Mock Version: 1.4.21 Mock Version: 1.4.21 ENTER ['do_with_status'](['bash', '--login', '-c', '/usr/bin/rpmbuild -bs --target riscv64 --nodeps /builddir/build/SPECS/gap-pkg-digraphs.spec'], chrootPath='/var/lib/mock/f33-build-279475-51688/root'env={'TERM': 'vt100', 'SHELL': '/bin/bash', 'HOME': '/builddir', 'HOSTNAME': 'mock', 'PATH': '/usr/bin:/bin:/usr/sbin:/sbin', 'PROMPT_COMMAND': 'printf "\\033]0;\\007"', 'PS1': ' \\s-\\v\\$ ', 'LANG': 'en_US.UTF-8'}shell=Falselogger=timeout=432000uid=987gid=135user='mockbuild'nspawn_args=[]unshare_net=TrueprintOutput=False) Executing command: ['bash', '--login', '-c', '/usr/bin/rpmbuild -bs --target riscv64 --nodeps /builddir/build/SPECS/gap-pkg-digraphs.spec'] with env {'TERM': 'vt100', 'SHELL': '/bin/bash', 'HOME': '/builddir', 'HOSTNAME': 'mock', 'PATH': '/usr/bin:/bin:/usr/sbin:/sbin', 'PROMPT_COMMAND': 'printf "\\033]0;\\007"', 'PS1': ' \\s-\\v\\$ ', 'LANG': 'en_US.UTF-8'} and shell False Building target platforms: riscv64 Building for target riscv64 setting SOURCE_DATE_EPOCH=1590537600 Wrote: /builddir/build/SRPMS/gap-pkg-digraphs-1.2.1-1.fc33.src.rpm Child return code was: 0 ENTER ['do_with_status'](['bash', '--login', '-c', '/usr/bin/rpmbuild -bb --target riscv64 --nodeps /builddir/build/SPECS/gap-pkg-digraphs.spec'], chrootPath='/var/lib/mock/f33-build-279475-51688/root'env={'TERM': 'vt100', 'SHELL': '/bin/bash', 'HOME': '/builddir', 'HOSTNAME': 'mock', 'PATH': '/usr/bin:/bin:/usr/sbin:/sbin', 'PROMPT_COMMAND': 'printf "\\033]0;\\007"', 'PS1': ' \\s-\\v\\$ ', 'LANG': 'en_US.UTF-8'}shell=Falselogger=timeout=432000uid=987gid=135user='mockbuild'nspawn_args=[]unshare_net=TrueprintOutput=False) Executing command: ['bash', '--login', '-c', '/usr/bin/rpmbuild -bb --target riscv64 --nodeps /builddir/build/SPECS/gap-pkg-digraphs.spec'] with env {'TERM': 'vt100', 'SHELL': '/bin/bash', 'HOME': '/builddir', 'HOSTNAME': 'mock', 'PATH': '/usr/bin:/bin:/usr/sbin:/sbin', 'PROMPT_COMMAND': 'printf "\\033]0;\\007"', 'PS1': ' \\s-\\v\\$ ', 'LANG': 'en_US.UTF-8'} and shell False Building target platforms: riscv64 Building for target riscv64 setting SOURCE_DATE_EPOCH=1590537600 Executing(%prep): /bin/sh -e /var/tmp/rpm-tmp.kRCoMH + umask 022 + cd /builddir/build/BUILD + cd /builddir/build/BUILD + rm -rf digraphs-1.2.1 + /usr/bin/gzip -dc /builddir/build/SOURCES/digraphs-1.2.1.tar.gz + /usr/bin/tar -xof - + STATUS=0 + '[' 0 -ne 0 ']' + cd digraphs-1.2.1 + /usr/bin/chmod -Rf a+rX,u+w,g-w,o-w . + rm -fr extern/edge-addition-planarity-suite-Version_3.0.0.5 + RPM_EC=0 ++ jobs -p + exit 0 Executing(%build): /bin/sh -e /var/tmp/rpm-tmp.6hB0KJ + umask 022 + cd /builddir/build/BUILD + cd digraphs-1.2.1 + export LC_ALL=C.UTF-8 + LC_ALL=C.UTF-8 + CFLAGS='-O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection' + export CFLAGS + CXXFLAGS='-O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection' + export CXXFLAGS + FFLAGS='-O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -I/usr/lib64/gfortran/modules' + export FFLAGS + FCFLAGS='-O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -I/usr/lib64/gfortran/modules' + export FCFLAGS + LDFLAGS='-Wl,-z,relro -Wl,--as-needed -Wl,-z,now -specs=/usr/lib/rpm/redhat/redhat-hardened-ld' + export LDFLAGS + LT_SYS_LIBRARY_PATH=/usr/lib64: + export LT_SYS_LIBRARY_PATH + CC=gcc + export CC + CXX=g++ + export CXX + '[' '%{_lto_cflags}x' '!=' x ']' ++ find . -type f -name configure -print + for file in $(find . -type f -name configure -print) + /usr/bin/sed -r --in-place=.backup 's/^char \(\*f\) \(\) = /__attribute__ ((used)) char (*f) () = /g' ./configure + diff -u ./configure.backup ./configure + mv ./configure.backup ./configure + /usr/bin/sed -r --in-place=.backup 's/^char \(\*f\) \(\);/__attribute__ ((used)) char (*f) ();/g' ./configure + diff -u ./configure.backup ./configure + mv ./configure.backup ./configure + /usr/bin/sed -r --in-place=.backup 's/^char \$2 \(\);/__attribute__ ((used)) char \$2 ();/g' ./configure + diff -u ./configure.backup ./configure --- ./configure.backup 2020-05-27 11:11:23.000000000 -0400 +++ ./configure 2020-06-09 06:31:44.774192655 -0400 @@ -1842,7 +1842,7 @@ #ifdef __cplusplus extern "C" #endif -char $2 (); +__attribute__ ((used)) char $2 (); /* The GNU C library defines this for functions which it implements to always fail with ENOSYS. Some functions are actually named something starting with __ and the normal name is an alias. */ + /usr/bin/sed --in-place=.backup '1{$!N;$!N};$!N;s/int x = 1;\nint y = 0;\nint z;\nint nan;/volatile int x = 1; volatile int y = 0; volatile int z, nan;/;P;D' ./configure + diff -u ./configure.backup ./configure + mv ./configure.backup ./configure + /usr/bin/sed --in-place=.backup 's#^lt_cv_sys_global_symbol_to_cdecl=.*#lt_cv_sys_global_symbol_to_cdecl="sed -n -e '\''s/^T .* \\(.*\\)$/extern int \\1();/p'\'' -e '\''s/^$symcode* .* \\(.*\\)$/extern char \\1;/p'\''"#' ./configure + diff -u ./configure.backup ./configure --- ./configure.backup 2020-06-09 06:31:44.774192655 -0400 +++ ./configure 2020-06-09 06:31:45.804192582 -0400 @@ -6919,7 +6919,7 @@ # Transform an extracted symbol line into a proper C declaration. # Some systems (esp. on ia64) link data and code symbols differently, # so use this general approach. -lt_cv_sys_global_symbol_to_cdecl="sed -n"\ +lt_cv_sys_global_symbol_to_cdecl="sed -n -e 's/^T .* \(.*\)$/extern int \1();/p' -e 's/^$symcode* .* \(.*\)$/extern char \1;/p'" $lt_cdecl_hook\ " -e 's/^T .* \(.*\)$/extern int \1();/p'"\ " -e 's/^$symcode$symcode* .* \(.*\)$/extern char \1;/p'" @@ -19352,7 +19352,7 @@ compiler='`$ECHO "$compiler" | $SED "$delay_single_quote_subst"`' GCC='`$ECHO "$GCC" | $SED "$delay_single_quote_subst"`' lt_cv_sys_global_symbol_pipe='`$ECHO "$lt_cv_sys_global_symbol_pipe" | $SED "$delay_single_quote_subst"`' -lt_cv_sys_global_symbol_to_cdecl='`$ECHO "$lt_cv_sys_global_symbol_to_cdecl" | $SED "$delay_single_quote_subst"`' +lt_cv_sys_global_symbol_to_cdecl="sed -n -e 's/^T .* \(.*\)$/extern int \1();/p' -e 's/^$symcode* .* \(.*\)$/extern char \1;/p'" lt_cv_sys_global_symbol_to_import='`$ECHO "$lt_cv_sys_global_symbol_to_import" | $SED "$delay_single_quote_subst"`' lt_cv_sys_global_symbol_to_c_name_address='`$ECHO "$lt_cv_sys_global_symbol_to_c_name_address" | $SED "$delay_single_quote_subst"`' lt_cv_sys_global_symbol_to_c_name_address_lib_prefix='`$ECHO "$lt_cv_sys_global_symbol_to_c_name_address_lib_prefix" | $SED "$delay_single_quote_subst"`' + '[' 1 = 1 ']' +++ dirname ./configure ++ find . -name config.guess -o -name config.sub + for i in $(find $(dirname ./configure) -name config.guess -o -name config.sub) ++ basename ./cnf/config.sub + '[' -f /usr/lib/rpm/redhat/config.sub ']' + /usr/bin/rm -f ./cnf/config.sub ++ basename ./cnf/config.sub + /usr/bin/cp -fv /usr/lib/rpm/redhat/config.sub ./cnf/config.sub '/usr/lib/rpm/redhat/config.sub' -> './cnf/config.sub' + for i in $(find $(dirname ./configure) -name config.guess -o -name config.sub) ++ basename ./cnf/config.guess + '[' -f /usr/lib/rpm/redhat/config.guess ']' + /usr/bin/rm -f ./cnf/config.guess ++ basename ./cnf/config.guess + /usr/bin/cp -fv /usr/lib/rpm/redhat/config.guess ./cnf/config.guess '/usr/lib/rpm/redhat/config.guess' -> './cnf/config.guess' + '[' 1 = 1 ']' + '[' x '!=' 'x-Wl,-z,now -specs=/usr/lib/rpm/redhat/redhat-hardened-ld' ']' ++ find . -name ltmain.sh + for i in $(find . -name ltmain.sh) + /usr/bin/sed -i.backup -e 's~compiler_flags=$~compiler_flags="-Wl,-z,now -specs=/usr/lib/rpm/redhat/redhat-hardened-ld"~' ./cnf/ltmain.sh + ./configure --build=riscv64-redhat-linux-gnu --host=riscv64-redhat-linux-gnu --program-prefix= --disable-dependency-tracking --prefix=/usr --exec-prefix=/usr --bindir=/usr/bin --sbindir=/usr/sbin --sysconfdir=/etc --datadir=/usr/share --includedir=/usr/include --libdir=/usr/lib64 --libexecdir=/usr/libexec --localstatedir=/var --sharedstatedir=/var/lib --mandir=/usr/share/man --infodir=/usr/share/info --with-gaproot=/usr/lib/gap --disable-silent-rules --with-external-planarity --without-intrinsics checking build system type... riscv64-redhat-linux-gnu checking host system type... riscv64-redhat-linux-gnu checking for a BSD-compatible install... /usr/bin/install -c checking whether build environment is sane... yes checking for a thread-safe mkdir -p... /usr/bin/mkdir -p checking for gawk... gawk checking whether make sets $(MAKE)... yes checking whether make supports nested variables... yes checking whether make supports nested variables... (cached) yes checking whether make supports the include directive... yes (GNU style) checking for riscv64-redhat-linux-gnu-gcc... gcc checking whether the C compiler works... yes checking for C compiler default output file name... a.out checking for suffix of executables... checking whether we are cross compiling... no checking for suffix of object files... o checking whether we are using the GNU C compiler... yes checking whether gcc accepts -g... yes checking for gcc option to accept ISO C89... none needed checking whether gcc understands -c and -o together... yes checking dependency style of gcc... none checking for riscv64-redhat-linux-gnu-ar... no checking for riscv64-redhat-linux-gnu-lib... no checking for riscv64-redhat-linux-gnu-link... no checking for ar... ar checking the archiver (ar) interface... ar checking for gcc option to accept ISO C99... none needed checking whether we are using the GNU C++ compiler... yes checking whether g++ accepts -g... yes checking dependency style of g++... none checking how to print strings... printf checking for a sed that does not truncate output... /usr/bin/sed checking for grep that handles long lines and -e... /usr/bin/grep checking for egrep... /usr/bin/grep -E checking for fgrep... /usr/bin/grep -F checking for ld used by gcc... /usr/bin/ld checking if the linker (/usr/bin/ld) is GNU ld... yes checking for BSD- or MS-compatible name lister (nm)... /usr/bin/nm -B checking the name lister (/usr/bin/nm -B) interface... BSD nm checking whether ln -s works... yes checking the maximum length of command line arguments... 1572864 checking how to convert riscv64-redhat-linux-gnu file names to riscv64-redhat-linux-gnu format... func_convert_file_noop checking how to convert riscv64-redhat-linux-gnu file names to toolchain format... func_convert_file_noop checking for /usr/bin/ld option to reload object files... -r checking for riscv64-redhat-linux-gnu-objdump... no checking for objdump... objdump checking how to recognize dependent libraries... pass_all checking for riscv64-redhat-linux-gnu-dlltool... no checking for dlltool... no checking how to associate runtime and link libraries... printf %s\n checking for riscv64-redhat-linux-gnu-ar... ar checking for archiver @FILE support... @ checking for riscv64-redhat-linux-gnu-strip... no checking for strip... strip checking for riscv64-redhat-linux-gnu-ranlib... no checking for ranlib... ranlib checking command to parse /usr/bin/nm -B output from gcc object... ./configure: line 6844: -e 's/^T .* \(.*\)$/extern int \1();/p' -e 's/^[ABCDGIRSTW][ABCDGIRSTW]* .* \(.*\)$/extern char \1;/p': No such file or directory ok checking for sysroot... no checking for a working dd... /usr/bin/dd checking how to truncate binary pipes... /usr/bin/dd bs=4096 count=1 checking for riscv64-redhat-linux-gnu-mt... no checking for mt... no checking if : is a manifest tool... no checking how to run the C preprocessor... gcc -E checking for ANSI C header files... yes checking for sys/types.h... yes checking for sys/stat.h... yes checking for stdlib.h... yes checking for string.h... yes checking for memory.h... yes checking for strings.h... yes checking for inttypes.h... yes checking for stdint.h... yes checking for unistd.h... yes checking for dlfcn.h... yes checking for objdir... .libs checking if gcc supports -fno-rtti -fno-exceptions... no checking for gcc option to produce PIC... -fPIC -DPIC checking if gcc PIC flag -fPIC -DPIC works... yes checking if gcc static flag -static works... no checking if gcc supports -c -o file.o... yes checking if gcc supports -c -o file.o... (cached) yes checking whether the gcc linker (/usr/bin/ld) supports shared libraries... yes checking whether -lc should be explicitly linked in... no checking dynamic linker characteristics... GNU/Linux ld.so checking how to hardcode library paths into programs... immediate checking for shl_load... no checking for shl_load in -ldld... no checking for dlopen... no checking for dlopen in -ldl... yes checking whether a program can dlopen itself... yes checking whether a statically linked program can dlopen itself... yes checking whether stripping libraries is possible... yes checking if libtool supports shared libraries... yes checking whether to build shared libraries... yes checking whether to build static libraries... no checking how to run the C++ preprocessor... g++ -E checking for ld used by g++... /usr/bin/ld checking if the linker (/usr/bin/ld) is GNU ld... yes checking whether the g++ linker (/usr/bin/ld) supports shared libraries... yes checking for g++ option to produce PIC... -fPIC -DPIC checking if g++ PIC flag -fPIC -DPIC works... yes checking if g++ static flag -static works... no checking if g++ supports -c -o file.o... yes checking if g++ supports -c -o file.o... (cached) yes checking whether the g++ linker (/usr/bin/ld) supports shared libraries... yes checking dynamic linker characteristics... (cached) GNU/Linux ld.so checking how to hardcode library paths into programs... immediate checking for GAP root directory... /usr/lib/gap checking for GAP architecture... checking whether to enable debug mode... no checking whether to enable stats mode... no checking whether to build with code coverage support... no checking whether enable compiler warnings... no checking whether to use external planarity... yes checking for gp_InitGraph in -lplanarity... yes checking planarity/graph.h usability... yes checking planarity/graph.h presence... yes checking for planarity/graph.h... yes checking whether to use external bliss... no configure: compiler intrinsics will not be used even if available checking that generated files are newer than configure... done configure: creating ./config.status config.status: creating Makefile config.status: creating src/_pkgconfig.h config.status: executing depfiles commands config.status: executing src/digraphs-config.h commands config.status: creating src/digraphs-config.h - prefix DIGRAPHS for src/_pkgconfig.h defines config.status: executing libtool commands + /usr/bin/make -O -j8 V=1 VERBOSE=1 make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.2.1' /bin/sh ./libtool --tag=CXX --mode=compile g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c -o extern/bliss-0.73/digraphs_la-uintseqhash.lo `test -f 'extern/bliss-0.73/uintseqhash.cc' || echo './'`extern/bliss-0.73/uintseqhash.cc libtool: compile: g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c extern/bliss-0.73/uintseqhash.cc -fPIC -DPIC -o extern/bliss-0.73/.libs/digraphs_la-uintseqhash.o make[1]: Leaving directory '/builddir/build/BUILD/digraphs-1.2.1' make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.2.1' /bin/sh ./libtool --tag=CXX --mode=compile g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c -o extern/bliss-0.73/digraphs_la-timer.lo `test -f 'extern/bliss-0.73/timer.cc' || echo './'`extern/bliss-0.73/timer.cc libtool: compile: g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c extern/bliss-0.73/timer.cc -fPIC -DPIC -o extern/bliss-0.73/.libs/digraphs_la-timer.o make[1]: Leaving directory '/builddir/build/BUILD/digraphs-1.2.1' extern/bliss-0.73/timer.cc: In member function ‘void bliss_digraphs::Timer::reset()’: extern/bliss-0.73/timer.cc:39:24: warning: ‘clkticks.tms::tms_utime’ is used uninitialized in this function [-Wuninitialized] 39 | ((double) clkticks.tms_utime + (double) clkticks.tms_stime) / | ~~~~~~~~~^~~~~~~~~ extern/bliss-0.73/timer.cc:39:54: warning: ‘clkticks.tms::tms_stime’ is used uninitialized in this function [-Wuninitialized] 39 | ((double) clkticks.tms_utime + (double) clkticks.tms_stime) / | ~~~~~~~~~^~~~~~~~~ extern/bliss-0.73/timer.cc: In member function ‘double bliss_digraphs::Timer::get_duration()’: extern/bliss-0.73/timer.cc:50:24: warning: ‘clkticks.tms::tms_utime’ is used uninitialized in this function [-Wuninitialized] 50 | ((double) clkticks.tms_utime + (double) clkticks.tms_stime) / | ~~~~~~~~~^~~~~~~~~ extern/bliss-0.73/timer.cc:50:54: warning: ‘clkticks.tms::tms_stime’ is used uninitialized in this function [-Wuninitialized] 50 | ((double) clkticks.tms_utime + (double) clkticks.tms_stime) / | ~~~~~~~~~^~~~~~~~~ make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.2.1' /bin/sh ./libtool --tag=CXX --mode=compile g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c -o extern/bliss-0.73/digraphs_la-defs.lo `test -f 'extern/bliss-0.73/defs.cc' || echo './'`extern/bliss-0.73/defs.cc libtool: compile: g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c extern/bliss-0.73/defs.cc -fPIC -DPIC -o extern/bliss-0.73/.libs/digraphs_la-defs.o make[1]: Leaving directory '/builddir/build/BUILD/digraphs-1.2.1' make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.2.1' /bin/sh ./libtool --tag=CXX --mode=compile g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c -o extern/bliss-0.73/digraphs_la-heap.lo `test -f 'extern/bliss-0.73/heap.cc' || echo './'`extern/bliss-0.73/heap.cc libtool: compile: g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c extern/bliss-0.73/heap.cc -fPIC -DPIC -o extern/bliss-0.73/.libs/digraphs_la-heap.o make[1]: Leaving directory '/builddir/build/BUILD/digraphs-1.2.1' make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.2.1' /bin/sh ./libtool --tag=CXX --mode=compile g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c -o extern/bliss-0.73/digraphs_la-utils.lo `test -f 'extern/bliss-0.73/utils.cc' || echo './'`extern/bliss-0.73/utils.cc libtool: compile: g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c extern/bliss-0.73/utils.cc -fPIC -DPIC -o extern/bliss-0.73/.libs/digraphs_la-utils.o make[1]: Leaving directory '/builddir/build/BUILD/digraphs-1.2.1' make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.2.1' /bin/sh ./libtool --tag=CXX --mode=compile g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c -o extern/bliss-0.73/digraphs_la-orbit.lo `test -f 'extern/bliss-0.73/orbit.cc' || echo './'`extern/bliss-0.73/orbit.cc libtool: compile: g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c extern/bliss-0.73/orbit.cc -fPIC -DPIC -o extern/bliss-0.73/.libs/digraphs_la-orbit.o make[1]: Leaving directory '/builddir/build/BUILD/digraphs-1.2.1' make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.2.1' /bin/sh ./libtool --tag=CC --mode=compile gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -g -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -fexceptions -fstack-protector-strong -grecord-gcc-switches -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c -o src/digraphs_la-bitarray.lo `test -f 'src/bitarray.c' || echo './'`src/bitarray.c libtool: compile: gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -g -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -fexceptions -fstack-protector-strong -grecord-gcc-switches -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c src/bitarray.c -fPIC -DPIC -o src/.libs/digraphs_la-bitarray.o make[1]: Leaving directory '/builddir/build/BUILD/digraphs-1.2.1' make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.2.1' /bin/sh ./libtool --tag=CC --mode=compile gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -g -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -fexceptions -fstack-protector-strong -grecord-gcc-switches -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c -o src/digraphs_la-conditions.lo `test -f 'src/conditions.c' || echo './'`src/conditions.c libtool: compile: gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -g -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -fexceptions -fstack-protector-strong -grecord-gcc-switches -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c src/conditions.c -fPIC -DPIC -o src/.libs/digraphs_la-conditions.o make[1]: Leaving directory '/builddir/build/BUILD/digraphs-1.2.1' make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.2.1' /bin/sh ./libtool --tag=CC --mode=compile gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -g -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -fexceptions -fstack-protector-strong -grecord-gcc-switches -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c -o src/digraphs_la-perms.lo `test -f 'src/perms.c' || echo './'`src/perms.c libtool: compile: gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -g -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -fexceptions -fstack-protector-strong -grecord-gcc-switches -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c src/perms.c -fPIC -DPIC -o src/.libs/digraphs_la-perms.o make[1]: Leaving directory '/builddir/build/BUILD/digraphs-1.2.1' make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.2.1' /bin/sh ./libtool --tag=CC --mode=compile gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -g -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -fexceptions -fstack-protector-strong -grecord-gcc-switches -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c -o src/digraphs_la-homos-graphs.lo `test -f 'src/homos-graphs.c' || echo './'`src/homos-graphs.c libtool: compile: gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -g -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -fexceptions -fstack-protector-strong -grecord-gcc-switches -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c src/homos-graphs.c -fPIC -DPIC -o src/.libs/digraphs_la-homos-graphs.o make[1]: Leaving directory '/builddir/build/BUILD/digraphs-1.2.1' make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.2.1' /bin/sh ./libtool --tag=CXX --mode=compile g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c -o extern/bliss-0.73/digraphs_la-bliss_C.lo `test -f 'extern/bliss-0.73/bliss_C.cc' || echo './'`extern/bliss-0.73/bliss_C.cc libtool: compile: g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c extern/bliss-0.73/bliss_C.cc -fPIC -DPIC -o extern/bliss-0.73/.libs/digraphs_la-bliss_C.o make[1]: Leaving directory '/builddir/build/BUILD/digraphs-1.2.1' extern/bliss-0.73/bliss_C.cc: In function ‘void fill_size(BlissStats*, const bliss_digraphs::Stats&)’: extern/bliss-0.73/bliss_C.cc:156:21: warning: comparison of integer expressions of different signedness: ‘int’ and ‘std::vector::size_type’ {aka ‘long unsigned int’} [-Wsign-compare] 156 | for(int i = 0; i < sizes.size(); ++i) { | ~~^~~~~~~~~~~~~~ make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.2.1' /bin/sh ./libtool --tag=CC --mode=compile gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -g -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -fexceptions -fstack-protector-strong -grecord-gcc-switches -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c -o src/digraphs_la-planar.lo `test -f 'src/planar.c' || echo './'`src/planar.c libtool: compile: gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -g -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -fexceptions -fstack-protector-strong -grecord-gcc-switches -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c src/planar.c -fPIC -DPIC -o src/.libs/digraphs_la-planar.o make[1]: Leaving directory '/builddir/build/BUILD/digraphs-1.2.1' make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.2.1' /bin/sh ./libtool --tag=CC --mode=compile gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -g -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -fexceptions -fstack-protector-strong -grecord-gcc-switches -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c -o src/digraphs_la-schreier-sims.lo `test -f 'src/schreier-sims.c' || echo './'`src/schreier-sims.c libtool: compile: gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -g -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -fexceptions -fstack-protector-strong -grecord-gcc-switches -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c src/schreier-sims.c -fPIC -DPIC -o src/.libs/digraphs_la-schreier-sims.o make[1]: Leaving directory '/builddir/build/BUILD/digraphs-1.2.1' make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.2.1' /bin/sh ./libtool --tag=CC --mode=compile gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -g -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -fexceptions -fstack-protector-strong -grecord-gcc-switches -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c -o src/digraphs_la-digraphs.lo `test -f 'src/digraphs.c' || echo './'`src/digraphs.c libtool: compile: gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -g -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -fexceptions -fstack-protector-strong -grecord-gcc-switches -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c src/digraphs.c -fPIC -DPIC -o src/.libs/digraphs_la-digraphs.o make[1]: Leaving directory '/builddir/build/BUILD/digraphs-1.2.1' src/digraphs.c: In function ‘FLOYD_WARSHALL.constprop’: src/digraphs.c:1210:13: warning: ‘adj’ may be used uninitialized in this function [-Wmaybe-uninitialized] 1210 | free(adj); | ^~~~~~~~~ make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.2.1' /bin/sh ./libtool --tag=CXX --mode=compile g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c -o extern/bliss-0.73/digraphs_la-partition.lo `test -f 'extern/bliss-0.73/partition.cc' || echo './'`extern/bliss-0.73/partition.cc libtool: compile: g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c extern/bliss-0.73/partition.cc -fPIC -DPIC -o extern/bliss-0.73/.libs/digraphs_la-partition.o make[1]: Leaving directory '/builddir/build/BUILD/digraphs-1.2.1' make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.2.1' /bin/sh ./libtool --tag=CC --mode=compile gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -g -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -fexceptions -fstack-protector-strong -grecord-gcc-switches -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c -o src/digraphs_la-homos.lo `test -f 'src/homos.c' || echo './'`src/homos.c libtool: compile: gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -g -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -fexceptions -fstack-protector-strong -grecord-gcc-switches -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c src/homos.c -fPIC -DPIC -o src/.libs/digraphs_la-homos.o make[1]: Leaving directory '/builddir/build/BUILD/digraphs-1.2.1' make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.2.1' /bin/sh ./libtool --tag=CXX --mode=compile g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c -o extern/bliss-0.73/digraphs_la-graph.lo `test -f 'extern/bliss-0.73/graph.cc' || echo './'`extern/bliss-0.73/graph.cc libtool: compile: g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -c extern/bliss-0.73/graph.cc -fPIC -DPIC -o extern/bliss-0.73/.libs/digraphs_la-graph.o make[1]: Leaving directory '/builddir/build/BUILD/digraphs-1.2.1' make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.2.1' /bin/sh ./libtool --tag=CXX --mode=link g++ -I./extern/ -O2 -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -fasynchronous-unwind-tables -fstack-clash-protection -Wl,-z,relro -Wl,--as-needed -module -avoid-version -Wl,-z,relro -Wl,--as-needed -Wl,-z,now -specs=/usr/lib/rpm/redhat/redhat-hardened-ld -o digraphs.la -rpath /usr/lib64 src/digraphs_la-digraphs.lo src/digraphs_la-bitarray.lo src/digraphs_la-conditions.lo src/digraphs_la-homos.lo src/digraphs_la-homos-graphs.lo src/digraphs_la-perms.lo src/digraphs_la-planar.lo src/digraphs_la-schreier-sims.lo extern/bliss-0.73/digraphs_la-defs.lo extern/bliss-0.73/digraphs_la-graph.lo extern/bliss-0.73/digraphs_la-partition.lo extern/bliss-0.73/digraphs_la-orbit.lo extern/bliss-0.73/digraphs_la-uintseqhash.lo extern/bliss-0.73/digraphs_la-heap.lo extern/bliss-0.73/digraphs_la-timer.lo extern/bliss-0.73/digraphs_la-utils.lo extern/bliss-0.73/digraphs_la-bliss_C.lo -lplanarity libtool: link: g++ -fPIC -DPIC -shared -nostdlib /usr/lib/gcc/riscv64-redhat-linux/10/crti.o /usr/lib/gcc/riscv64-redhat-linux/10/crtbeginS.o src/.libs/digraphs_la-digraphs.o src/.libs/digraphs_la-bitarray.o src/.libs/digraphs_la-conditions.o src/.libs/digraphs_la-homos.o src/.libs/digraphs_la-homos-graphs.o src/.libs/digraphs_la-perms.o src/.libs/digraphs_la-planar.o src/.libs/digraphs_la-schreier-sims.o extern/bliss-0.73/.libs/digraphs_la-defs.o extern/bliss-0.73/.libs/digraphs_la-graph.o extern/bliss-0.73/.libs/digraphs_la-partition.o extern/bliss-0.73/.libs/digraphs_la-orbit.o extern/bliss-0.73/.libs/digraphs_la-uintseqhash.o extern/bliss-0.73/.libs/digraphs_la-heap.o extern/bliss-0.73/.libs/digraphs_la-timer.o extern/bliss-0.73/.libs/digraphs_la-utils.o extern/bliss-0.73/.libs/digraphs_la-bliss_C.o -lplanarity -L/usr/lib/gcc/riscv64-redhat-linux/10 -L/lib64/lp64d/../lib64/lp64d -L/usr/lib64/lp64d/../lib64/lp64d -L/lib/../lib64/lp64d -L/usr/lib/../lib64/lp64d -L/lib64/lp64d -L/usr/lib64/lp64d -lstdc++ -lm -lc -lgcc_s /usr/lib/gcc/riscv64-redhat-linux/10/crtendS.o /usr/lib/gcc/riscv64-redhat-linux/10/crtn.o -Wl,-z,now -specs=/usr/lib/rpm/redhat/redhat-hardened-ld -O2 -g -grecord-gcc-switches -fstack-protector-strong -Wl,-z -Wl,relro -Wl,--as-needed -Wl,-z -Wl,relro -Wl,--as-needed -Wl,-z -Wl,now -Wl,-soname -Wl,digraphs.so -o .libs/digraphs.so libtool: link: ( cd ".libs" && rm -f "digraphs.la" && ln -s "../digraphs.la" "digraphs.la" ) make[1]: Leaving directory '/builddir/build/BUILD/digraphs-1.2.1' make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.2.1' /usr/bin/mkdir -p ./bin/riscv64-redhat-linux-gnu-default64-kv7 ./bin/lib cp .libs/digraphs.so /builddir/build/BUILD/digraphs-1.2.1/bin/riscv64-redhat-linux-gnu-default64-kv7/ SUCCESS! make[1]: Leaving directory '/builddir/build/BUILD/digraphs-1.2.1' + mkdir ../pkg + ln -s ../digraphs-1.2.1 ../pkg + gap -l '/builddir/build/BUILD/digraphs-1.2.1/..;/usr/lib/gap' ┌───────┐ GAP 4.11.0 of 29-Feb-2020 │ GAP │ https://www.gap-system.org └───────┘ Architecture: riscv64-redhat-linux-gnu-default64-kv7 Configuration: gmp 6.2.0, GASMAN, readline Loading the library and packages ... #I autpgrp package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I alnuth package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I crisp package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I ctbllib package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I factint package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I fga package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I irredsol package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I laguna package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I polenta package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I polycyclic package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I resclasses package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I sophus package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I tomlib package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') Packages: GAPDoc 1.6.3, PrimGrp 3.4.1, SmallGrp 1.4.1, TransGrp 2.0.5 Try '??help' for help. See also '?copyright', '?cite' and '?authors' gap> gap> gap> gap> gap> gap> gap> gap> gap> "Digraphs" gap> gap> true gap> gap> > > > > > > > > > > > > > > > > [ "attr.xml", "cliques.xml", "constructors.xml", "digraph.xml", "display.xml", "examples.xml", "grahom.xml", "grape.xml", "io.xml", "isomorph.xml", "labels.xml", "oper.xml", "orbits.xml", "planar.xml", "prop.xml", "utils.xml", "../PackageInfo.g" ] gap> gap> > > > #I Composing XML document . . . #I Parsing XML document . . . #I Checking XML structure . . . #I Text version (also produces labels for hyperlinks): #I First run, collecting cross references, index, toc, bib and so on . . . #I Table of contents complete. #I Producing the index . . . #I Reading bibliography data files . . . #I BibTeX format: digraphs #I checking and translating to BibXMLext . . . #I Writing bibliography . . . #I Second run through document . . . #I Producing simplified search strings and labels for hyperlinks . . . #I Constructing LaTeX version and calling pdflatex: #I Writing LaTeX file, 4 x pdflatex with bibtex and makeindex, #I Writing manual.six file ... #I Finally the HTML version . . . #I First run, collecting cross references, index, toc, bib and so on . . . #I Table of contents complete. #I Producing the index . . . #I Writing bibliography . . . #I Second run through document . . . #I - also HTML version for MathJax . . . #I First run, collecting cross references, index, toc, bib and so on . . . #I Table of contents complete. #I Producing the index . . . #I Writing bibliography . . . #I Second run through document . . . rec( Name := "digraphs", attributes := rec( ), bibdata := "digraphs", bibentries := [ , , , , , ], bibkeys := [ "BM06", "CK86", "Gab00", "JK07", "MP14", "vLS81" ], biblabels := [ "BM06", "CK86", "Gab00", "JK07", "MP14", "vLS81" ], bibpath := dir("/builddir/build/BUILD/digraphs-1.2.1/../pkg/digraphs-1.2.1/d\ oc/"), bibstrings := [ [ 0, 0 ] ], bibtext := "\n

\n

\n[BM06] Boyer, J. M.\ and Myrvold, W. J.,\n On the Cutting Edge: Simplified\ O(n) Planarity by Edge\n Addition,\n in Gr\ aph Algorithms and Applications 5,\n {WORLD} {S\ CIENTIFIC}\n (2006),\n 241--273.\n

\n\n\n

\ \n

\n[CK86] Calder\ bank, R. and Kantor, W. M.,\n The geometry of two-weig\ ht codes,\n Bull. London Math. Soc.,\n 18 (2)\n (1986),\n 97--122.\n

\n\n\n

\

\n

\n[Gab00] Gabow, H. N.,\n Path-based depth-first search for strong and biconnected\n \ components,\n Information Processing Letters,\n 74 (34)\n (\ 2000),\n 107 - 114.\ \n

\n\n\n

\n

\n[JK07] Junttila, T. and\ Kaski, P. (Applegate, D., Brodal, G. S., Panario,\ D. and Sedgewick, R., Eds.),\n Engineering an effi\ cient canonical labeling tool for large and\n sparse graphs,\n \ in Proceedings of the Ninth Workshop on Algorithm Eng\ ineering and\n Experiments and the Fourth Workshop on Analytic Algorithms and\ \n Combinatorics,\n SIAM\n\ (2007),\n 135--149\ .\n

\n\n\n

\n

\n[MP14] McKay, B. D. an\ d Piperno, A.,\n Practical graph isomorphism, II,\ \n Journal of Symbolic Computation,\n 60 (0)\n (2014),\n 94 - 112.\n

\n\n\n

\n

\n[vLS81\ ] van Lint, J. H. and Schrijver, A.,\n <\ i class='BibTitle'>Construction of strongly regular graphs, two-weight codes a\ nd\n partial geometries by finite fields,\n Combinatorica,\n 1 (1)\n (1981),\n 63--73.\n

\n\n", bookname := "digraphs", chapsectlinks := rec( 1 := "\n", 2 := "
2 Installing Digraphs\n\n\n
 2.\ 3 Compiling the kernel module\n\n\n
&nb\ sp;2.4 Rebuilding the documentation\n\n\n\n", 3 := "\n
 3.3 \ New digraphs from old\n\n
\n
 &nb\ sp;3.3-1 DigraphImmutableCo\ py
\n
  \ 3.3-2 DigraphImmutableCopyI\ fImmutable
\n
&nbs\ p; 3.3-3 InducedSubdig\ raph
\n
 &nbs\ p;3.3-4 ReducedDigraph<\ /span>\n
  \ 3.3-5 MaximalSymmetricSubdigraph
\n
  
3.3-6 MaximalAntiSymmetricSubdi\ graph
\n
 &nb\ sp;3.3-7 UndirectedSpanning\ Forest
\n
 &n\ bsp;3.3-8 QuotientDigraph
\n
  
3.3-9 DigraphReverse\ \n
  3.3-10 DigraphDual
\n
  3.3-11 DigraphSymmetricClosure
\n
  3.3-12 DigraphTransitiveClosure
\n
  3.3-13 DigraphTransitiveReduction
\n
  3.3-14 DigraphAddVertex\n
  3.3-15 DigraphAddVertices
\n
  3.3-16 DigraphAddEdge
\n
  3.3-17 DigraphAddEdgeOrbit
\n\
  3.3-18 DigraphAddEdges
\n
<\ span class=\"nocss\">  
3.3-19 DigraphRemoveVertex\n
  
3.3-20 DigraphRemoveVertices\n
  
3.3-21 DigraphRemoveEdge\n
  3.\ 3-22 DigraphRemoveEdgeOrbit
\n
  3.\ 3-23 DigraphRemoveEdges
\n
  3.3-2\ 4 DigraphRemoveLoops
\n
  3.3-25 Di\ graphRemoveAllMultipleEdges
\n
  3.\ 3-26 DigraphReverseEdges
\n
  3.3-2\ 7 DigraphDisjointUnion
\n
  3.3-28 \ DigraphEdgeUnion
\n
  3.3-29 Digra\ phJoin
\n
 &n\ bsp;3.3-30 DigraphCartesian\ Product
\n
 &\ nbsp;3.3-31 DigraphDirectPr\ oduct
\n
 &nb\ sp;3.3-32 DigraphCartesianP\ roductProjections
\n
  3.3-33 Digra\ phDirectProductProjections
\n
  3.3\ -34 LineDigraph
\n
  3.3-35 LineUnd\ irectedDigraph
\n
\   3.3-36 DoubleDi\ graph
\n
 &nb\ sp;3.3-37 BipartiteDoubleDi\ graph
\n
 &nb\ sp;3.3-38 DigraphAddAllLoop\ s
\n
  <\ /span>3.3-39 DistanceDigraph\n
  <\ a href=\"chap3_mj.html#X86F9CCEA839ABC48\">3.3-40 DigraphClosure
\n<\ span class=\"ContSS\">
  3.3-41 DigraphMycielskian
\n
\n\n\n", 4 := "\n", 5 := "
5 Attributes and operations\n\n\n\n\n
 5.5 Associated s\ emigroups\n\n
\n
  5.5-1 AsSemigroup
\n
<\ span class=\"nocss\">  
5.5-2 AsSemigroup\n
\n\n
\n", 6 := "
6 Properties of digraphs\n
 6.1 Edge propertie\ s\n\n\n\n\n
 6.4 Planarity\n\n\n\n", 7 := "
7 Homomorphisms\n\n\n\n
\n", 8 := "\n", 9 := "\n", A := "
A \n Grape to Digraphs Command Map\n \n\n\n\n\n\n\n\n\n" ), chapsectlinkstext := rec( 1 := "\n", 2 := "
2 Installing Digraphs\n\n\n
 2.\ 3 Compiling the kernel module\n\n\n
&nb\ sp;2.4 Rebuilding the documentation\n\n\n\n", 3 := "\n
 3.3 \ New digraphs from old\n\n
\n
 &nb\ sp;3.3-1 DigraphImmutableCo\ py
\n
  \ 3.3-2 DigraphImmutableCopyI\ fImmutable
\n
&nbs\ p; 3.3-3 InducedSubdig\ raph
\n
 &nbs\ p;3.3-4 ReducedDigraph<\ /span>\n
  \ 3.3-5 MaximalSymmetricSubdigraph
\n
  
3.3-6 MaximalAntiSymmetricSubdi\ graph
\n
 &nb\ sp;3.3-7 UndirectedSpanning\ Forest
\n
 &n\ bsp;3.3-8 QuotientDigraph
\n
  
3.3-9 DigraphReverse\ \n
  3.3-10 DigraphDual
\n
  3.3-11 DigraphSymmetricClosure
\n
  3.3-12 DigraphTransitiveClosure
\n
  3.3-13 DigraphTransitiveReduction
\n
  3.3-14 DigraphAddVertex\n
  3.3-15 DigraphAddVertices
\n
  3.3-16 DigraphAddEdge
\n
  3.3-17 DigraphAddEdgeOrbit
\n\
  3.3-18 DigraphAddEdges
\n
<\ span class=\"nocss\">  
3.3-19 DigraphRemoveVertex\n
  
3.3-20 DigraphRemoveVertices\n
  
3.3-21 DigraphRemoveEdge\n
  3.\ 3-22 DigraphRemoveEdgeOrbit
\n
  3.\ 3-23 DigraphRemoveEdges
\n
  3.3-2\ 4 DigraphRemoveLoops
\n
  3.3-25 Di\ graphRemoveAllMultipleEdges
\n
  3.\ 3-26 DigraphReverseEdges
\n
  3.3-2\ 7 DigraphDisjointUnion
\n
  3.3-28 \ DigraphEdgeUnion
\n
  3.3-29 Digra\ phJoin
\n
 &n\ bsp;3.3-30 DigraphCartesian\ Product
\n
 &\ nbsp;3.3-31 DigraphDirectPr\ oduct
\n
 &nb\ sp;3.3-32 DigraphCartesianP\ roductProjections
\n
  3.3-33 Digra\ phDirectProductProjections
\n
  3.3\ -34 LineDigraph
\n
  3.3-35 LineUnd\ irectedDigraph
\n
\   3.3-36 DoubleDi\ graph
\n
 &nb\ sp;3.3-37 BipartiteDoubleDi\ graph
\n
 &nb\ sp;3.3-38 DigraphAddAllLoop\ s
\n
  <\ /span>3.3-39 DistanceDigraph\n
  <\ a href=\"chap3_mj.html#X86F9CCEA839ABC48\">3.3-40 DigraphClosure
\n<\ span class=\"ContSS\">
  3.3-41 DigraphMycielskian
\n
\n\n\n", 4 := "\n", 5 := "
5 Attributes and operations\n\n\n\n\n
 5.5 Associated s\ emigroups\n\n
\n
  5.5-1 AsSemigroup
\n
<\ span class=\"nocss\">  
5.5-2 AsSemigroup\n
\n\n
\n", 6 := "
6 Properties of digraphs\n
 6.1 Edge propertie\ s\n\n\n\n\n
 6.4 Planarity\n\n\n\n", 7 := "
7 Homomorphisms\n\n\n\n
\n", 8 := "\n", 9 := "\n", A := "
A \n Grape to Digraphs Command Map\n \n\n\n\n\n\n\n\n\n" ), chaptitle := rec( 1 := "\n The Digraphs package\n ", 2 := "Installing Digraphs<\ /strong>", 3 := "Creating digraphs", 4 := "Operators", 5 := "Attributes and operations", 6 := "Properties of digraphs", 7 := "Homomorphisms", 8 := "Finding cliques and independent sets", 9 := "Visualising and IO", A := "\n Grape to Digraphs Command Map\n " ), content := [ rec( content := "Book SYSTEM \"gapdoc.dtd\"\n [ Digraphs\">\n http://www.maths.qmul.ac.uk/~leonard/grape/Grape\">\n http://www.tcs.tkk.fi/Software/bliss/bliss\">\n https://github.com/graph-algorithms/edge-addition-planarity-suiteedge-addition-planarity-suite\">\n ht\ tp://pallini.di.uniroma1.it/nauty\">\n https://github.com/gap-packages/NautyTracesInter\ faceNautyTracesInterface\">\n \n http://gap-p\ ackages.github.io/io/\nIO\">\n \n http://http:/\ /gap-packages.github.io/orb/\n Orb\">\n https://github.com/gap-packages/datastructuresdatastructures\">\n \n\n\n\n\n\n\n\n\n\n ]", count := [ 0, 0, 0, 1 ], name := "XMLDOCTYPE", root := ~ ), rec( attributes := rec( Name := "digraphs" ), content := [ rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ) ], count := [ 0, 0, 0, 1 ], name := "Title", next := 2023, root := ~, start := 1998, stop := 2022 ), rec( attributes := rec( ), content := [ rec( content := "Version 1.2.1", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], name := "Version", next := 2062, root := ~, start := 2026, stop := 2061 ), rec( attributes := rec( ), content := [ rec( content := "Jan De Beule\n ", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "jdebeule@cage.ugent.be", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "Email", next := 2128, root := ~, start := 2091, stop := 2127 ), rec( content := "\n ", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "http://homepages.vub.ac.b\ e/~jdbeule", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "Homepage", next := 2189, root := ~, start := 2133, stop := 2188 ), rec( content := "\n ", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], name := "Author", next := 2201, root := ~, start := 2066, stop := 2200 ), rec( attributes := rec( ), content := [ rec( content := "Julius Jonušas\n ", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "julius.jonusas@tuwien.ac.\ at", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "Email", next := 2279, root := ~, start := 2237, stop := 2278 ), rec( content := "\n ", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "http://julius.jonusas.wor\ k", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "Homepage", next := 2331, root := ~, start := 2284, stop := 2330 ), rec( content := "\n ", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], name := "Author", next := 2343, root := ~, start := 2205, stop := 2342 ), rec( attributes := rec( ), content := [ rec( content := "James D. Mitchell\n ", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "jdm3@st-and.ac.uk", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "Email", next := 2409, root := ~, start := 2377, stop := 2408 ), rec( content := "\n ", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "http://www-groups.mcs.st-\ andrews.ac.uk/~jamesm", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "Homepage", next := 2481, root := ~, start := 2414, stop := 2480 ), rec( content := "\n ", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], name := "Author", next := 2493, root := ~, start := 2347, stop := 2492 ), rec( attributes := rec( ), content := [ rec( content := "Michael Torpey\n ", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "mct25@st-andrews.ac.uk", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "Email", next := 2561, root := ~, start := 2524, stop := 2560 ), rec( content := "\n ", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "https://mtorpey.github.io\ ", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "Homepage", next := 2612, root := ~, start := 2566, stop := 2611 ), rec( content := "\n ", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], name := "Author", next := 2624, root := ~, start := 2497, stop := 2623 ), rec( attributes := rec( ), content := [ rec( content := "Wilf A. Wilson\n ", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "gap@wilf-wilson.net", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "Email", next := 2689, root := ~, start := 2655, stop := 2688 ), rec( content := "\n ", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "http://wilf.me", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "Homepage", next := 2729, root := ~, start := 2694, stop := 2728 ), rec( content := "\n ", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], name := "Author", next := 2741, root := ~, start := 2628, stop := 2740 ), rec( attributes := rec( ), content := [ rec( content := "Stuart Burrell", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], name := "Author", next := 2776, root := ~, start := 2745, stop := 2775 ), rec( attributes := rec( ), content := [ rec( content := "Reinis Cirpons", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], name := "Author", next := 2811, root := ~, start := 2780, stop := 2810 ), rec( attributes := rec( ), content := [ rec( content := "Luke Elliott", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], name := "Author", next := 2844, root := ~, start := 2815, stop := 2843 ), rec( attributes := rec( ), content := [ rec( content := "Max Horn", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], name := "Author", next := 2873, root := ~, start := 2848, stop := 2872 ), rec( attributes := rec( ), content := [ rec( content := "Christopher Jefferson", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], name := "Author", next := 2915, root := ~, start := 2877, stop := 2914 ), rec( attributes := rec( ), content := [ rec( content := "Markus Pfeiffer", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], name := "Author", next := 2951, root := ~, start := 2919, stop := 2950 ), rec( attributes := rec( ), content := [ rec( content := "Chris Russell", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], name := "Author", next := 2985, root := ~, start := 2955, stop := 2984 ), rec( attributes := rec( ), content := [ rec( content := "Finn Smith", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], name := "Author", next := 3016, root := ~, start := 2989, stop := 3015 ), rec( attributes := rec( ), content := [ rec( content := "Murray White", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], name := "Author", next := 3049, root := ~, start := 3020, stop := 3048 ), rec( attributes := rec( ), content := [ rec( content := "© 2014-20 by\n Jan De Beule, \ Julius Jonušas, James D. Mitchell, Michael\n Torpey, Wilf A. Wilson et al.\ ", count := [ 0, 0, 1, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "P", next := 3199, root := ~, start := 3195, stop := 3198 ), rec( content := "\n\n ", count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " is free software; you can redis\ tribute it and/or modify it\n under the terms of the ", count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Text := "GNU General Public License" ), content := [ rec( content := "\n http://www.fsf.org/\ licenses/gpl.html", count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "URL", next := 3388, root := ~, start := 3302, stop := 3387 ), rec( content := " as published by the Free Softwa\ re\n Foundation; either version 3 of the License, or (at your option) any l\ ater\n version.\n ", count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 1 ], name := "Copyright", next := 3529, root := ~, start := 3053, stop := 3528 ), rec( attributes := rec( ), content := [ rec( content := "\n The ", count := [ 0, 0, 2, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 0, 0, 2, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 2, 1 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " package is a ", count := [ 0, 0, 2, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "GAP", count := [ 0, 0, 2, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 2, 1 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " package containing methods for \ graphs,\n digraphs, and multidigraphs.\n ", count := [ 0, 0, 2, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 2, 1 ], name := "Abstract", next := 3667, root := ~, start := 3533, stop := 3666 ), rec( attributes := rec( ), content := [ rec( content := "\n We would like to thank Chri\ stopher Jefferson for his help in including \n ", count := [ 0, 0, 3, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "bliss" ) , content := [ rec( content := "http://www.tcs.tk\ k.fi/Software/bliss/", count := [ 0, 0, 3, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 3, 1 ], mathmode := "Text", name := "URL", next := 81, root := ~, start := 17, stop := 80 ) ], count := [ 0, 0, 3, 1 ], name := "Alt", next := 87, root := ~, start := 1, stop := 86 ), rec( attributes := rec( Only := "Text" ), content := [ rec( attributes := rec( ), content := [ rec( content := "bliss", count := [ 0, 0, 3, 1 ], name := "PCDATA", root := ~ ) ], count := [ 0, 0, 3, 1 ], name := "Package", next := 131, root := ~, start := 107, stop := 130 ) ], count := [ 0, 0, 3, 1 ], mathmode := "Text", name := "Alt", next := 137, root := ~, start := 87, stop := 136 ), rec( content := " in ", count := [ 0, 0, 3, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 0, 0, 3, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 3, 1 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := ".\n\n This package's methods \ for computing digraph homomorphisms are based on work\n by Max Neunhöffer,\ and independently Artur Schäfer.\n ", count := [ 0, 0, 3, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 3, 1 ], name := "Acknowledgements", next := 3962, root := ~, start := 3671, stop := 3961 ) ], count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "TitlePage", next := 3976, root := ~, start := 1984, stop := 3975 ), rec( attributes := rec( ), content := 0, count := [ 0, 0, 4, 1 ], mathmode := "Text", name := "TableOfContents", next := 3997, root := ~, start := 3979, stop := 3996 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 0, 0, 4, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "The Digraphs package" ), content := [ rec( content := "\n ", count := [ 1, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\n The ", count := [ 1, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 1, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 0, 0, 2 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " package\n ", count := [ 1, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 0, 0, 2 ], mathmode := "Text", name := "Heading", next := 4098, root := ~, start := 4049, stop := 4097 ), rec( content := "\n ", count := [ 1, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "Digraphs" ), content := [ rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 1, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 0, 0, 3 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " package overview", count := [ 1, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 0, 0, 3 ], mathmode := "Text", name := "Index", next := 4158, root := ~, start := 4101, stop := 4157 ), rec( content := "\n\n", count := [ 1, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Introduction", count := [ 1, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 2 ], mathmode := "Text", name := "Heading", next := 4200, root := ~, start := 4169, stop := 4199 ), rec( content := "\n\n This is the manual\ for version 1.2.1 of the ", count := [ 1, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 1, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 3 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " package.\n This packag\ e was developed at the University of St Andrews by:\n ", count := [ 1, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Jan De Be\ ule,", count := [ 1, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 5 ], name := "Item", next := 4376, root := ~, start := 4350, stop := 4375 ), rec( attributes := rec( ), content := [ rec( content := "Julius Jo\ nušas,", count := [ 1, 1, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 7 ], name := "Item", next := 4414, root := ~, start := 4381, stop := 4413 ), rec( attributes := rec( ), content := [ rec( content := "James D. \ Mitchell,", count := [ 1, 1, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 9 ], name := "Item", next := 4450, root := ~, start := 4419, stop := 4449 ), rec( attributes := rec( ), content := [ rec( content := "Michael C\ . Torpey, and", count := [ 1, 1, 0, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 11 ], name := "Item", next := 4490, root := ~, start := 4455, stop := 4489 ), rec( attributes := rec( ), content := [ rec( content := "Wilf A. W\ ilson.", count := [ 1, 1, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 13 ], name := "Item", next := 4523, root := ~, start := 4495, stop := 4522 ) ], count := [ 1, 1, 0, 4 ], mathmode := "Text", name := "List", next := 4533, root := ~, start := 4339, stop := 4532 ), rec( content := "\n Additional contribut\ ions were made by:\n ", count := [ 1, 1, 0, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Stuart Bu\ rrell,", count := [ 1, 1, 0, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 17 ], name := "Item", next := 4616, root := ~, start := 4588, stop := 4615 ), rec( attributes := rec( ), content := [ rec( content := "Reinis Ci\ rpons,", count := [ 1, 1, 0, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 19 ], name := "Item", next := 4649, root := ~, start := 4621, stop := 4648 ), rec( attributes := rec( ), content := [ rec( content := "Luke Elli\ ott,", count := [ 1, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 21 ], name := "Item", next := 4680, root := ~, start := 4654, stop := 4679 ), rec( attributes := rec( ), content := [ rec( content := "Max Horn,\ ", count := [ 1, 1, 0, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 23 ], name := "Item", next := 4707, root := ~, start := 4685, stop := 4706 ), rec( attributes := rec( ), content := [ rec( content := "Christoph\ er Jefferson,", count := [ 1, 1, 0, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 25 ], name := "Item", next := 4747, root := ~, start := 4712, stop := 4746 ), rec( attributes := rec( ), content := [ rec( content := "Markus Pf\ eiffer,", count := [ 1, 1, 0, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 27 ], name := "Item", next := 4781, root := ~, start := 4752, stop := 4780 ), rec( attributes := rec( ), content := [ rec( content := "Chris Rus\ sell,", count := [ 1, 1, 0, 29 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 29 ], name := "Item", next := 4813, root := ~, start := 4786, stop := 4812 ), rec( attributes := rec( ), content := [ rec( content := "Finn Smit\ h, and", count := [ 1, 1, 0, 31 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 31 ], name := "Item", next := 4846, root := ~, start := 4818, stop := 4845 ), rec( attributes := rec( ), content := [ rec( content := "Maria Tsa\ lakou,", count := [ 1, 1, 0, 33 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 33 ], name := "Item", next := 4879, root := ~, start := 4851, stop := 4878 ), rec( attributes := rec( ), content := [ rec( content := "Murray Wh\ yte.", count := [ 1, 1, 0, 35 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 35 ], name := "Item", next := 4910, root := ~, start := 4884, stop := 4909 ) ], count := [ 1, 1, 0, 16 ], mathmode := "Text", name := "List", next := 4920, root := ~, start := 4577, stop := 4919 ), rec( content := "\n\n The ", count := [ 1, 1, 0, 37 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 1, 1, 0, 37 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 37 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " package contains a vari\ ety of methods for efficiently creating\n and storing mutable and immutable d\ igraphs and computing information about\n them. Full explanations of all t\ he functions contained in the package are\n provided below. ", count := [ 1, 1, 0, 37 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "P", next := 5182, root := ~, start := 5178, stop := 5181 ), rec( content := "\n\n If the ", count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" ), content := [ rec( content := "http://ww\ w.maths.qmul.ac.uk/~leonard/grape/", count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 ) ], count := [ 1, 1, 0, 38 ], name := "Alt", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes := rec( ), content := [ rec( content := "Grape", count := [ 1, 1, 0, 38 ], name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 38 ], name := "Package", next := 137, root := ~, start := 113, stop := 136 ) ], count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), rec( content := " package is available, i\ t will be loaded automatically.\n Digraphs created with the ", count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " package can be converte\ d to ", count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" ), content := [ rec( content := "http://ww\ w.maths.qmul.ac.uk/~leonard/grape/", count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 ) ], count := [ 1, 1, 0, 38 ], name := "Alt", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes := rec( ), content := [ rec( content := "Grape", count := [ 1, 1, 0, 38 ], name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 38 ], name := "Package", next := 137, root := ~, start := 113, stop := 136 ) ], count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), rec( content := "\n graphs with ", count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Graph" ) , content := 0, count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "Ref", next := 5364, root := ~, start := 5345, stop := 5363 ), rec( content := ", and conversely ", count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" ), content := [ rec( content := "http://ww\ w.maths.qmul.ac.uk/~leonard/grape/", count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 ) ], count := [ 1, 1, 0, 38 ], name := "Alt", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes := rec( ), content := [ rec( content := "Grape", count := [ 1, 1, 0, 38 ], name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 38 ], name := "Package", next := 137, root := ~, start := 113, stop := 136 ) ], count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), rec( content := " graphs can be\n conver\ ted to ", count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " objects with ", count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph" ), content := 0, count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "Ref", next := 5463, root := ~, start := 5442, stop := 5462 ), rec( content := ". ", count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" ), content := [ rec( content := "http://ww\ w.maths.qmul.ac.uk/~leonard/grape/", count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 ) ], count := [ 1, 1, 0, 38 ], name := "Alt", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes := rec( ), content := [ rec( content := "Grape", count := [ 1, 1, 0, 38 ], name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 38 ], name := "Package", next := 137, root := ~, start := 113, stop := 136 ) ], count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), rec( content := " is not\n required for \ ", count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " to run. ", count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "P", next := 5519, root := ~, start := 5515, stop := 5518 ), rec( content := "\n\n The ", count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "bliss" ), content := [ rec( content := "http://ww\ w.tcs.tkk.fi/Software/bliss/", count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "URL", next := 81, root := ~, start := 17, stop := 80 ) ], count := [ 1, 1, 0, 39 ], name := "Alt", next := 87, root := ~, start := 1, stop := 86 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes := rec( ), content := [ rec( content := "bliss", count := [ 1, 1, 0, 39 ], name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 39 ], name := "Package", next := 131, root := ~, start := 107, stop := 130 ) ], count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "Alt", next := 137, root := ~, start := 87, stop := 136 ), rec( content := " tool ", count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "JK07" ), content := 0, count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "Cite", next := 5558, root := ~, start := 5540, stop := 5557 ), rec( content := " is included in this pac\ kage. It\n is an open-source tool for computing automorphism groups and cano\ nical forms\n of graphs, written by Tommi Junttila and Petteri Kaski. Several\ of the methods\n in the ", count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " package rely on ", count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "bliss" ), content := [ rec( content := "http://ww\ w.tcs.tkk.fi/Software/bliss/", count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "URL", next := 81, root := ~, start := 17, stop := 80 ) ], count := [ 1, 1, 0, 39 ], name := "Alt", next := 87, root := ~, start := 1, stop := 86 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes := rec( ), content := [ rec( content := "bliss", count := [ 1, 1, 0, 39 ], name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 39 ], name := "Package", next := 131, root := ~, start := 107, stop := 130 ) ], count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "Alt", next := 137, root := ~, start := 87, stop := 136 ), rec( content := ". If the ", count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "NautyTracesInte\ rface" ), content := [ rec( content := "https://github.com/gap-packages/NautyT\ racesInterface", count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], count := [ 1, 1, 0, 39 ], name := "Alt", next := 117, root := ~, start := 1, stop := 116 ) , rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes := rec( ), content := [ rec( content := "NautyTrac\ esInterface", count := [ 1, 1, 0, 39 ], name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 39 ], name := "Package", next := 176, root := ~, start := 137, stop := 175 ) ], count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "Alt", next := 182, root := ~, start := 117, stop := 181 ), rec( content := "\n package for GAP is a\ vailable then it is also possible to use ", count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "nauty" ), content := [ rec( content := "http://pa\ llini.di.uniroma1.it/", count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "URL", next := 74, root := ~, start := 17, stop := 73 ) ], count := [ 1, 1, 0, 39 ], name := "Alt", next := 80, root := ~, start := 1, stop := 79 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes := rec( ), content := [ rec( content := "nauty", count := [ 1, 1, 0, 39 ], name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 39 ], name := "Package", next := 124, root := ~, start := 100, stop := 123 ) ], count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "Alt", next := 130, root := ~, start := 80, stop := 129 ), rec( content := " ", count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "MP14" ), content := 0, count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "Cite", next := 5920, root := ~, start := 5898, stop := 5919 ), rec( content := " for computing automorph\ ism groups and canonical forms\n in ", count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := ". See Section \n ", count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Sect := "Isomorphisms and canoni\ cal labellings" ), content := 0, count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "Ref", next := 6058, root := ~, start := 6007, stop := 6057 ), rec( content := " for more details. \n \ ", count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := 0, count := [ 1, 1, 0, 40 ], mathmode := "Text", name := "P", next := 6085, root := ~, start := 6081, stop := 6084 ), rec( content := "\n\n From version 1.0.0\ of this package, digraphs can be either mutable or immutable.\n Mutable digr\ aphs can be changed in-place by many of the methods in the\n package, which a\ voids unnecessary copying. Immutable digraphs cannot be\n changed in-place, b\ ut their advantage is that the value of an attribute of\n an immutable digrap\ h is only ever computed once. Mutable digraphs can be\n converted into immuta\ ble digraphs in-place using ", count := [ 1, 1, 0, 40 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "ref", Func := "MakeImmutable" ), content := 0, count := [ 1, 1, 0, 40 ], mathmode := "Text", name := "Ref", next := 6566, root := ~, start := 6520, stop := 6565 ), rec( content := ". One of the motivation\ s for introducing mutable\n digraphs in version 1.0.0 was that in practice th\ e authors often wanted\n to create a digraph and immediately modify it (remov\ ing certain edges,\n loops, and so on). Before version 1.0.0, this involved c\ opying the digraph\n several times, with each copy being discarded almost imm\ ediately.\n From version 1.0.0, this unnecessary copying can be eliminated by\ \n first creating a mutable digraph, then changing it in-place, and finally\ \n converting the mutable digraph to an immutable one in-place\n (if desirab\ le).\n\n ", count := [ 1, 1, 0, 40 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "Definitions" ), content := [ rec( attributes := rec( ), content := [ rec( content := "Definitio\ ns", count := [ 1, 1, 1, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 2 ], mathmode := "Text", name := "Heading", next := 7197, root := ~, start := 7167, stop := 7196 ), rec( content := "\n\n For the \ purposes of this package and its documentation, the following\n definitions\ apply: ", count := [ 1, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "P", next := 7300, root := ~, start := 7296, stop := 7299 ), rec( content := "\n\n A ", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "digraph", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "E", next := 7322, root := ~, start := 7308, stop := 7321 ), rec( content := " ", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "E=(E^0,E^\ 1,r,s)", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "M", next := 7345, root := ~, start := 7323, stop := 7344 ), rec( content := ", also known as \ a ", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "directed\\ n graph", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "E", next := 7390, root := ~, start := 7363, stop := 7389 ), rec( content := ", consists of a \ set of vertices ", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "E^0", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "M", next := 7432, root := ~, start := 7422, stop := 7431 ), rec( content := " and a set of ed\ ges\n ", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "E^1", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "M", next := 7466, root := ~, start := 7456, stop := 7465 ), rec( content := " together with f\ unctions ", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s, r: E^1\ \\to E^0", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "M", next := 7515, root := ~, start := 7491, stop := 7514 ), rec( content := ", called the\n \ ", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "source", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "E", next := 7545, root := ~, start := 7532, stop := 7544 ), rec( content := " and ", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "range", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "E", next := 7562, root := ~, start := 7550, stop := 7561 ), rec( content := ", respectively.\\ n\n The source and range of an edge is respectively the values of ", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s, r", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "M", next := 7656, root := ~, start := 7645, stop := 7655 ), rec( content := " at\n that ed\ ge.\n\n An edge is called a ", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "loop", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "E", next := 7711, root := ~, start := 7700, stop := 7710 ), rec( content := " if its source a\ nd range are the same.\n\n A digraph is called a ", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "multidigr\ aph", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "E", next := 7796, root := ~, start := 7777, stop := 7795 ), rec( content := " if there exist \ two or more edges\n with the same source and the same range. ", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "P", next := 7879, root := ~, start := 7875, stop := 7878 ), rec( content := "\n\n A ", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "directed \ walk", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "E", next := 7907, root := ~, start := 7887, stop := 7906 ), rec( content := " on a digraph is\ a sequence of alternating vertices\n and edges ", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "(v_1, e_1\ , v_2, e_2, ..., e_{n-1}, v_n)", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "M", next := 8019, root := ~, start := 7973, stop := 8018 ), rec( content := " such that each \ edge\n ", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e_i", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "M", next := 8054, root := ~, start := 8044, stop := 8053 ), rec( content := " has source ", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v_i", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "M", next := 8076, root := ~, start := 8066, stop := 8075 ), rec( content := " and range ", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v_{i+1}", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "M", next := 8101, root := ~, start := 8087, stop := 8100 ), rec( content := ". A ", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "directed\\ n path", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "E", next := 8131, root := ~, start := 8105, stop := 8130 ), rec( content := " is a directed w\ alk where no vertex (and hence no edge) is\n repeated. A ", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "directed \ circuit", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "E", next := 8230, root := ~, start := 8207, stop := 8229 ), rec( content := " is a directed w\ alk where ", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v_1 =\n \ v_n", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "M", next := 8278, root := ~, start := 8256, stop := 8277 ), rec( content := ", and a ", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "directed \ cycle", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "E", next := 8307, root := ~, start := 8286, stop := 8306 ), rec( content := " is a directed c\ ircuit where where no\n vertex is repeated, except for ", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v_1 = v_n\ ", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "M", next := 8396, root := ~, start := 8380, stop := 8395 ), rec( content := ". ", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "P", next := 8403, root := ~, start := 8399, stop := 8402 ), rec( content := "\n\n The ", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "length", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "E", next := 8426, root := ~, start := 8413, stop := 8425 ), rec( content := " of a directed w\ alk ", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "(v_1, e_1\ , v_2, e_2, ..., e_{n-1},\n v_n)", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "M", next := 8498, root := ~, start := 8446, stop := 8497 ), rec( content := " is equal to ", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n-1", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "M", next := 8521, root := ~, start := 8511, stop := 8520 ), rec( content := ", the number of \ edges it contains. A\n directed walk (or path) ", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "(v_1, e_1\ , v_2, e_2, ..., e_{n-1}, v_n)", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "M", next := 8633, root := ~, start := 8587, stop := 8632 ), rec( content := " is\n sometim\ es called a directed walk (or path) ", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "from vert\ ex ", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ _1", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "M", next := 8709, root := ~, start := 8699, stop := 8708 ), rec( content := " to\n \ vertex ", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ _n", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "M", next := 8736, root := ~, start := 8726, stop := 8735 ) ], count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "E", next := 8740, root := ~, start := 8684, stop := 8739 ), rec( content := ". A directed wa\ lk of zero length, i.e. a sequence\n ", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "(v)", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "M", next := 8805, root := ~, start := 8795, stop := 8804 ), rec( content := " for some vertex\ ", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "v", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "M", next := 8830, root := ~, start := 8822, stop := 8829 ), rec( content := ", is called ", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "trivial", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "E", next := 8856, root := ~, start := 8842, stop := 8855 ), rec( content := ". A trivial\n \ directed walk is considered to be both a circuit and a cycle, as is the\n \ empty directed walk ", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "()", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "M", next := 8977, root := ~, start := 8968, stop := 8976 ), rec( content := ". A ", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "simple ci\ rcuit", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "E", next := 9002, root := ~, start := 8981, stop := 9001 ), rec( content := " is another name\ for a\n non-trivial and non-empty directed cycle.", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 1, 1, 1, 7 ], mathmode := "Text", name := "P", next := 9074, root := ~, start := 9070, stop := 9073 ), rec( content := "\n\n ", count := [ 1, 1, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 1, 1 ], mathmode := "Text", name := "Subsection", next := 9091, root := ~, start := 7135, stop := 9090 ), rec( content := "\n ", count := [ 1, 1, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 1, 0, 1 ], mathmode := "Text", name := "Section", next := 9104, root := ~, start := 4160, stop := 9103 ), rec( content := "\n", count := [ 1, 1, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 0, 0, 1 ], mathmode := "Text", name := "Chapter", next := 9115, root := ~, start := 4008, stop := 9114 ), rec( content := "\n ", count := [ 1, 1, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := " intro ", count := [ 1, 1, 1, 7 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n ", count := [ 1, 1, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "Installing Digraphs" ) , content := [ rec( content := "\n ", count := [ 2, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Installing ", count := [ 2, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 2, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 0, 0, 2 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ) ], count := [ 2, 0, 0, 2 ], mathmode := "Text", name := "Heading", next := 9214, root := ~, start := 9174, stop := 9213 ), rec( content := "\n\n ", count := [ 2, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "For those in a hurry" ), content := [ rec( content := "\n ", count := [ 2, 1, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "For those in a hu\ rry", count := [ 2, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 2 ], mathmode := "Text", name := "Heading", next := 9300, root := ~, start := 9261, stop := 9299 ), rec( content := "\n In this section we\ give a brief description of how to start using\n ", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := ".", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 2, 1, 0, 4 ], mathmode := "Text", name := "P", next := 9390, root := ~, start := 9386, stop := 9389 ), rec( content := "\n\n It is assumed th\ at you have a working copy of ", count := [ 2, 1, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "GAP", count := [ 2, 1, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 4 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " with version number\n \ 4.9.0 or higher. The most up-to-date version of ", count := [ 2, 1, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "GAP", count := [ 2, 1, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 4 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " and instructions\n o\ n how to install it can be obtained from the main ", count := [ 2, 1, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "GAP", count := [ 2, 1, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 4 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " webpage\n ", count := [ 2, 1, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "http://www.gap-sy\ stem.org", count := [ 2, 1, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 4 ], mathmode := "Text", name := "URL", next := 9656, root := ~, start := 9620, stop := 9655 ), rec( content := ".", count := [ 2, 1, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 2, 1, 0, 5 ], mathmode := "Text", name := "P", next := 9661, root := ~, start := 9657, stop := 9660 ), rec( content := "\n\n The following is\ a summary of the steps that should lead to a\n successful installation of \ ", count := [ 2, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 2, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 5 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := ":\n\n ", count := [ 2, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "\n \ ensure that the ", count := [ 2, 1, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "IO" ), content := [ rec( content := "\n http://gap-packages\ .github.io/io/\n", count := [ 2, 1, 0, 7 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 2, 1, 0, 7 ], mathmode := "Text", name := "URL", next := 78, root := ~, start := 17, stop := 77 ) ], count := [ 2, 1, 0, 7 ], name := "Alt", next := 84, root := ~, start := 1, stop := 83 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "IO", count := [ 2, 1, 0, 7 ], name := \ "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 7 ], name := "Package", next := 122, root := ~, start := 101 , stop := 121 ) ], count := [ 2, 1, 0, 7 ], mathmode := "Text", name := "Alt", next := 128, root := ~, start := 84, stop := 127 ), rec( content := " package\ version 4.5.1 or higher is available.\n ", count := [ 2, 1, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "IO" ), content := [ rec( content := "\n http://gap-packages\ .github.io/io/\n", count := [ 2, 1, 0, 7 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 2, 1, 0, 7 ], mathmode := "Text", name := "URL", next := 78, root := ~, start := 17, stop := 77 ) ], count := [ 2, 1, 0, 7 ], name := "Alt", next := 84, root := ~, start := 1, stop := 83 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "IO", count := [ 2, 1, 0, 7 ], name := \ "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 7 ], name := "Package", next := 122, root := ~, start := 101 , stop := 121 ) ], count := [ 2, 1, 0, 7 ], mathmode := "Text", name := "Alt", next := 128, root := ~, start := 84, stop := 127 ), rec( content := " must be\ compiled before ", count := [ 2, 1, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphs", count := [ 2, 1, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 7 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " can be \ loaded.\n ", count := [ 2, 1, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 7 ], name := "Item", next := 9952, root := ~, start := 9791, stop := 9951 ), rec( attributes := rec( ), content := [ rec( content := "\n \ ensure that the ", count := [ 2, 1, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "Orb" ), content := [ rec( content := "\n http://http://gap-\ packages.github.io/orb/", count := [ 2, 1, 0, 9 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 9 ], mathmode := "Text", name := "URL\ ", next := 86, root := ~, start := 17, stop := 85 ), rec( content := "\n " , count := [ 2, 1, 0, 9 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 9 ], name := "Alt", next := 98, root := ~, start := 1, stop := 97 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "Orb", count := [ 2, 1, 0, 9 ], name :=\ "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 9 ], name := "Package", next := 137, root := ~, start := 115 , stop := 136 ) ], count := [ 2, 1, 0, 9 ], mathmode := "Text", name := "Alt", next := 143, root := ~, start := 98, stop := 142 ), rec( content := " package\ version 4.8.2 or higher is available.\n ", count := [ 2, 1, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "Orb" ), content := [ rec( content := "\n http://http://gap-\ packages.github.io/orb/", count := [ 2, 1, 0, 9 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 9 ], mathmode := "Text", name := "URL\ ", next := 86, root := ~, start := 17, stop := 85 ), rec( content := "\n " , count := [ 2, 1, 0, 9 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 9 ], name := "Alt", next := 98, root := ~, start := 1, stop := 97 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "Orb", count := [ 2, 1, 0, 9 ], name :=\ "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 9 ], name := "Package", next := 137, root := ~, start := 115 , stop := 136 ) ], count := [ 2, 1, 0, 9 ], mathmode := "Text", name := "Alt", next := 143, root := ~, start := 98, stop := 142 ), rec( content := " has bet\ ter performance when compiled, but although compilation is\n recommende\ d, it is not required to be compiled for ", count := [ 2, 1, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphs", count := [ 2, 1, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 9 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " to be\n\ loaded.\n ", count := [ 2, 1, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 9 ], name := "Item", next := 10232, root := ~, start := 9960, stop := 10231 ), rec( attributes := rec( ), content := [ rec( content := " ensure t\ hat the ", count := [ 2, 1, 0, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "datastructures" ), content := [ rec( content := "https://github\ .com/gap-packages/datastructures", count := [ 2, 1, 0, 11 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 11 ], mathmode := "Tex\ t", name := "URL", next := 103, root := ~, start := 17, stop := 102 ) ], count := [ 2, 1, 0, 11 ], name := "Alt", next := 109, root := ~, start := 1, stop := 108 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "datastructures", count := [ 2, 1, 0, 1\ 1 ], name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 11 ], name := "Packa\ ge", next := 162, root := ~, start := 129, stop := 161 ) ], count := [ 2, 1, 0, 11 ], mathmode := "Text", name := "Alt", next := 168, root := ~, start := 109, stop := 167 ), rec( content := " package\ version\n 0.2.5 or higher is available. \n ", count := [ 2, 1, 0, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 11 ], name := "Item", next := 10361, root := ~, start := 10240, stop := 10360 ), rec( attributes := rec( ), content := [ rec( content := "\n \ ", count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "T\ his step is optional:", count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "B", next := 10413, root := ~, start := 10384, stop := 10412 ), rec( content := " certain\ functions in ", count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphs", count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " require\ \n the ", count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\ c.uk/~leonard/grape/", count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "\ PCDATA", root := ~ ) ], count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "URL\ ", next := 87, root := ~, start := 17, stop := 86 ) ], count := [ 2, 1, 0, 13 ], name := "Alt", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "Grape", count := [ 2, 1, 0, 13 ], name\ := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 13 ], name := "Package", next := 137, root := ~, start := 113 , stop := 136 ) ], count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), rec( content := " package\ to be available; see Section\n ", count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Subsect := "The \ Grape package" ), content := 0, count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "Ref", next := 10553, root := ~, start := 10519, stop := 10552 ), rec( content := " for ful\ l details. To use these\n functions make sure\n that the ", count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\ c.uk/~leonard/grape/", count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "\ PCDATA", root := ~ ) ], count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "URL\ ", next := 87, root := ~, start := 17, stop := 86 ) ], count := [ 2, 1, 0, 13 ], name := "Alt", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "Grape", count := [ 2, 1, 0, 13 ], name\ := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 13 ], name := "Package", next := 137, root := ~, start := 113 , stop := 136 ) ], count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), rec( content := " package\ version 4.8.1 or higher is available.\n If ", count := [ 2, 1, 0, 13 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\ c.uk/~leonard/grape/", count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "\ PCDATA", root := ~ ) ], count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "URL\ ", next := 87, root := ~, start := 17, stop := 86 ) ], count := [ 2, 1, 0, 13 ], name := "Alt", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "Grape", count := [ 2, 1, 0, 13 ], name\ := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 13 ], name := "Package", next := 137, root := ~, start := 113 , stop := 136 ) ], count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), rec( content := " is not \ available, then ", count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphs", count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " can be \ used as normal with\n the exception that the functions listed in Subsec\ tion\n ", count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Subsect := "The \ Grape package" ), content := 0, count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "Ref", next := 10875, root := ~, start := 10841, stop := 10874 ), rec( content := " will no\ t work.\n ", count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 13 ], name := "Item", next := 10904, root := ~, start := 10369, stop := 10903 ), rec( attributes := rec( ), content := [ rec( content := "\n \ ", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "T\ his step is optional:", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "B", next := 10962, root := ~, start := 10933, stop := 10961 ), rec( content := " certain\ functions in ", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphs", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " require\ \n the ", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\ github.com/gap-packages/NautyTracesInterface", count := [ 2, 1, 0, 15 ], mathm\ ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 15 ], mathmode := \ "Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], count := [ 2, 1, 0, 15 ], name := "Alt", next := 117, root := ~, start := 1, stop := 116 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "NautyTracesInterface", count := [ 2, 1\ , 0, 15 ], name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 15 ], name := "Pac\ kage", next := 176, root := ~, start := 137, stop := 175 ) ], count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "Alt", next := 182, root := ~, start := 117, stop := 181 ), rec( content := " package\ to be available.\n ", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := " TODO \n\ see Section\n for full d\ etails. ", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "XMLCOMMENT" , root := ~ ), rec( content := "\n \ If you want to make use of these functions, please ensure that the\n \ ", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\ github.com/gap-packages/NautyTracesInterface", count := [ 2, 1, 0, 15 ], mathm\ ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 15 ], mathmode := \ "Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], count := [ 2, 1, 0, 15 ], name := "Alt", next := 117, root := ~, start := 1, stop := 116 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "NautyTracesInterface", count := [ 2, 1\ , 0, 15 ], name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 15 ], name := "Pac\ kage", next := 176, root := ~, start := 137, stop := 175 ) ], count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "Alt", next := 182, root := ~, start := 117, stop := 181 ), rec( content := " package\ version 0.2 or\n higher is available. If ", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\ github.com/gap-packages/NautyTracesInterface", count := [ 2, 1, 0, 15 ], mathm\ ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 15 ], mathmode := \ "Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], count := [ 2, 1, 0, 15 ], name := "Alt", next := 117, root := ~, start := 1, stop := 116 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "NautyTracesInterface", count := [ 2, 1\ , 0, 15 ], name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 15 ], name := "Pac\ kage", next := 176, root := ~, start := 137, stop := 175 ) ], count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "Alt", next := 182, root := ~, start := 117, stop := 181 ), rec( content := " is not \ available,\n then ", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphs", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " can be \ used as normal with the exception that \n functions whose names conta\ in ", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "N\ auty", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "Q", next := 11521, root := ~, start := 11509, stop := 11520 ), rec( content := " will no\ t work.\n ", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 15 ], name := "Item", next := 11550, root := ~, start := 10918, stop := 11549 ), rec( attributes := rec( ), content := [ rec( content := "\n \ download the package archive ", count := [ 2, 1, 0, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraphs-1.2.1.tar.gz", count := [ 2, 1, 0, 17 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 2, 1, 0, 17 ], mathmode := "Text", name := "F", next := 11629, root := ~, start := 11602, stop := 11628 ), rec( content := " from\n \ ", count := [ 2, 1, 0, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Text := "the Dig\ raph package webpage" ), content := [ rec( content := "http://gap-packages.git\ hub.io/Digraphs/", count := [ 2, 1, 0, 17 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 2, 1, 0, 17 ], mathmode := "Text", name := "URL", next := 11728, root := ~, start := 11643, stop := 11727 ), rec( content := ".\n \ ", count := [ 2, 1, 0, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 17 ], name := "Item", next := 11743, root := ~, start := 11558, stop := 11742 ), rec( attributes := rec( ), content := [ rec( content := "\n \ unzip and untar the file, this should create a directory called\n ", count := [ 2, 1, 0, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraphs-1.2.1", count := [ 2, 1, 0, 19 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 2, 1, 0, 19 ], mathmode := "Text", name := "F", next := 11858, root := ~, start := 11838, stop := 11857 ), rec( content := ".\n \ ", count := [ 2, 1, 0, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 19 ], name := "Item", next := 11873, root := ~, start := 11751, stop := 11872 ), rec( attributes := rec( ), content := [ rec( content := "\n \ locate the ", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ kg", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "F", next := 11917, root := ~, start := 11907, stop := 11916 ), rec( content := " directo\ ry of your ", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ AP", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " directo\ ry, which contains\n the directories ", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ib", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "F", next := 12002, root := ~, start := 11992, stop := 12001 ), rec( content := ", ", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ oc", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "F", next := 12014, root := ~, start := 12004, stop := 12013 ), rec( content := " and so \ on. Move the directory\n ", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraphs-1.2.1", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "F", next := 12073, root := ~, start := 12053, stop := 12072 ), rec( content := " into th\ e ", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ kg", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "F", next := 12093, root := ~, start := 12083, stop := 12092 ), rec( content := " directo\ ry.\n ", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 21 ], name := "Item", next := 12118, root := ~, start := 11881, stop := 12117 ), rec( attributes := rec( ), content := [ rec( content := "\n \ it is necessary to compile the ", count := [ 2, 1, 0, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphs", count := [ 2, 1, 0, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 23 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " package\ .\n Inside the ", count := [ 2, 1, 0, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ kg/digraphs-1.2.1", count := [ 2, 1, 0, 23 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 2, 1, 0, 23 ], mathmode := "Text", name := "F", next := 12235, root := ~, start := 12211, stop := 12234 ), rec( content := " directo\ ry, type\n ", count := [ 2, 1, 0, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ n./configure\nmake", count := [ 2, 1, 0, 24 ], name := "PCDATA", root := ~ ) ] , count := [ 2, 1, 0, 24 ], mathmode := "Text", name := "Listing", next := 12308, root := ~, start := 12260, stop := 12307 ), rec( content := "\n \ Further information about this step can be found in Section\n ", count := [ 2, 1, 0, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Sect := "Compili\ ng the kernel module" ), content := 0, count := [ 2, 1, 0, 25 ], mathmode := "Text", name := "Ref", next := 12426, root := ~, start := 12385, stop := 12425 ), rec( content := ".\n \ ", count := [ 2, 1, 0, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 23 ], name := "Item", next := 12441, root := ~, start := 12126, stop := 12440 ), rec( attributes := rec( ), content := [ rec( content := "\n \ start ", count := [ 2, 1, 0, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ AP", count := [ 2, 1, 0, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 27 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " in the \ usual way (i.e. type ", count := [ 2, 1, 0, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ ap", count := [ 2, 1, 0, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 27 ], mathmode := "Text", name := "C", next := 12514, root := ~, start := 12504, stop := 12513 ), rec( content := " at the \ command line).\n ", count := [ 2, 1, 0, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 27 ], name := "Item", next := 12550, root := ~, start := 12449, stop := 12549 ), rec( attributes := rec( ), content := [ rec( content := "\n \ type ", count := [ 2, 1, 0, 29 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "L\ oadPackage(\"digraphs\");", count := [ 2, 1, 0, 29 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 2, 1, 0, 29 ], mathmode := "Text", name := "C", next := 12609, root := ~, start := 12578, stop := 12608 ), rec( content := "\n \ ", count := [ 2, 1, 0, 29 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 29 ], name := "Item", next := 12623, root := ~, start := 12558, stop := 12622 ) ], count := [ 2, 1, 0, 6 ], mathmode := "Text", name := "List", next := 12635, root := ~, start := 9777, stop := 12634 ), rec( content := "\n\n If you want to c\ heck that the package is working correctly, you\n should run some of the te\ sts described in Section\n ", count := [ 2, 1, 0, 31 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Sect := "Testing your installati\ on" ), content := 0, count := [ 2, 1, 0, 31 ], mathmode := "Text", name := "Ref", next := 12802, root := ~, start := 12763, stop := 12801 ), rec( content := ".\n ", count := [ 2, 1, 0, 31 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 1 ], mathmode := "Text", name := "Section", next := 12816, root := ~, start := 9218, stop := 12815 ), rec( content := "\n\n ", count := [ 2, 1, 0, 31 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := "********************************\ **************************************", count := [ 2, 1, 0, 31 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n ", count := [ 2, 1, 0, 31 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := "********************************\ **************************************", count := [ 2, 1, 0, 31 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n\n ", count := [ 2, 1, 0, 31 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "Optional package dependencies"\ ), content := [ rec( content := "\n ", count := [ 2, 2, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Optional package \ dependencies", count := [ 2, 2, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 2, 0, 2 ], mathmode := "Text", name := "Heading", next := 13081, root := ~, start := 13033, stop := 13080 ), rec( content := "\n\n ", count := [ 2, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := "************************\ ********************************************", count := [ 2, 2, 0, 3 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n\n The ", count := [ 2, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 2, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 2, 0, 3 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " package is written in " , count := [ 2, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "GAP", count := [ 2, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 2, 0, 3 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " and C code and requires\ the\n ", count := [ 2, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "IO" ), content := [ rec( content := "\n ht\ tp://gap-packages.github.io/io/\n", count := [ 2, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 2, 0, 3 ], mathmode := "Text", name := "URL", next := 78, root := ~, start := 17, stop := 77 ) ], count := [ 2, 2, 0, 3 ], name := "Alt", next := 84, root := ~, start := 1, stop := 83 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes := rec( ), content := [ rec( content := "IO", count := [ 2, 2, 0, 3 ], name := "PCDATA", root := ~ ) ], count := [ 2, 2, 0, 3 ], name := "Package", next := 122, root := ~, start := 101, stop := 121 ) ], count := [ 2, 2, 0, 3 ], mathmode := "Text", name := "Alt", next := 128, root := ~, start := 84, stop := 127 ), rec( content := " package. The ", count := [ 2, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "IO" ), content := [ rec( content := "\n ht\ tp://gap-packages.github.io/io/\n", count := [ 2, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 2, 0, 3 ], mathmode := "Text", name := "URL", next := 78, root := ~, start := 17, stop := 77 ) ], count := [ 2, 2, 0, 3 ], name := "Alt", next := 84, root := ~, start := 1, stop := 83 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes := rec( ), content := [ rec( content := "IO", count := [ 2, 2, 0, 3 ], name := "PCDATA", root := ~ ) ], count := [ 2, 2, 0, 3 ], name := "Package", next := 122, root := ~, start := 101, stop := 121 ) ], count := [ 2, 2, 0, 3 ], mathmode := "Text", name := "Alt", next := 128, root := ~, start := 84, stop := 127 ), rec( content := " package is used to read\ and write transformations,\n partial permutations, and bipartitions to a f\ ile. ", count := [ 2, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 2, 2, 0, 4 ], mathmode := "Text", name := "P", next := 13376, root := ~, start := 13372, stop := 13375 ), rec( content := "\n\n ", count := [ 2, 2, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := "************************\ ********************************************", count := [ 2, 2, 0, 4 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n\n ", count := [ 2, 2, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "The Grape package" ), content := [ rec( content := "\n ", count := [ 2, 2, 1, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "The Grape\ package", count := [ 2, 2, 1, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 2, 1, 2 ], mathmode := "Text", name := "Heading", next := 13544, root := ~, start := 13508, stop := 13543 ), rec( content := "\n\n The ", count := [ 2, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" ), content := [ rec( content := "h\ ttp://www.maths.qmul.ac.uk/~leonard/grape/", count := [ 2, 2, 1, 3 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 2, 1, 3 ], mathmode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 ) ], count := [ 2, 2, 1, 3 ], name := "Alt", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := rec( Only := "Text" ), content := [ rec( attributes := rec( ) , content := [ rec( content := "G\ rape", count := [ 2, 2, 1, 3 ], name := "PCDATA", root := ~ ) ], count := [ 2, 2, 1, 3 ], name := "Package", next := 137, root := ~, start := 113, stop := 136 ) ], count := [ 2, 2, 1, 3 ], mathmode := "Text", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), rec( content := " package must be\ available for the following operations to be\n available:\n\n ", count := [ 2, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( attributes :=\ rec( Oper := "Graph" ), content := 0, count := [ 2, 2, 1, 5 ], mathmode := "T\ ext", name := "Ref", next := 13689, root := ~, start := 13670, stop := 13688 ) , rec( content := "\ with a digraph argument", count := [ 2, 2, 1, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 2, 2, 1, 5 ], name := "Item", next := 13720, root := ~, start := 13664, stop := 13719 ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( Attr := "AsGraph" ), content := 0, count := [ 2, 2, 1, 7 ], mathmode := \ "Text", name := "Ref", next := 13756, root := ~, start := 13735, stop := 13755\ ), rec( content := " with a digraph argument", count := [ 2, 2, 1, 7 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 2, 1, 7 ], name := "Item", next := 13787, root := ~, start := 13729, stop := 13786 ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( Oper := "Digraph" ), content := 0, count := [ 2, 2, 1, 9 ], mathmode := \ "Text", name := "Ref", next := 13823, root := ~, start := 13802, stop := 13822\ ), rec( content := " with a ", count := [ 2, 2, 1, 9 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attri\ butes := rec( Text := "Grape" ), content := [ rec( content := "http://www.math\ s.qmul.ac.uk/~leonard/grape/", count := [ 2, 2, 1, 9 ], mathmode := "Text", na\ me := "PCDATA", root := ~ ) ], count := [ 2, 2, 1, 9 ], mathmode := "Text", name\ := "URL", next := 87, root := ~, start := 17, stop := 86 ) ], count := [ 2, 2, 1, 9 ], name := "Alt\ ", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := rec( Only := \ "Text" ), content := [ rec( attributes := rec( ), content := [ rec( content :\ = "Grape", count := [ 2, 2, 1, 9 ], name := "PCDATA", root := ~ ) ], count := [ \ 2, 2, 1, 9 ], name := "Package", next := 137, root := ~, start := 113, stop :=\ 136 ) ], count := [ 2, 2, 1, 9 ], mathmode := "Text", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), rec( content := "\ graph argument", count := [ 2, 2, 1, 9 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 2, 2, 1, 9 ], name := "Item", next := 13860, root := ~, start := 13796, stop := 13859 ) ], count := [ 2, 2, 1, 4 ], mathmode := "Text", name := "List", next := 13874, root := ~, start := 13649, stop := 13873 ), rec( content := "\n\n If ", count := [ 2, 2, 1, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" ), content := [ rec( content := "h\ ttp://www.maths.qmul.ac.uk/~leonard/grape/", count := [ 2, 2, 1, 11 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 2, 1, 11 ], mathmode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 ) ], count := [ 2, 2, 1, 11 ], name := "Alt", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := rec( Only := "Text" ), content := [ rec( attributes := rec( ) , content := [ rec( content := "G\ rape", count := [ 2, 2, 1, 11 ], name := "PCDATA", root := ~ ) ], count := [ 2, 2, 1, 11 ], name := "Package", next := 137, root := ~, start := 113, stop := 136 ) ], count := [ 2, 2, 1, 11 ], mathmode := "Text", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), rec( content := " is not availabl\ e, then ", count := [ 2, 2, 1, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs" , count := [ 2, 2, 1, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 2, 1, 11 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " can be used as \ normal with\n the exception that the functions above will not work.\n \ ", count := [ 2, 2, 1, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 2, 1, 1 ], mathmode := "Text", name := "Subsection", next := 14031, root := ~, start := 13463, stop := 14030 ), rec( content := "\n ", count := [ 2, 2, 1, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 2, 0, 1 ], mathmode := "Text", name := "Section", next := 14044, root := ~, start := 12981, stop := 14043 ), rec( content := "\n\n ", count := [ 2, 2, 1, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := "********************************\ **************************************", count := [ 2, 2, 1, 11 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n ", count := [ 2, 2, 1, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := "********************************\ **************************************", count := [ 2, 2, 1, 11 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n\n ", count := [ 2, 2, 1, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "Compiling the kernel module" ) , content := [ rec( content := "\n ", count := [ 2, 3, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Compiling the ker\ nel module", count := [ 2, 3, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 3, 0, 2 ], mathmode := "Text", name := "Heading", next := 14305, root := ~, start := 14259, stop := 14304 ), rec( content := "\n The ", count := [ 2, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 2, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 3, 0, 3 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " package has a ", count := [ 2, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "GAP", count := [ 2, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 3, 0, 3 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " kernel component in\n \ C which should be compiled. This component contains certain low-level\n f\ unctions required by ", count := [ 2, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 2, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 3, 0, 3 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := ".\n ", count := [ 2, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 2, 3, 0, 4 ], mathmode := "Text", name := "P", next := 14485, root := ~, start := 14481, stop := 14484 ), rec( content := "\n\n It is not possib\ le to use the ", count := [ 2, 3, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 2, 3, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 3, 0, 4 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " package without compili\ ng it.", count := [ 2, 3, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 2, 3, 0, 5 ], mathmode := "Text", name := "P", next := 14565, root := ~, start := 14561, stop := 14564 ), rec( content := "\n\n To compile the k\ ernel component inside the ", count := [ 2, 3, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "pkg/digraphs-1.2.\ 1", count := [ 2, 3, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 3, 0, 5 ], mathmode := "Text", name := "F", next := 14638, root := ~, start := 14614, stop := 14637 ), rec( content := "\n directory, type\n" , count := [ 2, 3, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\n\n./configure\n\ make", count := [ 2, 3, 0, 6 ], name := "PCDATA", root := ~ ) ], count := [ 2, 3, 0, 6 ], mathmode := "Text", name := "Listing", next := 14708, root := ~, start := 14659, stop := 14707 ), rec( content := "\n ", count := [ 2, 3, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 2, 3, 0, 8 ], mathmode := "Text", name := "P", next := 14717, root := ~, start := 14713, stop := 14716 ), rec( content := "\n\n If you installed\ the package in another 'pkg' directory than the standard 'pkg'\n directory\ in your ", count := [ 2, 3, 0, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "GAP", count := [ 2, 3, 0, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 3, 0, 8 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " installation, then you \ have to do two things. Firstly\n during compilation you have to use the opt\ ion '--with-gaproot=PATH' of the\n 'configure' script where 'PATH' is a pat\ h to the main GAP root directory (if\n not given the default '../..' is ass\ umed).", count := [ 2, 3, 0, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 2, 3, 0, 9 ], mathmode := "Text", name := "P", next := 15095, root := ~, start := 15091, stop := 15094 ), rec( content := "\n\n If you installed\ ", count := [ 2, 3, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "GAP", count := [ 2, 3, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 3, 0, 9 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " on several architecture\ s, you must execute the\n configure/make step for each of the architectures\ . You can either do this\n immediately after configuring and compiling GAP \ itself on this architecture, or\n alternatively set the environment\n va\ riable 'CONFIGNAME' to the name of the configuration you used when compiling\n\ GAP before running './configure'. Note however that your compiler choice \ and\n flags (environment variables 'CC' and 'CFLAGS') need to be chosen to \ match the\n setup of the original GAP compilation. For example you have to \ specify 32-bit\n or 64-bit mode correctly!\n ", count := [ 2, 3, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 3, 0, 1 ], mathmode := "Text", name := "Section", next := 15743, root := ~, start := 14209, stop := 15742 ), rec( content := "\n\n ", count := [ 2, 3, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := "********************************\ **************************************", count := [ 2, 3, 0, 9 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n ", count := [ 2, 3, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := "********************************\ **************************************", count := [ 2, 3, 0, 9 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n\n ", count := [ 2, 3, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "Rebuilding the documentation" ), content := [ rec( content := "\n ", count := [ 2, 4, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Rebuilding the do\ cumentation", count := [ 2, 4, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 4, 0, 2 ], mathmode := "Text", name := "Heading", next := 16006, root := ~, start := 15959, stop := 16005 ), rec( content := "\n The ", count := [ 2, 4, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 2, 4, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 4, 0, 3 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " package comes complete \ with pdf, html, and text versions of\n the documentation. However, you migh\ t find it necessary, at some point, to\n rebuild the documentation. To rebu\ ild the documentation, please use the\n function ", count := [ 2, 4, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "DigraphsMakeDoc" ), content := 0, count := [ 2, 4, 0, 3 ], mathmode := "Text", name := "Ref", next := 16283, root := ~, start := 16254, stop := 16282 ), rec( content := ".\n\n ", count := [ 2, 4, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "", Name := "DigraphsMakeDoc\ " ), content := 0, count := [ 2, 4, 1, 2 ], mathmode := "Text", name := "Func", next := 16342, root := ~, start := 16305, stop := 16341 ), rec( attributes := rec( ), content := [ rec( content := "Nothing", count := [ 2, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 4, 1, 3 ], mathmode := "Text", name := "Returns", next := 16371, root := ~, start := 16345, stop := 16370 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function should be called with no argument to compile the ", count := [ 2, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphs", count := [ 2, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 4, 1, 3 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := "\n do\ cumentation.\n ", count := [ 2, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 4, 1, 3 ], mathmode := "Text", name := "Description", next := 16501, root := ~, start := 16374, stop := 16500 ) ], count := [ 2, 4, 1, 1 ], mathmode := "Text", name := "ManSection", next := 16515, root := ~, start := 16290, stop := 16514 ), rec( content := "\n\n ", count := [ 2, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 4, 0, 1 ], mathmode := "Text", name := "Section", next := 16529, root := ~, start := 15908, stop := 16528 ), rec( content := "\n\n ", count := [ 2, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := "********************************\ **************************************", count := [ 2, 4, 1, 3 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n ", count := [ 2, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := "********************************\ **************************************", count := [ 2, 4, 1, 3 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n\n ", count := [ 2, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "Testing your installation" ), content := [ rec( content := "\n ", count := [ 2, 5, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Testing your inst\ allation", count := [ 2, 5, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 0, 2 ], mathmode := "Text", name := "Heading", next := 16786, root := ~, start := 16742, stop := 16785 ), rec( content := "\n\n In this section \ we describe how to test that ", count := [ 2, 5, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 2, 5, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 0, 3 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " is working as\n inte\ nded. To test that ", count := [ 2, 5, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 2, 5, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 0, 3 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " is installed correctly \ use\n ", count := [ 2, 5, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "DigraphsTestInstall" ), content := 0, count := [ 2, 5, 0, 3 ], mathmode := "Text", name := "Ref", next := 16965, root := ~, start := 16932, stop := 16964 ), rec( content := " or for more extensive t\ ests use\n ", count := [ 2, 5, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "DigraphsTestStandard" ) , content := 0, count := [ 2, 5, 0, 3 ], mathmode := "Text", name := "Ref", next := 17036, root := ~, start := 17002, stop := 17035 ), rec( content := ". ", count := [ 2, 5, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 2, 5, 0, 4 ], mathmode := "Text", name := "P", next := 17042, root := ~, start := 17038, stop := 17041 ), rec( content := "\n\n If something goe\ s wrong, then please review the instructions in Section ", count := [ 2, 5, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Sect := "For those in a hurry" ) , content := 0, count := [ 2, 5, 0, 4 ], mathmode := "Text", name := "Ref", next := 17160, root := ~, start := 17120, stop := 17159 ), rec( content := " and ensure that ", count := [ 2, 5, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 2, 5, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 0, 4 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " has been\n properly \ installed. If you continue having problems, please use the ", count := [ 2, 5, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Text := "issue tracker" ), content := [ rec( content := "https://github.co\ m/gap-packages/Digraphs/issues", count := [ 2, 5, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 0, 4 ], mathmode := "Text", name := "URL", next := 17355, root := ~, start := 17270, stop := 17354 ), rec( content := "\n to report the issu\ es you are having.\n\n ", count := [ 2, 5, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "", Name := "DigraphsTestIns\ tall" ), content := 0, count := [ 2, 5, 1, 2 ], mathmode := "Text", name := "Func", next := 17458, root := ~, start := 17417, stop := 17457 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "K", next := 17481, root := ~, start := 17470, stop := 17480 ), rec( content := " or ", count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "K", next := 17497, root := ~, start := 17485, stop := 17496 ), rec( content := ".", count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "Returns", next := 17508, root := ~, start := 17461, stop := 17507 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function can be called without arguments to test your installation of\n " , count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphs", count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " is work\ ing correctly. These tests should take no more than a\n few seconds to comp\ lete. To test more comprehensively that\n ", count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphs", count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " is work\ ing correctly, use ", count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sTestStandard" ), content := 0, count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "Ref", next := 17819, root := ~, start := 17785, stop := 17818 ), rec( content := ".\n ", count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "Description", next := 17837, root := ~, start := 17511, stop := 17836 ) ], count := [ 2, 5, 1, 1 ], mathmode := "Text", name := "ManSection", next := 17851, root := ~, start := 17402, stop := 17850 ), rec( content := "\n\n ", count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "", Name := "DigraphsTestSta\ ndard" ), content := 0, count := [ 2, 5, 2, 2 ], mathmode := "Text", name := "Func", next := 17914, root := ~, start := 17872, stop := 17913 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 2, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 2, 3 ], mathmode := "Text", name := "K", next := 17937, root := ~, start := 17926, stop := 17936 ), rec( content := " or ", count := [ 2, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 2, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 2, 3 ], mathmode := "Text", name := "K", next := 17953, root := ~, start := 17941, stop := 17952 ), rec( content := ".", count := [ 2, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 2, 3 ], mathmode := "Text", name := "Returns", next := 17964, root := ~, start := 17917, stop := 17963 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function can be called without arguments to test all of the methods\n inc\ luded in ", count := [ 2, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphs", count := [ 2, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 2, 3 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := ".\n T\ hese tests should take less than a minute to complete. ", count := [ 2, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 2, 5, 2, 4 ], mathmode := "Text", name := "P", next := 18150, root := ~, start := 18146, stop := 18149 ), rec( content := "\n\n \ To quickly test that ", count := [ 2, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphs", count := [ 2, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 2, 4 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " is inst\ alled correctly use ", count := [ 2, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sTestInstall" ), content := 0, count := [ 2, 5, 2, 4 ], mathmode := "Text", name := "Ref", next := 18252, root := ~, start := 18215, stop := 18251 ), rec( content := ". For a\ more thorough test, use ", count := [ 2, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sTestExtreme" ), content := 0, count := [ 2, 5, 2, 4 ], mathmode := "Text", name := "Ref", next := 18322, root := ~, start := 18285, stop := 18321 ), rec( content := ".\n ", count := [ 2, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 2, 3 ], mathmode := "Text", name := "Description", next := 18340, root := ~, start := 17967, stop := 18339 ) ], count := [ 2, 5, 2, 1 ], mathmode := "Text", name := "ManSection", next := 18354, root := ~, start := 17857, stop := 18353 ), rec( content := "\n\n ", count := [ 2, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "", Name := "DigraphsTestExt\ reme" ), content := 0, count := [ 2, 5, 3, 2 ], mathmode := "Text", name := "Func", next := 18416, root := ~, start := 18375, stop := 18415 ), rec( attributes := rec( ), content := [ rec( content := "Nothing." , count := [ 2, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 3, 3 ], mathmode := "Text", name := "Returns", next := 18446, root := ~, start := 18419, stop := 18445 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function should be called with no argument. It executes a series of\n ver\ y demanding tests, which measure the performance of a variety of\n function\ s on large examples. These tests take a long time to\n complete, at least \ several minutes. ", count := [ 2, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "P", next := 18722, root := ~, start := 18718, stop := 18721 ), rec( content := "\n\n \ For these tests to complete, the digraphs library ", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraphs-lib", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "C", next := 18797, root := ~, start := 18778, stop := 18796 ), rec( content := " must\n \ be downloaded and placed in the ", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraphs", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "C", next := 18854, root := ~, start := 18839, stop := 18853 ), rec( content := " directo\ ry in a subfolder\n named ", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraphs-lib", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "F", next := 18909, root := ~, start := 18890, stop := 18908 ), rec( content := ".\n T\ his library can be found on the ", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphs", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " website\ .\n ", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 3, 3 ], mathmode := "Text", name := "Description", next := 18984, root := ~, start := 18449, stop := 18983 ) ], count := [ 2, 5, 3, 1 ], mathmode := "Text", name := "ManSection", next := 18998, root := ~, start := 18360, stop := 18997 ), rec( content := "\n\n\n ", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 0, 1 ], mathmode := "Text", name := "Section", next := 19013, root := ~, start := 16694, stop := 19012 ), rec( content := "\n\n ", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := "********************************\ **************************************", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n ", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := "********************************\ **************************************", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n\n\n", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 0, 0, 1 ], mathmode := "Text", name := "Chapter", next := 19187, root := ~, start := 9134, stop := 19186 ), rec( content := "\n ", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := " installing ", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n ", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "Creating digraphs" ), content := [ rec( attributes := rec( ), content := [ rec( content := "Creating digraphs", count := [ 3, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 0, 0, 2 ], mathmode := "Text", name := "Heading", next := 19282, root := ~, start := 19246, stop := 19281 ), rec( content := "\n\n In this chapter we describ\ e how to create digraphs.", count := [ 3, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 0, 0, 4 ], mathmode := "Text", name := "P", next := 19341, root := ~, start := 19337, stop := 19340 ), rec( content := "\n\n ", count := [ 3, 0, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Creating digraphs\ ", count := [ 3, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 0, 2 ], mathmode := "Text", name := "Heading", next := 19390, root := ~, start := 19354, stop := 19389 ), rec( content := "\n ", count := [ 3, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Name := "IsDigraph", Type := "Category" ), content := 0, count := [ 3, 1, 1, 2 ], mathmode := "Text", name := "Filt", next := 19450, root := ~, start := 19410, stop := 19449 ), rec( attributes := rec( ), content := [ rec( content := "\n Eve\ ry digraph in ", count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphs", count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " belong\ s to the category\n ", count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sDigraph", count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "C", next := 19549, root := ~, start := 19533, stop := 19548 ), rec( content := ". Some \ basic attributes and operations for digraphs\n are ", count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Vertices" ), content := 0, count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "Ref", next := 19639, root := ~, start := 19610, stop := 19638 ), rec( content := ", ", count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Edges" ), content := 0, count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "Ref", next := 19667, root := ~, start := 19641, stop := 19666 ), rec( content := ", and\n \ ", count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "OutNeig\ hbours" ), content := 0, count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "Ref", next := 19704, root := ~, start := 19677, stop := 19703 ), rec( content := ".\n " , count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "Description", next := 19724, root := ~, start := 19453, stop := 19723 ) ], count := [ 3, 1, 1, 1 ], mathmode := "Text", name := "ManSection", next := 19738, root := ~, start := 19395, stop := 19737 ), rec( content := "\n\n ", count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Name := "IsMutableDigrap\ h", Type := "Category" ), content := 0, count := [ 3, 1, 2, 2 ], mathmode := "Text", name := "Filt", next := 19806, root := ~, start := 19759, stop := 19805 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sMutableDigraph", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "C", next := 19850, root := ~, start := 19827, stop := 19849 ), rec( content := " is a sy\ nonym for ", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsDigra\ ph" ), content := 0, count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "Ref", next := 19892, root := ~, start := 19868, stop := 19891 ), rec( content := " and ", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "ref\ ", Filt := "IsMutable" ), content := 0, count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "Ref", next := 19940, root := ~, start := 19897, stop := 19939 ), rec( content := ". A mut\ able digraph may be changed\n in-place by methods in the ", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphs", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " package\ , and is not attribute-storing\n – see ", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "ref\ ", Filt := "IsAttributeStoringRep" ), content := 0, count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "Ref", next := 20119, root := ~, start := 20068, stop := 20118 ), rec( content := ".\n " , count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 2, 4 ], mathmode := "Text", name := "P", next := 20129, root := ~, start := 20125, stop := 20128 ), rec( content := "\n\n \ A mutable digraph may be converted into an immutable attribute-storing\n di\ graph by calling ", count := [ 3, 1, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "ref\ ", Func := "MakeImmutable" ), content := 0, count := [ 3, 1, 2, 4 ], mathmode := "Text", name := "Ref", next := 20271, root := ~, start := 20229, stop := 20270 ), rec( content := " on the\\ n digraph.\n ", count := [ 3, 1, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "Description", next := 20310, root := ~, start := 19809, stop := 20309 ) ], count := [ 3, 1, 2, 1 ], mathmode := "Text", name := "ManSection", next := 20324, root := ~, start := 19744, stop := 20323 ), rec( content := "\n\n ", count := [ 3, 1, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Name := "IsImmutableDigr\ aph", Type := "Category" ), content := 0, count := [ 3, 1, 3, 2 ], mathmode := "Text", name := "Filt", next := 20394, root := ~, start := 20345, stop := 20393 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 3, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sImmutableDigraph", count := [ 3, 1, 3, 3 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 3, 1, 3, 3 ], mathmode := "Text", name := "C", next := 20440, root := ~, start := 20415, stop := 20439 ), rec( content := " is a su\ bcategory of ", count := [ 3, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsDigra\ ph" ), content := 0, count := [ 3, 1, 3, 3 ], mathmode := "Text", name := "Ref", next := 20485, root := ~, start := 20461, stop := 20484 ), rec( content := ".\n D\ igraphs that lie in ", count := [ 3, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sImmutableDigraph", count := [ 3, 1, 3, 3 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 3, 1, 3, 3 ], mathmode := "Text", name := "C", next := 20537, root := ~, start := 20512, stop := 20536 ), rec( content := " are imm\ utable and\n attribute-storing. In particular, they lie in\n ", count := [ 3, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "ref\ ", Filt := "IsAttributeStoringRep" ), content := 0, count := [ 3, 1, 3, 3 ], mathmode := "Text", name := "Ref", next := 20661, root := ~, start := 20610, stop := 20660 ), rec( content := ". ", count := [ 3, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 3, 4 ], mathmode := "Text", name := "P", next := 20667, root := ~, start := 20663, stop := 20666 ), rec( content := "\n\n \ A mutable digraph may be converted to an immutable\n digraph that lies in t\ he category ", count := [ 3, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sImmutableDigraph", count := [ 3, 1, 3, 4 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 3, 1, 3, 4 ], mathmode := "Text", name := "C", next := 20787, root := ~, start := 20762, stop := 20786 ), rec( content := " by call\ ing\n ", count := [ 3, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "ref\ ", Func := "MakeImmutable" ), content := 0, count := [ 3, 1, 3, 4 ], mathmode := "Text", name := "Ref", next := 20845, root := ~, start := 20803, stop := 20844 ), rec( content := " on the \ digraph.", count := [ 3, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 3, 5 ], mathmode := "Text", name := "P", next := 20865, root := ~, start := 20861, stop := 20864 ), rec( content := "\n\n \ The operation ", count := [ 3, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ MutableCopy" ), content := 0, count := [ 3, 1, 3, 5 ], mathmode := "Text", name := "Ref", next := 20917, root := ~, start := 20885, stop := 20916 ), rec( content := " can be \ used\n to construct a mutable copy of an immutable digraph. It is however n\ ot\n possible to convert an immutable digraph into a mutable digraph in-pla\ ce.\n ", count := [ 3, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 3, 3 ], mathmode := "Text", name := "Description", next := 21099, root := ~, start := 20397, stop := 21098 ) ], count := [ 3, 1, 3, 1 ], mathmode := "Text", name := "ManSection", next := 21113, root := ~, start := 20330, stop := 21112 ), rec( content := "\n\n ", count := [ 3, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Name := "IsCayleyDigraph\ ", Type := "Category" ), content := 0, count := [ 3, 1, 4, 2 ], mathmode := "Text", name := "Filt", next := 21180, root := ~, start := 21134, stop := 21179 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 3, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sCayleyDigraph", count := [ 3, 1, 4, 3 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 3, 1, 4, 3 ], mathmode := "Text", name := "C", next := 21223, root := ~, start := 21201, stop := 21222 ), rec( content := " is a su\ bcategory of ", count := [ 3, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sDigraph", count := [ 3, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 4, 3 ], mathmode := "Text", name := "C", next := 21260, root := ~, start := 21244, stop := 21259 ), rec( content := ". Digrap\ hs that\n are Cayley digraphs of a group and that are constructed by the op\ eration\n ", count := [ 3, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "CayleyD\ igraph" ), content := 0, count := [ 3, 1, 4, 3 ], mathmode := "Text", name := "Ref", next := 21384, root := ~, start := 21357, stop := 21383 ), rec( content := " are con\ structed in this category, and are\n always immutable.\n ", count := [ 3, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 4, 3 ], mathmode := "Text", name := "Description", next := 21467, root := ~, start := 21183, stop := 21466 ) ], count := [ 3, 1, 4, 1 ], mathmode := "Text", name := "ManSection", next := 21481, root := ~, start := 21119, stop := 21480 ), rec( content := "\n\n ", count := [ 3, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Name := "IsDigraphWithAd\ jacencyFunction", Type := "Category" ), content := 0, count := [ 3, 1, 5, 2 ], mathmode := "Text", name := "Filt", next := 21563, root := ~, start := 21502, stop := 21562 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 3, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sDigraphWithAdjacencyFunction", count := [ 3, 1, 5, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 1, 5, 3 ], mathmode := "Text", name := "C", next := 21621, root := ~, start := 21584, stop := 21620 ), rec( content := " is a su\ bcategory of ", count := [ 3, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sDigraph", count := [ 3, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 5, 3 ], mathmode := "Text", name := "C", next := 21658, root := ~, start := 21642, stop := 21657 ), rec( content := ".\n D\ igraphs that are ", count := [ 3, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ reated", count := [ 3, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 5, 3 ], mathmode := "Text", name := "E", next := 21696, root := ~, start := 21682, stop := 21695 ), rec( content := " using a\ n adjacency function are constructed\n in this category.\n ", count := [ 3, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 5, 3 ], mathmode := "Text", name := "Description", next := 21779, root := ~, start := 21566, stop := 21778 ) ], count := [ 3, 1, 5, 1 ], mathmode := "Text", name := "ManSection", next := 21793, root := ~, start := 21487, stop := 21792 ), rec( content := "\n\n ", count := [ 3, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Name := "DigraphByOutNei\ ghboursType" ), content := 0, count := [ 3, 1, 6, 2 ], mathmode := "Text", name := "Var", next := 21854, root := ~, start := 21814, stop := 21853 ), rec( attributes := rec( Name := "DigraphFamily" ), content := 0, count := [ 3, 1, 6, 4 ], mathmode := "Text", name := "Fam", next := 21884, root := ~, start := 21857, stop := 21883 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ type of all digraphs is ", count := [ 3, 1, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphByOutNeighboursType", count := [ 3, 1, 6, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 1, 6, 5 ], mathmode := "Text", name := "C", next := 21966, root := ~, start := 21933, stop := 21965 ), rec( content := ".\n T\ he family of all digraphs is ", count := [ 3, 1, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphFamily", count := [ 3, 1, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 6, 5 ], mathmode := "Text", name := "C", next := 22022, root := ~, start := 22002, stop := 22021 ), rec( content := ".\n ", count := [ 3, 1, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 6, 5 ], mathmode := "Text", name := "Description", next := 22040, root := ~, start := 21887, stop := 22039 ) ], count := [ 3, 1, 6, 1 ], mathmode := "Text", name := "ManSection", next := 22054, root := ~, start := 21799, stop := 22053 ), rec( content := "\n\n ", count := [ 3, 1, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "[filt,] obj[, so\ urce, range]", Name := "Digraph" ), content := 0, count := [ 3, 1, 7, 2 ], mathmode := "Text", name := "Oper", next := 22136, root := ~, start := 22075, stop := 22135 ), rec( attributes := rec( Arg := "[filt,] list, fu\ nc", Label := "for a list and function", Name := "Digraph" ), content := 0, count := [ 3, 1, 7, 4 ], mathmode := "Text", name := "Oper", next := 22229, root := ~, start := 22139, stop := 22228 ), rec( attributes := rec( Arg := "[filt,] G, list,\ act, adj", Label := "for a group, list, function, and function", Name := "Digraph" ), content := 0, count := [ 3, 1, 7, 6 ], mathmode := "Text", name := "Oper", next := 22346, root := ~, start := 22232, stop := 22345 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "Returns", next := 22378, root := ~, start := 22349, stop := 22377 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ the optional first argument ", count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "A", next := 22441, root := ~, start := 22430, stop := 22440 ), rec( content := " is pres\ ent, then this should\n specify the category or representation the digraph \ being created will\n belong to. For example, if ", count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "A", next := 22587, root := ~, start := 22576, stop := 22586 ), rec( content := " is ", count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "Ref", next := 22621, root := ~, start := 22591, stop := 22620 ), rec( content := ",\n t\ hen the digraph being created will be mutable, if ", count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "A", next := 22689, root := ~, start := 22678, stop := 22688 ), rec( content := " is ", count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "Ref", next := 22729, root := ~, start := 22693, stop := 22728 ), rec( content := ", then t\ he digraph will be immutable. \n If the optional first argument ", count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "A", next := 22814, root := ~, start := 22803, stop := 22813 ), rec( content := " is not \ present, then ", count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "Ref", next := 22872, root := ~, start := 22836, stop := 22871 ), rec( content := " is used\ by default.\n ", count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "for a list (i.e. an adjacency list)", coun\ t := [ 3, 1, 7, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 8 ], name := "Mar\ k", next := 22958, root := ~, start := 22910, stop := 22957 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n if ", count := [ 3, 1, 7, 9\ ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(\ ), content := [ rec( content := "obj", count := [ 3, 1, 7, 9 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 9 ], mathmode := \ "Text", name := "A", next := 22993, root := ~, start := 22983, stop := 22992 ) , rec( cont\ ent := " is a list of lists of positive integers in\n the range from ", coun\ t := [ 3, 1, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "1", count := [ 3, 1, 7, 9 ], \ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 9 ], math\ mode := "Text", name := "C", next := 23068, root := ~, start := 23060, stop :=\ 23067 ), rec( content := " to ", count := [ 3, 1, 7, 9 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "Length(", count := [ 3, 1, 7, 9 ], mathmode := "Text", name := "PCDATA"\ , root := ~ ), rec( attributes := rec( ), content := [ rec( content := "obj",\ count := [ 3, 1, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ],\ count := [ 3, 1, 7, 9 ], mathmode := "Text", name := "A", next := 23092, root\ := ~, start := 23082, stop := 23091 ), rec( content := ")", count := [ 3, 1, \ 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, \ 7, 9 ], mathmode := "Text", name := "C", next := 23097, root := ~, start := 23\ 072, stop := 23096 ), rec( content := ", then this function\n returns t\ he digraph with vertices\n ", count := [ 3, 1, 7, 9 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ re\ c( content := "E ^ 0 = ", count := [ 3, 1, 7, 9 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 9 ], mathmode := "Text", name :=\ "M", next := 23183, root := ~, start := 23168, stop := 23182 ), rec( attribut\ es := rec( ), content := [ rec( content := "[1 .. Length(", count := [ 3, 1, \ 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := \ rec( ), content := [ rec( content := "obj", count := [ 3, 1, 7, 9 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 9 ], mathmode\ := "Text", name := "A", next := 23209, root := ~, start := 23199, stop := 232\ 08 ), rec( content := ")]", count := [ 3, 1, 7, 9 ], mathmode := "Text", name \ := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 9 ], mathmode := "Text", name \ := "C", next := 23215, root := ~, start := 23183, stop := 23214 ), rec( conten\ t := ",\n and edges corresponding to the entries of ", count := [ 3, 1,\ 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :=\ rec( ), content := [ rec( content := "obj", count := [ 3, 1, 7, 9 ], mathmod\ e := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 9 ], mathmod\ e := "Text", name := "A", next := 23277, root := ~, start := 23267, stop := 23\ 276 ), rec( content := ". ", count := [ 3, 1, 7, 9 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ \ 3, 1, 7, 10 ], mathmode := "Text", name := "P", next := 23283, root := ~, star\ t := 23279, stop := 23282 ), rec( content := "\n\n More precisely, ther\ e is an edge from vertex ", count := [ 3, 1, 7, 10 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "i", count := [ 3, 1, 7, 10 ], mathmode := "Text", name := "PCDATA", roo\ t := ~ ) ], count := [ 3, 1, 7, 10 ], mathmode := "Text", name := "C", next :=\ 23346, root := ~, start := 23338, stop := 23345 ), rec( content := " to ", coun\ t := [ 3, 1, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "j", count := [ 3, 1, 7, 10 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 10 ] , math\ mode := "Text", name := "C", next := 23358, root := ~, start := 23350, stop :=\ 23357 ), rec( content := " if and\n only if ", count := [ 3, 1, 7, 10 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "j", count := [ 3, 1, 7, 10 ], mathmode := "Text", na\ me := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 10 ], mathmode := "Text", name\ := "C", next := 23390, root := ~, start := 23382, stop := 23389 ), rec( conte\ nt := " is in ", count := [ 3, 1, 7, 10 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := re\ c( ), content := [ rec( content := "obj", count := [ 3, 1, 7, 10 ], mathmode \ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 10 ], mathmode\ := "Text", name := "A", next := 23410, root := ~, start := 23400, stop := 234\ 09 ), rec( content := "[i]", count := [ 3, 1, 7, 10 ], mathmode := "Text", nam\ e := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 10 ], mathmode := "Text", name\ := "C", next := 23417, root := ~, start := 23397, stop := 23416 ), rec( conte\ nt := "; the source of this edge is\n ", count := [ 3, 1, 7, 10 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "i", count := [ 3, 1, 7, 10 ], mathmode := "Text", na\ me := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 10 ], mathmode := "Text", name\ := "C", next := 23462, root := ~, start := 23454, stop := 23461 ), rec( conte\ nt := " and the range is ", count := [ 3, 1, 7, 10 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "j", count := [ 3, 1, 7, 10 ], mathmode := "Text", name := "PCDATA", roo\ t := ~ ) ], count := [ 3, 1, 7, 10 ], mathmode := "Text", name := "C", next :=\ 23488, root := ~, start := 23480, stop := 23487 ), rec( content := ". If ", coun\ t := [ 3, 1, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "j", count := [ 3, 1, 7, 10 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 10 ] , math\ mode := "Text", name := "C", next := 23501, root := ~, start := 23493, stop :=\ 23500 ), rec( content := " occurs in\n ", count := [ 3, 1, 7, 10 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( attributes := rec( ), content := [ rec( content := "obj", count\ := [ 3, 1, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 3, 1, 7, 10 ], mathmode := "Text", name := "A", next := 23533, root := \ ~, start := 23523, stop := 23532 ), rec( content := "[i]", count := [ 3, 1, 7,\ 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7\ , 10 ], mathmode := "Text", name := "C", next := 23540, root := ~, start := 23\ 520, stop := 23539 ), rec( content := " with multiplicity ", count := [ 3, 1, \ 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :=\ rec( ), content := [ rec( content := "k", count := [ 3, 1, 7, 10 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 10 ], mathmod\ e := "Text", name := "C", next := 23567, root := ~, start := 23559, stop := 23\ 566 ), rec( content := ", then there are ", count := [ 3, 1, 7, 10 ], mathmode\ := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content\ := [ rec( content := "k", count := [ 3, 1, 7, 10 ], mathmode := "Text", name \ := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 10 ], mathmode := "Text", name\ := "C", next := 23592, root := ~, start := 23584, stop := 23591 ), rec( conte\ nt := "\n edges from ", count := [ 3, 1, 7, 10 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "i", count := [ 3, 1, 7, 10 ], mathmode := "Text", name := "PCDATA", roo\ t := ~ ) ], count := [ 3, 1, 7, 10 ], mathmode := "Text", name := "C", next :=\ 23620, root := ~, start := 23612, stop := 23619 ), rec( content := " to ", coun\ t := [ 3, 1, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "j", count := [ 3, 1, 7, 10 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 10 ] , math\ mode := "Text", name := "C", next := 23632, root := ~, start := 23624, stop :=\ 23631 ), rec( content := ".\n ", count := [ 3, 1, 7, 10 ], mathmode := "\ Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 9 ], name := "Item\ ", next := 23647, root := ~, start := 22965, stop := 23646 ), rec( attributes :\ = rec( ), content := [ rec( content := "for three lists", count := [ 3, 1, 7,\ 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 11 ], name := "Mar\ k", next := 23683, root := ~, start := 23655, stop := 23682 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n if ", count := [ 3, 1, 7, 1\ 2 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec\ ( ), content := [ rec( content := "obj", count := [ 3, 1, 7, 12 ], mathmode :\ = "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 12 ], mathmode \ := "Text", name := "A", next := 23718, root := ~, start := 23708, stop := 2371\ 7 ), rec( content := " is a duplicate-free list, and ", count := [ 3, 1, 7, 12\ ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(\ ), content := [ rec( content := "source", count := [ 3, 1, 7, 12 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 12 ], mathmod\ e := "Text", name := "A", next := 23762, root := ~, start := 23749, stop := 23\ 761 ), rec( content := " and\n ", count := [ 3, 1, 7, 12 ], mathmode :=\ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content :=\ [ rec( content := "range", count := [ 3, 1, 7, 12 ], mathmode := "Text", name\ := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 12 ], mathmode := "Text", name\ := "A", next := 23787, root := ~, start := 23775, stop := 23786 ), rec( conte\ nt := " are lists of equal length consisting of positive integers\n in \ the list ", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "[1 .. Lengt\ h(", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~\ ), rec( attributes := rec( ), content := [ rec( content := "obj", count := [\ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := \ [ 3, 1, 7, 12 ], mathmode := "Text", name := "A", next := 23892, root := ~, st\ art := 23882, stop := 23891 ), rec( content := ")]", count := [ 3, 1, 7, 12 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 12 ] , math\ mode := "Text", name := "C", next := 23898, root := ~, start := 23866, stop :=\ 23897 ), rec( content := ", then this function\n returns a digraph wit\ h vertices\n ", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "\ PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content :=\ "E ^ 0 = ", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", r\ oot := ~ ) ], count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "M", next \ := 23982, root := ~, start := 23967, stop := 23981 ), rec( attributes := rec( \ ), content := [ rec( content := "[1 .. Length(", count := [ 3, 1, 7, 12 ], ma\ thmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), c\ ontent := [ rec( content := "obj", count := [ 3, 1, 7, 12 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 12 ], mathmode := "Tex\ t", name := "A", next := 24008, root := ~, start := 23998, stop := 24007 ), re\ c( content := ")]", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "C" , next\ := 24014, root := ~, start := 23982, stop := 24013 ), rec( content := ", and\ \n ", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "Length(", c\ ount := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), re\ c( attributes := rec( ), content := [ rec( content := "source", count := [ 3,\ 1, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3\ , 1, 7, 12 ], mathmode := "Text", name := "A", next := 24051, root := ~, start\ := 24038, stop := 24050 ), rec( content := ")", count := [ 3, 1, 7, 12 ], mat\ hmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 12 ], math\ mode := "Text", name := "C", next := 24056, root := ~, start := 24028, stop :=\ 24055 ), rec( content := " edges. For each ", count := [ 3, 1, 7, 12 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "i", count := [ 3, 1, 7, 12 ], mathmode := "Text", na\ me := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 12 ], mathmode := "Text", name\ := "C", next := 24082, root := ~, start := 24074, stop := 24081 ), rec( conte\ nt := " in\n ", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "\ PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content :=\ "[1 .. Length(", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "sou\ rce", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", root := \ ~ ) ], count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "A", next := 2412\ 3, root := ~, start := 24110, stop := 24122 ), rec( content := ")]", count := \ [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :=\ [ 3, 1, 7, 12 ], mathmode := "Text", name := "C", next := 24129, root := ~, star\ t := 24094, stop := 24128 ), rec( content := " there exists an edge with sourc\ e\n vertex ", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PC\ DATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\ source[i]", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", ro\ ot := ~ ) ], count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "C", next :\ = 24194, root := ~, start := 24178, stop := 24193 ), rec( content := " and ran\ ge vertex ", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "range[i]", \ count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 3, 1, 7, 12 ], mathmode := "Text", name := "C", next := 24227, root := \ ~, start := 24212, stop := 24226 ), rec( content := ".\n See ", count :\ = [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( Attr := "DigraphSource" ), content := 0, count := [ 3, 1, 7, 12\ ], mathmode := "Text", name := "Ref", next := 24268, root := ~, start := 2424\ 1, stop := 24267 ), rec( content := " and ", count := [ 3, 1, 7, 12 ], mathmod\ e := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "D\ igraphRange" ), content := 0, count := [ 3, 1, 7, 12 ], mathmode := "Text", name\ := "Ref", next := 24299, root := ~, start := 24273, stop := 24298 ), rec( cont\ ent := ".\n ", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "P\ CDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1\ , 7, 13 ], mathmode := "Text", name := "P", next := 24313, root := ~, start :=\ 24309, stop := 24312 ), rec( content := "\n\n The vertices of the digr\ aph will be labelled by the elements of\n ", count := [ 3, 1, 7, 13 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "obj", count := [ 3, 1, 7, 13 ], mathmode := "Text", \ name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 13 ], mathmode := "Text", name\ := "A", next := 24405, root := ~, start := 24395, stop := 24404 ), rec( conte\ nt := ".\n ", count := [ 3, 1, 7, 13 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 3, 1, 7, 12 ], name := "Item", next := 24420, root := ~, start := 236\ 90, stop := 24419 ), rec( attributes := rec( ), content := [ rec( content := \ "for an integer, and two lists", count := [ 3, 1, 7, 14 ], mathmode := "Text", name\ := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 14 ], name := "Mark", next := 2447\ 0, root := ~, start := 24428, stop := 24469 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "\n if ", count := [ 3, 1, 7, 15 ], mathmode := "Text", name := \ "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content :\ = "obj", count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDATA", root \ := ~ ) ], count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "A", next := 2\ 4505, root := ~, start := 24495, stop := 24504 ), rec( content := " is an inte\ ger, and ", count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "source", co\ unt := [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 3, 1, 7, 15 ], mathmode := "Text", name := "A", next := 24538, root := \ ~, start := 24525, stop := 24537 ), rec( content := " and\n ", count :=\ [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "range", count := [ 3, 1, 7, 1\ 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, \ 15 ], mathmode := "Text", name := "A", next := 24563, root := ~, start := 2455\ 1, stop := 24562 ), rec( content := " are lists of equal length consisting of \ positive integers\n in the list ", count := [ 3, 1, 7, 15 ], mathmode :\ = "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content :\ = [ rec( content := "[1 .. ", count := [ 3, 1, 7, 15 ], mathmode := "Text", na\ me := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( con\ tent := "obj", count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDATA",\ root := ~ ) ], count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "A", nex\ t := 24661, root := ~, start := 24651, stop := 24660 ), rec( content := "]", c\ ount := [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 3, 1, 7, 15 ], mathmode := "Text", name := "C", next := 24666, root := \ ~, start := 24642, stop := 24665 ), rec( content := ", then this function\n \ returns a digraph with vertices\n ", count := [ 3, 1, 7, 15 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "E ^ 0 = ", count := [ 3, 1, 7, 15 ], mathmode := "Te\ xt", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 15 ], mathmode := "T\ ext", name := "M", next := 24750, root := ~, start := 24735, stop := 24749 ), rec( attr\ ibutes := rec( ), content := [ rec( content := "[1 .. ", count := [ 3, 1, 7, \ 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\ c( ), content := [ rec( content := "obj", count := [ 3, 1, 7, 15 ], mathmode \ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 15 ], mathmode\ := "Text", name := "A", next := 24769, root := ~, start := 24759, stop := 247\ 68 ), rec( content := "]", count := [ 3, 1, 7, 15 ], mathmode := "Text", name \ := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 15 ], mathmode := "Text", name\ := "C", next := 24774, root := ~, start := 24750, stop := 24773 ), rec( conte\ nt := ", and\n ", count := [ 3, 1, 7, 15 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content \ := "Length(", count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDATA", \ root := ~ ), rec( attributes := rec( ), content := [ rec( content := "source"\ , count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) \ ], count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "A", next := 24811, r\ oot := ~, start := 24798, stop := 24810 ), rec( content := ")", count := [ 3, \ 1, 7, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3,\ 1, 7, 15 ], mathmode := "Text", name := "C", next := 24816, root := ~, start \ := 24788, stop := 24815 ), rec( content := " edges. For each ", count := [ 3,\ 1, 7, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribute\ s := rec( ), content := [ rec( content := "i", count := [ 3, 1, 7, 15 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 15 ], math\ mode := "Text", name := "C", next := 24842, root := ~, start := 24834, stop :=\ 24841 ), rec( content := " in\n ", count := [ 3, 1, 7, 15 ], mathmode \ := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content \ := [ rec( content := "[1 .. Length(", count := [ 3, 1, 7, 15 ], mathmode := "T\ ext", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ \ rec( content := "source", count := [ 3, 1, 7, 15 ], mathmode := "Text", name :\ = "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 15 ], mathmode := "Text", name \ := "A", next := 24883, root := ~, start := 24870, stop := 24882 ), rec( conten\ t := ")]", count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDATA", roo\ t := ~ ) ], count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "C", next :=\ 24889, root := ~, start := 24854, stop := 24888 ), rec( content := " there ex\ ists an edge with source\n vertex ", count := [ 3, 1, 7, 15 ], mathmode\ := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content\ := [ rec( content := "source[i]", count := [ 3, 1, 7, 15 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 15 ], mathmode := "Tex\ t", name := "C", next := 24954, root := ~, start := 24938, stop := 24953 ), rec( cont\ ent := " and range vertex ", count := [ 3, 1, 7, 15 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "range[i]", count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "C", next\ := 24987, root := ~, start := 24972, stop := 24986 ), rec( content := ".\n \ See ", count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( Attr := "DigraphSource" ), content := 0, coun\ t := [ 3, 1, 7, 15 ], mathmode := "Text", name := "Ref", next := 25028, root :\ = ~, start := 25001, stop := 25027 ), rec( content := " and ", count := [ 3, 1\ , 7, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes \ := rec( Attr := "DigraphRange" ), content := 0, count := [ 3, 1, 7, 15 ], math\ mode := "Text", name := "Ref", next := 25059, root := ~, start := 25033, stop \ := 25058 ), rec( content := ".\n ", count := [ 3, 1, 7, 15 ], mathmode :=\ "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 15 ], name := "Ite\ m", next := 25074, root := ~, start := 24477, stop := 25073 ), rec( attributes :\ = rec( ), content := [ rec( content := "for a list and a function", count := [ \ 3, 1, 7, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 16 ], name := "Mar\ k", next := 25120, root := ~, start := 25082, stop := 25119 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n if ", count := [ 3, 1, 7, 1\ 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec\ ( ), content := [ rec( content := "list", count := [ 3, 1, 7, 17 ], mathmode \ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 17 ], mathmode\ := "Text", name := "A", next := 25156, root := ~, start := 25145, stop := 251\ 55 ), rec( content := " is a list and ", count := [ 3, 1, 7, 17 ], mathmode :=\ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content :=\ [ rec( content := "func", count := [ 3, 1, 7, 17 ], mathmode := "Text", name \ := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 17 ], mathmode := "Text", name\ := "A", next := 25182, root := ~, start := 25171, stop := 25181 ), rec( conte\ nt := " is a function taking 2\n arguments that are elements of ", coun\ t := [ 3, 1, 7, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "list", count := [ 3, 1, 7, 17\ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 1\ 7 ], mathmode := "Text", name := "A", next := 25256, root := ~, start := 25245 , stop\ := 25255 ), rec( content := ", and ", count := [ 3, 1, 7, 17 ], mathmode := "\ Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ \ rec( content := "func", count := [ 3, 1, 7, 17 ], mathmode := "Text", name := \ "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 17 ], mathmode := "Text", name :=\ "A", next := 25273, root := ~, start := 25262, stop := 25272 ), rec( content \ := " returns\n ", count := [ 3, 1, 7, 17 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content \ := "true", count := [ 3, 1, 7, 17 ], mathmode := "Text", name := "PCDATA", roo\ t := ~ ) ], count := [ 3, 1, 7, 17 ], mathmode := "Text", name := "K", next :=\ 25301, root := ~, start := 25290, stop := 25300 ), rec( content := " or ", coun\ t := [ 3, 1, 7, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "false", count := [ 3, 1, 7, 1\ 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, \ 17 ], mathmode := "Text", name := "K", next := 25317, root := ~, start := 2530\ 5, stop := 25316 ), rec( content := ", then this operation creates a digraph w\ ith\n vertices ", count := [ 3, 1, 7, 17 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content \ := "[1 .. Length(", count := [ 3, 1, 7, 17 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 3, 1, 7, 17 ], mathmode := "Text", name := "PCDATA", root := \ ~ ) ], count := [ 3, 1, 7, 17 ], mathmode := "Text", name := "A", next := 2540\ 6, root := ~, start := 25395, stop := 25405 ), rec( content := ")]", count := \ [ 3, 1, 7, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :=\ [ 3, 1, 7, 17 ], mathmode := "Text", name := "C", next := 25412, root := ~, star\ t := 25379, stop := 25411 ), rec( content := " and an edge from vertex\n \ ", count := [ 3, 1, 7, 17 ], mathmode := "Text", name := "PCDATA", root := ~\ ), rec( attributes := rec( ), content := [ rec( content := "i", count := [ 3\ , 1, 7, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ \ 3, 1, 7, 17 ], mathmode := "Text", name := "C", next := 25453, root := ~, star\ t := 25445, stop := 25452 ), rec( content := " to vertex ", count := [ 3, 1, 7\ , 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\ c( ), content := [ rec( content := "j", count := [ 3, 1, 7, 17 ], mathmode :=\ "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 17 ], mathmode :\ = "Text", name := "C", next := 25472, root := ~, start := 25464, stop := 25471\ ), rec( content := " if and only if\n ", count := [ 3, 1, 7, 17 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( attributes := rec( ), content := [ rec( content := "func", coun\ t := [ 3, 1, 7, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], cou\ nt := [ 3, 1, 7, 17 ], mathmode := "Text", name := "A", next := 25510, root :=\ ~, start := 25499, stop := 25509 ), rec( content := "(", count := [ 3, 1, 7, \ 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\ c( ), content := [ rec( content := "list", count := [ 3, 1, 7, 17 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 17 ], mathmod\ e := "Text", name := "A", next := 25522, root := ~, start := 25511, stop := 25\ 521 ), rec( content := "[i], ", count := [ 3, 1, 7, 17 ], mathmode := "Text", \ name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( c\ ontent := "list", count := [ 3, 1, 7, 17 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 3, 1, 7, 17 ], mathmode := "Text", name := "A", \ next := 25538, root := ~, start := 25527, stop := 25537 ), rec( content := "[j\ ])", count := [ 3, 1, 7, 17 ], mathmode := "Text", name := "PCDATA", root := ~\ ) ], count := [ 3, 1, 7, 17 ], mathmode := "Text", name := "C", next := 25546 , root\ := ~, start := 25496, stop := 25545 ), rec( content := " returns ", count := [ \ 3, 1, 7, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\ tes := rec( ), content := [ rec( content := "true", count := [ 3, 1, 7, 17 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 17 ] , math\ mode := "Text", name := "K", next := 25566, root := ~, start := 25555, stop :=\ 25565 ), rec( content := ".\n ", count := [ 3, 1, 7, 17 ], mathmode := "\ Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 17 ], name := "Ite\ m", next := 25581, root := ~, start := 25127, stop := 25580 ), rec( attributes :\ = rec( ), content := [ rec( content := "for a group, a list, and two function\ s", count := [ 3, 1, 7, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 18 ], name := "Mar\ k", next := 25640, root := ~, start := 25589, stop := 25639 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n The arguments will be ", coun\ t := [ 3, 1, 7, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "G, list, act, adj", count := \ [ 3, 1, 7, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :=\ [ 3, 1, 7, 19 ], mathmode := "Text", name := "A", next := 25708, root := ~, star\ t := 25684, stop := 25707 ), rec( content := ". ", count := [ 3, 1, 7, 19 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := 0, count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "P", next := 2\ 5714, root := ~, start := 25710, stop := 25713 ), rec( content := "\n\n \ Let ", count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root :\ = ~ ), rec( attributes := rec( ), content := [ rec( content := "G", count := \ [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :=\ [ 3, 1, 7, 20 ], mathmode := "Text", name := "A", next := 25736, root := ~, star\ t := 25728, stop := 25735 ), rec( content := " be a group acting on the object\ s in ", count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root :\ = ~ ), rec( attributes := rec( ), content := [ rec( content := "list", count \ := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count\ := [ 3, 1, 7, 20 ], mathmode := "Text", name := "A", next := 25784, root := ~ , star\ t := 25773, stop := 25783 ), rec( content := " via\n the action ", coun\ t := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "act", count := [ 3, 1, 7, 20 \ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 20\ ], mathmode := "Text", name := "A", next := 25818, root := ~, start := 25808, stop\ := 25817 ), rec( content := ", and let ", count := [ 3, 1, 7, 20 ], mathmode \ := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content \ := [ rec( content := "adj", count := [ 3, 1, 7, 20 ], mathmode := "Text", name\ := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 20 ], mathmode := "Text", name\ := "A", next := 25838, root := ~, start := 25828, stop := 25837 ), rec( conte\ nt := " be a function taking\n two objects from ", count := [ 3, 1, 7, \ 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\ c( ), content := [ rec( content := "list", count := [ 3, 1, 7, 20 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 20 ], mathmod\ e := "Text", name := "A", next := 25896, root := ~, start := 25885, stop := 25\ 895 ), rec( content := " as arguments and returning ", count := [ 3, 1, 7, 20 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "true", count := [ 3, 1, 7, 20 ], mathmode := "Text",\ name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 20 ], mathmode := "Text" , name\ := "C", next := 25935, root := ~, start := 25924, stop := 25934 ), rec( conte\ nt := " or\n ", count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "\ PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content :=\ "false", count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "C", next := \ 25959, root := ~, start := 25947, stop := 25958 ), rec( content := ". The func\ tion ", count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root :\ = ~ ), rec( attributes := rec( ), content := [ rec( content := "adj", count :\ = [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count \ := [ 3, 1, 7, 20 ], mathmode := "Text", name := "A", next := 25984, root := ~, star\ t := 25974, stop := 25983 ), rec( content := " will describe the adjacency\n \ between objects from ", count := [ 3, 1, 7, 20 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "list", count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", \ root := ~ ) ], count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "A", next\ := 26053, root := ~, start := 26042, stop := 26052 ), rec( content := ", whic\ h is invariant under the action of\n ", count := [ 3, 1, 7, 20 ], mathm\ ode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "G", count := [ 3, 1, 7, 20 ], mathmode := "Text", na\ me := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 20 ], mathmode := "Text", name\ := "A", next := 26110, root := ~, start := 26102, stop := 26109 ), rec( conte\ nt := ". This variant of the constructor returns a digraph with\n verti\ ces the objects of ", count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "P\ CDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := \ "list", count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root :\ = ~ ) ], count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "A", next := 26\ 210, root := ~, start := 26199, stop := 26209 ), rec( content := " and directe\ d edges ", count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "[x, y]", co\ unt := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 3, 1, 7, 20 ], mathmode := "Text", name := "C", next := 26243, root := \ ~, start := 26230, stop := 26242 ), rec( content := "\n when ", count :\ = [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "f(x, y)", count := [ 3, 1, 7,\ 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7\ , 20 ], mathmode := "Text", name := "C", next := 26271, root := ~, start := 26\ 257, stop := 26270 ), rec( content := " is ", count := [ 3, 1, 7, 20 ], mathmo\ de := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), conte\ nt := [ rec( content := "true", count := [ 3, 1, 7, 20 ], mathmode := "Text", \ name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 20 ], mathmode := "Text", name\ := "C", next := 26286, root := ~, start := 26275, stop := 26285 ), rec( conte\ nt := ". ", count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 7, 21 ], math\ mode := "Text", name := "P", next := 26292, root := ~, start := 26288, stop :=\ 26291 ), rec( content := "\n\n The action of the group ", count := [ 3\ , 1, 7, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribut\ es := rec( ), content := [ rec( content := "G", count := [ 3, 1, 7, 21 ], mat\ hmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 21 ], math\ mode := "Text", name := "A", next := 26334, root := ~, start := 26326, stop :=\ 26333 ), rec( content := " on the objects in ", count := [ 3, 1, 7, 21 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "list", count := [ 3, 1, 7, 21 ], mathmode := "Text",\ name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 21 ], mathmode := "Text" , name\ := "A", next := 26364, root := ~, start := 26353, stop := 26363 ), rec( conte\ nt := " is stored\n in the attribute ", count := [ 3, 1, 7, 21 ], mathm\ ode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := \ "DigraphGroup" ), content := 0, count := [ 3, 1, 7, 21 ], mathmode := "Text", name\ := "Ref", next := 26426, root := ~, start := 26400, stop := 26425 ), rec( cont\ ent := ", and is used to speed up\n operations like ", count := [ 3, 1,\ 7, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( Attr := "DigraphDiameter" ), content := 0, count := [ 3, 1, 7, 21 ], math\ mode := "Text", name := "Ref", next := 26505, root := ~, start := 26476, stop \ := 26504 ), rec( content := ".\n ", count := [ 3, 1, 7, 21 ], mathmode :=\ "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 19 ], name := "Ite\ m", next := 26520, root := ~, start := 25647, stop := 26519 ), rec( attributes :\ = rec( ), content := [ rec( content := "for a Grape package graph", count := [ \ 3, 1, 7, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 22 ], name := "Mar\ k", next := 26566, root := ~, start := 26528, stop := 26565 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n if ", count := [ 3, 1, 7, 2\ 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec\ ( ), content := [ rec( content := "obj", count := [ 3, 1, 7, 23 ], mathmode :\ = "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 23 ], mathmode \ := "Text", name := "A", next := 26601, root := ~, start := 26591, stop := 2660\ 0 ), rec( content := " is a ", count := [ 3, 1, 7, 23 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content :=\ [ rec( attributes := rec( Text := "Grape" ), content := [ rec( content := "ht\ tp://www.maths.qmul.ac.uk/~leonard/grape/", count := [ 3, 1, 7, 23 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 23 ], mathmod\ e := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 ) ] , coun\ t := [ 3, 1, 7, 23 ], name := "Alt", next := 93, root := ~, start := 1, stop :\ = 92 ), rec( attributes := rec( Only := "Text" ), content := [ rec( attributes\ := rec( ), content := [ rec( content := "Grape", count := [ 3, 1, 7, 23 ], n\ ame := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 23 ], name := "Package", n\ ext := 137, root := ~, start := 113, stop := 136 ) ], count := [ 3, 1, 7, 23 ] , math\ mode := "Text", name := "Alt", next := 143, root := ~, start := 93, stop := 14\ 2 ), rec( content := " package graph (i.e. a record for which the\n fun\ ction ", count := [ 3, 1, 7, 23 ], mathmode := "Text", name := "PCDATA", root \ := ~ ), rec( attributes := rec( ), content := [ rec( content := "IsGraph", co\ unt := [ 3, 1, 7, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 3, 1, 7, 23 ], mathmode := "Text", name := "C", next := 26689, root := \ ~, start := 26675, stop := 26688 ), rec( content := " returns ", count := [ 3,\ 1, 7, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribute\ s := rec( ), content := [ rec( content := "true", count := [ 3, 1, 7, 23 ], m\ athmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 23 ], math\ mode := "Text", name := "K", next := 26709, root := ~, start := 26698, stop :=\ 26708 ), rec( content := "), then this function returns\n a digraph is\ omorphic to ", count := [ 3, 1, 7, 23 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "obj", count\ := [ 3, 1, 7, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 3, 1, 7, 23 ], mathmode := "Text", name := "A", next := 26781, root := \ ~, start := 26771, stop := 26780 ), rec( content := ".\n ", count := [ 3,\ 1, 7, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 23 ], name := "Ite\ m", next := 26796, root := ~, start := 26573, stop := 26795 ), rec( attributes :\ = rec( ), content := [ rec( content := "for a binary relation", count := [ 3,\ 1, 7, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 24 ], name := "Mar\ k", next := 26838, root := ~, start := 26804, stop := 26837 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n if ", count := [ 3, 1, 7, 2\ 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec\ ( ), content := [ rec( content := "obj", count := [ 3, 1, 7, 25 ], mathmode :\ = "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 25 ], mathmode \ := "Text", name := "A", next := 26873, root := ~, start := 26863, stop := 2687\ 2 ), rec( content := " is a binary relation on the points ", count := [ 3, 1, \ 7, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :=\ rec( ), content := [ rec( content := "[1 .. n]", count := [ 3, 1, 7, 25 ], m\ athmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 25 ], math\ mode := "Text", name := "C", next := 26924, root := ~, start := 26909, stop :=\ 26923 ), rec( content := " for\n some posititve integer ", count := [ \ 3, 1, 7, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\ tes := rec( ), content := [ rec( content := "n", count := [ 3, 1, 7, 25 ], ma\ thmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 25 ], math\ mode := "Text", name := "M", next := 26968, root := ~, start := 26960, stop :=\ 26967 ), rec( content := ", then this function returns the digraph\n d\ efined by ", count := [ 3, 1, 7, 25 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "obj", count\ := [ 3, 1, 7, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 3, 1, 7, 25 ], mathmode := "Text", name := "A", next := 27038, root := \ ~, start := 27028, stop := 27037 ), rec( content := ". Specifically, this func\ tion returns a digraph\n which has ", count := [ 3, 1, 7, 25 ], mathmod\ e := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), conten\ t := [ rec( content := "n", count := [ 3, 1, 7, 25 ], mathmode := "Text", name\ := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 25 ], mathmode := "Text", name\ := "M", next := 27112, root := ~, start := 27104, stop := 27111 ), rec( conte\ nt := " vertices, and which has an edge with source ", count := [ 3, 1, 7, 25 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "i", count := [ 3, 1, 7, 25 ], mathmode := "Text", na\ me := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 25 ], mathmode := "Text", name\ := "C", next := 27165, root := ~, start := 27157, stop := 27164 ), rec( conte\ nt := "\n and range ", count := [ 3, 1, 7, 25 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "j", count := [ 3, 1, 7, 25 ], mathmode := "Text", name := "PCDATA", roo\ t := ~ ) ], count := [ 3, 1, 7, 25 ], mathmode := "Text", name := "C", next :=\ 27192, root := ~, start := 27184, stop := 27191 ), rec( content := " if and o\ nly if ", count := [ 3, 1, 7, 25 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "[i,j]", cou\ nt := [ 3, 1, 7, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 3, 1, 7, 25 ], mathmode := "Text", name := "C", next := 27220, root := \ ~, start := 27208, stop := 27219 ), rec( content := " is a pair in\n th\ e binary relation ", count := [ 3, 1, 7, 25 ], mathmode := "Text", name := "PC\ DATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\ obj", count := [ 3, 1, 7, 25 ], mathmode := "Text", name := "PCDATA", root := \ ~ ) ], count := [ 3, 1, 7, 25 ], mathmode := "Text", name := "A", next := 2727\ 2, root := ~, start := 27262, stop := 27271 ), rec( content := ".\n ", coun\ t := [ 3, 1, 7, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 25 ], name := "Ite\ m", next := 27287, root := ~, start := 26845, stop := 27286 ) ], count := [ 3, 1, 7, 8 ], mathmode := "Text", name := "List", next := 27299, root := ~, start := 22897, stop := 27298 ), rec( content := "\n\n \ ", count := [ 3, 1, 7, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := Digraph([\n> [2, 5, 8, 10], [2, 3, 4, 2, 5, 6, 8, 9, 10], [1],\n> \ [3, 5, 7, 8, 10], [2, 5, 7], [3, 6, 7, 9, 10], [1, 4],\n> [1, 5, 9], [1, 2, 7,\ 8], [3, 5]]);\n\ngap> gr :\ = Digraph([\"a\", \"b\", \"c\"], [\"a\"], [\"b\"]);\n\ngap> gr := Digraph(5, [1, 2, 2, 4, 1, 1], [2, 3, 5, 5, 1, \ 1]);\n\ngap> Petersen := Grap\ h(SymmetricGroup(5), [[1, 2]], OnSets,\n> function(x, y) return Intersection(x\ , y) = []; end);;\ngap> Digraph(Petersen);\n\ngap> gr := Digraph([1 .. 10], ReturnTrue);\n", count := [ 3, 1, 7, 28 ], name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 28 ], mathmode := "Text", name := "Example", next := 28041, root := ~, start := 27305, stop := 28040 ), rec( content := "\n\n \ The next example illustrates the uses of the fourth and fifth variants of\n \ this constructor. The resulting digraph is a strongly regular graph, and\ \n it is actually the point graph of the van Lint-Schrijver partial\n \ geometry, ", count := [ 3, 1, 7, 29 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "vLS81" ) , content := 0, count := [ 3, 1, 7, 29 ], mathmode := "Text", name := "Cite", next := 28308, root := ~, start := 28289, stop := 28307 ), rec( content := ". The a\ lgebraic description\n is taken from the seminal paper of Calderbank and \ Kantor ", count := [ 3, 1, 7, 29 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "CK86" ), content := 0, count := [ 3, 1, 7, 29 ], mathmode := "Text", name := "Cite", next := 28426, root := ~, start := 28400, stop := 28425 ), rec( content := ".\n", count := [ 3, 1, 7, 29 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> f := GF(3 ^ 4);\nGF(3^4)\ngap> gamma := First(f, x -> Order(x) = 5);\nZ(\ 3^4)^64\ngap> L := Union([Zero(f)], List(Group(gamma)));\n[ 0*Z(3), Z(3)^0, Z(\ 3^4)^16, Z(3^4)^32, Z(3^4)^48, Z(3^4)^64 ]\ngap> omega := Union(List(L, x -> L\ ist(Difference(L, [x]), y -> x - y)));\n[ Z(3)^0, Z(3), Z(3^4)^5, Z(3^4)^7, Z(\ 3^4)^8, Z(3^4)^13, Z(3^4)^15, \n Z(3^4)^16, Z(3^4)^21, Z(3^4)^23, Z(3^4)^24, \ Z(3^4)^29, Z(3^4)^31, \n Z(3^4)^32, Z(3^4)^37, Z(3^4)^39, Z(3^4)^45, Z(3^4)^4\ 7, Z(3^4)^48, \n Z(3^4)^53, Z(3^4)^55, Z(3^4)^56, Z(3^4)^61, Z(3^4)^63, Z(3^4\ )^64, \n Z(3^4)^69, Z(3^4)^71, Z(3^4)^72, Z(3^4)^77, Z(3^4)^79 ]\ngap> adj :=\ function(x, y)\n> return x - y in omega;\n> end;\nfunction( x, y ) ... end\ \ngap> digraph := Digraph(AsList(f), adj);\n\ngap> group := Group(Z(3));;\ngap> act := \\*;\n\ngap> digraph := Digraph(group, List(f), act, adj);\n\n", count := [ 3, 1, 7, 30 ], name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 30 ], mathmode := "Text", name := "Example", next := 29396, root := ~, start := 28428, stop := 29395 ), rec( content := "\n ", count := [ 3, 1, 7, 31 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "Description", next := 29413, root := ~, start := 22381, stop := 29412 ) ], count := [ 3, 1, 7, 1 ], mathmode := "Text", name := "ManSection", next := 29427, root := ~, start := 22060, stop := 29426 ), rec( content := "\n\n ", count := [ 3, 1, 7, 31 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "[filt, ]list", Name := "DigraphByAdjace\ ncyMatrix" ), content := 0, count := [ 3, 1, 8, 2 ], mathmode := "Text", name := "Oper", next := 29506, root := ~, start := 29448, stop := 29505 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "Returns", next := 29538, root := ~, start := 29509, stop := 29537 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ the optional first argument ", count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "A", next := 29601, root := ~, start := 29590, stop := 29600 ), rec( content := " is pres\ ent, then this should\n specify the category or representation the digraph \ being created will\n belong to. For example, if ", count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "A", next := 29747, root := ~, start := 29736, stop := 29746 ), rec( content := " is ", count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "Ref", next := 29781, root := ~, start := 29751, stop := 29780 ), rec( content := ",\n t\ hen the digraph being created will be mutable, if ", count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "A", next := 29849, root := ~, start := 29838, stop := 29848 ), rec( content := " is ", count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "Ref", next := 29889, root := ~, start := 29853, stop := 29888 ), rec( content := ", then t\ he digraph will be immutable. \n If the optional first argument ", count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "A", next := 29974, root := ~, start := 29963, stop := 29973 ), rec( content := " is not \ present, then ", count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "Ref", next := 30032, root := ~, start := 29996, stop := 30031 ), rec( content := " is used\ by default.", count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 8, 4 ], mathmode := "Text", name := "P", next := 30056, root := ~, start := 30052, stop := 30055 ), rec( content := "\n\n \ If ", count := [ 3, 1, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 3, 1, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 8, 4 ], mathmode := "Text", name := "A", next := 30076, root := ~, start := 30065, stop := 30075 ), rec( content := " is the \ adjacency matrix of a digraph in the sense of\n ", count := [ 3, 1, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Adjacen\ cyMatrix" ), content := 0, count := [ 3, 1, 8, 4 ], mathmode := "Text", name := "Ref", next := 30163, root := ~, start := 30134, stop := 30162 ), rec( content := ", then t\ his operation returns the digraph\n which is defined by ", count := [ 3, 1, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 3, 1, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 8, 4 ], mathmode := "Text", name := "A", next := 30240, root := ~, start := 30229, stop := 30239 ), rec( content := ". ", count := [ 3, 1, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "P", next := 30246, root := ~, start := 30242, stop := 30245 ), rec( content := "\n\n \ Alternatively, if ", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "A", next := 30281, root := ~, start := 30270, stop := 30280 ), rec( content := " is a sq\ uare boolean matrix, then this\n operation returns the digraph with ", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "L\ ength(", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "C", next := 30373, root := ~, start := 30359, stop := 30372 ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "A", next := 30384, root := ~, start := 30373, stop := 30383 ), rec( attributes := rec( ), content := [ rec( content := ")\ ", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "C", next := 30392, root := ~, start := 30384, stop := 30391 ), rec( content := "\n ve\ rtices which has the edge ", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ i,j]", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "C", next := 30437, root := ~, start := 30425, stop := 30436 ), rec( content := " if and \ only if\n ", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "A", next := 30468, root := ~, start := 30457, stop := 30467 ), rec( attributes := rec( ), content := [ rec( content := "[\ i][j]", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "C", next := 30481, root := ~, start := 30468, stop := 30480 ), rec( content := " is ", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "K", next := 30496, root := ~, start := 30485, stop := 30495 ), rec( content := ". ", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 8, 6 ], mathmode := "Text", name := "P", next := 30502, root := ~, start := 30498, stop := 30501 ), rec( content := "\n\n \ ", count := [ 3, 1, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> DigraphByAdjacencyMatrix([\n> [0, 1, 0, 2, 0],\n> [1, 1, 1, 0, 1],\n> [0\ , 3, 2, 1, 1],\n> [0, 0, 1, 0, 1],\n> [2, 0, 0, 0, 0]]);\n\ngap> D := DigraphByAdjacencyMatrix([\n> [true,\ false, true],\n> [false, false, true],\n> [false, true, false]]);\n\ngap> OutNeighbours(D);\n[ [ 1, 3 ], [ 3 ],\ [ 2 ] ]\ngap> D := DigraphByAdjacencyMatrix(IsMutableDigraph, \n> [[true, fal\ se, true],\n> [false, false, true],\n> [false, true, false]]);\n\n", count := [ 3, 1, 8, 7 ], name := "PCDATA", root := ~ ) ], count := [ 3, 1, 8, 7 ], mathmode := "Text", name := "Example", next := 31098, root := ~, start := 30508, stop := 31097 ), rec( content := "\n ", count := [ 3, 1, 8, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "Description", next := 31115, root := ~, start := 29541, stop := 31114 ) ], count := [ 3, 1, 8, 1 ], mathmode := "Text", name := "ManSection", next := 31129, root := ~, start := 29433, stop := 31128 ), rec( content := "\n\n ", count := [ 3, 1, 8, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "[filt, ]list[, n\ ]", Name := "DigraphByEdges" ), content := 0, count := [ 3, 1, 9, 2 ], mathmode := "Text", name := "Oper", next := 31203, root := ~, start := 31150, stop := 31202 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "Returns", next := 31235, root := ~, start := 31206, stop := 31234 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ the optional first argument ", count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "A", next := 31298, root := ~, start := 31287, stop := 31297 ), rec( content := " is pres\ ent, then this should\n specify the category or representation the digraph \ being created will\n belong to. For example, if ", count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "A", next := 31444, root := ~, start := 31433, stop := 31443 ), rec( content := " is ", count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "Ref", next := 31478, root := ~, start := 31448, stop := 31477 ), rec( content := ",\n t\ hen the digraph being created will be mutable, if ", count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "A", next := 31546, root := ~, start := 31535, stop := 31545 ), rec( content := " is ", count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "Ref", next := 31586, root := ~, start := 31550, stop := 31585 ), rec( content := ", then t\ he digraph will be immutable. \n If the optional first argument ", count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "A", next := 31671, root := ~, start := 31660, stop := 31670 ), rec( content := " is not \ present, then ", count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "Ref", next := 31729, root := ~, start := 31693, stop := 31728 ), rec( content := " is used\ by default.", count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 9, 4 ], mathmode := "Text", name := "P", next := 31753, root := ~, start := 31749, stop := 31752 ), rec( content := "\n\n \ If ", count := [ 3, 1, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 3, 1, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 9, 4 ], mathmode := "Text", name := "A", next := 31773, root := ~, start := 31762, stop := 31772 ), rec( content := " is list\ of pairs of positive integers, then this function\n returns the digraph wi\ th the minimum number of vertices ", count := [ 3, 1, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 3, 1, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 9, 4 ], mathmode := "Text", name := "C", next := 31900, root := ~, start := 31892, stop := 31899 ), rec( content := " such th\ at\n its list equal ", count := [ 3, 1, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 3, 1, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 9, 4 ], mathmode := "Text", name := "A", next := 31941, root := ~, start := 31930, stop := 31940 ), rec( content := ".", count := [ 3, 1, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "P", next := 31946, root := ~, start := 31942, stop := 31945 ), rec( content := "\n\n \ If the optional second argument ", count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "A", next := 31992, root := ~, start := 31984, stop := 31991 ), rec( content := " is a po\ sitive integer with\n ", count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "n", count := [ 3, 1, 9, 5 ], mathmode \ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 9, 5 ], mathmode := \ "Text", name := "A", next := 32035, root := ~, start := 32027, stop := 32034 ) , rec( content := "\ >= m", count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "C", next := 32044, root := ~, start := 32024, stop := 32043 ), rec( content := " (with " , count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "C", next := 32059, root := ~, start := 32051, stop := 32058 ), rec( content := " defined\ as above),\n then this function returns the digraph with ", count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "A", next := 32135, root := ~, start := 32127, stop := 32134 ), rec( content := " vertice\ s and list\n ", count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "A", next := 32169, root := ~, start := 32158, stop := 32168 ), rec( content := ". ", count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 9, 6 ], mathmode := "Text", name := "P", next := 32175, root := ~, start := 32171, stop := 32174 ), rec( content := "\n\n \ See ", count := [ 3, 1, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Edges" ), content := 0, count := [ 3, 1, 9, 6 ], mathmode := "Text", name := "Ref", next := 32211, root := ~, start := 32185, stop := 32210 ), rec( content := ".\n\n \ ", count := [ 3, 1, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> DigraphByEdges(\n> [[1, 3], [2, 1], [2, 3], [2, 5], [3, 6],\n> [4, 6], \ [5, 2], [5, 4], [5, 6], [6, 6]]);\n\ngap> DigraphByEdges(\n> [[1, 3], [2, 1], [2, 3], [2, 5], [3, 6],\n> [4, 6\ ], [5, 2], [5, 4], [5, 6], [6, 6]], 12);\n\ngap> DigraphByEdges(IsMutableDigraph, \n> [[1, 3], [2, 1], [2, 3],\ [2, 5], [3, 6],\n> [4, 6], [5, 2], [5, 4], [5, 6], [6, 6]], 12);\n\n", count := [ 3, 1, 9, 7 ], name := "PCDAT\ A", root := ~ ) ], count := [ 3, 1, 9, 7 ], mathmode := "Text", name := "Example", next := 32741, root := ~, start := 32218, stop := 32740 ), rec( content := "\n ", count := [ 3, 1, 9, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "Description", next := 32758, root := ~, start := 31238, stop := 32757 ) ], count := [ 3, 1, 9, 1 ], mathmode := "Text", name := "ManSection", next := 32772, root := ~, start := 31135, stop := 32771 ), rec( content := "\n\n ", count := [ 3, 1, 9, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "G, edges[, n]", Name := "EdgeOrbitsDigra\ ph" ), content := 0, count := [ 3, 1, 10, 2 ], mathmode := "Text", name := "Oper", next := 32845, root := ~, start := 32793, stop := 32844 ), rec( attributes := rec( ), content := [ rec( content := "\n An \ immutable digraph.\n ", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "Returns", next := 32896, root := ~, start := 32848, stop := 32895 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "A", next := 32928, root := ~, start := 32920, stop := 32927 ), rec( content := " is a pe\ rmutation group, ", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dges", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "A", next := 32965, root := ~, start := 32953, stop := 32964 ), rec( content := " is an e\ dge or list of\n edges, and ", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "A", next := 33011, root := ~, start := 33003, stop := 33010 ), rec( content := " is a no\ n-negative integer such that ", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "A", next := 33056, root := ~, start := 33048, stop := 33055 ), rec( content := " fixes\n\ ", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ 1 .. ", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "n", count := [ 3, 1, 10, 3 ], mathmod\ e := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 10, 3 ], mathmode := \ "Text", name := "A", next := 33084, root := ~, start := 33076, stop := 33083 ) , rec( content := "\ ]", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "C", next := 33089, root := ~, start := 33067, stop := 33088 ), rec( content := " setwise\ , then\n this operation returns an immutable digraph with ", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "A", next := 33165, root := ~, start := 33157, stop := 33164 ), rec( content := " vertice\ s and the union\n of the orbits of the edges in ", count := [ 3, 1, 10, 3 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := " \ edges ", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "A", next := 33237, root := ~, start := 33223, stop := 33236 ), rec( content := " under t\ he action of the\n permutation group ", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "A", next := 33292, root := ~, start := 33284, stop := 33291 ), rec( content := ". An ed\ ge in this context is simply a pair of\n positive integers.\n ", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 10, 4 ], mathmode := "Text", name := "P", next := 33370, root := ~, start := 33366, stop := 33369 ), rec( content := "\n\n \ If the optional third argument ", count := [ 3, 1, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 1, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 10, 4 ], mathmode := "Text", name := "A", next := 33415, root := ~, start := 33407, stop := 33414 ), rec( content := " is not \ present, then the largest\n moved point of the permutation group ", count := [ 3, 1, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 3, 1, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 10, 4 ], mathmode := "Text", name := "A", next := 33498, root := ~, start := 33490, stop := 33497 ), rec( content := " is used\ by default.", count := [ 3, 1, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 10, 5 ], mathmode := "Text", name := "P", next := 33522, root := ~, start := 33518, stop := 33521 ), rec( content := "\n\n \ ", count := [ 3, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> digraph := EdgeOrbitsDigraph(Group((1, 3), (1, 2)(3, 4)),\n> \ [[1, 2], [4, 5]], 5);\n\ngap> OutNeighbours(digraph);\n[ [ 2, 4, 5 ], [ 1, 3, 5 ], [ 2, 4,\ 5 ], [ 1, 3, 5 ], [ ] ]\ngap> RepresentativeOutNeighbours(digraph);\n[ [ 2, \ 4, 5 ], [ ] ]\n", count := [ 3, 1, 10, 6 ], name := "PCDATA", root := ~ ) ], count := [ 3, 1, 10, 6 ], mathmode := "Text", name := "Example", next := 33880, root := ~, start := 33528, stop := 33879 ), rec( content := "\n ", count := [ 3, 1, 10, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "Description", next := 33897, root := ~, start := 32899, stop := 33896 ) ], count := [ 3, 1, 10, 1 ], mathmode := "Text", name := "ManSection", next := 33911, root := ~, start := 32778, stop := 33910 ), rec( content := "\n\n ", count := [ 3, 1, 10, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "[filt, ]list", Name := "DigraphByInNeig\ hbours" ), content := 0, count := [ 3, 1, 11, 2 ], mathmode := "Text", name := "Oper", next := 33987, root := ~, start := 33932, stop := 33986 ), rec( attributes := rec( Arg := "[filt, ]list", Name := "DigraphByInNeig\ hbors" ), content := 0, count := [ 3, 1, 11, 4 ], mathmode := "Text", name := "Oper", next := 34044, root := ~, start := 33990, stop := 34043 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "Returns", next := 34076, root := ~, start := 34047, stop := 34075 ), rec( attributes := rec( ), content := [ rec( content := "\n If th\ e optional first argument ", count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "A", next := 34137, root := ~, start := 34126, stop := 34136 ), rec( content := " is pres\ ent, then this should\n specify the category or representation the digraph be\ ing created will\n belong to. For example, if ", count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "A", next := 34279, root := ~, start := 34268, stop := 34278 ), rec( content := " is ", count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "Ref", next := 34313, root := ~, start := 34283, stop := 34312 ), rec( content := ",\n the\ n the digraph being created will be mutable, if ", count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "A", next := 34379, root := ~, start := 34368, stop := 34378 ), rec( content := " is ", count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "Ref", next := 34417, root := ~, start := 34383, stop := 34416 ), rec( content := ", then t\ he digraph will be immutable. \n If the optional first argument ", count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "A", next := 34500, root := ~, start := 34489, stop := 34499 ), rec( content := " is not \ present, then ", count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "Ref", next := 34556, root := ~, start := 34522, stop := 34555 ), rec( content := " is used\ by default.", count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "P", next := 34580, root := ~, start := 34576, stop := 34579 ), rec( content := "\n\n If\ ", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "A", next := 34598, root := ~, start := 34587, stop := 34597 ), rec( content := " is a li\ st of lists of positive integers list the range\n ", count := [ 3, 1, 11, 6 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ 1 .. Length(", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "list", count := [ 3, 1, 11, 6 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 6 ], mathmode := \ "Text", name := "A", next := 34683, root := ~, start := 34672, stop := 34682 ) , rec( content := "\ )]", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "C", next := 34689, root := ~, start := 34656, stop := 34688 ), rec( content := ", then t\ his function returns the\n digraph with vertices ", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "E\ ^0=", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "M", next := 34757, root := ~, start := 34746, stop := 34756 ), rec( attributes := rec( ), content := [ rec( content := "[\ 1 .. Length(", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "list", count := [ 3, 1, 11, 6 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 6 ], mathmode := \ "Text", name := "A", next := 34784, root := ~, start := 34773, stop := 34783 ) , rec( content := "\ )]", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "C", next := 34790, root := ~, start := 34757, stop := 34789 ), rec( content := ", and\n \ edges corresponding to the entries of ", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "A", next := 34847, root := ~, start := 34836, stop := 34846 ), rec( content := ". More p\ recisely, there is an\n edge with source vertex ", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "C", next := 34911, root := ~, start := 34903, stop := 34910 ), rec( content := " and ran\ ge vertex ", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "C", next := 34937, root := ~, start := 34929, stop := 34936 ), rec( content := " if ", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "C", next := 34949, root := ~, start := 34941, stop := 34948 ), rec( content := " is list\ \n ", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "list", count := [ 3, 1, 11, 6 ], mathm\ ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 6 ], mathmode := \ "Text", name := "A", next := 34974, root := ~, start := 34963, stop := 34973 ) , rec( content := "\ [j]", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "C", next := 34981, root := ~, start := 34960, stop := 34980 ), rec( content := ". ", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "P", next := 34987, root := ~, start := 34983, stop := 34986 ), rec( content := "\n\n If\ ", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "C", next := 35002, root := ~, start := 34994, stop := 35001 ), rec( content := " occurs \ list ", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "list", count := [ 3, 1, 11, 7 ], mathm\ ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 7 ], mathmode := \ "Text", name := "A", next := 35029, root := ~, start := 35018, stop := 35028 ) , rec( content := "\ [j]", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "C", next := 35036, root := ~, start := 35015, stop := 35035 ), rec( content := " with mu\ ltiplicity ", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "k\ ", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "C", next := 35063, root := ~, start := 35055, stop := 35062 ), rec( content := ",\n the\ n there are ", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "k\ ", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "C", next := 35090, root := ~, start := 35082, stop := 35089 ), rec( content := " multipl\ e edges from ", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "C", next := 35119, root := ~, start := 35111, stop := 35118 ), rec( content := " to ", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "C", next := 35131, root := ~, start := 35123, stop := 35130 ), rec( content := ". ", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 11, 8 ], mathmode := "Text", name := "P", next := 35137, root := ~, start := 35133, stop := 35136 ), rec( content := "\n\n Se\ e ", count := [ 3, 1, 11, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "InNeigh\ bours" ), content := 0, count := [ 3, 1, 11, 8 ], mathmode := "Text", name := "Ref", next := 35171, root := ~, start := 35145, stop := 35170 ), rec( content := ".\n\n \ ", count := [ 3, 1, 11, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := DigraphByInNeighbours([\n> [2, 5, 8, 10], [2, 3, 4, 5, 6, 8, 9, 10]\ ,\n> [1], [3, 5, 7, 8, 10], [2, 5, 7], [3, 6, 7, 9, 10], [1, 4],\n> [1, 5, 9],\ [1, 2, 7, 8], [3, 5]]);\n\ngap>\ D := DigraphByInNeighbours([[2, 3, 2], [1], [1, 2, 3]]);\n\ngap> D := DigraphByInNeighbours(IsMutableDigra\ ph, \n> [[2, 3, 2], [1], [1, 2, 3]]);\n\n", count := [ 3, 1, 11, 9 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 1, 11, 9 ], mathmode := "Text", name := "Example", next := 35707, root := ~, start := 35178, stop := 35706 ), rec( content := "\n ", count := [ 3, 1, 11, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "Description", next := 35724, root := ~, start := 34079, stop := 35723 ) ], count := [ 3, 1, 11, 1 ], mathmode := "Text", name := "ManSection", next := 35738, root := ~, start := 33917, stop := 35737 ), rec( content := "\n\n ", count := [ 3, 1, 11, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "G[, gens]", Name := "CayleyDigraph" ), content := 0, count := [ 3, 1, 12, 2 ], mathmode := "Text", name := "Oper", next := 35803, root := ~, start := 35759, stop := 35802 ), rec( attributes := rec( ), content := [ rec( content := "An immuta\ ble digraph.", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "Returns", next := 35846, root := ~, start := 35806, stop := 35845 ), rec( attributes := rec( ), content := [ rec( content := "\n Let\ ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "A", next := 35879, root := ~, start := 35871, stop := 35878 ), rec( content := " be any \ group and let ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ ens", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "A", next := 35912, root := ~, start := 35901, stop := 35911 ), rec( content := " be a li\ st of elements of\n ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "A", next := 35950, root := ~, start := 35942, stop := 35949 ), rec( content := ". This o\ peration returns an immutable digraph that corresponds to\n the Cayley grap\ h of ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "A", next := 36048, root := ~, start := 36040, stop := 36047 ), rec( content := " with re\ spect\n ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ ens", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "A", next := 36077, root := ~, start := 36066, stop := 36076 ), rec( content := ". The ve\ rtices are the elements of ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "A", next := 36120, root := ~, start := 36112, stop := 36119 ), rec( content := ". There \ exists an edge\n from the vertex ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "C", next := 36171, root := ~, start := 36163, stop := 36170 ), rec( content := " to the \ vertex ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "C", next := 36194, root := ~, start := 36186, stop := 36193 ), rec( content := " if and \ only if there exists\n a generator ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "C", next := 36247, root := ~, start := 36239, stop := 36246 ), rec( content := " in ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ ens", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "A", next := 36262, root := ~, start := 36251, stop := 36261 ), rec( content := " such th\ at ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ * g = y", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "C", next := 36289, root := ~, start := 36273, stop := 36288 ), rec( content := ". ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 12, 4 ], mathmode := "Text", name := "P", next := 36295, root := ~, start := 36291, stop := 36294 ), rec( content := "\n\n \ ", count := [ 3, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( content := " FIXME W\ hat is the correspondence between vertices and elements? ", count := [ 3, 1, 12, 4 ], mathmode := "Text", name := "XMLCOMMENT" , root := ~ ), rec( content := "\n\n \ If the optional second argument ", count := [ 3, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ ens", count := [ 3, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 12, 4 ], mathmode := "Text", name := "A", next := 36422, root := ~, start := 36411, stop := 36421 ), rec( content := " is not \ present, then the\n generators of ", count := [ 3, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 3, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 12, 4 ], mathmode := "Text", name := "A", next := 36474, root := ~, start := 36466, stop := 36473 ), rec( content := " are use\ d by default.", count := [ 3, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 12, 5 ], mathmode := "Text", name := "P", next := 36499, root := ~, start := 36495, stop := 36498 ), rec( content := "\n\n \ The digraph created by this operation belongs to the category ", count := [ 3, 1, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsCayle\ yDigraph" ), content := 0, count := [ 3, 1, 12, 5 ], mathmode := "Text", name := "Ref", next := 36602, root := ~, start := 36567, stop := 36601 ), rec( content := ", the gr\ oup ", count := [ 3, 1, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 3, 1, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 12, 5 ], mathmode := "Text", name := "A", next := 36622, root := ~, start := 36614, stop := 36621 ), rec( content := " can be \ recovered from the\n digraph using ", count := [ 3, 1, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "GroupOf\ CayleyDigraph" ), content := 0, count := [ 3, 1, 12, 5 ], mathmode := "Text", name := "Ref", next := 36701, root := ~, start := 36667, stop := 36700 ), rec( content := ", and th\ e generators\n ", count := [ 3, 1, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ ens", count := [ 3, 1, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 12, 5 ], mathmode := "Text", name := "A", next := 36737, root := ~, start := 36726, stop := 36736 ), rec( content := " can be \ obtained using ", count := [ 3, 1, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Generat\ orsOfCayleyDigraph" ), content := 0, count := [ 3, 1, 12, 5 ], mathmode := "Text", name := "Ref", next := 36799, root := ~, start := 36760, stop := 36798 ), rec( content := ".", count := [ 3, 1, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 12, 6 ], mathmode := "Text", name := "P", next := 36804, root := ~, start := 36800, stop := 36803 ), rec( content := "\n\n \ Note that this function can only return an immutable digraph.\n\n ", count := [ 3, 1, 12, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> G := DihedralGroup(8);\n\ngap> Cay\ leyDigraph(G);\n\ngap> G := Dihed\ ralGroup(IsPermGroup, 8);\nGroup([ (1,2,3,4), (2,4) ])\ngap> CayleyDigraph(G);\ \n\ngap> digraph := CayleyDigraph\ (G, [()]);\n\ngap> GroupOfCayleyDi\ graph(digraph) = G;\ntrue\ngap> GeneratorsOfCayleyDigraph(digraph);\n[ () ]", count := [ 3, 1, 12, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 1, 12, 7 ], mathmode := "Text", name := "Example", next := 37360, root := ~, start := 36877, stop := 37359 ), rec( content := "\n ", count := [ 3, 1, 12, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "Description", next := 37377, root := ~, start := 35849, stop := 37376 ) ], count := [ 3, 1, 12, 1 ], mathmode := "Text", name := "ManSection", next := 37391, root := ~, start := 35744, stop := 37390 ), rec( content := "\n\n ", count := [ 3, 1, 12, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 0, 1 ], mathmode := "Text", name := "Section", next := 37405, root := ~, start := 19345, stop := 37404 ), rec( content := "\n\n ", count := [ 3, 1, 12, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Changing represen\ tations", count := [ 3, 2, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 0, 2 ], mathmode := "Text", name := "Heading", next := 37461, root := ~, start := 37418, stop := 37460 ), rec( content := "\n ", count := [ 3, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "AsBinaryRelatio\ n" ), content := 0, count := [ 3, 2, 1, 2 ], mathmode := "Text", name := "Oper", next := 37526, root := ~, start := 37481, stop := 37525 ), rec( attributes := rec( ), content := [ rec( content := "A binary \ relation.", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "Returns", next := 37566, root := ~, start := 37529, stop := 37565 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "A", next := 37604, root := ~, start := 37590, stop := 37603 ), rec( content := " is a di\ graph with a positive number of vertices\n ", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "M", next := 37665, root := ~, start := 37657, stop := 37664 ), rec( content := ", and no\ multiple edges, then this operation returns a binary\n relation on the poi\ nts ", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ 1..n]", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "C", next := 37767, root := ~, start := 37754, stop := 37766 ), rec( content := ".\n T\ he pair ", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ i,j]", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "C", next := 37794, root := ~, start := 37782, stop := 37793 ), rec( content := " is in t\ he binary relation if and only if\n ", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ i,j]", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "C", next := 37852, root := ~, start := 37840, stop := 37851 ), rec( content := " is an e\ dge in ", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "A", next := 37881, root := ~, start := 37867, stop := 37880 ), rec( content := ".\n " , count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 2, 1, 4 ], mathmode := "Text", name := "P", next := 37891, root := ~, start := 37887, stop := 37890 ), rec( content := "\n", count := [ 3, 2, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[3, 2], [1, 2], [2], [3, 4]]);\n\ngap> AsBinaryRelation(D);\nBinary Relation on 4 points\n", count := [ 3, 2, 1, 5 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 2, 1, 5 ], mathmode := "Text", name := "Example", next := 38073, root := ~, start := 37892, stop := 38072 ), rec( content := "\n ", count := [ 3, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "Description", next := 38090, root := ~, start := 37569, stop := 38089 ) ], count := [ 3, 2, 1, 1 ], mathmode := "Text", name := "ManSection", next := 38104, root := ~, start := 37466, stop := 38103 ), rec( content := "\n\n ", count := [ 3, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "[filt, ]trans[, \ n]", Name := "AsDigraph" ), content := 0, count := [ 3, 2, 2, 2 ], mathmode := "Text", name := "Oper", next := 38174, root := ~, start := 38125, stop := 38173 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ , or ", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "K", next := 38211, root := ~, start := 38200, stop := 38210 ), rec( content := ".", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "Returns", next := 38222, root := ~, start := 38177, stop := 38221 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ the optional first argument ", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "A", next := 38285, root := ~, start := 38274, stop := 38284 ), rec( content := " is pres\ ent, then this should\n specify the category or representation the digraph \ being created will\n belong to. For example, if ", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "A", next := 38431, root := ~, start := 38420, stop := 38430 ), rec( content := " is ", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "Ref", next := 38465, root := ~, start := 38435, stop := 38464 ), rec( content := ",\n t\ hen the digraph being created will be mutable, if ", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "A", next := 38533, root := ~, start := 38522, stop := 38532 ), rec( content := " is ", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "Ref", next := 38573, root := ~, start := 38537, stop := 38572 ), rec( content := ", then t\ he digraph will be immutable. \n If the optional first argument ", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "A", next := 38658, root := ~, start := 38647, stop := 38657 ), rec( content := " is not \ present, then ", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "Ref", next := 38716, root := ~, start := 38680, stop := 38715 ), rec( content := " is used\ by default.", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "P", next := 38740, root := ~, start := 38736, stop := 38739 ), rec( content := "\n\n \ If ", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rans", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "A", next := 38761, root := ~, start := 38749, stop := 38760 ), rec( content := " is a tr\ ansformation, and ", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "A", next := 38795, root := ~, start := 38787, stop := 38794 ), rec( content := " is a no\ n-negative integer\n such that the restriction of ", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rans", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "A", next := 38867, root := ~, start := 38855, stop := 38866 ), rec( content := " to ", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ 1 .. ", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "n", count := [ 3, 2, 2, 4 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 4 ], mathmode := \ "Text", name := "A", next := 38888, root := ~, start := 38880, stop := 38887 ) , rec( content := "\ ]", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "C", next := 38893, root := ~, start := 38871, stop := 38892 ), rec( content := " defines\ \n a transformation of ", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ 1 .. ", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "n", count := [ 3, 2, 2, 4 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 4 ], mathmode := \ "Text", name := "A", next := 38943, root := ~, start := 38935, stop := 38942 ) , rec( content := "\ ]", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "C", next := 38948, root := ~, start := 38926, stop := 38947 ), rec( content := ", then " , count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A\ sDigraph", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "C", next := 38971, root := ~, start := 38955, stop := 38970 ), rec( content := "\n re\ turns the functional digraph with ", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "A", next := 39020, root := ~, start := 39012, stop := 39019 ), rec( content := " vertice\ s defined by\n ", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rans", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "A", next := 39057, root := ~, start := 39045, stop := 39056 ), rec( content := ". See ", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsFunct\ ionalDigraph" ), content := 0, count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "Ref", next := 39096, root := ~, start := 39063, stop := 39095 ), rec( content := ".\n " , count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "P", next := 39106, root := ~, start := 39102, stop := 39105 ), rec( content := "\n\n \ Specifically, the digraph returned by ", count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A\ sDigraph", count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "C", next := 39166, root := ~, start := 39150, stop := 39165 ), rec( content := " has ", count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "A", next := 39180, root := ~, start := 39172, stop := 39179 ), rec( content := " edges:\\ n for each vertex ", count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ", count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "C", next := 39216, root := ~, start := 39208, stop := 39215 ), rec( content := " in ", count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ 1 .. ", count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "n", count := [ 3, 2, 2, 5 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 5 ], mathmode := \ "Text", name := "A", next := 39237, root := ~, start := 39229, stop := 39236 ) , rec( content := "\ ]", count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "C", next := 39242, root := ~, start := 39220, stop := 39241 ), rec( content := ", there \ is a unique edge\n with source ", count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ", count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "C", next := 39291, root := ~, start := 39283, stop := 39290 ), rec( content := "; this e\ dge has range ", count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ^", count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes :\ = rec( ), content := [ rec( content := "trans", count := [ 3, 2, 2, 5 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 5 ], mathmode := \ "Text", name := "A", next := 39330, root := ~, start := 39318, stop := 39329 ) ], count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "C", next := 39334, root := ~, start := 39313, stop := 39333 ), rec( content := ".\n " , count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "P", next := 39344, root := ~, start := 39340, stop := 39343 ), rec( content := "\n\n \ If the optional second argument ", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "A", next := 39390, root := ~, start := 39382, stop := 39389 ), rec( content := " is not \ supplied, then the degree of\n the transformation ", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rans", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "A", next := 39462, root := ~, start := 39450, stop := 39461 ), rec( content := " is used\ by default. If the restriction of\n ", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rans", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "A", next := 39522, root := ~, start := 39510, stop := 39521 ), rec( content := " to ", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ 1 .. ", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "n", count := [ 3, 2, 2, 6 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 6 ], mathmode := \ "Text", name := "A", next := 39543, root := ~, start := 39535, stop := 39542 ) , rec( content := "\ ]", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "C", next := 39548, root := ~, start := 39526, stop := 39547 ), rec( content := " does no\ t define a transformation of\n ", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ 1 .. ", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "n", count := [ 3, 2, 2, 6 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 6 ], mathmode := \ "Text", name := "A", next := 39606, root := ~, start := 39598, stop := 39605 ) , rec( content := "\ ]", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "C", next := 39611, root := ~, start := 39589, stop := 39610 ), rec( content := ", then " , count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A\ sDigraph(", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "trans", count := [ 3, 2, 2, 6 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 6 ], mathmode := \ "Text", name := "A", next := 39643, root := ~, start := 39631, stop := 39642 ) , rec( content := "\ , ", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "n", count := [ 3, 2, 2, 6 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 6 ], mathmode := \ "Text", name := "A", next := 39653, root := ~, start := 39645, stop := 39652 ) , rec( content := "\ )", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "C", next := 39658, root := ~, start := 39618, stop := 39657 ), rec( content := "\n re\ turns ", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "K", next := 39682, root := ~, start := 39671, stop := 39681 ), rec( content := ".\n\n \ ", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> f := Transformation([4, 3, 3, 1, 7, 9, 10, 4, 2, 3]);\nTransformation( [\ 4, 3, 3, 1, 7, 9, 10, 4, 2, 3 ] )\ngap> AsDigraph(f);\n\ngap> AsDigraph(f, 4);\n\ngap> AsDigraph(f, 5);\nfail\ngap> b := BinaryRelationOnPoi\ nts(\n> [[3], [1, 3, 5], [1], [1, 2, 4], [2, 3, 5]]);\nBinary Relation on 5 po\ ints\ngap> D := AsDigraph(b);\n\n\ ", count := [ 3, 2, 2, 7 ], name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 7 ], mathmode := "Text", name := "Example", next := 40175, root := ~, start := 39689, stop := 40174 ), rec( content := "\n ", count := [ 3, 2, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "Description", next := 40192, root := ~, start := 38225, stop := 40191 ) ], count := [ 3, 2, 2, 1 ], mathmode := "Text", name := "ManSection", next := 40206, root := ~, start := 38110, stop := 40205 ), rec( content := "\n\n ", count := [ 3, 2, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "Graph" ), content := 0, count := [ 3, 2, 3, 2 ], mathmode := "Text", name := "Oper", next := 40261, root := ~, start := 40227, stop := 40260 ), rec( attributes := rec( ), content := [ rec( content := "A ", count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\ c.uk/~leonard/grape/", count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "P\ CDATA", root := ~ ) ], count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "URL\ ", next := 87, root := ~, start := 17, stop := 86 ) ], count := [ 3, 2, 3, 3 ] , name := "Alt", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "Grape", count := [ 3, 2, 3, 3 ], name \ := "PCDATA", root := ~ ) ], count := [ 3, 2, 3, 3 ], name := "Package", next := 137, root := ~, start := 113 , stop := 136 ) ], count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), rec( content := " package\ graph.", count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "Returns", next := 40307, root := ~, start := 40264, stop := 40306 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "A", next := 40345, root := ~, start := 40331, stop := 40344 ), rec( content := " is a mu\ table or immutable digraph without multiple edges, then this operation\n re\ turns a ", count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\ c.uk/~leonard/grape/", count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "P\ CDATA", root := ~ ) ], count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "URL\ ", next := 87, root := ~, start := 17, stop := 86 ) ], count := [ 3, 2, 3, 3 ] , name := "Alt", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "Grape", count := [ 3, 2, 3, 3 ], name \ := "PCDATA", root := ~ ) ], count := [ 3, 2, 3, 3 ], name := "Package", next := 137, root := ~, start := 113 , stop := 136 ) ], count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), rec( content := " package\ graph that is isomorphic to ", count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "A", next := 40496, root := ~, start := 40482, stop := 40495 ), rec( content := ". ", count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "P", next := 40502, root := ~, start := 40498, stop := 40501 ), rec( content := "\n\n \ If ", count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "A", next := 40525, root := ~, start := 40511, stop := 40524 ), rec( content := " is a mu\ ltidigraph, then since ", count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\ c.uk/~leonard/grape/", count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "P\ CDATA", root := ~ ) ], count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "URL\ ", next := 87, root := ~, start := 17, stop := 86 ) ], count := [ 3, 2, 3, 4 ] , name := "Alt", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "Grape", count := [ 3, 2, 3, 4 ], name \ := "PCDATA", root := ~ ) ], count := [ 3, 2, 3, 4 ], name := "Package", next := 137, root := ~, start := 113 , stop := 136 ) ], count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), rec( content := " does no\ t support\n multiple edges, the multiple edges will be reduced to a single \ edge in the\n result. In order words, for a multidigraph this operation wil\ l return the\n same as ", count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ raph(DigraphRemoveAllMultipleEdges(", count := [ 3, 2, 3, 4 ], mathmode := "Te\ xt", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "C", next := 40793, root := ~, start := 40750, stop := 40792 ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "A", next := 40807, root := ~, start := 40793, stop := 40806 ), rec( attributes := rec( ), content := [ rec( content := ")\ )", count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "C", next := 40816, root := ~, start := 40807, stop := 40815 ), rec( content := ".\n\n \ ", count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> Petersen := Graph(SymmetricGroup(5), [[1, 2]], OnSets,\n> function(x, y)\ return Intersection(x, y) = []; end);;\ngap> Display(Petersen);\nrec(\n adja\ cencies := [ [ 3, 5, 8 ] ],\n group := \n Group( [ ( 1, 2, 3, 5, 7)( 4, 6, \ 8, 9,10), ( 2, 4)( 6, 9)( 7,10) \n ] ),\n isGraph := true,\n names := [ \ [ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 1, 3 ], [ 4, 5 ], \n [ 2, 4 ], [ 1, 5 ], \ [ 3, 5 ], [ 1, 4 ], [ 2, 5 ] ],\n order := 10,\n representatives := [ 1 ],\n\ schreierVector := [ -1, 1, 1, 2, 1, 1, 1, 1, 2, 2 ] )\ngap> Digraph(Petersen\ );\n\ngap> Graph(last) = Peterse\ n;\ntrue", count := [ 3, 2, 3, 5 ], name := "PCDATA", root := ~ ) ], count := [ 3, 2, 3, 5 ], mathmode := "Text", name := "Example", next := 41469, root := ~, start := 40823, stop := 41468 ), rec( content := "\n ", count := [ 3, 2, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "Description", next := 41486, root := ~, start := 40310, stop := 41485 ) ], count := [ 3, 2, 3, 1 ], mathmode := "Text", name := "ManSection", next := 41500, root := ~, start := 40212, stop := 41499 ), rec( content := "\n\n ", count := [ 3, 2, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "AsGraph" ), content := 0, count := [ 3, 2, 4, 2 ], mathmode := "Text", name := "Attr", next := 41557, root := ~, start := 41521, stop := 41556 ), rec( attributes := rec( ), content := [ rec( content := "A ", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\ c.uk/~leonard/grape/", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "P\ CDATA", root := ~ ) ], count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "URL\ ", next := 87, root := ~, start := 17, stop := 86 ) ], count := [ 3, 2, 4, 3 ] , name := "Alt", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "Grape", count := [ 3, 2, 4, 3 ], name \ := "PCDATA", root := ~ ) ], count := [ 3, 2, 4, 3 ], name := "Package", next := 137, root := ~, start := 113 , stop := 136 ) ], count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), rec( content := " package\ graph.", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "Returns", next := 41603, root := ~, start := 41560, stop := 41602 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "A", next := 41641, root := ~, start := 41627, stop := 41640 ), rec( content := " is a di\ graph, then this method returns the same as\n ", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Graph" ), content := 0, count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "Ref", next := 41716, root := ~, start := 41697, stop := 41715 ), rec( content := ", except\ that if ", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "A", next := 41747, root := ~, start := 41733, stop := 41746 ), rec( content := " is immu\ table, then the\n result will be stored as a mutable attribute of ", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "A", next := 41837, root := ~, start := 41823, stop := 41836 ), rec( content := ".\n I\ n this latter case, when ", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A\ sGraph(", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "C", next := 41884, root := ~, start := 41869, stop := 41883 ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "A", next := 41898, root := ~, start := 41884, stop := 41897 ), rec( attributes := rec( ), content := [ rec( content := ")\ ", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "C", next := 41906, root := ~, start := 41898, stop := 41905 ), rec( content := " is call\ ed\n subsequently, the same ", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ AP", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " object \ will be returned as before.\n\n ", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 2], [3], []]);\n\ngap> G := AsGraph(D);\nrec( adjacencies := [ [ 1, 2 ], [ 3 ], [ ] ], \ group := Group(()), \n isGraph := true, names := [ 1 .. 3 ], order := 3, \n \ representatives := [ 1, 2, 3 ], schreierVector := [ -1, -2, -3 ] )\n", count := [ 3, 2, 4, 4 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 2, 4, 4 ], mathmode := "Text", name := "Example", next := 42317, root := ~, start := 41990, stop := 42316 ), rec( content := "\n ", count := [ 3, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "Description", next := 42334, root := ~, start := 41606, stop := 42333 ) ], count := [ 3, 2, 4, 1 ], mathmode := "Text", name := "ManSection", next := 42348, root := ~, start := 41506, stop := 42347 ), rec( content := "\n\n ", count := [ 3, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "AsTransformatio\ n" ), content := 0, count := [ 3, 2, 5, 2 ], mathmode := "Text", name := "Attr", next := 42414, root := ~, start := 42369, stop := 42413 ), rec( attributes := rec( ), content := [ rec( content := "A transfo\ rmation, or ", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "K", next := 42458, root := ~, start := 42447, stop := 42457 ) ], count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "Returns", next := 42468, root := ~, start := 42417, stop := 42467 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "A", next := 42506, root := ~, start := 42492, stop := 42505 ), rec( content := " is a fu\ nctional digraph, then ", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A\ sTransformation", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "C", next := 42560, root := ~, start := 42537, stop := 42559 ), rec( content := "\n re\ turns the transformation which is defined by ", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "A", next := 42626, root := ~, start := 42612, stop := 42625 ), rec( content := ". See " , count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsFunct\ ionalDigraph" ), content := 0, count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "Ref", next := 42672, root := ~, start := 42633, stop := 42671 ), rec( content := ". Otherw\ ise,\n ", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A\ sTransformation(", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "C", next := 42713, root := ~, start := 42689, stop := 42712 ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "A", next := 42727, root := ~, start := 42713, stop := 42726 ), rec( attributes := rec( ), content := [ rec( content := ")\ ", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "C", next := 42735, root := ~, start := 42727, stop := 42734 ), rec( content := " returns\ ", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "K", next := 42755, root := ~, start := 42744, stop := 42754 ), rec( content := ". ", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "P", next := 42762, root := ~, start := 42758, stop := 42761 ), rec( content := "\n\n \ If ", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "A", next := 42785, root := ~, start := 42771, stop := 42784 ), rec( content := " is a fu\ nctional digraph with ", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "M", next := 42823, root := ~, start := 42815, stop := 42822 ), rec( content := " vertice\ s, then\n ", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A\ sTransformation(", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "C", next := 42867, root := ~, start := 42843, stop := 42866 ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "A", next := 42881, root := ~, start := 42867, stop := 42880 ), rec( attributes := rec( ), content := [ rec( content := ")\ ", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "C", next := 42889, root := ~, start := 42881, stop := 42888 ), rec( content := " will re\ turn the\n transformation ", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "C", next := 42933, root := ~, start := 42925, stop := 42932 ), rec( content := " of degr\ ee at most ", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "M", next := 42960, root := ~, start := 42952, stop := 42959 ), rec( content := " where f\ or each ", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "1\ \n \\leq i \\leq n", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "M", next := 43004, root := ~, start := 42976, stop := 43003 ), rec( content := ", ", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ^ f", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "C", next := 43018, root := ~, start := 43006, stop := 43017 ), rec( content := " is equa\ l to the unique out-neighbour of\n vertex ", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "C", next := 43078, root := ~, start := 43070, stop := 43077 ), rec( content := " in ", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "A", next := 43096, root := ~, start := 43082, stop := 43095 ), rec( content := ".\n\n \ ", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1], [3], [2]]);\n\ngap> AsTransformation(D);\nTransformation( [ 1, 3, 2 ] )\ngap> D := Cycl\ eDigraph(IsMutableDigraph, 3);\n\nga\ p> AsTransformation(D);\nTransformation( [ 2, 3, 1 ] )\ngap> AsPermutation(las\ t);\n(1,2,3)\ngap> D := Digraph([[2, 3], [], []]);\n\ngap> AsTransformation(D);\nfail", count := [ 3, 2, 5, 5 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 2, 5, 5 ], mathmode := "Text", name := "Example", next := 43562, root := ~, start := 43103, stop := 43561 ), rec( content := "\n ", count := [ 3, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "Description", next := 43579, root := ~, start := 42471, stop := 43578 ) ], count := [ 3, 2, 5, 1 ], mathmode := "Text", name := "ManSection", next := 43593, root := ~, start := 42354, stop := 43592 ), rec( content := "\n\n ", count := [ 3, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 0, 1 ], mathmode := "Text", name := "Section", next := 43607, root := ~, start := 37409, stop := 43606 ), rec( content := "\n\n ", count := [ 3, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "New digraphs from\ old", count := [ 3, 3, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 0, 2 ], mathmode := "Text", name := "Heading", next := 43660, root := ~, start := 43620, stop := 43659 ), rec( content := "\n ", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphImmutabl\ eCopy" ), content := 0, count := [ 3, 3, 1, 2 ], mathmode := "Text", name := "Oper", next := 43729, root := ~, start := 43680, stop := 43728 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphMutableC\ opy" ), content := 0, count := [ 3, 3, 1, 4 ], mathmode := "Text", name := "Oper", next := 43779, root := ~, start := 43732, stop := 43778 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphCopySame\ Mutability" ), content := 0, count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "Oper", next := 43836, root := ~, start := 43782, stop := 43835 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphCopy" ), content := 0, count := [ 3, 3, 1, 8 ], mathmode := "Text", name := "Oper", next := 43879, root := ~, start := 43839, stop := 43878 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 9 ], mathmode := "Text", name := "Returns", next := 43911, root := ~, start := 43882, stop := 43910 ), rec( attributes := rec( ), content := [ rec( content := "\n Eac\ h of these operations returns a new copy of ", count := [ 3, 3, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 9 ], mathmode := "Text", name := "A", next := 43993, root := ~, start := 43979, stop := 43992 ), rec( content := ",\n o\ f the appropriate mutability, retaining none of the attributes or\n propert\ ies of ", count := [ 3, 3, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 9 ], mathmode := "Text", name := "A", next := 44098, root := ~, start := 44084, stop := 44097 ), rec( content := ". ", count := [ 3, 3, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 1, 10 ], mathmode := "Text", name := "P", next := 44104, root := ~, start := 44100, stop := 44103 ), rec( content := "\n\n \ ", count := [ 3, 3, 1, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "D\ igraphCopy", count := [ 3, 3, 1, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 10 ], mathmode := "Text", name := "C", next := 44128, root := ~, start := 44110, stop := 44127 ), rec( content := " is a sy\ nonym for ", count := [ 3, 3, 1, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphCopySameMutability", count := [ 3, 3, 1, 10 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 1, 10 ], mathmode := "Text", name := "C", next := 44178, root := ~, start := 44146, stop := 44177 ), rec( content := ".\n", count := [ 3, 3, 1, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CycleDigraph(10);\n\ngap>\ DigraphCopy(D) = D;\ntrue\ngap> IsIdenticalObj(DigraphCopy(D), D);\nfalse\nga\ p> DigraphMutableCopy(D);\n\n", count := [ 3, 3, 1, 11 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 1, 11 ], mathmode := "Text", name := "Example", next := 44432, root := ~, start := 44180, stop := 44431 ), rec( content := "\n ", count := [ 3, 3, 1, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 9 ], mathmode := "Text", name := "Description", next := 44449, root := ~, start := 43914, stop := 44448 ) ], count := [ 3, 3, 1, 1 ], mathmode := "Text", name := "ManSection", next := 44463, root := ~, start := 43665, stop := 44462 ), rec( content := "\n\n ", count := [ 3, 3, 1, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphImmutabl\ eCopyIfImmutable" ), content := 0, count := [ 3, 3, 2, 2 ], mathmode := "Text", name := "Oper", next := 44544, root := ~, start := 44484, stop := 44543 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphImmutabl\ eCopyIfMutable" ), content := 0, count := [ 3, 3, 2, 4 ], mathmode := "Text", name := "Oper", next := 44605, root := ~, start := 44547, stop := 44604 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphMutableC\ opyIfMutable" ), content := 0, count := [ 3, 3, 2, 6 ], mathmode := "Text", name := "Oper", next := 44664, root := ~, start := 44608, stop := 44663 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphMutableC\ opyIfImmutable" ), content := 0, count := [ 3, 3, 2, 8 ], mathmode := "Text", name := "Oper", next := 44725, root := ~, start := 44667, stop := 44724 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 2, 9 ], mathmode := "Text", name := "Returns", next := 44757, root := ~, start := 44728, stop := 44756 ), rec( attributes := rec( ), content := [ rec( content := "\n Eac\ h of these operations returns either the original argument\n ", count := [ 3, 3, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 2, 9 ], mathmode := "Text", name := "A", next := 44858, root := ~, start := 44844, stop := 44857 ), rec( content := ", or a n\ ew copy of ", count := [ 3, 3, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 2, 9 ], mathmode := "Text", name := "A", next := 44891, root := ~, start := 44877, stop := 44890 ), rec( content := " of the \ appropriate\n mutability, according to the mutability of ", count := [ 3, 3, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 2, 9 ], mathmode := "Text", name := "A", next := 44972, root := ~, start := 44958, stop := 44971 ), rec( content := ".\n", count := [ 3, 3, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> C := CycleDigraph(10);\n\ngap>\ D := DigraphImmutableCopyIfImmutable(C);\n\ngap> IsIdenticalObj(C, D);\nfalse\ngap> C = D;\ntrue\ngap> D := D\ igraphImmutableCopyIfMutable(C);\n\n\ gap> IsIdenticalObj(C, D);\ntrue\ngap> C = D;\ntrue\ngap> D := DigraphMutableC\ opyIfMutable(C);\n\ngap> IsMutableDi\ graph(D);\nfalse\ngap> D := DigraphMutableCopyIfImmutable(C);\n\ngap> IsMutableDigraph(D);\ntrue\ngap> C := Cycl\ eDigraph(IsMutableDigraph, 10);\n\ \ngap> D := DigraphImmutableCopyIfImmutable(C);\n\ngap> IsIdenticalObj(C, D);\ntrue\ngap> C = D;\ntrue\ngap> D :\ = DigraphImmutableCopyIfMutable(C);\n\ngap> IsIdenticalObj(C, D);\nfalse\ngap> C = D;\ntrue\ngap> D := Digraph\ MutableCopyIfMutable(C);\n\ngap> I\ sMutableDigraph(D);\ntrue\ngap> D := DigraphMutableCopyIfImmutable(C);\n\ngap> IsIdenticalObj(C, D);\ntrue\ngap>\ IsMutableDigraph(D);\ntrue", count := [ 3, 3, 2, 10 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 2, 10 ], mathmode := "Text", name := "Example", next := 46234, root := ~, start := 44974, stop := 46233 ), rec( content := "\n ", count := [ 3, 3, 2, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 2, 9 ], mathmode := "Text", name := "Description", next := 46251, root := ~, start := 44760, stop := 46250 ) ], count := [ 3, 3, 2, 1 ], mathmode := "Text", name := "ManSection", next := 46265, root := ~, start := 44469, stop := 46264 ), rec( content := "\n\n ", count := [ 3, 3, 2, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, verts", Name := "InducedSubdigra\ ph" ), content := 0, count := [ 3, 3, 3, 2 ], mathmode := "Text", name := "Oper", next := 46339, root := ~, start := 46286, stop := 46338 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "Returns", next := 46371, root := ~, start := 46342, stop := 46370 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "A", next := 46409, root := ~, start := 46395, stop := 46408 ), rec( content := " is a di\ graph, and ", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ erts", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "A", next := 46440, root := ~, start := 46428, stop := 46439 ), rec( content := " is a su\ bset of the\n vertices of ", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "A", next := 46490, root := ~, start := 46476, stop := 46489 ), rec( content := ", then t\ his operation returns a digraph\n constructed from ", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "A", next := 46565, root := ~, start := 46551, stop := 46564 ), rec( content := " by reta\ ining precisely those vertices in\n ", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ erts", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "A", next := 46623, root := ~, start := 46611, stop := 46622 ), rec( content := ", and th\ ose edges whose source and range vertices are both\n contained in ", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ erts", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "A", next := 46711, root := ~, start := 46699, stop := 46710 ), rec( content := ". ", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 3, 4 ], mathmode := "Text", name := "P", next := 46717, root := ~, start := 46713, stop := 46716 ), rec( content := "\n\n \ The vertices of the induced subdigraph are\n ", count := [ 3, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ 1..Length(verts)]", count := [ 3, 3, 3, 4 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 3, 3, 3, 4 ], mathmode := "Text", name := "C", next := 46795, root := ~, start := 46770, stop := 46794 ), rec( content := " but the\ original vertex labels can be\n accessed via ", count := [ 3, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ VertexLabels" ), content := 0, count := [ 3, 3, 3, 4 ], mathmode := "Text", name := "Ref", next := 46884, root := ~, start := 46851, stop := 46883 ), rec( content := ". ", count := [ 3, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "P", next := 46890, root := ~, start := 46886, stop := 46889 ), rec( content := "\n\n \ If ", count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "A", next := 46913, root := ~, start := 46899, stop := 46912 ), rec( content := " belongs\ to ", count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "Ref", next := 46955, root := ~, start := 46925, stop := 46954 ), rec( content := ", then\n\ ", count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "A", next := 46980, root := ~, start := 46966, stop := 46979 ), rec( content := " is modi\ fied in place. If ", count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "A", next := 47020, root := ~, start := 47006, stop := 47019 ), rec( content := " belongs\ to ", count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "Ref", next := 47070, root := ~, start := 47032, stop := 47069 ), rec( content := ", a new \ immutable digraph containing the\n appropriate\n vertices and edges is r\ eturned.", count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 3, 6 ], mathmode := "Text", name := "P", next := 47166, root := ~, start := 47162, stop := 47165 ), rec( content := "\n\n \ ", count := [ 3, 3, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 1, 2, 3, 4, 4], [1, 3, 4], [3, 1], [1, 1]]);\n\ngap> InducedSubdigraph(D, [1, 3, 4\ ]);\n\ngap> DigraphVertices(l\ ast);\n[ 1 .. 3 ]\ngap> D := DigraphMutableCopy(D);\n\ngap> new := InducedSubdigraph(D, [1, 3, 4]);\n\ngap> D = new;\ntrue\n", count := [ 3, 3, 3, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 3, 7 ], mathmode := "Text", name := "Example", next := 47644, root := ~, start := 47172, stop := 47643 ), rec( content := "\n ", count := [ 3, 3, 3, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "Description", next := 47661, root := ~, start := 46374, stop := 47660 ) ], count := [ 3, 3, 3, 1 ], mathmode := "Text", name := "ManSection", next := 47675, root := ~, start := 46271, stop := 47674 ), rec( content := "\n\n ", count := [ 3, 3, 3, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "ReducedDigraph"\ ), content := 0, count := [ 3, 3, 4, 2 ], mathmode := "Text", name := "Oper", next := 47739, root := ~, start := 47696, stop := 47738 ), rec( attributes := rec( Arg := "digraph", Name := "ReducedDigraphA\ ttr" ), content := 0, count := [ 3, 3, 4, 4 ], mathmode := "Text", name := "Attr", next := 47789, root := ~, start := 47742, stop := 47788 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 4, 5 ], mathmode := "Text", name := "Returns", next := 47821, root := ~, start := 47792, stop := 47820 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function returns a digraph isomorphic to the subdigraph of\n ", count := [ 3, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 4, 5 ], mathmode := "Text", name := "A", next := 47924, root := ~, start := 47910, stop := 47923 ), rec( content := " induced\ by the set of non-isolated vertices,\n i.e. the set of those vertices of " , count := [ 3, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 4, 5 ], mathmode := "Text", name := "A", next := 48022, root := ~, start := 48008, stop := 48021 ), rec( content := " which a\ re the source or\n range of some edge in ", count := [ 3, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 4, 5 ], mathmode := "Text", name := "A", next := 48087, root := ~, start := 48073, stop := 48086 ), rec( content := ".\n S\ ee ", count := [ 3, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Induced\ Subdigraph" ), content := 0, count := [ 3, 3, 4, 5 ], mathmode := "Text", name := "Ref", next := 48128, root := ~, start := 48097, stop := 48127 ), rec( content := ".\n " , count := [ 3, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 4, 6 ], mathmode := "Text", name := "P", next := 48138, root := ~, start := 48134, stop := 48137 ), rec( content := "\n\n \ The ordering of the remaining vertices of ", count := [ 3, 3, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 4, 6 ], mathmode := "Text", name := "A", next := 48200, root := ~, start := 48186, stop := 48199 ), rec( content := " is pres\ erved, as are\n the labels of the remaining vertices and edges;\n see ", count := [ 3, 3, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ VertexLabels" ), content := 0, count := [ 3, 3, 4, 6 ], mathmode := "Text", name := "Ref", next := 48315, root := ~, start := 48282, stop := 48314 ), rec( content := " and ", count := [ 3, 3, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ EdgeLabels" ), content := 0, count := [ 3, 3, 4, 6 ], mathmode := "Text", name := "Ref", next := 48351, root := ~, start := 48320, stop := 48350 ), rec( content := ".\n T\ his can allow one to match a vertex in the reduced digraph to the\n corresp\ onding vertex in ", count := [ 3, 3, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 4, 6 ], mathmode := "Text", name := "A", next := 48466, root := ~, start := 48452, stop := 48465 ), rec( content := ".\n " , count := [ 3, 3, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 4, 7 ], mathmode := "Text", name := "P", next := 48476, root := ~, start := 48472, stop := 48475 ), rec( content := "\n\n \ If ", count := [ 3, 3, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 4, 7 ], mathmode := "Text", name := "A", next := 48499, root := ~, start := 48485, stop := 48498 ), rec( content := " is immu\ table, then a new immutable digraph is returned.\n Otherwise, the isolated \ vertices of the mutable digraph ", count := [ 3, 3, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 4, 7 ], mathmode := "Text", name := "A", next := 48630, root := ~, start := 48616, stop := 48629 ), rec( content := " are\n \ removed in-place.\n ", count := [ 3, 3, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 2], [], [], [1, 4], []]);\n\ngap> R := ReducedDigraph(D);\n\ngap> OutNeighbours(R);\n[ [ 1, 2 ], [ ], [ 1, 3 ] ]\ngap> Di\ graphEdges(D);\n[ [ 1, 1 ], [ 1, 2 ], [ 4, 1 ], [ 4, 4 ] ]\ngap> DigraphEdges(\ R);\n[ [ 1, 1 ], [ 1, 2 ], [ 3, 1 ], [ 3, 3 ] ]\ngap> DigraphVertexLabel(R, 3)\ ;\n4\ngap> DigraphVertexLabel(R, 2);\n2\ngap> D := Digraph(IsMutableDigraph, [\ [], [3], [2]]);\n\ngap> ReducedDigra\ ph(D);\n\ngap> D;\n\n", count := [ 3, 3, 4, 8 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 4, 8 ], mathmode := "Text", name := "Example", next := 49323, root := ~, start := 48661, stop := 49322 ), rec( content := "\n ", count := [ 3, 3, 4, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 4, 5 ], mathmode := "Text", name := "Description", next := 49340, root := ~, start := 47824, stop := 49339 ) ], count := [ 3, 3, 4, 1 ], mathmode := "Text", name := "ManSection", next := 49354, root := ~, start := 47681, stop := 49353 ), rec( content := "\n\n ", count := [ 3, 3, 4, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "MaximalSymmetri\ cSubdigraph" ), content := 0, count := [ 3, 3, 5, 2 ], mathmode := "Text", name := "Oper", next := 49430, root := ~, start := 49375, stop := 49429 ), rec( attributes := rec( Arg := "digraph", Name := "MaximalSymmetri\ cSubdigraphAttr" ), content := 0, count := [ 3, 3, 5, 4 ], mathmode := "Text", name := "Attr", next := 49492, root := ~, start := 49433, stop := 49491 ), rec( attributes := rec( Arg := "digraph", Name := "MaximalSymmetri\ cSubdigraphWithoutLoops" ), content := 0, count := [ 3, 3, 5, 6 ], mathmode := "Text", name := "Oper", next := 49562, root := ~, start := 49495, stop := 49561 ), rec( attributes := rec( Arg := "digraph", Name := "MaximalSymmetri\ cSubdigraphWithoutLoopsAttr" ), content := 0, count := [ 3, 3, 5, 8 ], mathmode := "Text", name := "Attr", next := 49636, root := ~, start := 49565, stop := 49635 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "Returns", next := 49668, root := ~, start := 49639, stop := 49667 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "A", next := 49706, root := ~, start := 49692, stop := 49705 ), rec( content := " is a di\ graph, then ", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "M\ aximalSymmetricSubdigraph", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "C", next := 49759, root := ~, start := 49726, stop := 49758 ), rec( content := "\n re\ turns a symmetric digraph without multiple edges which has the same\n verte\ x set as ", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "A", next := 49866, root := ~, start := 49852, stop := 49865 ), rec( content := ", and wh\ ose edge list is formed from\n ", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "A", next := 49921, root := ~, start := 49907, stop := 49920 ), rec( content := " by igno\ ring the multiplicity of edges, and by ignoring\n edges ", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ u,v]", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "C", next := 49999, root := ~, start := 49987, stop := 49998 ), rec( content := " for whi\ ch there does not exist an edge ", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ v,u]", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "C", next := 50051, root := ~, start := 50039, stop := 50050 ), rec( content := ".\n " , count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 5, 10 ], mathmode := "Text", name := "P", next := 50061, root := ~, start := 50057, stop := 50060 ), rec( content := "\n\n \ The digraph returned by ", count := [ 3, 3, 5, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "M\ aximalSymmetricSubdigraphWithoutLoops", count := [ 3, 3, 5, 10 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 5, 10 ], mathmode := "Text", name := "C", next := 50136, root := ~, start := 50091, stop := 50135 ), rec( content := " is\n \ the same, except that loops are removed.", count := [ 3, 3, 5, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 5, 11 ], mathmode := "Text", name := "P", next := 50188, root := ~, start := 50184, stop := 50187 ), rec( content := "\n \n\ If ", count := [ 3, 3, 5, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 5, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 5, 11 ], mathmode := "Text", name := "A", next := 50215, root := ~, start := 50201, stop := 50214 ), rec( content := " is immu\ table, then a new immutable digraph is returned.\n Otherwise, the mutable d\ igraph ", count := [ 3, 3, 5, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 5, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 5, 11 ], mathmode := "Text", name := "A", next := 50321, root := ~, start := 50307, stop := 50320 ), rec( content := " is chan\ ged in-place into such\n a digraph described above.", count := [ 3, 3, 5, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 5, 12 ], mathmode := "Text", name := "P", next := 50386, root := ~, start := 50382, stop := 50385 ), rec( content := "\n\n \ See ", count := [ 3, 3, 5, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsSymme\ tricDigraph" ), content := 0, count := [ 3, 3, 5, 12 ], mathmode := "Text", name := "Ref", next := 50428, root := ~, start := 50396, stop := 50427 ), rec( content := ", ", count := [ 3, 3, 5, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsMulti\ Digraph" ), content := 0, count := [ 3, 3, 5, 12 ], mathmode := "Text", name := "Ref", next := 50458, root := ~, start := 50430, stop := 50457 ), rec( content := ", and\n \ ", count := [ 3, 3, 5, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "Digraph\ HasLoops" ), content := 0, count := [ 3, 3, 5, 12 ], mathmode := "Text", name := "Ref", next := 50497, root := ~, start := 50468, stop := 50496 ), rec( content := " for mor\ e information.\n ", count := [ 3, 3, 5, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[2, 2], [1, 3], [4], [3, 1]]);\n\ngap> not IsSymmetricDigraph(D) and IsMultiDigraph(D);\ \ntrue\ngap> OutNeighbours(D);\n[ [ 2, 2 ], [ 1, 3 ], [ 4 ], [ 3, 1 ] ]\ngap> \ S := MaximalSymmetricSubdigraph(D);\n\ngap> IsSymmetricDigraph(S) and not IsMultiDigraph(S);\ntrue\nga\ p> OutNeighbours(S);\n[ [ 2 ], [ 1 ], [ 4 ], [ 3 ] ]\ngap> D := CycleDigraph(I\ sMutableDigraph, 3);\n\ngap> Maximal\ SymmetricSubdigraph(D);\n\ngap> D;\n\n", count := [ 3, 3, 5, 13 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 5, 13 ], mathmode := "Text", name := "Example", next := 51199, root := ~, start := 50524, stop := 51198 ), rec( content := "\n ", count := [ 3, 3, 5, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "Description", next := 51216, root := ~, start := 49671, stop := 51215 ) ], count := [ 3, 3, 5, 1 ], mathmode := "Text", name := "ManSection", next := 51230, root := ~, start := 49360, stop := 51229 ), rec( content := "\n\n ", count := [ 3, 3, 5, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "MaximalAntiSymm\ etricSubdigraph" ), content := 0, count := [ 3, 3, 6, 2 ], mathmode := "Text", name := "Oper", next := 51310, root := ~, start := 51251, stop := 51309 ), rec( attributes := rec( Arg := "digraph", Name := "MaximalAntiSymm\ etricSubdigraphAttr" ), content := 0, count := [ 3, 3, 6, 4 ], mathmode := "Text", name := "Attr", next := 51376, root := ~, start := 51313, stop := 51375 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "Returns", next := 51408, root := ~, start := 51379, stop := 51407 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "A", next := 51446, root := ~, start := 51432, stop := 51445 ), rec( content := " is a di\ graph, then ", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "M\ aximalAntiSymmetricSubdigraph", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "C", next := 51503, root := ~, start := 51466, stop := 51502 ), rec( content := "\n re\ turns an anti-symmetric subdigraph of ", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "A", next := 51562, root := ~, start := 51548, stop := 51561 ), rec( content := " formed \ by\n retaining the vertices of ", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "A", next := 51617, root := ~, start := 51603, stop := 51616 ), rec( content := ", discar\ ding any duplicate edges,\n and discarding any edge ", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ i,j]", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "C", next := 51691, root := ~, start := 51679, stop := 51690 ), rec( content := " of ", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "A", next := 51709, root := ~, start := 51695, stop := 51708 ), rec( content := " where " , count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ > j", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "C", next := 51728, root := ~, start := 51716, stop := 51727 ), rec( content := "\n an\ d the reverse edge ", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ j,i]", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "C", next := 51766, root := ~, start := 51754, stop := 51765 ), rec( content := " is an e\ dge of ", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "A", next := 51795, root := ~, start := 51781, stop := 51794 ), rec( content := ".\n I\ n other words, for every\n symmetric pair of edges ", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ i,j]", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "C", next := 51867, root := ~, start := 51855, stop := 51866 ), rec( content := " and ", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ j,i]", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "C", next := 51884, root := ~, start := 51872, stop := 51883 ), rec( content := " in ", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "A", next := 51902, root := ~, start := 51888, stop := 51901 ), rec( content := ", where \ \n ", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "C", next := 51923, root := ~, start := 51915, stop := 51922 ), rec( content := " and ", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "C", next := 51936, root := ~, start := 51928, stop := 51935 ), rec( content := " are dis\ tinct, it discards the the edge\n ", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ \\max(i,j),\\min(i,j)]", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "M", next := 52008, root := ~, start := 51980, stop := 52007 ), rec( content := ".\n " , count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 6, 6 ], mathmode := "Text", name := "P", next := 52018, root := ~, start := 52014, stop := 52017 ), rec( content := "\n\n \ If ", count := [ 3, 3, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 6, 6 ], mathmode := "Text", name := "A", next := 52041, root := ~, start := 52027, stop := 52040 ), rec( content := " is immu\ table, then a new immutable digraph is returned.\n Otherwise, the mutable d\ igraph ", count := [ 3, 3, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 6, 6 ], mathmode := "Text", name := "A", next := 52147, root := ~, start := 52133, stop := 52146 ), rec( content := " is chan\ ged in-place. ", count := [ 3, 3, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 6, 7 ], mathmode := "Text", name := "P", next := 52173, root := ~, start := 52169, stop := 52172 ), rec( content := "\n\n \ See ", count := [ 3, 3, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsAntis\ ymmetricDigraph" ), content := 0, count := [ 3, 3, 6, 7 ], mathmode := "Text", name := "Ref", next := 52219, root := ~, start := 52183, stop := 52218 ), rec( content := " for mor\ e information.\n ", count := [ 3, 3, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[2, 2], [1, 3], [4], [3, 1]]);\n\ngap> not IsAntiSymmetricDigraph(D) and IsMultiDigraph\ (D);\ntrue\ngap> OutNeighbours(D);\n[ [ 2, 2 ], [ 1, 3 ], [ 4 ], [ 3, 1 ] ]\ng\ ap> D := MaximalAntiSymmetricSubdigraph(D);\n\ngap> IsAntiSymmetricDigraph(D) and not IsMultiDigra\ ph(D);\ntrue\ngap> OutNeighbours(D);\n[ [ 2 ], [ 3 ], [ 4 ], [ 1 ] ]\ngap> D :\ = Digraph(IsMutableDigraph, [[2], [1]]);\n\ngap> MaximalAntiSymmetricSubdigraph(D);\n\ngap> D;\n\n", count := [ 3, 3, 6, 8 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 6, 8 ], mathmode := "Text", name := "Example", next := 52949, root := ~, start := 52246, stop := 52948 ), rec( content := "\n ", count := [ 3, 3, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "Description", next := 52966, root := ~, start := 51411, stop := 52965 ) ], count := [ 3, 3, 6, 1 ], mathmode := "Text", name := "ManSection", next := 52980, root := ~, start := 51236, stop := 52979 ), rec( content := "\n\n ", count := [ 3, 3, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "UndirectedSpann\ ingForest" ), content := 0, count := [ 3, 3, 7, 2 ], mathmode := "Text", name := "Oper", next := 53054, root := ~, start := 53001, stop := 53053 ), rec( attributes := rec( Arg := "digraph", Name := "UndirectedSpann\ ingForestAttr" ), content := 0, count := [ 3, 3, 7, 4 ], mathmode := "Text", name := "Attr", next := 53114, root := ~, start := 53057, stop := 53113 ), rec( attributes := rec( Arg := "digraph", Name := "UndirectedSpann\ ingTree" ), content := 0, count := [ 3, 3, 7, 6 ], mathmode := "Text", name := "Oper", next := 53168, root := ~, start := 53117, stop := 53167 ), rec( attributes := rec( Arg := "digraph", Name := "UndirectedSpann\ ingTreeAttr" ), content := 0, count := [ 3, 3, 7, 8 ], mathmode := "Text", name := "Attr", next := 53226, root := ~, start := 53171, stop := 53225 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ , or ", count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "K", next := 53263, root := ~, start := 53252, stop := 53262 ), rec( content := ".", count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "Returns", next := 53274, root := ~, start := 53229, stop := 53273 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "A", next := 53312, root := ~, start := 53298, stop := 53311 ), rec( content := " is a di\ graph with at least one vertex, then\n ", count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "U\ ndirectedSpanningForest", count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "C", next := 53392, root := ~, start := 53361, stop := 53391 ), rec( content := " returns\ an undirected spanning forest of\n ", count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "A", next := 53452, root := ~, start := 53438, stop := 53451 ), rec( content := ", otherw\ ise this attribute returns ", count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "K", next := 53498, root := ~, start := 53487, stop := 53497 ), rec( content := ". See ", count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "IsUndir\ ectedSpanningForest" ), content := 0, count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "Ref", next := 53551, root := ~, start := 53504, stop := 53550 ), rec( content := " for the\ definition of an undirected\n spanning forest.", count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "P", next := 53612, root := ~, start := 53608, stop := 53611 ), rec( content := "\n\n \ If ", count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "A", next := 53635, root := ~, start := 53621, stop := 53634 ), rec( content := " is a di\ graph with at least one vertex and whose ", count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Maximal\ SymmetricSubdigraph" ), content := 0, count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "Ref", next := 53730, root := ~, start := 53684, stop := 53729 ), rec( content := " is conn\ ected (see ", count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsConne\ ctedDigraph" ), content := 0, count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "Ref", next := 53788, root := ~, start := 53749, stop := 53787 ), rec( content := "), then \ ", count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "U\ ndirectedSpanningTree", count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "C", next := 53825, root := ~, start := 53796, stop := 53824 ), rec( content := " returns\ \n an undirected spanning tree of ", count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "A", next := 53883, root := ~, start := 53869, stop := 53882 ), rec( content := ", otherw\ ise this attribute\n returns ", count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "K", next := 53933, root := ~, start := 53922, stop := 53932 ), rec( content := ". See " , count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "IsUndir\ ectedSpanningTree" ), content := 0, count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "Ref", next := 53979, root := ~, start := 53940, stop := 53978 ), rec( content := " for the\ \n definition of an undirected spanning tree.", count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 7, 11 ], mathmode := "Text", name := "P", next := 54038, root := ~, start := 54034, stop := 54037 ), rec( content := "\n\n \ If ", count := [ 3, 3, 7, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 7, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 7, 11 ], mathmode := "Text", name := "A", next := 54061, root := ~, start := 54047, stop := 54060 ), rec( content := " is immu\ table, then an immutable digraph is returned.\n Otherwise, the mutable digr\ aph ", count := [ 3, 3, 7, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 7, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 7, 11 ], mathmode := "Text", name := "A", next := 54164, root := ~, start := 54150, stop := 54163 ), rec( content := " is chan\ ged in-place into an\n undirected spanning tree of ", count := [ 3, 3, 7, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 7, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 7, 11 ], mathmode := "Text", name := "A", next := 54239, root := ~, start := 54225, stop := 54238 ), rec( content := ".", count := [ 3, 3, 7, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 7, 12 ], mathmode := "Text", name := "P", next := 54244, root := ~, start := 54240, stop := 54243 ), rec( content := "\n\n \ Note that for an immutable digraph that has known undirected spanning tree,\n \ the attribute ", count := [ 3, 3, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "U\ ndirectedSpanningTree", count := [ 3, 3, 7, 12 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 7, 12 ], mathmode := "Text", name := "C", next := 54373, root := ~, start := 54344, stop := 54372 ), rec( content := " returns\ the same digraph as\n the attribute ", count := [ 3, 3, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "U\ ndirectedSpanningForest", count := [ 3, 3, 7, 12 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 7, 12 ], mathmode := "Text", name := "C", next := 54451, root := ~, start := 54420, stop := 54450 ), rec( content := ".\n\n \ ", count := [ 3, 3, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 2, 1, 3], [1], [4], [3, 4, 3]]);\n\ngap> UndirectedSpanningTree(D);\nfail\ngap> for\ est := UndirectedSpanningForest(D);\n\ngap> OutNeighbours(forest);\n[ [ 2 ], [ 1 ], [ 4 ], [ 3 ] ]\nga\ p> IsUndirectedSpanningForest(D, forest);\ntrue\ngap> DigraphConnectedComponen\ ts(forest).comps;\n[ [ 1, 2 ], [ 3, 4 ] ]\ngap> DigraphConnectedComponents(Max\ imalSymmetricSubdigraph(D)).comps;\n[ [ 1, 2 ], [ 3, 4 ] ]\ngap> UndirectedSpa\ nningForest(MaximalSymmetricSubdigraph(D))\n> = forest;\ntrue\ngap> D := Compl\ eteDigraph(4);\n\ngap> tree := Und\ irectedSpanningTree(D);\n\ngap> IsUndirectedSpanningTree(D, tree);\ntrue\ngap> tree = UndirectedSpanni\ ngForest(D);\ntrue\ngap> UndirectedSpanningForest(EmptyDigraph(0));\nfail\ngap\ > D := PetersenGraph(IsMutableDigraph);\n\ngap> UndirectedSpanningTree(D);\n\ngap> D;\n\n", count := [ 3, 3, 7, 13 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 7, 13 ], mathmode := "Text", name := "Example", next := 55613, root := ~, start := 54458, stop := 55612 ), rec( content := "\n ", count := [ 3, 3, 7, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "Description", next := 55630, root := ~, start := 53277, stop := 55629 ) ], count := [ 3, 3, 7, 1 ], mathmode := "Text", name := "ManSection", next := 55644, root := ~, start := 52986, stop := 55643 ), rec( content := "\n\n ", count := [ 3, 3, 7, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, p", Name := "QuotientDigraph\ " ), content := 0, count := [ 3, 3, 8, 2 ], mathmode := "Text", name := "Oper", next := 55712, root := ~, start := 55665, stop := 55711 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "Returns", next := 55744, root := ~, start := 55715, stop := 55743 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "A", next := 55782, root := ~, start := 55768, stop := 55781 ), rec( content := " is a di\ graph, and ", count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ ", count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "A", next := 55809, root := ~, start := 55801, stop := 55808 ), rec( content := " is a pa\ rtition of the vertices\n of ", count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "A", next := 55862, root := ~, start := 55848, stop := 55861 ), rec( content := ", then t\ his operation returns a digraph constructed by\n amalgamating all vertices \ of ", count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "A", next := 55964, root := ~, start := 55950, stop := 55963 ), rec( content := " which l\ ie in the same part of\n ", count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ ", count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "A", next := 56007, root := ~, start := 55999, stop := 56006 ), rec( content := ".\n " , count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 8, 4 ], mathmode := "Text", name := "P", next := 56017, root := ~, start := 56013, stop := 56016 ), rec( content := "\n\n \ A partition of the vertices of ", count := [ 3, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 4 ], mathmode := "Text", name := "A", next := 56068, root := ~, start := 56054, stop := 56067 ), rec( content := " is a li\ st of non-empty\n disjoint lists, such that the union of all the sub-lists \ is equal\n to vertex set of ", count := [ 3, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 4 ], mathmode := "Text", name := "A", next := 56197, root := ~, start := 56183, stop := 56196 ), rec( content := ". In par\ ticular, each vertex must appear\n in precisely one sub-list.\n ", count := [ 3, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "P", next := 56277, root := ~, start := 56273, stop := 56276 ), rec( content := "\n\n \ The vertices of ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "A", next := 56313, root := ~, start := 56299, stop := 56312 ), rec( content := " in part\ ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "C", next := 56330, root := ~, start := 56322, stop := 56329 ), rec( content := " of ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "A", next := 56342, root := ~, start := 56334, stop := 56341 ), rec( content := " will be\ come\n vertex ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "C", next := 56374, root := ~, start := 56366, stop := 56373 ), rec( content := " in the \ quotient, and there exists some edge in ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "A", next := 56436, root := ~, start := 56422, stop := 56435 ), rec( content := "\n wi\ th source in part ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "C", next := 56469, root := ~, start := 56461, stop := 56468 ), rec( content := " and ran\ ge in part ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "C", next := 56496, root := ~, start := 56488, stop := 56495 ), rec( content := " if and \ only if there\n is an edge from ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "C", next := 56546, root := ~, start := 56538, stop := 56545 ), rec( content := " to ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "C", next := 56558, root := ~, start := 56550, stop := 56557 ), rec( content := " in the \ quotient.\n In particular, this means that the quotient of a digraph has no\ multiple edges.\n which was a change introduced in version 1.0.0 of the ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphs", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " package\ .\n ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "P", next := 56746, root := ~, start := 56742, stop := 56745 ), rec( content := "\n\n \ If ", count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "A", next := 56769, root := ~, start := 56755, stop := 56768 ), rec( content := " belongs\ to ", count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "Ref", next := 56811, root := ~, start := 56781, stop := 56810 ), rec( content := ", then\n\ ", count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "A", next := 56836, root := ~, start := 56822, stop := 56835 ), rec( content := " is modi\ fied in place. If ", count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "A", next := 56876, root := ~, start := 56862, stop := 56875 ), rec( content := " belongs\ to ", count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "Ref", next := 56926, root := ~, start := 56888, stop := 56925 ), rec( content := ", a new \ immutable digraph with the above\n properties is returned.", count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 8, 7 ], mathmode := "Text", name := "P", next := 56998, root := ~, start := 56994, stop := 56997 ), rec( content := "\n\n \ ", count := [ 3, 3, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[2, 1], [4], [1], [1, 3, 4]]);\n\ngap> DigraphVertices(D);\n[ 1 .. 4 ]\ngap> DigraphEdges(D)\ ;\n[ [ 1, 2 ], [ 1, 1 ], [ 2, 4 ], [ 3, 1 ], [ 4, 1 ], [ 4, 3 ], \n [ 4, 4 ] \ ]\ngap> p := [[1], [2, 4], [3]];\n[ [ 1 ], [ 2, 4 ], [ 3 ] ]\ngap> quo := Quot\ ientDigraph(D, p);\n\ngap> Digraph\ Vertices(quo);\n[ 1 .. 3 ]\ngap> DigraphEdges(quo);\n[ [ 1, 1 ], [ 1, 2 ], [ 2\ , 1 ], [ 2, 2 ], [ 2, 3 ], [ 3, 1 ] ]\ngap> QuotientDigraph(EmptyDigraph(0), [\ ]);\n\n", count := [ 3, 3, 8, 8 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 8, 8 ], mathmode := "Text", name := "Example", next := 57612, root := ~, start := 57004, stop := 57611 ), rec( content := "\n ", count := [ 3, 3, 8, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "Description", next := 57629, root := ~, start := 55747, stop := 57628 ) ], count := [ 3, 3, 8, 1 ], mathmode := "Text", name := "ManSection", next := 57643, root := ~, start := 55650, stop := 57642 ), rec( content := "\n\n ", count := [ 3, 3, 8, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphReverse"\ ), content := 0, count := [ 3, 3, 9, 2 ], mathmode := "Text", name := "Oper", next := 57707, root := ~, start := 57664, stop := 57706 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphReverseA\ ttr" ), content := 0, count := [ 3, 3, 9, 4 ], mathmode := "Text", name := "Attr", next := 57757, root := ~, start := 57710, stop := 57756 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 9, 5 ], mathmode := "Text", name := "Returns", next := 57789, root := ~, start := 57760, stop := 57788 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ reverse of a digraph is the digraph formed by reversing the orientation\n \ of each of its edges, i.e. for every edge ", count := [ 3, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ i, j]", count := [ 3, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 9, 5 ], mathmode := "Text", name := "C", next := 57945, root := ~, start := 57932, stop := 57944 ), rec( content := " of a di\ graph, the\n reverse contains the corresponding edge ", count := [ 3, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ j, i]", count := [ 3, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 9, 5 ], mathmode := "Text", name := "C", next := 58021, root := ~, start := 58008, stop := 58020 ), rec( content := ".", count := [ 3, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "P", next := 58026, root := ~, start := 58022, stop := 58025 ), rec( content := "\n\n \ ", count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphReverse", count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "C", next := 58053, root := ~, start := 58032, stop := 58052 ), rec( content := " returns\ the reverse of the digraph ", count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "A", next := 58103, root := ~, start := 58089, stop := 58102 ), rec( content := ". If\n \ ", count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "A", next := 58126, root := ~, start := 58112, stop := 58125 ), rec( content := " is immu\ table, then a new immutable digraph is returned. Otherwise,\n the mutable d\ igraph ", count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "A", next := 58232, root := ~, start := 58218, stop := 58231 ), rec( content := " is chan\ ged in-place into its reverse.\n ", count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[3], [1, 3, 5], [1], [1, 2, 4], [2, 3, 5]]);\n\ngap> DigraphReverse(D);\n\ngap> OutNeighbours(last);\n[ [ 2, 3, 4 ], [ 4, 5 \ ], [ 1, 2, 5 ], [ 4 ], [ 2, 5 ] ]\ngap> D := Digraph([[2, 4], [1], [4], [3, 4]\ ]);\n\ngap> DigraphEdges(D);\n[ [ \ 1, 2 ], [ 1, 4 ], [ 2, 1 ], [ 3, 4 ], [ 4, 3 ], [ 4, 4 ] ]\ngap> DigraphEdges(\ DigraphReverse(D));\n[ [ 1, 2 ], [ 2, 1 ], [ 3, 4 ], [ 4, 1 ], [ 4, 3 ], [ 4, \ 4 ] ]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n\ngap> OutNeighbours(D);\n[ [ 2 ], [ 3 ], [ 1 ] ]\ngap> Digra\ phReverse(D);\n\ngap> OutNeighbours(\ D);\n[ [ 3 ], [ 1 ], [ 2 ] ]\n", count := [ 3, 3, 9, 7 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 9, 7 ], mathmode := "Text", name := "Example", next := 59096, root := ~, start := 58275, stop := 59095 ), rec( content := "\n ", count := [ 3, 3, 9, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 9, 5 ], mathmode := "Text", name := "Description", next := 59113, root := ~, start := 57792, stop := 59112 ) ], count := [ 3, 3, 9, 1 ], mathmode := "Text", name := "ManSection", next := 59127, root := ~, start := 57649, stop := 59126 ), rec( content := "\n\n ", count := [ 3, 3, 9, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphDual" ), content := 0, count := [ 3, 3, 10, 2 ], mathmode := "Text", name := "Oper", next := 59188, root := ~, start := 59148, stop := 59187 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphDualAttr\ " ), content := 0, count := [ 3, 3, 10, 4 ], mathmode := "Text", name := "Attr", next := 59235, root := ~, start := 59191, stop := 59234 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "Returns", next := 59267, root := ~, start := 59238, stop := 59266 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ ", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ ual", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "E", next := 59303, root := ~, start := 59292, stop := 59302 ), rec( content := " of ", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "A", next := 59321, root := ~, start := 59307, stop := 59320 ), rec( content := " has the\ same vertices as ", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "A", next := 59361, root := ~, start := 59347, stop := 59360 ), rec( content := ",\n a\ nd there is an edge in the dual from ", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "C", next := 59413, root := ~, start := 59405, stop := 59412 ), rec( content := " to ", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "C", next := 59425, root := ~, start := 59417, stop := 59424 ), rec( content := "\n wh\ enever there is no edge from ", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "C", next := 59469, root := ~, start := 59461, stop := 59468 ), rec( content := " to ", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "C", next := 59481, root := ~, start := 59473, stop := 59480 ), rec( content := " in ", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "A", next := 59499, root := ~, start := 59485, stop := 59498 ), rec( content := ".\n T\ he ", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ ual", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "E", next := 59520, root := ~, start := 59509, stop := 59519 ), rec( content := " is some\ times called the ", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ omplement", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "E", next := 59562, root := ~, start := 59545, stop := 59561 ), rec( content := ".", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 10, 6 ], mathmode := "Text", name := "P", next := 59567, root := ~, start := 59563, stop := 59566 ), rec( content := "\n\n \ ", count := [ 3, 3, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "D\ igraphDual", count := [ 3, 3, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 10, 6 ], mathmode := "Text", name := "C", next := 59591, root := ~, start := 59573, stop := 59590 ), rec( content := " returns\ the dual of the digraph ", count := [ 3, 3, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 10, 6 ], mathmode := "Text", name := "A", next := 59638, root := ~, start := 59624, stop := 59637 ), rec( content := ". If\n \ ", count := [ 3, 3, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 10, 6 ], mathmode := "Text", name := "A", next := 59661, root := ~, start := 59647, stop := 59660 ), rec( content := " is an i\ mmutable digraph, then a new immutable digraph is\n returned. Otherwise, th\ e mutable digraph ", count := [ 3, 3, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 10, 6 ], mathmode := "Text", name := "A", next := 59778, root := ~, start := 59764, stop := 59777 ), rec( content := " is chan\ ged in-place\n into its dual.\n ", count := [ 3, 3, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[2, 3], [], [4, 6], [5], [],\n> [7, 8, 9], [], [], []]);\n\ \ngap> DigraphDual(D);\n\ngap> D := CycleDigraph(IsMutableDigraph, \ 3);\n\ngap> DigraphDual(D);\n\ngap> D;\n\n", count := [ 3, 3, 10, 7 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 10, 7 ], mathmode := "Text", name := "Example", next := 60244, root := ~, start := 59822, stop := 60243 ), rec( content := "\n ", count := [ 3, 3, 10, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "Description", next := 60261, root := ~, start := 59270, stop := 60260 ) ], count := [ 3, 3, 10, 1 ], mathmode := "Text", name := "ManSection", next := 60275, root := ~, start := 59133, stop := 60274 ), rec( content := "\n\n ", count := [ 3, 3, 10, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphSymmetri\ cClosure" ), content := 0, count := [ 3, 3, 11, 2 ], mathmode := "Text", name := "Oper", next := 60348, root := ~, start := 60296, stop := 60347 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphSymmetri\ cClosureAttr" ), content := 0, count := [ 3, 3, 11, 4 ], mathmode := "Text", name := "Attr", next := 60407, root := ~, start := 60351, stop := 60406 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 11, 5 ], mathmode := "Text", name := "Returns", next := 60439, root := ~, start := 60410, stop := 60438 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 11, 5 ], mathmode := "Text", name := "A", next := 60477, root := ~, start := 60463, stop := 60476 ), rec( content := " is a di\ graph, then this attribute gives the minimal\n symmetric digraph which has \ the same vertices and contains all the edges of\n ", count := [ 3, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 11, 5 ], mathmode := "Text", name := "A", next := 60628, root := ~, start := 60614, stop := 60627 ), rec( content := ".", count := [ 3, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "P", next := 60633, root := ~, start := 60629, stop := 60632 ), rec( content := "\n \n\ A digraph is ", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ymmetric", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "E", next := 60672, root := ~, start := 60656, stop := 60671 ), rec( content := " if its \ adjacency matrix \n ", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Adjacen\ cyMatrix" ), content := 0, count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "Ref", next := 60731, root := ~, start := 60702, stop := 60730 ), rec( content := " is symm\ etric. For a digraph with multiple\n edges this means that there are the sa\ me number of edges from a vertex\n ", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "C", next := 60861, root := ~, start := 60853, stop := 60860 ), rec( content := " to a ve\ rtex ", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "C", next := 60882, root := ~, start := 60874, stop := 60881 ), rec( content := " as ther\ e are from ", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "C", next := 60909, root := ~, start := 60901, stop := 60908 ), rec( content := " to ", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "C", next := 60921, root := ~, start := 60913, stop := 60920 ), rec( content := "; \n \ see ", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsSymme\ tricDigraph" ), content := 0, count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "Ref", next := 60964, root := ~, start := 60932, stop := 60963 ), rec( content := ".", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 11, 7 ], mathmode := "Text", name := "P", next := 60969, root := ~, start := 60965, stop := 60968 ), rec( content := "\n\n \ If ", count := [ 3, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 11, 7 ], mathmode := "Text", name := "A", next := 60992, root := ~, start := 60978, stop := 60991 ), rec( content := " is immu\ table, then a new immutable digraph is returned.\n Otherwise, the mutable d\ igraph ", count := [ 3, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 11, 7 ], mathmode := "Text", name := "A", next := 61098, root := ~, start := 61084, stop := 61097 ), rec( content := " is chan\ ged in-place into its\n symmetric closure.\n", count := [ 3, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 2, 3], [2, 4], [1], [3, 4]]);\n\ngap> D := DigraphSymmetricClosure(D);\n\ngap> IsSymmetricDigraph(D);\ntrue\nga\ p> List(OutNeighbours(D), AsSet);\n[ [ 1, 2, 3 ], [ 1, 2, 4 ], [ 1, 4 ], [ 2, \ 3, 4 ] ]\ngap> D := Digraph([[2, 2], [1]]);\n\ngap> D := DigraphSymmetricClosure(D);\n\ngap> OutNeighbours(D);\n[ [ 2, 2 ], [ \ 1, 1 ] ]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n\ngap> DigraphSymmetricClosure(D);\n\ngap> D;\n\n", count := [ 3, 3, 11, 8 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 11, 8 ], mathmode := "Text", name := "Example", next := 61939, root := ~, start := 61151, stop := 61938 ), rec( content := "\n ", count := [ 3, 3, 11, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 11, 5 ], mathmode := "Text", name := "Description", next := 61956, root := ~, start := 60442, stop := 61955 ) ], count := [ 3, 3, 11, 1 ], mathmode := "Text", name := "ManSection", next := 61970, root := ~, start := 60281, stop := 61969 ), rec( content := "\n\n ", count := [ 3, 3, 11, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphTransiti\ veClosure" ), content := 0, count := [ 3, 3, 12, 2 ], mathmode := "Text", name := "Oper", next := 62044, root := ~, start := 61991, stop := 62043 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphTransiti\ veClosureAttr" ), content := 0, count := [ 3, 3, 12, 4 ], mathmode := "Text", name := "Attr", next := 62104, root := ~, start := 62047, stop := 62103 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphReflexiv\ eTransitiveClosure" ), content := 0, count := [ 3, 3, 12, 6 ], mathmode := "Text", name := "Oper", next := 62169, root := ~, start := 62107, stop := 62168 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphReflexiv\ eTransitiveClosureAttr" ), content := 0, count := [ 3, 3, 12, 8 ], mathmode := "Text", name := "Attr", next := 62238, root := ~, start := 62172, stop := 62237 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 12, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 12, 9 ], mathmode := "Text", name := "Returns", next := 62270, root := ~, start := 62241, stop := 62269 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 3, 12, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 12, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 12, 9 ], mathmode := "Text", name := "A", next := 62308, root := ~, start := 62294, stop := 62307 ), rec( content := " is a di\ graph with no multiple edges, then these\n attributes return the (reflexive\ ) transitive closure of ", count := [ 3, 3, 12, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 12, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 12, 9 ], mathmode := "Text", name := "A", next := 62431, root := ~, start := 62417, stop := 62430 ), rec( content := ".", count := [ 3, 3, 12, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "P", next := 62436, root := ~, start := 62432, stop := 62435 ), rec( content := "\n\n \ A digraph is ", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "r\ eflexive", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "E", next := 62471, root := ~, start := 62455, stop := 62470 ), rec( content := " if it h\ as a loop at every vertex, and it is\n ", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ ransitive", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "E", next := 62537, root := ~, start := 62520, stop := 62536 ), rec( content := " if when\ ever ", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ i,j]", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "C", next := 62562, root := ~, start := 62550, stop := 62561 ), rec( content := " and ", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ j,k]", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "C", next := 62579, root := ~, start := 62567, stop := 62578 ), rec( content := " are edg\ es of\n ", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "A", next := 62611, root := ~, start := 62597, stop := 62610 ), rec( content := ", ", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ i,k]", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "C", next := 62625, root := ~, start := 62613, stop := 62624 ), rec( content := " is also\ an edge. The ", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "(\ reflexive)\n transitive closure", count := [ 3, 3, 12, 10 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "E", next := 62691, root := ~, start := 62648, stop := 62690 ), rec( content := " of a di\ graph ", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "A", next := 62719, root := ~, start := 62705, stop := 62718 ), rec( content := " is the \ least\n (reflexive and) transitive digraph containing ", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "A", next := 62797, root := ~, start := 62783, stop := 62796 ), rec( content := ".", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 12, 11 ], mathmode := "Text", name := "P", next := 62802, root := ~, start := 62798, stop := 62801 ), rec( content := "\n\n \ If ", count := [ 3, 3, 12, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 12, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 12, 11 ], mathmode := "Text", name := "A", next := 62825, root := ~, start := 62811, stop := 62824 ), rec( content := " is immu\ table, then a new immutable digraph is returned.\n Otherwise, the mutable d\ igraph ", count := [ 3, 3, 12, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 12, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 12, 11 ], mathmode := "Text", name := "A", next := 62931, root := ~, start := 62917, stop := 62930 ), rec( content := " is chan\ ged in-place into its\n (reflexive) transitive closure.", count := [ 3, 3, 12, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "P", next := 63000, root := ~, start := 62996, stop := 62999 ), rec( content := "\n\n \ Let ", count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "M", next := 63018, root := ~, start := 63010, stop := 63017 ), rec( content := " be the \ number of vertices of ", count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "A", next := 63062, root := ~, start := 63048, stop := 63061 ), rec( content := ", and le\ t\n ", count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "M", next := 63084, root := ~, start := 63076, stop := 63083 ), rec( content := " be the \ number of edges. For an arbitrary digraph, these\n attributes will use a v\ ersion of the Floyd-Warshall algorithm, with\n complexity ", count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (n^3)", count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "M", next := 63242, root := ~, start := 63229, stop := 63241 ), rec( content := ".\n\n \ However, for a topologically sortable digraph [see ", count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ TopologicalSort" ), content := 0, count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "Ref", next := 63342, root := ~, start := 63300, stop := 63341 ), rec( content := "], these\ attributes will use methods\n with complexity ", count := [ 3, 3, 12, 12 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (m + n + m \\cdot n)", count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "M", next := 63426, root := ~, start := 63399, stop := 63425 ), rec( content := " when th\ is is faster.", count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 12, 13 ], mathmode := "Text", name := "P", next := 63451, root := ~, start := 63447, stop := 63450 ), rec( content := "\n\n \ ", count := [ 3, 3, 12, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := DigraphFromDiSparse6String(\".H`eOWR`Ul^\");\n\ngap> IsReflexiveDigraph(D) or IsTransitiveDigraph(D);\ \nfalse\ngap> OutNeighbours(D);\n[ [ 4, 6 ], [ 1, 3 ], [ ], [ 5 ], [ ], [ 7,\ 8, 9 ], [ ], [ ], \n [ ] ]\ngap> T := DigraphTransitiveClosure(D);\n\ngap> OutNeighbours(T);\n[\ [ 4, 6, 5, 7, 8, 9 ], [ 1, 3, 4, 5, 6, 7, 8, 9 ], [ ], [ 5 ], \n [ ], [ 7,\ 8, 9 ], [ ], [ ], [ ] ]\ngap> RT := DigraphReflexiveTransitiveClosure(D);\ \n\ngap> OutNeighbours(R\ T);\n[ [ 4, 6, 5, 7, 8, 9, 1 ], [ 1, 3, 4, 5, 6, 7, 8, 9, 2 ], [ 3 ], \n [ 5,\ 4 ], [ 5 ], [ 7, 8, 9, 6 ], [ 7 ], [ 8 ], [ 9 ] ]\ngap> D := CycleDigraph(IsM\ utableDigraph, 3);\n\ngap> DigraphRe\ flexiveTransitiveClosure(D);\n\ngap>\ D;\n\n", count := [ 3, 3, 12, 14 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 12, 14 ], mathmode := "Text", name := "Example", next := 64447, root := ~, start := 63457, stop := 64446 ), rec( content := "\n ", count := [ 3, 3, 12, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 12, 9 ], mathmode := "Text", name := "Description", next := 64464, root := ~, start := 62273, stop := 64463 ) ], count := [ 3, 3, 12, 1 ], mathmode := "Text", name := "ManSection", next := 64478, root := ~, start := 61976, stop := 64477 ), rec( content := "\n\n ", count := [ 3, 3, 12, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphTransiti\ veReduction" ), content := 0, count := [ 3, 3, 13, 2 ], mathmode := "Text", name := "Oper", next := 64554, root := ~, start := 64499, stop := 64553 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphTransiti\ veReductionAttr" ), content := 0, count := [ 3, 3, 13, 4 ], mathmode := "Text", name := "Attr", next := 64616, root := ~, start := 64557, stop := 64615 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphReflexiv\ eTransitiveReduction" ), content := 0, count := [ 3, 3, 13, 6 ], mathmode := "Text", name := "Oper", next := 64683, root := ~, start := 64619, stop := 64682 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphReflexiv\ eTransitiveReductionAttr" ), content := 0, count := [ 3, 3, 13, 8 ], mathmode := "Text", name := "Attr", next := 64754, root := ~, start := 64686, stop := 64753 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 13, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 13, 9 ], mathmode := "Text", name := "Returns", next := 64786, root := ~, start := 64757, stop := 64785 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 3, 13, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 13, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 13, 9 ], mathmode := "Text", name := "A", next := 64824, root := ~, start := 64810, stop := 64823 ), rec( content := " is a to\ pologically sortable digraph\n [see ", count := [ 3, 3, 13, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ TopologicalSort" ), content := 0, count := [ 3, 3, 13, 9 ], mathmode := "Text", name := "Ref", next := 64906, root := ~, start := 64870, stop := 64905 ), rec( content := "]\n w\ ith no multiple edges, then these operations return the\n (reflexive) tran\ sitive reduction of ", count := [ 3, 3, 13, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 13, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 13, 9 ], mathmode := "Text", name := "A", next := 65024, root := ~, start := 65010, stop := 65023 ), rec( content := ".", count := [ 3, 3, 13, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 13, 10 ], mathmode := "Text", name := "P", next := 65029, root := ~, start := 65025, stop := 65028 ), rec( content := "\n\n \ The (reflexive) transitive reduction of such a digraph is the unique\n leas\ t subgraph such that the (reflexive) transitive closure of the\n subgraph i\ s equal to the (reflexive) transitive closure of ", count := [ 3, 3, 13, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 13, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 13, 10 ], mathmode := "Text", name := "A", next := 65252, root := ~, start := 65238, stop := 65251 ), rec( content := "\n [s\ ee ", count := [ 3, 3, 13, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ ReflexiveTransitiveClosure" ), content := 0, count := [ 3, 3, 13, 10 ], mathmode := "Text", name := "Ref", next := 65309, root := ~, start := 65262, stop := 65308 ), rec( content := "].\n \ In order words, it is the least subgraph of ", count := [ 3, 3, 13, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 13, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 13, 10 ], mathmode := "Text", name := "A", next := 65374, root := ~, start := 65360, stop := 65373 ), rec( content := " which\n\ retains the same reachability as ", count := [ 3, 3, 13, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 13, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 13, 10 ], mathmode := "Text", name := "A", next := 65432, root := ~, start := 65418, stop := 65431 ), rec( content := ".", count := [ 3, 3, 13, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 13, 11 ], mathmode := "Text", name := "P", next := 65437, root := ~, start := 65433, stop := 65436 ), rec( content := "\n\n \ If ", count := [ 3, 3, 13, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 13, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 13, 11 ], mathmode := "Text", name := "A", next := 65460, root := ~, start := 65446, stop := 65459 ), rec( content := " is immu\ table, then a new immutable digraph is returned.\n Otherwise, the mutable d\ igraph ", count := [ 3, 3, 13, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 13, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 13, 11 ], mathmode := "Text", name := "A", next := 65566, root := ~, start := 65552, stop := 65565 ), rec( content := " is chan\ ged in-place into its\n (reflexive) transitive reduction.", count := [ 3, 3, 13, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 13, 12 ], mathmode := "Text", name := "P", next := 65637, root := ~, start := 65633, stop := 65636 ), rec( content := "\n\n \ Let ", count := [ 3, 3, 13, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 3, 13, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 13, 12 ], mathmode := "Text", name := "M", next := 65655, root := ~, start := 65647, stop := 65654 ), rec( content := " be the \ number of vertices of an arbitrary digraph, and let\n ", count := [ 3, 3, 13, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 3, 3, 13, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 13, 12 ], mathmode := "Text", name := "M", next := 65731, root := ~, start := 65723, stop := 65730 ), rec( content := " be the \ number of edges.\n Then these operations\n use methods with complexity " , count := [ 3, 3, 13, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (m + n + m \\cdot n)", count := [ 3, 3, 13, 12 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 13, 12 ], mathmode := "Text", name := "M", next := 65841, root := ~, start := 65814, stop := 65840 ), rec( content := ".\n " , count := [ 3, 3, 13, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 13, 13 ], mathmode := "Text", name := "P", next := 65851, root := ~, start := 65847, stop := 65850 ), rec( content := "\n ", count := [ 3, 3, 13, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 2, 3], [3], [3]]);;\ngap> DigraphHasLoops(D);\ntrue\ng\ ap> D1 := DigraphReflexiveTransitiveReduction(D);\n\ngap> DigraphHasLoops(D1);\nfalse\ngap> OutNeighbours(D1);\n\ [ [ 2 ], [ 3 ], [ ] ]\ngap> D2 := DigraphTransitiveReduction(D);\n\ngap> DigraphHasLoops(D2);\ntrue\ngap> OutNe\ ighbours(D2);\n[ [ 2, 1 ], [ 3 ], [ 3 ] ]\ngap> DigraphReflexiveTransitiveClos\ ure(D)\n> = DigraphReflexiveTransitiveClosure(D1);\ntrue\ngap> DigraphTransit\ iveClosure(D)\n> = DigraphTransitiveClosure(D2);\ntrue\ngap> D := Digraph(IsM\ utableDigraph, [[1], [1], [1, 2, 3]]);\n\ngap> DigraphReflexiveTransitiveReduction(D);\n\ngap> D;\n\n", count := [ 3, 3, 13, 14 ] , name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 13, 14 ], mathmode := "Text", name := "Example", next := 66711, root := ~, start := 65856, stop := 66710 ), rec( content := "\n ", count := [ 3, 3, 13, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 13, 9 ], mathmode := "Text", name := "Description", next := 66728, root := ~, start := 64789, stop := 66727 ) ], count := [ 3, 3, 13, 1 ], mathmode := "Text", name := "ManSection", next := 66742, root := ~, start := 64484, stop := 66741 ), rec( content := "\n\n ", count := [ 3, 3, 13, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph[, label \ ]", Name := "DigraphAddVertex" ), content := 0, count := [ 3, 3, 14, 2 ], mathmode := "Text", name := "Oper", next := 66818, root := ~, start := 66763, stop := 66817 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 14, 3 ], mathmode := "Text", name := "Returns", next := 66850, root := ~, start := 66821, stop := 66849 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ operation returns a digraph constructed from ", count := [ 3, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 14, 3 ], mathmode := "Text", name := "A", next := 66934, root := ~, start := 66920, stop := 66933 ), rec( content := " by addi\ ng a\n single new vertex, and no new edges. ", count := [ 3, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 14, 4 ], mathmode := "Text", name := "P", next := 66992, root := ~, start := 66988, stop := 66991 ), rec( content := "\n\n \ If the optional second argument ", count := [ 3, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ abel", count := [ 3, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 14, 4 ], mathmode := "Text", name := "A", next := 67042, root := ~, start := 67030, stop := 67041 ), rec( content := " is a ", count := [ 3, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ AP", count := [ 3, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 14, 4 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " object,\ \n then the new vertex will be labelled ", count := [ 3, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ abel", count := [ 3, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 14, 4 ], mathmode := "Text", name := "A", next := 67115, root := ~, start := 67103, stop := 67114 ), rec( content := ".\n " , count := [ 3, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "P", next := 67125, root := ~, start := 67121, stop := 67124 ), rec( content := "\n\n \ If ", count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "A", next := 67148, root := ~, start := 67134, stop := 67147 ), rec( content := " belongs\ to ", count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "Ref", next := 67190, root := ~, start := 67160, stop := 67189 ), rec( content := ", then t\ he\n vertex is added directly to ", count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "A", next := 67247, root := ~, start := 67233, stop := 67246 ), rec( content := ". If ", count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "A", next := 67266, root := ~, start := 67252, stop := 67265 ), rec( content := " belongs\ to\n ", count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "Ref", next := 67314, root := ~, start := 67282, stop := 67313 ), rec( content := ", an imm\ utable copy of ", count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "A", next := 67351, root := ~, start := 67337, stop := 67350 ), rec( content := " with\n \ the additional vertex is returned.", count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 14, 6 ], mathmode := "Text", name := "P", next := 67399, root := ~, start := 67395, stop := 67398 ), rec( content := "\n\n \ ", count := [ 3, 3, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CompleteDigraph(3);\n\n\ gap> new := DigraphAddVertex(D);\n\ \ngap> D = new;\nfalse\ngap> DigraphVertices(new);\n[ 1 .. 4 ]\ngap> new := Di\ graphAddVertex(D, Group([(1, 2)]));\n\ngap> DigraphVertexLabels(new);\n[ 1, 2, 3, Group([ (1,2) ]) ]\ngap> D := \ CompleteBipartiteDigraph(IsMutableDigraph, 2, 3);\n\ngap> new := DigraphAddVertex(D);\n\ngap> D = new;\ntrue\n", count := [ 3, 3, 14, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 14, 7 ], mathmode := "Text", name := "Example", next := 68004, root := ~, start := 67405, stop := 68003 ), rec( content := "\n ", count := [ 3, 3, 14, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 14, 3 ], mathmode := "Text", name := "Description", next := 68021, root := ~, start := 66853, stop := 68020 ) ], count := [ 3, 3, 14, 1 ], mathmode := "Text", name := "ManSection", next := 68035, root := ~, start := 66748, stop := 68034 ), rec( content := "\n\n ", count := [ 3, 3, 14, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, m", Label := "for a digraph \ and an integer", Name := "DigraphAddVertices" ), content := 0, count := [ 3, 3, 15, 2 ], mathmode := "Text", name := "Oper", next := 68147, root := ~, start := 68056, stop := 68146 ), rec( attributes := rec( Arg := "digraph, labels" , Label := "for a digraph \ and a list of labels", Name := "DigraphAddVertices" ), content := 0, count := [ 3, 3, 15, 4 ], mathmode := "Text", name := "Oper", next := 68252, root := ~, start := 68150, stop := 68251 ), rec( content := " The 3-argument \ version is deliberately undocumented. It is redundant,\n but it is inclu\ ded for backwards compatibility. ", count := [ 3, 3, 15, 5 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 15, 5 ], mathmode := "Text", name := "Returns", next := 68420, root := ~, start := 68391, stop := 68419 ), rec( attributes := rec( ), content := [ rec( content := "\n For\ a non-negative integer ", count := [ 3, 3, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 3, 3, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 15, 5 ], mathmode := "Text", name := "A", next := 68476, root := ~, start := 68468, stop := 68475 ), rec( content := ", this o\ peration returns a digraph\n constructed from ", count := [ 3, 3, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 15, 5 ], mathmode := "Text", name := "A", next := 68546, root := ~, start := 68532, stop := 68545 ), rec( content := " by addi\ ng ", count := [ 3, 3, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 3, 3, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 15, 5 ], mathmode := "Text", name := "A", next := 68565, root := ~, start := 68557, stop := 68564 ), rec( content := " new ver\ tices.\n ", count := [ 3, 3, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "P", next := 68588, root := ~, start := 68584, stop := 68587 ), rec( content := "\n\n \ Otherwise, if ", count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ abels", count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "A", next := 68621, root := ~, start := 68608, stop := 68620 ), rec( content := " is a li\ st\n consisting of ", count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "k\ ", count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "C", next := 68658, root := ~, start := 68650, stop := 68657 ), rec( content := " ", count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ AP", count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " objects\ , then this operation returns a\n digraph constructed from ", count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "A", next := 68747, root := ~, start := 68733, stop := 68746 ), rec( content := " by addi\ ng ", count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "k\ ", count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "C", next := 68766, root := ~, start := 68758, stop := 68765 ), rec( content := " new ver\ tices,\n which are labelled according to this list.\n ", count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "P", next := 68836, root := ~, start := 68832, stop := 68835 ), rec( content := "\n\n \ If ", count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "A", next := 68859, root := ~, start := 68845, stop := 68858 ), rec( content := " belongs\ to ", count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "Ref", next := 68901, root := ~, start := 68871, stop := 68900 ), rec( content := ", then t\ he\n vertices are added directly to ", count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "A", next := 68961, root := ~, start := 68947, stop := 68960 ), rec( content := ", which \ is changed in-place.\n If ", count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "A", next := 69011, root := ~, start := 68997, stop := 69010 ), rec( content := " belongs\ to ", count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "Ref", next := 69055, root := ~, start := 69023, stop := 69054 ), rec( content := ", then t\ he\n result is returned as an immutable digraph.\n ", count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 15, 8 ], mathmode := "Text", name := "P", next := 69122, root := ~, start := 69118, stop := 69121 ), rec( content := "\n\n \ ", count := [ 3, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CompleteDigraph(3);\n\n\ gap> new := DigraphAddVertices(D, 3);\n\ngap> DigraphVertices(new);\n[ 1 .. 6 ]\ngap> new := DigraphAddVertices(\ D, [Group([(1, 2)]), \"d\"]);\n\ng\ ap> DigraphVertexLabels(new);\n[ 1, 2, 3, Group([ (1,2) ]), \"d\" ]\ngap> Digr\ aphAddVertices(D, 0) = D;\ntrue\ngap> D := CompleteBipartiteDigraph(IsMutableD\ igraph, 2, 3);\n\ngap> new := Digra\ phAddVertices(D, 4);\n\ngap> D = ne\ w;\ntrue\n", count := [ 3, 3, 15, 9 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 15, 9 ], mathmode := "Text", name := "Example", next := 69771, root := ~, start := 69128, stop := 69770 ), rec( content := "\n ", count := [ 3, 3, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 15, 5 ], mathmode := "Text", name := "Description", next := 69788, root := ~, start := 68423, stop := 69787 ) ], count := [ 3, 3, 15, 1 ], mathmode := "Text", name := "ManSection", next := 69802, root := ~, start := 68041, stop := 69801 ), rec( content := "\n\n ", count := [ 3, 3, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, edge", Label := "for a digraph \ and an edge", Name := "DigraphAddEdge" ), content := 0, count := [ 3, 3, 16, 2 ], mathmode := "Text", name := "Oper", next := 69910, root := ~, start := 69823, stop := 69909 ), rec( attributes := rec( Arg := "digraph, src, ra\ n", Label := "for a digraph, source, and range", Name := "DigraphAddEdge" ), content := 0, count := [ 3, 3, 16, 4 ], mathmode := "Text", name := "Oper", next := 70011, root := ~, start := 69913, stop := 70010 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "Returns", next := 70043, root := ~, start := 70014, stop := 70042 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "e\ dge", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "A", next := 70078, root := ~, start := 70067, stop := 70077 ), rec( content := " is a pa\ ir of vertices of ", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "A", next := 70118, root := ~, start := 70104, stop := 70117 ), rec( content := ", or ", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ rc", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "A", next := 70133, root := ~, start := 70123, stop := 70132 ), rec( content := " and\n \ ", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "r\ an", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "A", next := 70152, root := ~, start := 70142, stop := 70151 ), rec( content := " are ver\ tices of ", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "A", next := 70183, root := ~, start := 70169, stop := 70182 ), rec( content := ",\n t\ hen this operation returns a digraph constructed from ", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "A", next := 70258, root := ~, start := 70244, stop := 70257 ), rec( content := "\n by\ adding a new edge with source ", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dge", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "A", next := 70307, root := ~, start := 70296, stop := 70306 ), rec( attributes := rec( ), content := [ rec( content := "[\ 1]", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "C", next := 70317, root := ~, start := 70307, stop := 70316 ), rec( content := " [", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ rc", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "A", next := 70329, root := ~, start := 70319, stop := 70328 ), rec( content := "] and ra\ nge\n ", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dge", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "A", next := 70356, root := ~, start := 70345, stop := 70355 ), rec( attributes := rec( ), content := [ rec( content := "[\ 2]", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "C", next := 70366, root := ~, start := 70356, stop := 70365 ), rec( content := " [", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "r\ an", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "A", next := 70378, root := ~, start := 70368, stop := 70377 ), rec( content := "].\n \ ", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := 0, count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "P", next := 70389, root := ~, start := 70385, stop := 70388 ), rec( content := "\n \n\ If ", count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "A", next := 70416, root := ~, start := 70402, stop := 70415 ), rec( content := " belongs\ to ", count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "Ref", next := 70458, root := ~, start := 70428, stop := 70457 ), rec( content := ", then t\ he edge\n is added directly to ", count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "A", next := 70513, root := ~, start := 70499, stop := 70512 ), rec( content := ". If ", count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "A", next := 70532, root := ~, start := 70518, stop := 70531 ), rec( content := " belongs\ to ", count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "Ref", next := 70582, root := ~, start := 70544, stop := 70581 ), rec( content := ", then a\ n immutable copy of ", count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "A", next := 70624, root := ~, start := 70610, stop := 70623 ), rec( content := " with th\ e\n additional edge is returned. ", count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 16, 7 ], mathmode := "Text", name := "P", next := 70672, root := ~, start := 70668, stop := 70671 ), rec( content := "\n\n \ ", count := [ 3, 3, 16, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D1 := Digraph([[2], [3], []]);\n\ngap> DigraphEdges(D1);\n[ [ 1, 2 ], [ 2, 3 ] ]\ngap> D2 := DigraphAddEdg\ e(D1, [3, 1]);\n\ngap> DigraphEdge\ s(D2);\n[ [ 1, 2 ], [ 2, 3 ], [ 3, 1 ] ]\ngap> D3 := DigraphAddEdge(D2, [2, 3]\ );\n\ngap> DigraphEdges(D3);\ \n[ [ 1, 2 ], [ 2, 3 ], [ 2, 3 ], [ 3, 1 ] ]\ngap> D := CycleDigraph(IsMutable\ Digraph, 4);\n\ngap> new := DigraphA\ ddEdge(D, [1, 3]);\n\ngap> DigraphEd\ ges(new);\n[ [ 1, 2 ], [ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ] ]\ngap> D = new;\ \ntrue\n", count := [ 3, 3, 16, 8 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 16, 8 ], mathmode := "Text", name := "Example", next := 71398, root := ~, start := 70678, stop := 71397 ), rec( content := "\n ", count := [ 3, 3, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "Description", next := 71415, root := ~, start := 70046, stop := 71414 ) ], count := [ 3, 3, 16, 1 ], mathmode := "Text", name := "ManSection", next := 71429, root := ~, start := 69808, stop := 71428 ), rec( content := "\n\n ", count := [ 3, 3, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, edge", Name := "DigraphAddEdgeO\ rbit" ), content := 0, count := [ 3, 3, 17, 2 ], mathmode := "Text", name := "Oper", next := 71504, root := ~, start := 71450, stop := 71503 ), rec( attributes := rec( ), content := [ rec( content := "\n A n\ ew digraph.\n ", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "Returns", next := 71548, root := ~, start := 71507, stop := 71547 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s operation returns a new digraph with the same vertices and edges as\n ", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "A", next := 71660, root := ~, start := 71646, stop := 71659 ), rec( content := " and wit\ h additional edges consisting of the orbit of the\n edge ", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dge", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "A", next := 71738, root := ~, start := 71727, stop := 71737 ), rec( content := " under t\ he action of the ", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Group" ), content := 0, count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "Ref", next := 71789, root := ~, start := 71763, stop := 71788 ), rec( content := " of\n \ ", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "A", next := 71811, root := ~, start := 71797, stop := 71810 ), rec( content := ". If ", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dge", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "A", next := 71828, root := ~, start := 71817, stop := 71827 ), rec( content := " is alre\ ady an edge in ", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "A", next := 71865, root := ~, start := 71851, stop := 71864 ), rec( content := ", then\n\ ", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "A", next := 71890, root := ~, start := 71876, stop := 71889 ), rec( content := " is retu\ rned unchanged. The argument ", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "A", next := 71941, root := ~, start := 71927, stop := 71940 ), rec( content := " must be\ \n an immutable digraph.\n ", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 17, 4 ], mathmode := "Text", name := "P", next := 71984, root := ~, start := 71980, stop := 71983 ), rec( content := "\n\n \ An edge is simply a pair of vertices of ", count := [ 3, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 17, 4 ], mathmode := "Text", name := "A", next := 72044, root := ~, start := 72030, stop := 72043 ), rec( content := ".\n\n \ ", count := [ 3, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr1 := CayleyDigraph(DihedralGroup(8));\n\ngap> gr2 := DigraphAddEdgeOrbit(gr1, [1, 8]);\n\ngap> DigraphEdges(gr1);\n[ [ 1, 2 ], [ 1, 3 ],\ [ 1, 4 ], [ 2, 1 ], [ 2, 8 ], [ 2, 6 ], \n [ 3, 5 ], [ 3, 4 ], [ 3, 7 ], [ 4\ , 6 ], [ 4, 7 ], [ 4, 1 ], \n [ 5, 3 ], [ 5, 2 ], [ 5, 8 ], [ 6, 4 ], [ 6, 5 \ ], [ 6, 2 ], \n [ 7, 8 ], [ 7, 1 ], [ 7, 3 ], [ 8, 7 ], [ 8, 6 ], [ 8, 5 ] ]\ \ngap> DigraphEdges(gr2);\n[ [ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 1, 8 ], [ 2, 1 ],\ [ 2, 8 ], \n [ 2, 6 ], [ 2, 3 ], [ 3, 5 ], [ 3, 4 ], [ 3, 7 ], [ 3, 2 ], \n \ [ 4, 6 ], [ 4, 7 ], [ 4, 1 ], [ 4, 5 ], [ 5, 3 ], [ 5, 2 ], \n [ 5, 8 ], [ 5\ , 4 ], [ 6, 4 ], [ 6, 5 ], [ 6, 2 ], [ 6, 7 ], \n [ 7, 8 ], [ 7, 1 ], [ 7, 3 \ ], [ 7, 6 ], [ 8, 7 ], [ 8, 6 ], \n [ 8, 5 ], [ 8, 1 ] ]\ngap> gr3 := Digraph\ RemoveEdgeOrbit(gr2, [1, 8]);\n\n\ gap> gr3 = gr1;\ntrue\n", count := [ 3, 3, 17, 5 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 17, 5 ], mathmode := "Text", name := "Example", next := 73020, root := ~, start := 72051, stop := 73019 ), rec( content := "\n ", count := [ 3, 3, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "Description", next := 73037, root := ~, start := 71551, stop := 73036 ) ], count := [ 3, 3, 17, 1 ], mathmode := "Text", name := "ManSection", next := 73051, root := ~, start := 71435, stop := 73050 ), rec( content := "\n\n ", count := [ 3, 3, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, edges", Name := "DigraphAddEdges\ " ), content := 0, count := [ 3, 3, 18, 2 ], mathmode := "Text", name := "Oper", next := 73123, root := ~, start := 73072, stop := 73122 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "Returns", next := 73155, root := ~, start := 73126, stop := 73154 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "e\ dges", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "A", next := 73191, root := ~, start := 73179, stop := 73190 ), rec( content := " is a (p\ ossibly empty) list of pairs of vertices of\n ", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "A", next := 73261, root := ~, start := 73247, stop := 73260 ), rec( content := ", then t\ his operation returns a digraph constructed from\n ", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "A", next := 73336, root := ~, start := 73322, stop := 73335 ), rec( content := " by addi\ ng the edges specified by ", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dges", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "A", next := 73382, root := ~, start := 73370, stop := 73381 ), rec( content := ". More\\ n precisely, for every ", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dge", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "C", next := 73426, root := ~, start := 73415, stop := 73425 ), rec( content := " in ", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dges", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "A", next := 73442, root := ~, start := 73430, stop := 73441 ), rec( content := ", a new \ edge\n will be added with source ", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dge[1]", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "C", next := 73499, root := ~, start := 73485, stop := 73498 ), rec( content := " and ran\ ge ", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dges[2]", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "C", next := 73525, root := ~, start := 73510, stop := 73524 ), rec( content := ".\n " , count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "P", next := 73535, root := ~, start := 73531, stop := 73534 ), rec( content := "\n\n \ If an edge is included in ", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dges", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "A", next := 73579, root := ~, start := 73567, stop := 73578 ), rec( content := " with mu\ ltiplicity ", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "k\ ", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "C", next := 73606, root := ~, start := 73598, stop := 73605 ), rec( content := ",\n t\ hen it will be added ", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "k\ ", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "C", next := 73642, root := ~, start := 73634, stop := 73641 ), rec( content := " times.\\ n\n If ", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "A", next := 73672, root := ~, start := 73658, stop := 73671 ), rec( content := " belongs\ to ", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "Ref", next := 73714, root := ~, start := 73684, stop := 73713 ), rec( content := ", then t\ he edges\n are added directly to ", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "A", next := 73771, root := ~, start := 73757, stop := 73770 ), rec( content := ". If ", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "A", next := 73790, root := ~, start := 73776, stop := 73789 ), rec( content := " belongs\ to ", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "Ref", next := 73840, root := ~, start := 73802, stop := 73839 ), rec( content := ", then t\ he result is returned as an immutable\n digraph.\n ", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 18, 5 ], mathmode := "Text", name := "P", next := 73907, root := ~, start := 73903, stop := 73906 ), rec( content := "\n\n \ ", count := [ 3, 3, 18, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> func := function(n)\n> local source, range, i;\n> source := [];\n> ra\ nge := [];\n> for i in [1 .. n - 2] do\n> Add(source, i);\n> Add(range\ , i + 1);\n> od;\n> return Digraph(n, source, range);\n> end;;\ngap> D := fu\ nc(1024);\n\ngap> new := Dig\ raphAddEdges(D,\n> [[1023, 1024], [1, 1024], [1023, 1024], [1024, 1]]);\n\ngap> D = new;\nfalse\ngap>\ D2 := DigraphMutableCopy(func(1024));\n\ngap> new := DigraphAddEdges(D2,\n> [[1023, 1024], [1, 1024], [1023\ , 1024], [1024, 1]]);\n\n\ gap> D2 = new;\ntrue\n", count := [ 3, 3, 18, 6 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 18, 6 ], mathmode := "Text", name := "Example", next := 74644, root := ~, start := 73913, stop := 74643 ), rec( content := "\n ", count := [ 3, 3, 18, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "Description", next := 74661, root := ~, start := 73158, stop := 74660 ) ], count := [ 3, 3, 18, 1 ], mathmode := "Text", name := "ManSection", next := 74675, root := ~, start := 73057, stop := 74674 ), rec( content := "\n\n ", count := [ 3, 3, 18, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, v", Name := "DigraphRemoveVe\ rtex" ), content := 0, count := [ 3, 3, 19, 2 ], mathmode := "Text", name := "Oper", next := 74747, root := ~, start := 74696, stop := 74746 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "Returns", next := 74779, root := ~, start := 74750, stop := 74778 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "A", next := 74811, root := ~, start := 74803, stop := 74810 ), rec( content := " is a ve\ rtex of ", count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "A", next := 74841, root := ~, start := 74827, stop := 74840 ), rec( content := ", then t\ his operation returns a\n digraph constructed from ", count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "A", next := 74916, root := ~, start := 74902, stop := 74915 ), rec( content := " by remo\ ving vertex ", count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "A", next := 74944, root := ~, start := 74936, stop := 74943 ), rec( content := ",\n a\ long with any edge whose source or range vertex is ", count := [ 3, 3, 19, 3 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "A", next := 75010, root := ~, start := 75002, stop := 75009 ), rec( content := ".", count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 19, 4 ], mathmode := "Text", name := "P", next := 75015, root := ~, start := 75011, stop := 75014 ), rec( content := "\n\n \ If ", count := [ 3, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 19, 4 ], mathmode := "Text", name := "A", next := 75038, root := ~, start := 75024, stop := 75037 ), rec( content := " has ", count := [ 3, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 19, 4 ], mathmode := "Text", name := "C", next := 75051, root := ~, start := 75043, stop := 75050 ), rec( content := " vertice\ s, then the vertices of the returned\n digraph are ", count := [ 3, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ 1..n-1]", count := [ 3, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 19, 4 ], mathmode := "Text", name := "C", next := 75127, root := ~, start := 75112, stop := 75126 ), rec( content := ", but th\ e original labels can be\n accessed via ", count := [ 3, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ VertexLabels" ), content := 0, count := [ 3, 3, 19, 4 ], mathmode := "Text", name := "Ref", next := 75210, root := ~, start := 75177, stop := 75209 ), rec( content := ". ", count := [ 3, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "P", next := 75216, root := ~, start := 75212, stop := 75215 ), rec( content := "\n\n \ If ", count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "A", next := 75239, root := ~, start := 75225, stop := 75238 ), rec( content := " belongs\ to ", count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "Ref", next := 75281, root := ~, start := 75251, stop := 75280 ), rec( content := ", then t\ he\n vertex is removed directly from ", count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "A", next := 75342, root := ~, start := 75328, stop := 75341 ), rec( content := ". If ", count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "A", next := 75361, root := ~, start := 75347, stop := 75360 ), rec( content := " belongs\ \n to ", count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "Ref", next := 75409, root := ~, start := 75377, stop := 75408 ), rec( content := ", an imm\ utable copy of ", count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "A", next := 75446, root := ~, start := 75432, stop := 75445 ), rec( content := "\n wi\ thout the vertex is returned.", count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 19, 6 ], mathmode := "Text", name := "P", next := 75486, root := ~, start := 75482, stop := 75485 ), rec( content := "\n\n \ ", count := [ 3, 3, 19, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([\"a\", \"b\", \"c\"],\n> [\"a\", \"a\", \ \"b\", \"c\", \"c\"],\n> [\"b\", \"c\", \"a\", \"a\", \"c\"])\ ;\n\ngap> DigraphVertexLabels(D);\ \n[ \"a\", \"b\", \"c\" ]\ngap> DigraphEdges(D);\n[ [ 1, 2 ], [ 1, 3 ], [ 2, 1\ ], [ 3, 1 ], [ 3, 3 ] ]\ngap> new := DigraphRemoveVertex(D, 2);\n\ngap> DigraphVertexLabels(new);\n[ \"a\", \"c\ \" ]\ngap> D := CycleDigraph(IsMutableDigraph, 5);\n\ngap> new := DigraphRemoveVertex(D, 1);\n\ngap> DigraphVertexLabels(D);\n[ 2, 3, 4, 5 ]\ngap> D =\ new;\ntrue\n", count := [ 3, 3, 19, 7 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 19, 7 ], mathmode := "Text", name := "Example", next := 76180, root := ~, start := 75492, stop := 76179 ), rec( content := "\n ", count := [ 3, 3, 19, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "Description", next := 76197, root := ~, start := 74782, stop := 76196 ) ], count := [ 3, 3, 19, 1 ], mathmode := "Text", name := "ManSection", next := 76211, root := ~, start := 74681, stop := 76210 ), rec( content := "\n\n ", count := [ 3, 3, 19, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, verts", Name := "DigraphRemoveVe\ rtices" ), content := 0, count := [ 3, 3, 20, 2 ], mathmode := "Text", name := "Oper", next := 76289, root := ~, start := 76232, stop := 76288 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "Returns", next := 76321, root := ~, start := 76292, stop := 76320 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "v\ erts", count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "A", next := 76357, root := ~, start := 76345, stop := 76356 ), rec( content := " is a (p\ ossibly empty) duplicate-free list of vertices of\n ", count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "A", next := 76433, root := ~, start := 76419, stop := 76432 ), rec( content := ", then t\ his operation returns a digraph constructed from\n ", count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "A", next := 76508, root := ~, start := 76494, stop := 76507 ), rec( content := " by remo\ ving every vertex in ", count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ erts", count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "A", next := 76549, root := ~, start := 76537, stop := 76548 ), rec( content := ", along \ with any edge\n whose source or range vertex is in ", count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ erts", count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "A", next := 76622, root := ~, start := 76610, stop := 76621 ), rec( content := ".", count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "P", next := 76627, root := ~, start := 76623, stop := 76626 ), rec( content := "\n\n \ If ", count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "A", next := 76650, root := ~, start := 76636, stop := 76649 ), rec( content := " has ", count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "C", next := 76663, root := ~, start := 76655, stop := 76662 ), rec( content := " vertice\ s, then the vertices of the new\n digraph are ", count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ 1 .. n-Length(", count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "vert\ s", count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 20, 4 ], mathmode := \ "Text", name := "A", next := 76749, root := ~, start := 76737, stop := 76748 ) , rec( content := "\ )]", count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "C", next := 76755, root := ~, start := 76719, stop := 76754 ), rec( content := ", but th\ e\n original labels can be accessed via ", count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ VertexLabels" ), content := 0, count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "Ref", next := 76838, root := ~, start := 76805, stop := 76837 ), rec( content := ". ", count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "P", next := 76844, root := ~, start := 76840, stop := 76843 ), rec( content := "\n\n \ If ", count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "A", next := 76867, root := ~, start := 76853, stop := 76866 ), rec( content := " belongs\ to ", count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "Ref", next := 76909, root := ~, start := 76879, stop := 76908 ), rec( content := ", then t\ he\n vertices are removed directly from ", count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "A", next := 76973, root := ~, start := 76959, stop := 76972 ), rec( content := ". If ", count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "A", next := 76992, root := ~, start := 76978, stop := 76991 ), rec( content := " belongs\ \n to ", count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "Ref", next := 77040, root := ~, start := 77008, stop := 77039 ), rec( content := ", an imm\ utable copy of ", count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "A", next := 77077, root := ~, start := 77063, stop := 77076 ), rec( content := "\n wi\ thout the vertices is returned.", count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 20, 6 ], mathmode := "Text", name := "P", next := 77119, root := ~, start := 77115, stop := 77118 ), rec( content := "\n\n \ ", count := [ 3, 3, 20, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[3], [1, 3, 5], [1], [1, 2, 4], [2, 3, 5]]);\n\ngap> SetDigraphVertexLabels(D, [\"a\", \"b\ \", \"c\", \"d\", \"e\"]);\ngap> new := DigraphRemoveVertices(D, [2, 4]);\n\ngap> DigraphVertexLabels(new);\n[ \ \"a\", \"c\", \"e\" ]\ngap> D := CycleDigraph(IsMutableDigraph, 5);\n\ngap> new := DigraphRemoveVertices(D, [1, 3]\ );\n\ngap> DigraphVertexLabels(D);\n[\ 2, 4, 5 ]\ngap> D = new;\ntrue\n", count := [ 3, 3, 20, 7 ], name := "PCDATA" , root := ~ ) ], count := [ 3, 3, 20, 7 ], mathmode := "Text", name := "Example", next := 77702, root := ~, start := 77125, stop := 77701 ), rec( content := "\n ", count := [ 3, 3, 20, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "Description", next := 77719, root := ~, start := 76324, stop := 77718 ) ], count := [ 3, 3, 20, 1 ], mathmode := "Text", name := "ManSection", next := 77733, root := ~, start := 76217, stop := 77732 ), rec( content := "\n\n ", count := [ 3, 3, 20, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, edge", Label := "for a digraph \ and an edge", Name := "DigraphRemoveEdge" ), content := 0, count := [ 3, 3, 21, 2 ], mathmode := "Text", name := "Oper", next := 77844, root := ~, start := 77754, stop := 77843 ), rec( attributes := rec( Arg := "digraph, src, ra\ n", Label := "for a digraph, source, and range", Name := "DigraphRemoveEdge" ) , content := 0, count := [ 3, 3, 21, 4 ], mathmode := "Text", name := "Oper", next := 77948, root := ~, start := 77847, stop := 77947 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "Returns", next := 77980, root := ~, start := 77951, stop := 77979 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "A", next := 78018, root := ~, start := 78004, stop := 78017 ), rec( content := " is a di\ graph with no multiple edges and ", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dge", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "A", next := 78070, root := ~, start := 78059, stop := 78069 ), rec( content := " is a\n \ pair of vertices of ", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "A", next := 78114, root := ~, start := 78100, stop := 78113 ), rec( content := ", or ", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ rc", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "A", next := 78129, root := ~, start := 78119, stop := 78128 ), rec( content := " and ", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "r\ an", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "A", next := 78144, root := ~, start := 78134, stop := 78143 ), rec( content := " are\n \ vertices of ", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "A", next := 78179, root := ~, start := 78165, stop := 78178 ), rec( content := ", then t\ his operation returns a digraph\n constructed from ", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "A", next := 78254, root := ~, start := 78240, stop := 78253 ), rec( content := " by remo\ ving the edge specified by\n ", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dge", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "A", next := 78304, root := ~, start := 78293, stop := 78303 ), rec( content := " or ", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ src, ran]", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "A", next := 78325, root := ~, start := 78308, stop := 78324 ), rec( content := ". ", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "P", next := 78331, root := ~, start := 78327, stop := 78330 ), rec( content := " \n\n \ If ", count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "A", next := 78356, root := ~, start := 78342, stop := 78355 ), rec( content := " belongs\ to ", count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "Ref", next := 78404, root := ~, start := 78368, stop := 78403 ), rec( content := ", then t\ he edge is removed directly from\n ", count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "A", next := 78463, root := ~, start := 78449, stop := 78462 ), rec( content := ". If ", count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "A", next := 78482, root := ~, start := 78468, stop := 78481 ), rec( content := " belongs\ to ", count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "Ref", next := 78532, root := ~, start := 78494, stop := 78531 ), rec( content := ", an imm\ utable copy of ", count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "A", next := 78569, root := ~, start := 78555, stop := 78568 ), rec( content := " without\ \n the edge is returned.\n ", count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "P", next := 78612, root := ~, start := 78608, stop := 78611 ), rec( content := "\n\n \ Note that if ", count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "A", next := 78645, root := ~, start := 78631, stop := 78644 ), rec( content := " belongs\ to ", count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "Ref", next := 78689, root := ~, start := 78657, stop := 78688 ), rec( content := ",\n t\ hen a new copy of ", count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "A", next := 78728, root := ~, start := 78714, stop := 78727 ), rec( content := " will be\ returned even if ", count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dge", count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "A", next := 78765, root := ~, start := 78754, stop := 78764 ), rec( content := " or \n \ ", count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ src, ran]", count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "A", next := 78791, root := ~, start := 78774, stop := 78790 ), rec( content := " does no\ t define an edge of ", count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "A", next := 78833, root := ~, start := 78819, stop := 78832 ), rec( content := ".", count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 21, 8 ], mathmode := "Text", name := "P", next := 78838, root := ~, start := 78834, stop := 78837 ), rec( content := "\n\n \ ", count := [ 3, 3, 21, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CycleDigraph(250000);\n\ngap> D := DigraphRemoveEdge(D, [250000, 1]);\n\ngap> new := DigraphRemoveEdge(D, [25000, 2]);;\nga\ p> new = D;\ntrue\ngap> IsIdenticalObj(new, D);\nfalse\ngap> D := DigraphMutab\ leCopy(D);;\ngap> new := DigraphRemoveEdge(D, 2500, 2);;\ngap> IsIdenticalObj(\ new, D);\ntrue\n", count := [ 3, 3, 21, 9 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 9 ], mathmode := "Text", name := "Example", next := 79268, root := ~, start := 78844, stop := 79267 ), rec( content := "\n ", count := [ 3, 3, 21, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "Description", next := 79285, root := ~, start := 77983, stop := 79284 ) ], count := [ 3, 3, 21, 1 ], mathmode := "Text", name := "ManSection", next := 79299, root := ~, start := 77739, stop := 79298 ), rec( content := "\n\n ", count := [ 3, 3, 21, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, edge", Name := "DigraphRemoveEd\ geOrbit" ), content := 0, count := [ 3, 3, 22, 2 ], mathmode := "Text", name := "Oper", next := 79377, root := ~, start := 79320, stop := 79376 ), rec( attributes := rec( ), content := [ rec( content := "\n A n\ ew digraph.\n ", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "Returns", next := 79421, root := ~, start := 79380, stop := 79420 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s operation returns a new digraph with the same vertices as\n ", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "A", next := 79523, root := ~, start := 79509, stop := 79522 ), rec( content := " and wit\ h the orbit of the edge ", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dge", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "A", next := 79566, root := ~, start := 79555, stop := 79565 ), rec( content := " (under \ the action\n of the ", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Group" ), content := 0, count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "Ref", next := 79622, root := ~, start := 79596, stop := 79621 ), rec( content := " of ", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "A", next := 79640, root := ~, start := 79626, stop := 79639 ), rec( content := ") remove\ d.\n If ", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dge", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "A", next := 79669, root := ~, start := 79658, stop := 79668 ), rec( content := " is not \ an edge in ", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "A", next := 79702, root := ~, start := 79688, stop := 79701 ), rec( content := ", then " , count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "A", next := 79723, root := ~, start := 79709, stop := 79722 ), rec( content := " is\n \ returned unchanged. The argument ", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "A", next := 79778, root := ~, start := 79764, stop := 79777 ), rec( content := " must be\ an immutable\n digraph.\n ", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 22, 4 ], mathmode := "Text", name := "P", next := 79821, root := ~, start := 79817, stop := 79820 ), rec( content := "\n\n \ An edge is simply a pair of vertices of ", count := [ 3, 3, 22, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 22, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 22, 4 ], mathmode := "Text", name := "A", next := 79881, root := ~, start := 79867, stop := 79880 ), rec( content := ".\n " , count := [ 3, 3, 22, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr1 := CayleyDigraph(DihedralGroup(8));\n\ngap> gr2 := DigraphAddEdgeOrbit(gr1, [1, 8]);\n\ngap> DigraphEdges(gr1);\n[ [ 1, 2 ], [ 1, 3 ],\ [ 1, 4 ], [ 2, 1 ], [ 2, 8 ], [ 2, 6 ], \n [ 3, 5 ], [ 3, 4 ], [ 3, 7 ], [ 4\ , 6 ], [ 4, 7 ], [ 4, 1 ], \n [ 5, 3 ], [ 5, 2 ], [ 5, 8 ], [ 6, 4 ], [ 6, 5 \ ], [ 6, 2 ], \n [ 7, 8 ], [ 7, 1 ], [ 7, 3 ], [ 8, 7 ], [ 8, 6 ], [ 8, 5 ] ]\ \ngap> DigraphEdges(gr2);\n[ [ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 1, 8 ], [ 2, 1 ],\ [ 2, 8 ], \n [ 2, 6 ], [ 2, 3 ], [ 3, 5 ], [ 3, 4 ], [ 3, 7 ], [ 3, 2 ], \n \ [ 4, 6 ], [ 4, 7 ], [ 4, 1 ], [ 4, 5 ], [ 5, 3 ], [ 5, 2 ], \n [ 5, 8 ], [ 5\ , 4 ], [ 6, 4 ], [ 6, 5 ], [ 6, 2 ], [ 6, 7 ], \n [ 7, 8 ], [ 7, 1 ], [ 7, 3 \ ], [ 7, 6 ], [ 8, 7 ], [ 8, 6 ], \n [ 8, 5 ], [ 8, 1 ] ]\ngap> gr3 := Digraph\ RemoveEdgeOrbit(gr2, [1, 8]);\n\n\ gap> gr3 = gr1;\ntrue\n", count := [ 3, 3, 22, 5 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 22, 5 ], mathmode := "Text", name := "Example", next := 80856, root := ~, start := 79887, stop := 80855 ), rec( content := "\n ", count := [ 3, 3, 22, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "Description", next := 80873, root := ~, start := 79424, stop := 80872 ) ], count := [ 3, 3, 22, 1 ], mathmode := "Text", name := "ManSection", next := 80887, root := ~, start := 79305, stop := 80886 ), rec( content := "\n\n ", count := [ 3, 3, 22, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, edges", Name := "DigraphRemoveEd\ ges" ), content := 0, count := [ 3, 3, 23, 2 ], mathmode := "Text", name := "Oper", next := 80962, root := ~, start := 80908, stop := 80961 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 3 ], mathmode := "Text", name := "Returns", next := 80994, root := ~, start := 80965, stop := 80993 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ one of the following holds:\n ", count := [ 3, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "\n ", count := [ 3, 3, 23, 5 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "digraph", count := [ 3, 3, 23, 5 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 5 ], mathmode := "Te\ xt", name := "A", next := 81092, root := ~, start := 81078, stop := 81091 ), rec( cont\ ent := " is a digraph with no multiple edges, and\n ", count := [ 3, 3,\ 23, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "edges", count := [ 3, 3, 23, 5 ], mat\ hmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 5 ], math\ mode := "Text", name := "A", next := 81154, root := ~, start := 81142, stop :=\ 81153 ), rec( content := " is a list of pairs of vertices of ", count := [ 3,\ 3, 23, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribute\ s := rec( ), content := [ rec( content := "digraph", count := [ 3, 3, 23, 5 ]\ , mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 5 ] , math\ mode := "Text", name := "A", next := 81203, root := ~, start := 81189, stop :=\ 81202 ), rec( content := ", or\n ", count := [ 3, 3, 23, 5 ], mathmode :\ = "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 5 ], name := "Ite\ m", next := 81221, root := ~, start := 81063, stop := 81220 ), rec( attributes :\ = rec( ), content := [ rec( content := " ", count := [ 3, 3, 23, 7 ], mathmod\ e := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), conten\ t := [ rec( content := "digraph", count := [ 3, 3, 23, 7 ], mathmode := "Text"\ , name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 7 ], mathmode := "Text\ ", name := "A", next := 81249, root := ~, start := 81235, stop := 81248 ), rec( cont\ ent := " is a digraph and ", count := [ 3, 3, 23, 7 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "edges", count := [ 3, 3, 23, 7 ], mathmode := "Text", name := "PCDATA",\ root := ~ ) ], count := [ 3, 3, 23, 7 ], mathmode := "Text", name := "A", next\ := 81279, root := ~, start := 81267, stop := 81278 ), rec( content := " is an\ empty list ", count := [ 3, 3, 23, 7 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 3, 3, 23, 7 ], name := "Item", next := 81304, root := ~, start := 812\ 28, stop := 81303 ) ], count := [ 3, 3, 23, 4 ], mathmode := "Text", name := "List", next := 81316, root := ~, start := 81050, stop := 81315 ), rec( content := "\n\n \ then this operation returns a digraph constructed from ", count := [ 3, 3, 23, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 23, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 9 ], mathmode := "Text", name := "A", next := 81391, root := ~, start := 81377, stop := 81390 ), rec( content := "\n by\ removing all of the edges specified by ", count := [ 3, 3, 23, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dges", count := [ 3, 3, 23, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 9 ], mathmode := "Text", name := "A", next := 81450, root := ~, start := 81438, stop := 81449 ), rec( content := "\n (s\ ee ", count := [ 3, 3, 23, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for a \ digraph and an edge", Oper := "DigraphRemoveEdge" ), content := 0, count := [ 3, 3, 23, 9 ], mathmode := "Text", name := "Ref", next := 81525, root := ~, start := 81460, stop := 81524 ), rec( content := ").\n \ ", count := [ 3, 3, 23, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := 0, count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "P", next := 81536, root := ~, start := 81532, stop := 81535 ), rec( content := "\n\n \ If ", count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "A", next := 81559, root := ~, start := 81545, stop := 81558 ), rec( content := " belongs\ to ", count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "Ref", next := 81601, root := ~, start := 81571, stop := 81600 ), rec( content := ", then t\ he edge\n is removed directly from ", count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "A", next := 81660, root := ~, start := 81646, stop := 81659 ), rec( content := ". If ", count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "A", next := 81679, root := ~, start := 81665, stop := 81678 ), rec( content := " belongs\ to ", count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "Ref", next := 81729, root := ~, start := 81691, stop := 81728 ), rec( content := ", the ed\ ge is removed from an immutable copy of\n ", count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "A", next := 81795, root := ~, start := 81781, stop := 81794 ), rec( content := " and thi\ s new digraph is returned.", count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 23, 11 ], mathmode := "Text", name := "P", next := 81833, root := ~, start := 81829, stop := 81832 ), rec( content := "\n\n \ Note that if ", count := [ 3, 3, 23, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dges", count := [ 3, 3, 23, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 11 ], mathmode := "Text", name := "A", next := 81864, root := ~, start := 81852, stop := 81863 ), rec( content := " is empt\ y, then this operation\n will always return ", count := [ 3, 3, 23, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 23, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 11 ], mathmode := "Text", name := "A", next := 81932, root := ~, start := 81918, stop := 81931 ), rec( content := " rather \ than a copy. Also, if any element\n of ", count := [ 3, 3, 23, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dges", count := [ 3, 3, 23, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 11 ], mathmode := "Text", name := "A", next := 81993, root := ~, start := 81981, stop := 81992 ), rec( content := " is inva\ lid (i.e. does not define an edge of ", count := [ 3, 3, 23, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 23, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 11 ], mathmode := "Text", name := "A", next := 82052, root := ~, start := 82038, stop := 82051 ), rec( content := ")\n t\ hen that element will simply be ignored.\n\n ", count := [ 3, 3, 23, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CycleDigraph(250000);\n\ngap> D := DigraphRemoveEdges(D, [[250000, 1]]);\n\ngap> D := DigraphMutableCopy(D);\n\ngap> new := DigraphRemoveEdges(D, [[1\ , 2], [2, 3], [3, 100]]);\n\ngap> new = D;\ntrue\n", count := [ 3, 3, 23, 12 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 12 ], mathmode := "Text", name := "Example", next := 82540, root := ~, start := 82105, stop := 82539 ), rec( content := "\n ", count := [ 3, 3, 23, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 3 ], mathmode := "Text", name := "Description", next := 82557, root := ~, start := 80997, stop := 82556 ) ], count := [ 3, 3, 23, 1 ], mathmode := "Text", name := "ManSection", next := 82571, root := ~, start := 80893, stop := 82570 ), rec( content := "\n\n ", count := [ 3, 3, 23, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphRemoveLo\ ops" ), content := 0, count := [ 3, 3, 24, 2 ], mathmode := "Text", name := "Oper", next := 82639, root := ~, start := 82592, stop := 82638 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphRemoveLo\ opsAttr" ), content := 0, count := [ 3, 3, 24, 4 ], mathmode := "Text", name := "Attr", next := 82693, root := ~, start := 82642, stop := 82692 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 24, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 24, 5 ], mathmode := "Text", name := "Returns", next := 82725, root := ~, start := 82696, stop := 82724 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 3, 24, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 24, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 24, 5 ], mathmode := "Text", name := "A", next := 82763, root := ~, start := 82749, stop := 82762 ), rec( content := " is a di\ graph, then this operation returns a\n digraph constructed from ", count := [ 3, 3, 24, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 24, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 24, 5 ], mathmode := "Text", name := "A", next := 82852, root := ~, start := 82838, stop := 82851 ), rec( content := " by remo\ ving every loop. A loop\n is an edge with equal source and range.", count := [ 3, 3, 24, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 24, 6 ], mathmode := "Text", name := "P", next := 82931, root := ~, start := 82927, stop := 82930 ), rec( content := "\n\n \ If ", count := [ 3, 3, 24, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 24, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 24, 6 ], mathmode := "Text", name := "A", next := 82954, root := ~, start := 82940, stop := 82953 ), rec( content := " is immu\ table, then a new immutable digraph is returned.\n Otherwise, the loops are\ removed from the mutable digraph ", count := [ 3, 3, 24, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 24, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 24, 6 ], mathmode := "Text", name := "A", next := 83087, root := ~, start := 83073, stop := 83086 ), rec( content := "\n in\ -place.\n ", count := [ 3, 3, 24, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 2, 4], [1, 4], [3, 4], [1, 4, 5], [1, 5]]);\n\ngap> DigraphRemoveLoops(D);\n\ngap> D := Digraph(IsMutableDigraph, [[1, 2]\ , [1]]);\n\ngap> DigraphRemoveLoops(\ D);\n\ngap> D;\n\n", count := [ 3, 3, 24, 7 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 24, 7 ], mathmode := "Text", name := "Example", next := 83541, root := ~, start := 83106, stop := 83540 ), rec( content := "\n ", count := [ 3, 3, 24, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 24, 5 ], mathmode := "Text", name := "Description", next := 83558, root := ~, start := 82728, stop := 83557 ) ], count := [ 3, 3, 24, 1 ], mathmode := "Text", name := "ManSection", next := 83572, root := ~, start := 82577, stop := 83571 ), rec( content := "\n\n ", count := [ 3, 3, 24, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphRemoveAl\ lMultipleEdges" ), content := 0, count := [ 3, 3, 25, 2 ], mathmode := "Text", name := "Oper", next := 83651, root := ~, start := 83593, stop := 83650 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphRemoveAl\ lMultipleEdgesAttr" ), content := 0, count := [ 3, 3, 25, 4 ], mathmode := "Text", name := "Attr", next := 83716, root := ~, start := 83654, stop := 83715 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 25, 5 ], mathmode := "Text", name := "Returns", next := 83748, root := ~, start := 83719, stop := 83747 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 25, 5 ], mathmode := "Text", name := "A", next := 83786, root := ~, start := 83772, stop := 83785 ), rec( content := " is a di\ graph, then this operation returns a\n digraph constructed from ", count := [ 3, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 25, 5 ], mathmode := "Text", name := "A", next := 83875, root := ~, start := 83861, stop := 83874 ), rec( content := " by remo\ ving all multiple edges.\n The result is the largest subdigraph of ", count := [ 3, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 25, 5 ], mathmode := "Text", name := "A", next := 83966, root := ~, start := 83952, stop := 83965 ), rec( content := " which d\ oes not\n contain multiple edges.", count := [ 3, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 25, 6 ], mathmode := "Text", name := "P", next := 84013, root := ~, start := 84009, stop := 84012 ), rec( content := "\n\n \ If ", count := [ 3, 3, 25, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 25, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 25, 6 ], mathmode := "Text", name := "A", next := 84036, root := ~, start := 84022, stop := 84035 ), rec( content := " is immu\ table, then a new immutable digraph is returned.\n Otherwise, the multiple \ edges of the mutable digraph ", count := [ 3, 3, 25, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 25, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 25, 6 ], mathmode := "Text", name := "A", next := 84164, root := ~, start := 84150, stop := 84163 ), rec( content := " are\n \ removed in-place.\n ", count := [ 3, 3, 25, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D1 := Digraph([[1, 2, 3, 2], [1, 1, 3], [2, 2, 2]]);\n\ngap> D2 := DigraphRemoveAllMultipleEdges(D1)\ ;\n\ngap> OutNeighbours(D2);\n[ [ \ 1, 2, 3 ], [ 1, 3 ], [ 2 ] ]\ngap> D := Digraph(IsMutableDigraph, [[2, 2], [1]\ ]);\n\ngap> DigraphRemoveAllMul\ tipleEdges(D);\n\ngap> D;\n\n", count := [ 3, 3, 25, 7 ], name := "PCDAT\ A", root := ~ ) ], count := [ 3, 3, 25, 7 ], mathmode := "Text", name := "Example", next := 84717, root := ~, start := 84195, stop := 84716 ), rec( content := "\n ", count := [ 3, 3, 25, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 25, 5 ], mathmode := "Text", name := "Description", next := 84734, root := ~, start := 83751, stop := 84733 ) ], count := [ 3, 3, 25, 1 ], mathmode := "Text", name := "ManSection", next := 84748, root := ~, start := 83578, stop := 84747 ), rec( content := "\n\n ", count := [ 3, 3, 25, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, edges", Label := "for a digraph \ and a list of edges", Name := "DigraphReverseEdges" ), content := 0, count := [ 3, 3, 26, 2 ], mathmode := "Text", name := "Oper", next := 84870, root := ~, start := 84769, stop := 84869 ), rec( attributes := rec( Arg := "digraph, edge", Label := "for a digraph \ and an edge", Name := "DigraphReverseEdge" ), content := 0, count := [ 3, 3, 26, 4 ], mathmode := "Text", name := "Oper", next := 84964, root := ~, start := 84873, stop := 84963 ), rec( attributes := rec( Arg := "digraph, src, ra\ n", Label := "for a digraph, source, and range", Name := "DigraphReverseEdge" ), content := 0, count := [ 3, 3, 26, 6 ], mathmode := "Text", name := "Oper", next := 85069, root := ~, start := 84967, stop := 85068 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "Returns", next := 85101, root := ~, start := 85072, stop := 85100 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "A", next := 85139, root := ~, start := 85125, stop := 85138 ), rec( content := " is a di\ graph without multiple edges, and ", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dges", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "A", next := 85193, root := ~, start := 85181, stop := 85192 ), rec( content := " is a\n \ list of pairs of vertices of ", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "A", next := 85246, root := ~, start := 85232, stop := 85245 ), rec( content := " (the en\ tries of each pair\n corresponding to the source and the range of an edge, \ respectively),\n then ", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphReverseEdges", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "C", next := 85381, root := ~, start := 85355, stop := 85380 ), rec( content := " returns\ a digraph constructed from\n ", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "A", next := 85435, root := ~, start := 85421, stop := 85434 ), rec( content := " by reve\ rsing the orientation of every edge specified by\n ", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dges", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "A", next := 85508, root := ~, start := 85496, stop := 85507 ), rec( content := ". If onl\ y one edge is to be reversed, then\n ", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphReverseEdge", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "C", next := 85580, root := ~, start := 85555, stop := 85579 ), rec( content := " can be \ used instead. In this case, the second\n argument should just be a single v\ ertex-pair, or the second and third\n arguments should be the source and ra\ nge of an edge respectively. ", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 26, 8 ], mathmode := "Text", name := "P", next := 85775, root := ~, start := 85771, stop := 85774 ), rec( content := "\n\n \ Note that even though ", count := [ 3, 3, 26, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 26, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 26, 8 ], mathmode := "Text", name := "A", next := 85817, root := ~, start := 85803, stop := 85816 ), rec( content := " cannot \ have multiple edges, the\n output may have multiple edges. ", count := [ 3, 3, 26, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "P", next := 85890, root := ~, start := 85886, stop := 85889 ), rec( content := "\n\n \ If ", count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "A", next := 85913, root := ~, start := 85899, stop := 85912 ), rec( content := " belongs\ to ", count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "Ref", next := 85955, root := ~, start := 85925, stop := 85954 ), rec( content := ", then t\ he edges\n are reversed in ", count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "A", next := 86006, root := ~, start := 85992, stop := 86005 ), rec( content := ". If ", count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "A", next := 86025, root := ~, start := 86011, stop := 86024 ), rec( content := " belongs\ to ", count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "Ref", next := 86075, root := ~, start := 86037, stop := 86074 ), rec( content := ", an imm\ utable copy of ", count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "A", next := 86112, root := ~, start := 86098, stop := 86111 ), rec( content := " with th\ e\n specified edges reversed is returned.", count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 26, 10 ], mathmode := "Text", name := "P", next := 86167, root := ~, start := 86163, stop := 86166 ), rec( content := "\n ", count := [ 3, 3, 26, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := DigraphFromDiSparse6String(\".Tg?i@s?t_e?_qEsC\");\n\ngap> DigraphEdges(D);\n[ [ 1, 2 ], [ 1, 7 ], [\ 1, 8 ], [ 5, 21 ], [ 7, 19 ], [ 9, 1 ], \n [ 11, 2 ], [ 21, 1 ] ]\ngap> new \ := DigraphReverseEdge(D, [7, 19]);\n\ngap> DigraphEdges(new);\n[ [ 1, 2 ], [ 1, 7 ], [ 1, 8 ], [ 5, 21 ], [ 9, \ 1 ], [ 11, 2 ], \n [ 19, 7 ], [ 21, 1 ] ]\ngap> D2 := DigraphMutableCopy(new)\ ;;\ngap> new := DigraphReverseEdges(D2, [[19, 7]]);;\ngap> D2 = new;\ntrue\nga\ p> D = new;\ntrue\n", count := [ 3, 3, 26, 11 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 26, 11 ], mathmode := "Text", name := "Example", next := 86750, root := ~, start := 86172, stop := 86749 ), rec( content := "\n ", count := [ 3, 3, 26, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "Description", next := 86767, root := ~, start := 85104, stop := 86766 ) ], count := [ 3, 3, 26, 1 ], mathmode := "Text", name := "ManSection", next := 86781, root := ~, start := 84754, stop := 86780 ), rec( content := "\n\n ", count := [ 3, 3, 26, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "D1, D2, ...", Label := "for an\n ar\ bitrary number of digraphs", Name := "DigraphDisjointUnion" ), content := 0, count := [ 3, 3, 27, 2 ], mathmode := "Text", name := "Func", next := 86903, root := ~, start := 86802, stop := 86902 ), rec( attributes := rec( Arg := "list", Label := "for a list of \ digraphs", Name := "DigraphDisjointUnion" ), content := 0, count := [ 3, 3, 27, 4 ], mathmode := "Text", name := "Func", next := 86983, root := ~, start := 86906, stop := 86982 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "Returns", next := 87015, root := ~, start := 86986, stop := 87014 ), rec( attributes := rec( ), content := [ rec( content := "\n In \ the first form, if ", count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 1", count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "A", next := 87067, root := ~, start := 87058, stop := 87066 ), rec( content := ", ", count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 2", count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "A", next := 87078, root := ~, start := 87069, stop := 87077 ), rec( content := ", etc. a\ re digraphs, then\n ", count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphDisjointUnion", count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "C", next := 87135, root := ~, start := 87108, stop := 87134 ), rec( content := " returns\ their disjoint union.\n\n In the second form, if ", count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "A", next := 87205, root := ~, start := 87194, stop := 87204 ), rec( content := " is a no\ n-empty list of digraphs, then\n ", count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphDisjointUnion", count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "C", next := 87275, root := ~, start := 87248, stop := 87274 ), rec( content := " returns\ the disjoint union of the digraphs\n contained in the list. ", count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 27, 6 ], mathmode := "Text", name := "P", next := 87351, root := ~, start := 87347, stop := 87350 ), rec( content := "\n\n \ For a disjoint union of digraphs, the vertex set is the disjoint union of\n \ the vertex sets, and the edge list is the disjoint union of the edge lists.\n\ ", count := [ 3, 3, 27, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "P", next := 87519, root := ~, start := 87515, stop := 87518 ), rec( content := "\n\n \ More specifically, for a collection of digraphs ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 1", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "A", next := 87582, root := ~, start := 87573, stop := 87581 ), rec( content := ", ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 2", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "A", next := 87593, root := ~, start := 87584, stop := 87592 ), rec( content := ",\n " , count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ ..", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "C", next := 87609, root := ~, start := 87599, stop := 87608 ), rec( content := ", the di\ sjoint union with have\n ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphNrVertices(", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "C", next := 87669, root := ~, start := 87644, stop := 87668 ), rec( attributes := rec( ), content := [ rec( content := "D\ 1", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "A", next := 87678, root := ~, start := 87669, stop := 87677 ), rec( attributes := rec( ), content := [ rec( content := ")\ ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "C", next := 87686, root := ~, start := 87678, stop := 87685 ), rec( content := " ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "+\ ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "C", next := 87695, root := ~, start := 87687, stop := 87694 ), rec( content := "\n ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphNrVertices(", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "C", next := 87725, root := ~, start := 87700, stop := 87724 ), rec( attributes := rec( ), content := [ rec( content := "D\ 2", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "A", next := 87734, root := ~, start := 87725, stop := 87733 ), rec( attributes := rec( ), content := [ rec( content := ")\ ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "C", next := 87742, root := ~, start := 87734, stop := 87741 ), rec( content := " ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "+\ ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "C", next := 87751, root := ~, start := 87743, stop := 87750 ), rec( content := " ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ ..", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "C", next := 87762, root := ~, start := 87752, stop := 87761 ), rec( content := " vertice\ s.\n The edges of ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 1", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "A", next := 87799, root := ~, start := 87790, stop := 87798 ), rec( content := " will re\ main unchanged, whilst the edges of the\n ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "C", next := 87859, root := ~, start := 87851, stop := 87858 ), rec( content := "th digra\ ph, ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "A", next := 87879, root := ~, start := 87871, stop := 87878 ), rec( attributes := rec( ), content := [ rec( content := "[\ i]", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "C", next := 87889, root := ~, start := 87879, stop := 87888 ), rec( content := ", will b\ e changed so that they\n belong to the vertices of the disjoint union corre\ sponding to\n ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "A", next := 87998, root := ~, start := 87990, stop := 87997 ), rec( attributes := rec( ), content := [ rec( content := "[\ i]", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "C", next := 88008, root := ~, start := 87998, stop := 88007 ), rec( content := ". In pa\ rticular, the edges of ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "A", next := 88047, root := ~, start := 88039, stop := 88046 ), rec( attributes := rec( ), content := [ rec( content := "[\ i]", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "C", next := 88057, root := ~, start := 88047, stop := 88056 ), rec( content := " will\n \ have their source and range increased by\n ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphNrVertices(", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "C", next := 88137, root := ~, start := 88112, stop := 88136 ), rec( attributes := rec( ), content := [ rec( content := "D\ 1", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "A", next := 88146, root := ~, start := 88137, stop := 88145 ), rec( attributes := rec( ), content := [ rec( content := ")\ ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "C", next := 88154, root := ~, start := 88146, stop := 88153 ), rec( content := " ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "+\ ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "C", next := 88163, root := ~, start := 88155, stop := 88162 ), rec( content := " ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ ..", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "C", next := 88174, root := ~, start := 88164, stop := 88173 ), rec( content := " ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "+\ ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "C", next := 88183, root := ~, start := 88175, stop := 88182 ), rec( content := "\n ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphNrVertices(", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "C", next := 88213, root := ~, start := 88188, stop := 88212 ), rec( attributes := rec( ), content := [ rec( content := "D\ ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "A", next := 88221, root := ~, start := 88213, stop := 88220 ), rec( attributes := rec( ), content := [ rec( content := "[\ i-1])", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "C", next := 88234, root := ~, start := 88221, stop := 88233 ), rec( content := ".\n\n \ ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 27, 8 ], mathmode := "Text", name := "P", next := 88245, root := ~, start := 88241, stop := 88244 ), rec( content := "\n\n \ Note that previously set ", count := [ 3, 3, 27, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ VertexLabels" ), content := 0, count := [ 3, 3, 27, 8 ], mathmode := "Text", name := "Ref", next := 88309, root := ~, start := 88276, stop := 88308 ), rec( content := " will be\ lost.", count := [ 3, 3, 27, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "P", next := 88327, root := ~, start := 88323, stop := 88326 ), rec( content := "\n\n \ If the first digraph ", count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 1", count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "A", next := 88363, root := ~, start := 88354, stop := 88362 ), rec( content := " [", count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist[1]", count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "A", next := 88379, root := ~, start := 88365, stop := 88378 ), rec( content := "] belong\ s to ", count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "Ref", next := 88426, root := ~, start := 88392, stop := 88425 ), rec( content := ", then " , count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 1", count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "A", next := 88442, root := ~, start := 88433, stop := 88441 ), rec( content := " [", count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist[1]", count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "A", next := 88458, root := ~, start := 88444, stop := 88457 ), rec( content := "] is mod\ ified in\n place to contain the appropriate vertices and edges. If ", count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "A", next := 88549, root := ~, start := 88535, stop := 88548 ), rec( content := " belongs\ \n to ", count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "Ref", next := 88597, root := ~, start := 88565, stop := 88596 ), rec( content := ", a new \ immutable digraph containing the\n appropriate vertices and edges is return\ ed.\n", count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D1 := CycleDigraph(3);\n\ngap> \ OutNeighbours(D1);\n[ [ 2 ], [ 3 ], [ 1 ] ]\ngap> D2 := CompleteDigraph(3);\n<\ immutable complete digraph with 3 vertices>\ngap> OutNeighbours(D2);\n[ [ 2, 3\ ], [ 1, 3 ], [ 1, 2 ] ]\ngap> union := DigraphDisjointUnion(D1, D2);\n\ngap> OutNeighbours(union);\n[ [ 2 ], [ \ 3 ], [ 1 ], [ 5, 6 ], [ 4, 6 ], [ 4, 5 ] ]\n", count := [ 3, 3, 27, 10 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 27, 10 ], mathmode := "Text", name := "Example", next := 89139, root := ~, start := 88686, stop := 89138 ), rec( content := "\n ", count := [ 3, 3, 27, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "Description", next := 89156, root := ~, start := 87018, stop := 89155 ) ], count := [ 3, 3, 27, 1 ], mathmode := "Text", name := "ManSection", next := 89170, root := ~, start := 86787, stop := 89169 ), rec( content := "\n\n ", count := [ 3, 3, 27, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "D1, D2, ...", Label := "for a positive\ number of digraphs", Name := "DigraphEdgeUnion" ), content := 0, count := [ 3, 3, 28, 2 ], mathmode := "Text", name := "Func", next := 89286, root := ~, start := 89191, stop := 89285 ), rec( attributes := rec( Arg := "list", Label := "for a list of \ digraphs", Name := "DigraphEdgeUnion" ), content := 0, count := [ 3, 3, 28, 4 ], mathmode := "Text", name := "Func", next := 89362, root := ~, start := 89289, stop := 89361 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "Returns", next := 89394, root := ~, start := 89365, stop := 89393 ), rec( attributes := rec( ), content := [ rec( content := "\n In \ the first form, if ", count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 1", count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "A", next := 89446, root := ~, start := 89437, stop := 89445 ), rec( content := ", ", count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 2", count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "A", next := 89457, root := ~, start := 89448, stop := 89456 ), rec( content := ", etc. a\ re digraphs, then\n ", count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphEdgeUnion", count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "C", next := 89510, root := ~, start := 89487, stop := 89509 ), rec( content := " returns\ their edge union.\n\n In the second form, if ", count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "A", next := 89576, root := ~, start := 89565, stop := 89575 ), rec( content := " is a no\ n-empty list of digraphs, then\n ", count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphEdgeUnion", count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "C", next := 89642, root := ~, start := 89619, stop := 89641 ), rec( content := " returns\ the edge union of the digraphs contained\n in the list. ", count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 28, 6 ], mathmode := "Text", name := "P", next := 89714, root := ~, start := 89710, stop := 89713 ), rec( content := "\n\n \ The vertex set of the edge union of a collection of digraphs is the\n ", count := [ 3, 3, 28, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ nion", count := [ 3, 3, 28, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 28, 6 ], mathmode := "Text", name := "E", next := 89804, root := ~, start := 89792, stop := 89803 ), rec( content := " of the \ vertex sets, whilst the edge list of the edge union is\n the ", count := [ 3, 3, 28, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ oncatenation", count := [ 3, 3, 28, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 28, 6 ], mathmode := "Text", name := "E", next := 89895, root := ~, start := 89875, stop := 89894 ), rec( content := " of the \ edge lists. The number of vertices of the\n edge union is equal to the ", count := [ 3, 3, 28, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ aximum", count := [ 3, 3, 28, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 28, 6 ], mathmode := "Text", name := "E", next := 89991, root := ~, start := 89977, stop := 89990 ), rec( content := " number \ of vertices of one of the\n digraphs, whilst the number of edges of the edg\ e union will equal the\n ", count := [ 3, 3, 28, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ um", count := [ 3, 3, 28, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 28, 6 ], mathmode := "Text", name := "E", next := 90113, root := ~, start := 90103, stop := 90112 ), rec( content := " of the \ number of edges of each digraph. ", count := [ 3, 3, 28, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 28, 7 ], mathmode := "Text", name := "P", next := 90158, root := ~, start := 90154, stop := 90157 ), rec( content := "\n\n \ Note that previously set ", count := [ 3, 3, 28, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ VertexLabels" ), content := 0, count := [ 3, 3, 28, 7 ], mathmode := "Text", name := "Ref", next := 90222, root := ~, start := 90189, stop := 90221 ), rec( content := " will be\ lost.\n ", count := [ 3, 3, 28, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "P", next := 90245, root := ~, start := 90241, stop := 90244 ), rec( content := "\n\n \ If the first digraph ", count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 1", count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "A", next := 90281, root := ~, start := 90272, stop := 90280 ), rec( content := " [", count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist[1]", count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "A", next := 90297, root := ~, start := 90283, stop := 90296 ), rec( content := "] belong\ s to ", count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "Ref", next := 90344, root := ~, start := 90310, stop := 90343 ), rec( content := ", then " , count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 1", count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "A", next := 90360, root := ~, start := 90351, stop := 90359 ), rec( content := " [", count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist[1]", count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "A", next := 90376, root := ~, start := 90362, stop := 90375 ), rec( content := "] is mod\ ified in\n place to contain the appropriate vertices and edges. If ", count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "A", next := 90467, root := ~, start := 90453, stop := 90466 ), rec( content := " belongs\ \n to ", count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "Ref", next := 90515, root := ~, start := 90483, stop := 90514 ), rec( content := ", a new \ immutable digraph containing the\n appropriate vertices and edges is return\ ed.\n", count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CycleDigraph(10);\n\ngap>\ DigraphEdgeUnion(D, D);\n\ \ngap> D1 := Digraph([[2], [1]]);\n\ngap> D2 := Digraph([[2, 3], [2], [1]]);\n\ngap> union := DigraphEdgeUnion(D1, D2);\n\ngap> OutNeighbours(union);\n[ [ 2, 2, 3 ], [ 1, 2 ],\ [ 1 ] ]\ngap> union = DigraphByEdges(\n> Concatenation(DigraphEdges(D1), Digr\ aphEdges(D2)));\ntrue\n", count := [ 3, 3, 28, 9 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 28, 9 ], mathmode := "Text", name := "Example", next := 91188, root := ~, start := 90604, stop := 91187 ), rec( content := "\n ", count := [ 3, 3, 28, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "Description", next := 91205, root := ~, start := 89397, stop := 91204 ) ], count := [ 3, 3, 28, 1 ], mathmode := "Text", name := "ManSection", next := 91219, root := ~, start := 89176, stop := 91218 ), rec( content := "\n\n ", count := [ 3, 3, 28, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "D1, D2, ...", Label := "for a positive\ number of digraphs", Name := "DigraphJoin" ), content := 0, count := [ 3, 3, 29, 2 ], mathmode := "Text", name := "Func", next := 91330, root := ~, start := 91240, stop := 91329 ), rec( attributes := rec( Arg := "list", Label := "for a list of \ digraphs", Name := "DigraphJoin" ), content := 0, count := [ 3, 3, 29, 4 ], mathmode := "Text", name := "Func", next := 91401, root := ~, start := 91333, stop := 91400 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "Returns", next := 91433, root := ~, start := 91404, stop := 91432 ), rec( attributes := rec( ), content := [ rec( content := "\n In \ the first form, if ", count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 1", count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "A", next := 91485, root := ~, start := 91476, stop := 91484 ), rec( content := ", ", count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 2", count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "A", next := 91496, root := ~, start := 91487, stop := 91495 ), rec( content := ", etc. a\ re digraphs, then\n ", count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphJoin", count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "C", next := 91544, root := ~, start := 91526, stop := 91543 ), rec( content := " returns\ their join.\n\n In the second form, if ", count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "A", next := 91604, root := ~, start := 91593, stop := 91603 ), rec( content := " is a no\ n-empty list of digraphs,\n then ", count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphJoin", count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "C", next := 91665, root := ~, start := 91647, stop := 91664 ), rec( content := " returns\ the join of the digraphs contained in the\n list. ", count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "P", next := 91730, root := ~, start := 91726, stop := 91729 ), rec( content := "\n\n \ The join of a collection of digraphs ", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 1", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "A", next := 91782, root := ~, start := 91773, stop := 91781 ), rec( content := ", ", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 2", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "A", next := 91793, root := ~, start := 91784, stop := 91792 ), rec( content := ", ", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ ..", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "C", next := 91805, root := ~, start := 91795, stop := 91804 ), rec( content := " is\n \ formed by first taking the ", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ DisjointUnion", Label := "for a list of digraphs" ), content := 0, count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "Ref", next := 91911, root := ~, start := 91840, stop := 91910 ), rec( content := " of the \ collection.\n\n In the disjoint union, if ", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ \\neq j", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "M", next := 91977, root := ~, start := 91962, stop := 91976 ), rec( content := " then th\ ere are no edges between\n vertices corresponding to digraphs ", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ ", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "A", next := 92057, root := ~, start := 92049, stop := 92056 ), rec( attributes := rec( ), content := [ rec( content := "[\ i]", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "C", next := 92067, root := ~, start := 92057, stop := 92066 ), rec( content := " and\n \ ", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ ", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "A", next := 92084, root := ~, start := 92076, stop := 92083 ), rec( attributes := rec( ), content := [ rec( content := "[\ j]", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "C", next := 92094, root := ~, start := 92084, stop := 92093 ), rec( content := " in the \ collection; the join is created by including\n all such edges.", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 29, 7 ], mathmode := "Text", name := "P", next := 92170, root := ~, start := 92166, stop := 92169 ), rec( content := "\n\n \ For example, the join of two empty digraphs is a complete bipartite\n digra\ ph.", count := [ 3, 3, 29, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 29, 8 ], mathmode := "Text", name := "P", next := 92260, root := ~, start := 92256, stop := 92259 ), rec( content := "\n\n \ Note that previously set ", count := [ 3, 3, 29, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ VertexLabels" ), content := 0, count := [ 3, 3, 29, 8 ], mathmode := "Text", name := "Ref", next := 92324, root := ~, start := 92291, stop := 92323 ), rec( content := " will be\ lost.\n ", count := [ 3, 3, 29, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "P", next := 92347, root := ~, start := 92343, stop := 92346 ), rec( content := "\n\n \ If the first digraph ", count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 1", count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "A", next := 92383, root := ~, start := 92374, stop := 92382 ), rec( content := " [", count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist[1]", count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "A", next := 92399, root := ~, start := 92385, stop := 92398 ), rec( content := "] belong\ s to ", count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "Ref", next := 92446, root := ~, start := 92412, stop := 92445 ), rec( content := ", then " , count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 1", count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "A", next := 92462, root := ~, start := 92453, stop := 92461 ), rec( content := " [", count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist[1]", count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "A", next := 92478, root := ~, start := 92464, stop := 92477 ), rec( content := "] is mod\ ified in\n place to contain the appropriate vertices and edges. If ", count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "A", next := 92569, root := ~, start := 92555, stop := 92568 ), rec( content := " belongs\ \n to ", count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "Ref", next := 92617, root := ~, start := 92585, stop := 92616 ), rec( content := ", a new \ immutable digraph containing the\n appropriate vertices and edges is return\ ed.\n", count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CompleteDigraph(3);\n\n\ gap> IsCompleteDigraph(DigraphJoin(D, D));\ntrue\ngap> D2 := CycleDigraph(3);\ \n\ngap> DigraphJoin(D, D2);\n\n", count := [ 3, 3, 29, 10 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 29, 10 ], mathmode := "Text", name := "Example", next := 93002, root := ~, start := 92706, stop := 93001 ), rec( content := "\n ", count := [ 3, 3, 29, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "Description", next := 93019, root := ~, start := 91436, stop := 93018 ) ], count := [ 3, 3, 29, 1 ], mathmode := "Text", name := "ManSection", next := 93033, root := ~, start := 91225, stop := 93032 ), rec( content := "\n\n ", count := [ 3, 3, 29, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "gr1, gr2, ...", Label := "for a positive\ number of digraphs", Name := "DigraphCartesianProduct" ), content := 0, count := [ 3, 3, 30, 2 ], mathmode := "Text", name := "Func", next := 93158, root := ~, start := 93054, stop := 93157 ), rec( attributes := rec( Arg := "list", Label := "for a list of \ digraphs", Name := "DigraphCartesianProduct" ), content := 0, count := [ 3, 3, 30, 4 ], mathmode := "Text", name := "Func", next := 93245, root := ~, start := 93161, stop := 93244 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 30, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 5 ], mathmode := "Text", name := "Returns", next := 93277, root := ~, start := 93248, stop := 93276 ), rec( attributes := rec( ), content := [ rec( content := "\n In \ the first form, if ", count := [ 3, 3, 30, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ r1", count := [ 3, 3, 30, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 5 ], mathmode := "Text", name := "A", next := 93330, root := ~, start := 93320, stop := 93329 ), rec( content := ", ", count := [ 3, 3, 30, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ r2", count := [ 3, 3, 30, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 5 ], mathmode := "Text", name := "A", next := 93342, root := ~, start := 93332, stop := 93341 ), rec( content := ", etc. a\ re digraphs, then\n ", count := [ 3, 3, 30, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphCartesianProduct", count := [ 3, 3, 30, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 30, 5 ], mathmode := "Text", name := "C", next := 93402, root := ~, start := 93372, stop := 93401 ), rec( content := " returns\ a digraph isomorphic to their\n Cartesian product.\n ", count := [ 3, 3, 30, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 30, 6 ], mathmode := "Text", name := "P", next := 93472, root := ~, start := 93468, stop := 93471 ), rec( content := "\n\n \ In the second form, if ", count := [ 3, 3, 30, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 3, 3, 30, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 6 ], mathmode := "Text", name := "A", next := 93512, root := ~, start := 93501, stop := 93511 ), rec( content := " is a no\ n-empty list of digraphs,\n then ", count := [ 3, 3, 30, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphCartesianProduct", count := [ 3, 3, 30, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 30, 6 ], mathmode := "Text", name := "C", next := 93585, root := ~, start := 93555, stop := 93584 ), rec( content := " returns\ a digraph isomorphic to the \n Cartesian product of the digraphs contained\ in the list.\n ", count := [ 3, 3, 30, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "P", next := 93692, root := ~, start := 93688, stop := 93691 ), rec( content := "\n \n \ Mathematically, the Cartesian product of two digraphs ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "C", next := 93761, root := ~, start := 93753, stop := 93760 ), rec( content := ", ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "H\ ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "C", next := 93771, root := ~, start := 93763, stop := 93770 ), rec( content := "\n is\ a digraph with vertex set ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "C\ artesian(DigraphVertices(G),\n DigraphVertices(H))", count := [ 3, 3, 30, 7 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "C", next := 93865, root := ~, start := 93805, stop := 93864 ), rec( content := " such th\ at there is an edge from ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ u, u']", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "C", next := 93912, root := ~, start := 93898, stop := 93911 ), rec( content := " to\n \ ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ v, v']", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "C", next := 93934, root := ~, start := 93920, stop := 93933 ), rec( content := " iff ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := " \ u = v ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "C", next := 93953, root := ~, start := 93939, stop := 93952 ), rec( content := " and the\ re is an edge from ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ '", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "C", next := 93989, root := ~, start := 93980, stop := 93988 ), rec( content := " to\n \ ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ '", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "C", next := 94006, root := ~, start := 93997, stop := 94005 ), rec( content := " in ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "H\ ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "C", next := 94018, root := ~, start := 94010, stop := 94017 ), rec( content := " or ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := " \ u' = v'", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "C", next := 94037, root := ~, start := 94022, stop := 94036 ), rec( content := " and the\ re is an edge from\n ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "C", next := 94076, root := ~, start := 94068, stop := 94075 ), rec( content := " to ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "C", next := 94088, root := ~, start := 94080, stop := 94087 ), rec( content := " in ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "C", next := 94100, root := ~, start := 94092, stop := 94099 ), rec( content := ".\n " , count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "P", next := 94110, root := ~, start := 94106, stop := 94109 ), rec( content := "\n\n \ Due to technical reasons, the digraph ", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ ", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "C", next := 94162, root := ~, start := 94154, stop := 94161 ), rec( content := " returne\ d by\n ", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphCartesianProduct", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "C", next := 94209, root := ~, start := 94179, stop := 94208 ), rec( content := " has ver\ tex set\n ", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ 1 .. DigraphNrVertices(G)*DigraphNrVertices(H)]", count := [ 3, 3, 30, 8 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "C", next := 94285, root := ~, start := 94229, stop := 94284 ), rec( content := " instead\ , and the\n exact\n method of encoding pairs of vertices into integers \ is implementation\n specific. The original vertex pair can be somewhat reg\ ained by using\n ", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ CartesianProductProjections" ), content := 0, count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "Ref", next := 94513, root := ~, start := 94465, stop := 94512 ), rec( content := ". In add\ ition,\n ", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ VertexLabels" ), content := 0, count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "Ref", next := 94565, root := ~, start := 94532, stop := 94564 ), rec( content := " are pre\ served: if vertex pair\n ", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ u,u']", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "C", next := 94613, root := ~, start := 94600, stop := 94612 ), rec( content := " was enc\ oded as ", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "C", next := 94637, root := ~, start := 94629, stop := 94636 ), rec( content := " then th\ e vertex label of ", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "C", next := 94671, root := ~, start := 94663, stop := 94670 ), rec( content := "\n wi\ ll be the pair of vertex labels of ", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "C", next := 94721, root := ~, start := 94713, stop := 94720 ), rec( content := " and ", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ '", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "C", next := 94735, root := ~, start := 94726, stop := 94734 ), rec( content := " i.e.\n \ ", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphVertexLabel(D,i) = [DigraphVertexLabel(G,u),\n DigraphVertexLabel(H\ ,u')]", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "C", next := 94835, root := ~, start := 94745, stop := 94834 ), rec( content := ".\n " , count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 30, 9 ], mathmode := "Text", name := "P", next := 94845, root := ~, start := 94841, stop := 94844 ), rec( content := "\n\n \ As the Cartesian product is associative, the Cartesian product of a collection\ \n of digraphs ", count := [ 3, 3, 30, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ r1", count := [ 3, 3, 30, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 9 ], mathmode := "Text", name := "A", next := 94957, root := ~, start := 94947, stop := 94956 ), rec( content := ", ", count := [ 3, 3, 30, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ r2", count := [ 3, 3, 30, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 9 ], mathmode := "Text", name := "A", next := 94969, root := ~, start := 94959, stop := 94968 ), rec( content := ", ", count := [ 3, 3, 30, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ ..", count := [ 3, 3, 30, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 9 ], mathmode := "Text", name := "C", next := 94981, root := ~, start := 94971, stop := 94980 ), rec( content := " is comp\ uted in the obvious \n fashion. \n ", count := [ 3, 3, 30, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 30, 10 ], mathmode := "Text", name := "P", next := 95032, root := ~, start := 95028, stop := 95031 ), rec( content := "\n\n", count := [ 3, 3, 30, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := ChainDigraph(4);\n\ngap> \ gr2 := CycleDigraph(3);\n\ngap> gr3 :\ = DigraphCartesianProduct(gr, gr2);\n\ngap> IsIsomorphicDigraph(gr3, \n> Digraph([[2, 5], [3, 6], [4, 7], [8],\ \n> [6, 9], [7, 10], [8, 11], [12],\n> [10, 1], [11, 2], [1\ 2, 3], [4]]));\ntrue\n", count := [ 3, 3, 30, 11 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 11 ], mathmode := "Text", name := "Example", next := 95466, root := ~, start := 95034, stop := 95465 ), rec( content := "\n ", count := [ 3, 3, 30, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 5 ], mathmode := "Text", name := "Description", next := 95483, root := ~, start := 93280, stop := 95482 ) ], count := [ 3, 3, 30, 1 ], mathmode := "Text", name := "ManSection", next := 95497, root := ~, start := 93039, stop := 95496 ), rec( content := "\n\n ", count := [ 3, 3, 30, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "gr1, gr2, ...", Label := "for a positive\ number of digraphs", Name := "DigraphDirectProduct" ), content := 0, count := [ 3, 3, 31, 2 ], mathmode := "Text", name := "Func", next := 95619, root := ~, start := 95518, stop := 95618 ), rec( attributes := rec( Arg := "list", Label := "for a list of \ digraphs", Name := "DigraphDirectProduct" ), content := 0, count := [ 3, 3, 31, 4 ], mathmode := "Text", name := "Func", next := 95703, root := ~, start := 95622, stop := 95702 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 5 ], mathmode := "Text", name := "Returns", next := 95735, root := ~, start := 95706, stop := 95734 ), rec( attributes := rec( ), content := [ rec( content := "\n In \ the first form, if ", count := [ 3, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ r1", count := [ 3, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 5 ], mathmode := "Text", name := "A", next := 95788, root := ~, start := 95778, stop := 95787 ), rec( content := ", ", count := [ 3, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ r2", count := [ 3, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 5 ], mathmode := "Text", name := "A", next := 95800, root := ~, start := 95790, stop := 95799 ), rec( content := ", etc. a\ re digraphs, then\n ", count := [ 3, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphDirectProduct", count := [ 3, 3, 31, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 31, 5 ], mathmode := "Text", name := "C", next := 95857, root := ~, start := 95830, stop := 95856 ), rec( content := " returns\ a digraph isomorphic to their direct\n product.\n ", count := [ 3, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 31, 6 ], mathmode := "Text", name := "P", next := 95924, root := ~, start := 95920, stop := 95923 ), rec( content := "\n\n \ In the second form, if ", count := [ 3, 3, 31, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 3, 3, 31, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 6 ], mathmode := "Text", name := "A", next := 95964, root := ~, start := 95953, stop := 95963 ), rec( content := " is a no\ n-empty list of digraphs, then\n ", count := [ 3, 3, 31, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphDirectProduct", count := [ 3, 3, 31, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 31, 6 ], mathmode := "Text", name := "C", next := 96034, root := ~, start := 96007, stop := 96033 ), rec( content := " returns\ a digraph isomorphic to the direct\n product of the digraphs contained in \ the list.\n ", count := [ 3, 3, 31, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "P", next := 96137, root := ~, start := 96133, stop := 96136 ), rec( content := "\n\n \ Mathematically, the direct product of two digraphs ", count := [ 3, 3, 31, 7 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "C", next := 96202, root := ~, start := 96194, stop := 96201 ), rec( content := ", ", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "H\ ", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "C", next := 96212, root := ~, start := 96204, stop := 96211 ), rec( content := " is a\n \ digraph with vertex set ", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "C\ artesian(DigraphVertices(G),\n DigraphVertices(H))", count := [ 3, 3, 31, 7 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "C", next := 96306, root := ~, start := 96246, stop := 96305 ), rec( content := " such th\ at there is an edge from ", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ u, u']", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "C", next := 96353, root := ~, start := 96339, stop := 96352 ), rec( content := "\n to\ ", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ v, v']", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "C", next := 96375, root := ~, start := 96361, stop := 96374 ), rec( content := " iff the\ re is an edge from ", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "C", next := 96410, root := ~, start := 96402, stop := 96409 ), rec( content := " to ", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "C", next := 96422, root := ~, start := 96414, stop := 96421 ), rec( content := " in\n \ ", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "C", next := 96438, root := ~, start := 96430, stop := 96437 ), rec( content := " and an \ edge from ", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ '", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "C", next := 96465, root := ~, start := 96456, stop := 96464 ), rec( content := " to ", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ '", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "C", next := 96478, root := ~, start := 96469, stop := 96477 ), rec( content := " in ", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "H\ ", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "C", next := 96490, root := ~, start := 96482, stop := 96489 ), rec( content := ". \n \ ", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := 0, count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "P", next := 96501, root := ~, start := 96497, stop := 96500 ), rec( content := " \n\n \ Due to technical reasons, the digraph ", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ ", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "C", next := 96554, root := ~, start := 96546, stop := 96553 ), rec( content := " returne\ d by\n ", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphDirectProduct", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "C", next := 96598, root := ~, start := 96571, stop := 96597 ), rec( content := " has ver\ tex set\n ", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ 1 .. DigraphNrVertices(G)*DigraphNrVertices(H)]", count := [ 3, 3, 31, 8 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "C", next := 96674, root := ~, start := 96618, stop := 96673 ), rec( content := " instead\ , and the\n exact method of encoding pairs of vertices into integers is imp\ lementation\n specific. The original vertex pair can be somewhat regained \ by using\n ", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ DirectProductProjections" ), content := 0, count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "Ref", next := 96894, root := ~, start := 96849, stop := 96893 ), rec( content := ". In add\ ition\n ", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ VertexLabels" ), content := 0, count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "Ref", next := 96945, root := ~, start := 96912, stop := 96944 ), rec( content := " are pre\ served: if vertex pair\n ", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ u,u']", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "C", next := 96993, root := ~, start := 96980, stop := 96992 ), rec( content := " was enc\ oded as ", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "C", next := 97017, root := ~, start := 97009, stop := 97016 ), rec( content := " then th\ e vertex label of ", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "C", next := 97051, root := ~, start := 97043, stop := 97050 ), rec( content := "\n wi\ ll be the pair of vertex labels of ", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "C", next := 97101, root := ~, start := 97093, stop := 97100 ), rec( content := " and ", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ '", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "C", next := 97115, root := ~, start := 97106, stop := 97114 ), rec( content := " i.e.\n \ ", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphVertexLabel(D,i) = [DigraphVertexLabel(G,u),\n DigraphVertexLabel(H,u\ ')]", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "C", next := 97213, root := ~, start := 97125, stop := 97212 ), rec( content := ".\n " , count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 31, 9 ], mathmode := "Text", name := "P", next := 97223, root := ~, start := 97219, stop := 97222 ), rec( content := "\n\n \ As the direct product is associative, the direct product of a collection \n \ of digraphs ", count := [ 3, 3, 31, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ r1", count := [ 3, 3, 31, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 9 ], mathmode := "Text", name := "A", next := 97329, root := ~, start := 97319, stop := 97328 ), rec( content := ", ", count := [ 3, 3, 31, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ r2", count := [ 3, 3, 31, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 9 ], mathmode := "Text", name := "A", next := 97341, root := ~, start := 97331, stop := 97340 ), rec( content := ", ", count := [ 3, 3, 31, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ ..", count := [ 3, 3, 31, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 9 ], mathmode := "Text", name := "C", next := 97353, root := ~, start := 97343, stop := 97352 ), rec( content := " is comp\ uted in the obvious \n fashion. \n ", count := [ 3, 3, 31, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 31, 10 ], mathmode := "Text", name := "P", next := 97404, root := ~, start := 97400, stop := 97403 ), rec( content := "\n\n", count := [ 3, 3, 31, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := ChainDigraph(4);\n\ngap> \ gr2 := CycleDigraph(3);\n\ngap> gr3 :\ = DigraphDirectProduct(gr, gr2);\n\ngap> IsIsomorphicDigraph(gr3, \n> Digraph([[6], [7], [8], [], \n> \ [10], [11], [12], [],\n> [2], [3], [4], []]));\ntrue\n", count := [ 3, 3, 31, 11 ] , name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 31, 11 ], mathmode := "Text", name := "Example", next := 97801, root := ~, start := 97406, stop := 97800 ), rec( content := "\n ", count := [ 3, 3, 31, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 5 ], mathmode := "Text", name := "Description", next := 97818, root := ~, start := 95738, stop := 97817 ) ], count := [ 3, 3, 31, 1 ], mathmode := "Text", name := "ManSection", next := 97832, root := ~, start := 95503, stop := 97831 ), rec( content := "\n\n ", count := [ 3, 3, 31, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphCartesia\ nProductProjections" ), content := 0, count := [ 3, 3, 32, 2 ], mathmode := "Text", name := "Attr", next := 97916, root := ~, start := 97853, stop := 97915 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ transformations.", count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "Returns", next := 97964, root := ~, start := 97919, stop := 97963 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "A", next := 98002, root := ~, start := 97988, stop := 98001 ), rec( content := " is a Ca\ rtesian product digraph, \n ", count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph = DigraphCartesianProduct(gr_1, gr_2, ... )", count := [ 3, 3, 32, 3 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "C", next := 98098, root := ~, start := 98040, stop := 98097 ), rec( content := ", then\n\ ", count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphCartesianProductProjections", count := [ 3, 3, 32, 3 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "C", next := 98150, root := ~, start := 98109, stop := 98149 ), rec( content := " returns\ a list ", count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ roj", count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "C", next := 98177, root := ~, start := 98166, stop := 98176 ), rec( content := "\n su\ ch that ", count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ roj[i]", count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "C", next := 98206, root := ~, start := 98192, stop := 98205 ), rec( content := " is the \ projection onto the ", count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "C", next := 98242, root := ~, start := 98234, stop := 98241 ), rec( content := "-th\n \ coordinate of the product.\n ", count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "P", next := 98285, root := ~, start := 98281, stop := 98284 ), rec( content := "\n\n \ A projection is an idempotent endomorphism of ", count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "A", next := 98351, root := ~, start := 98337, stop := 98350 ), rec( content := ". If\n \ ", count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ r1, gr2, ...", count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "C", next := 98380, root := ~, start := 98360, stop := 98379 ), rec( content := " are all\ loopless digraphs, then the induced \n subdigraph of ", count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "A", next := 98458, root := ~, start := 98444, stop := 98457 ), rec( content := " on the \ image of ", count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ roj[i]", count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "C", next := 98489, root := ~, start := 98475, stop := 98488 ), rec( content := " is \n \ isomorphic to ", count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ r_i", count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "C", next := 98523, root := ~, start := 98512, stop := 98522 ), rec( content := ".\n " , count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 32, 5 ], mathmode := "Text", name := "P", next := 98533, root := ~, start := 98529, stop := 98532 ), rec( content := "\n\n \ Currently this attribute is only set upon creating an immutable \n digraph \ via ", count := [ 3, 3, 32, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphCartesianProduct", count := [ 3, 3, 32, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 32, 5 ], mathmode := "Text", name := "C", next := 98650, root := ~, start := 98620, stop := 98649 ), rec( content := " and the\ re is no way \n of calculating it for other digraphs.\n ", count := [ 3, 3, 32, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 32, 6 ], mathmode := "Text", name := "P", next := 98722, root := ~, start := 98718, stop := 98721 ), rec( content := "\n\n \ For more information see\n ", count := [ 3, 3, 32, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ CartesianProduct", Label := "for a list of digraphs" ), content := 0, count := [ 3, 3, 32, 6 ], mathmode := "Text", name := "Ref", next := 98825, root := ~, start := 98757, stop := 98824 ), rec( content := " \n\n \ ", count := [ 3, 3, 32, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := DigraphCartesianProduct(ChainDigraph(3), CycleDigraph(4),\n> Digrap\ h([[2], [2]]));;\ngap> HasDigraphCartesianProductProjections(D);\ntrue\ngap> p\ roj := DigraphCartesianProductProjections(D);; Length(proj);\n3\ngap> IsIdempo\ tent(proj[2]);\ntrue\ngap> RankOfTransformation(proj[3]);\n2\ngap> S := ImageS\ etOfTransformation(proj[2]);;\ngap> IsIsomorphicDigraph(CycleDigraph(4), Induc\ edSubdigraph(D, S));\ntrue\n", count := [ 3, 3, 32, 7 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 32, 7 ], mathmode := "Text", name := "Example", next := 99268, root := ~, start := 98832, stop := 99267 ), rec( content := "\n ", count := [ 3, 3, 32, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "Description", next := 99285, root := ~, start := 97967, stop := 99284 ) ], count := [ 3, 3, 32, 1 ], mathmode := "Text", name := "ManSection", next := 99299, root := ~, start := 97838, stop := 99298 ), rec( content := "\n\n ", count := [ 3, 3, 32, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphDirectPr\ oductProjections" ), content := 0, count := [ 3, 3, 33, 2 ], mathmode := "Text", name := "Attr", next := 99380, root := ~, start := 99320, stop := 99379 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ transformations.", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "Returns", next := 99428, root := ~, start := 99383, stop := 99427 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "A", next := 99466, root := ~, start := 99452, stop := 99465 ), rec( content := " is a di\ rect product digraph, \n ", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph = DigraphDirectProduct(gr_1, gr_2, ... )", count := [ 3, 3, 33, 3 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "C", next := 99556, root := ~, start := 99501, stop := 99555 ), rec( content := ", then\n\ ", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphDirectProductProjections", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "C", next := 99605, root := ~, start := 99567, stop := 99604 ), rec( content := " returns\ a list ", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ roj", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "C", next := 99632, root := ~, start := 99621, stop := 99631 ), rec( content := "\n su\ ch that ", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ roj[i]", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "C", next := 99661, root := ~, start := 99647, stop := 99660 ), rec( content := " is the \ projection onto the ", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "C", next := 99697, root := ~, start := 99689, stop := 99696 ), rec( content := "-th\n \ coordinate of the product.\n ", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "P", next := 99740, root := ~, start := 99736, stop := 99739 ), rec( content := "\n\n \ A projection is an idempotent endomorphism of ", count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "A", next := 99806, root := ~, start := 99792, stop := 99805 ), rec( content := ". If\n \ ", count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ r1, gr2, ...", count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "C", next := 99835, root := ~, start := 99815, stop := 99834 ), rec( content := " are all\ loopless digraphs, then the image \n of ", count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "A", next := 99900, root := ~, start := 99886, stop := 99899 ), rec( content := " under " , count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ roj[i]", count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "C", next := 99921, root := ~, start := 99907, stop := 99920 ), rec( content := " is isom\ orphic to ", count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ r_i", count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "C", next := 99950, root := ~, start := 99939, stop := 99949 ), rec( content := ".\n " , count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 33, 5 ], mathmode := "Text", name := "P", next := 99960, root := ~, start := 99956, stop := 99959 ), rec( content := "\n\n \ Currently this attribute is only set upon creating an immutable\n digraph v\ ia ", count := [ 3, 3, 33, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphDirectProduct", count := [ 3, 3, 33, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 33, 5 ], mathmode := "Text", name := "C", next := 100073, root := ~, start := 100046, stop := 100072 ), rec( content := " and the\ re is no way of \n calculating it for other digraphs.\n ", count := [ 3, 3, 33, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 33, 6 ], mathmode := "Text", name := "P", next := 100145, root := ~, start := 100141, stop := 100144 ), rec( content := "\n\n \ For more information, see\n ", count := [ 3, 3, 33, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ DirectProduct", Label := "for a list of digraphs" ), content := 0, count := [ 3, 3, 33, 6 ], mathmode := "Text", name := "Ref", next := 100246, root := ~, start := 100181, stop := 100245 ), rec( content := " \n\n \ ", count := [ 3, 3, 33, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := DigraphDirectProduct(ChainDigraph(3), CycleDigraph(4),\n> Digraph([\ [2], [2]]));;\ngap> HasDigraphDirectProductProjections(D);\ntrue\ngap> proj :=\ DigraphDirectProductProjections(D);; Length(proj);\n3\ngap> IsIdempotent(proj\ [2]);\ntrue\ngap> RankOfTransformation(proj[3]);\n2\ngap> P := DigraphRemoveAl\ lMultipleEdges(\n> ReducedDigraph(OnDigraphs(D, proj[2])));; \ngap> IsIsomorph\ icDigraph(CycleDigraph(4), P);\ntrue\n", count := [ 3, 3, 33, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 33, 7 ], mathmode := "Text", name := "Example", next := 100698, root := ~, start := 100253, stop := 100697 ), rec( content := "\n ", count := [ 3, 3, 33, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "Description", next := 100715, root := ~, start := 99431, stop := 100714 ) ], count := [ 3, 3, 33, 1 ], mathmode := "Text", name := "ManSection", next := 100729, root := ~, start := 99305, stop := 100728 ), rec( content := "\n\n ", count := [ 3, 3, 33, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "LineDigraph" ), content := 0, count := [ 3, 3, 34, 2 ], mathmode := "Text", name := "Oper", next := 100790, root := ~, start := 100750, stop := 100789 ), rec( attributes := rec( Arg := "digraph", Name := "EdgeDigraph" ), content := 0, count := [ 3, 3, 34, 4 ], mathmode := "Text", name := "Oper", next := 100833, root := ~, start := 100793, stop := 100832 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "Returns", next := 100865, root := ~, start := 100836, stop := 100864 ), rec( attributes := rec( ), content := [ rec( content := "\n Giv\ en a digraph ", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "A", next := 100916, root := ~, start := 100902, stop := 100915 ), rec( content := ", the op\ eration returns the digraph\n obtained by associating a vertex with each ed\ ge of ", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "A", next := 101021, root := ~, start := 101007, stop := 101020 ), rec( content := ", and\n \ creating an edge from a vertex ", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "K", next := 101070, root := ~, start := 101062, stop := 101069 ), rec( content := " to a ve\ rtex ", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "K", next := 101091, root := ~, start := 101083, stop := 101090 ), rec( content := " if and \ only\n if the terminal vertex of the edge associated with ", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "K", next := 101167, root := ~, start := 101159, stop := 101166 ), rec( content := " is the \ start\n vertex of the edge associated with ", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "K", next := 101228, root := ~, start := 101220, stop := 101227 ), rec( content := ".", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 34, 6 ], mathmode := "Text", name := "P", next := 101233, root := ~, start := 101229, stop := 101232 ), rec( content := "\n\n \ Note that the returned digraph is always a new immutable digraph, and the\n \ argument ", count := [ 3, 3, 34, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 34, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 34, 6 ], mathmode := "Text", name := "A", next := 101340, root := ~, start := 101326, stop := 101339 ), rec( content := " is neve\ r modified.\n ", count := [ 3, 3, 34, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> LineDigraph(CompleteDigraph(3));\n\ngap> LineDigraph(ChainDigraph(3));\n\n", count := [ 3, 3, 34, 7 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 34, 7 ], mathmode := "Text", name := "Example", next := 101559, root := ~, start := 101364, stop := 101558 ), rec( content := "\n ", count := [ 3, 3, 34, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "Description", next := 101576, root := ~, start := 100868, stop := 101575 ) ], count := [ 3, 3, 34, 1 ], mathmode := "Text", name := "ManSection", next := 101590, root := ~, start := 100735, stop := 101589 ), rec( content := "\n\n ", count := [ 3, 3, 34, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "LineUndirectedD\ igraph" ), content := 0, count := [ 3, 3, 35, 2 ], mathmode := "Text", name := "Oper", next := 101661, root := ~, start := 101611, stop := 101660 ), rec( attributes := rec( Arg := "digraph", Name := "EdgeUndirectedD\ igraph" ), content := 0, count := [ 3, 3, 35, 4 ], mathmode := "Text", name := "Oper", next := 101714, root := ~, start := 101664, stop := 101713 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 35, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 35, 5 ], mathmode := "Text", name := "Returns", next := 101746, root := ~, start := 101717, stop := 101745 ), rec( attributes := rec( ), content := [ rec( content := "\n Giv\ en a symmetric digraph ", count := [ 3, 3, 35, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 35, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 35, 5 ], mathmode := "Text", name := "A", next := 101807, root := ~, start := 101793, stop := 101806 ), rec( content := ", the op\ eration returns the\n symmetric digraph obtained by associating a vertex wi\ th each edge of\n ", count := [ 3, 3, 35, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 35, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 35, 5 ], mathmode := "Text", name := "A", next := 101926, root := ~, start := 101912, stop := 101925 ), rec( content := ", ignori\ ng directions and multiplicites, and adding an edge\n between two vertices \ if and only if the corresponding edges have a vertex in\n common.", count := [ 3, 3, 35, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 35, 6 ], mathmode := "Text", name := "P", next := 102082, root := ~, start := 102078, stop := 102081 ), rec( content := "\n\n \ Note that the returned digraph is always a new immutable digraph, and the\n \ argument ", count := [ 3, 3, 35, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 35, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 35, 6 ], mathmode := "Text", name := "A", next := 102189, root := ~, start := 102175, stop := 102188 ), rec( content := " is neve\ r modified.\n ", count := [ 3, 3, 35, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> LineUndirectedDigraph(CompleteDigraph(3));\n\ngap> LineUndirectedDigraph(DigraphSymmetricClosure(ChainDigr\ aph(3)));\n\n", count := [ 3, 3, 35, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 35, 7 ], mathmode := "Text", name := "Example", next := 102453, root := ~, start := 102213, stop := 102452 ), rec( content := "\n ", count := [ 3, 3, 35, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 35, 5 ], mathmode := "Text", name := "Description", next := 102470, root := ~, start := 101749, stop := 102469 ) ], count := [ 3, 3, 35, 1 ], mathmode := "Text", name := "ManSection", next := 102484, root := ~, start := 101596, stop := 102483 ), rec( content := "\n\n ", count := [ 3, 3, 35, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DoubleDigraph" ), content := 0, count := [ 3, 3, 36, 2 ], mathmode := "Text", name := "Oper", next := 102547, root := ~, start := 102505, stop := 102546 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "Returns", next := 102579, root := ~, start := 102550, stop := 102578 ), rec( attributes := rec( ), content := [ rec( content := "\n Let\ ", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "A", next := 102618, root := ~, start := 102604, stop := 102617 ), rec( content := " be a di\ graph with vertex set ", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "V\ ", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "C", next := 102656, root := ~, start := 102648, stop := 102655 ), rec( content := ". This f\ unction\n returns the double digraph of ", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "A", next := 102720, root := ~, start := 102706, stop := 102719 ), rec( content := ". The ve\ rtex set of the double\n digraph is the orginal vertex set together with a \ duplicate. The edges are\n ", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ u_1, v_2]", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "C", next := 102851, root := ~, start := 102834, stop := 102850 ), rec( content := " and ", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ u_2, v_1]", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "C", next := 102873, root := ~, start := 102856, stop := 102872 ), rec( content := " if and \ only if ", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ u, v]", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "C", next := 102902, root := ~, start := 102889, stop := 102901 ), rec( content := " is an\n\ edge in ", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "A", next := 102935, root := ~, start := 102921, stop := 102934 ), rec( content := ", togeth\ er with the original edges and their\n duplicates.", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 36, 4 ], mathmode := "Text", name := "P", next := 102999, root := ~, start := 102995, stop := 102998 ), rec( content := "\n\n \ If ", count := [ 3, 3, 36, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 36, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 36, 4 ], mathmode := "Text", name := "A", next := 103022, root := ~, start := 103008, stop := 103021 ), rec( content := " is muta\ ble, then ", count := [ 3, 3, 36, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 36, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 36, 4 ], mathmode := "Text", name := "A", next := 103054, root := ~, start := 103040, stop := 103053 ), rec( content := " is modi\ fied in-place. If\n ", count := [ 3, 3, 36, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 36, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 36, 4 ], mathmode := "Text", name := "A", next := 103098, root := ~, start := 103084, stop := 103097 ), rec( content := " is immu\ table, then a new immutable digraph constructed as\n described above is ret\ urned.\n ", count := [ 3, 3, 36, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gamma := Digraph([[2], [3], [1]]);\n\ngap> DoubleDigraph(gamma);\n\n", count := [ 3, 3, 36, 5 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 36, 5 ], mathmode := "Text", name := "Example", next := 103384, root := ~, start := 103194, stop := 103383 ), rec( content := "\n ", count := [ 3, 3, 36, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "Description", next := 103401, root := ~, start := 102582, stop := 103400 ) ], count := [ 3, 3, 36, 1 ], mathmode := "Text", name := "ManSection", next := 103415, root := ~, start := 102490, stop := 103414 ), rec( content := "\n\n ", count := [ 3, 3, 36, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "BipartiteDouble\ Digraph" ), content := 0, count := [ 3, 3, 37, 2 ], mathmode := "Text", name := "Oper", next := 103487, root := ~, start := 103436, stop := 103486 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "Returns", next := 103519, root := ~, start := 103490, stop := 103518 ), rec( attributes := rec( ), content := [ rec( content := "\n Let\ ", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "A", next := 103558, root := ~, start := 103544, stop := 103557 ), rec( content := " be a di\ graph with vertex set ", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "V\ ", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "C", next := 103596, root := ~, start := 103588, stop := 103595 ), rec( content := ". This f\ unction\n returns the bipartite double digraph of ", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "A", next := 103670, root := ~, start := 103656, stop := 103669 ), rec( content := ". The ve\ rtex set of\n the double digraph is the original vertex set together with a\ duplicate. The\n edges are ", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ u_1, v_2]", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "C", next := 103802, root := ~, start := 103785, stop := 103801 ), rec( content := " and ", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ u_2, v_1]", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "C", next := 103824, root := ~, start := 103807, stop := 103823 ), rec( content := " if and \ only if ", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ u,\n v]", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "C", next := 103859, root := ~, start := 103840, stop := 103858 ), rec( content := " is an e\ dge in ", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "A", next := 103888, root := ~, start := 103874, stop := 103887 ), rec( content := ". The re\ sulting graph is bipartite,\n since the orignal edges are not included in t\ he resulting digraph.", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 37, 4 ], mathmode := "Text", name := "P", next := 103998, root := ~, start := 103994, stop := 103997 ), rec( content := "\n\n \ If ", count := [ 3, 3, 37, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 37, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 37, 4 ], mathmode := "Text", name := "A", next := 104021, root := ~, start := 104007, stop := 104020 ), rec( content := " is muta\ ble, then ", count := [ 3, 3, 37, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 37, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 37, 4 ], mathmode := "Text", name := "A", next := 104053, root := ~, start := 104039, stop := 104052 ), rec( content := " is modi\ fied in-place. If\n ", count := [ 3, 3, 37, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 37, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 37, 4 ], mathmode := "Text", name := "A", next := 104097, root := ~, start := 104083, stop := 104096 ), rec( content := " is immu\ table, then a new immutable digraph constructed as\n described above is ret\ urned.\n ", count := [ 3, 3, 37, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gamma := Digraph([[2], [3], [1]]);\n\ngap> BipartiteDoubleDigraph(gamma);\n\n", count := [ 3, 3, 37, 5 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 37, 5 ], mathmode := "Text", name := "Example", next := 104391, root := ~, start := 104193, stop := 104390 ), rec( content := "\n ", count := [ 3, 3, 37, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "Description", next := 104408, root := ~, start := 103522, stop := 104407 ) ], count := [ 3, 3, 37, 1 ], mathmode := "Text", name := "ManSection", next := 104422, root := ~, start := 103421, stop := 104421 ), rec( content := "\n\n ", count := [ 3, 3, 37, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphAddAllLo\ ops" ), content := 0, count := [ 3, 3, 38, 2 ], mathmode := "Text", name := "Oper", next := 104490, root := ~, start := 104443, stop := 104489 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphAddAllLo\ opsAttr" ), content := 0, count := [ 3, 3, 38, 4 ], mathmode := "Text", name := "Attr", next := 104544, root := ~, start := 104493, stop := 104543 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 38, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 38, 5 ], mathmode := "Text", name := "Returns", next := 104576, root := ~, start := 104547, stop := 104575 ), rec( attributes := rec( ), content := [ rec( content := "\n For\ a digraph ", count := [ 3, 3, 38, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 38, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 38, 5 ], mathmode := "Text", name := "A", next := 104625, root := ~, start := 104611, stop := 104624 ), rec( content := " this op\ eration returns a new digraph constructed\n from ", count := [ 3, 3, 38, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 38, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 38, 5 ], mathmode := "Text", name := "A", next := 104698, root := ~, start := 104684, stop := 104697 ), rec( content := ", such t\ hat a loop is added for every vertex which did not\n have a loop in ", count := [ 3, 3, 38, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 38, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 38, 5 ], mathmode := "Text", name := "A", next := 104790, root := ~, start := 104776, stop := 104789 ), rec( content := ".", count := [ 3, 3, 38, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 38, 6 ], mathmode := "Text", name := "P", next := 104795, root := ~, start := 104791, stop := 104794 ), rec( content := "\n\n \ If ", count := [ 3, 3, 38, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 38, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 38, 6 ], mathmode := "Text", name := "A", next := 104818, root := ~, start := 104804, stop := 104817 ), rec( content := " is immu\ table, then a new immutable digraph is returned.\n Otherwise, the loops are\ added to the loopless vertices of the mutable digraph\n ", count := [ 3, 3, 38, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 38, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 38, 6 ], mathmode := "Text", name := "A", next := 104976, root := ~, start := 104962, stop := 104975 ), rec( content := " in-plac\ e.\n ", count := [ 3, 3, 38, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := EmptyDigraph(13);\n\ngap>\ D := DigraphAddAllLoops(D);\n\ngap> OutNeighbours(D);\n[ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], \ [ 7 ], [ 8 ], [ 9 ], \n [ 10 ], [ 11 ], [ 12 ], [ 13 ] ]\ngap> D := Digraph([\ [1, 2, 3], [1, 3], [1]]);\n\ngap> \ D := DigraphAddAllLoops(D);\n\ngap> OutNeighbours(D);\n[ [ 1, 2, 3 ], [ 1, 3, 2 ], [ 1, 3 ] ]\ngap> D \ := CycleDigraph(IsMutableDigraph, 3);\n\ngap> DigraphAddAllLoops(D);\n\n\ gap> D;\n\n", count := [ 3, 3, 38, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 38, 7 ], mathmode := "Text", name := "Example", next := 105758, root := ~, start := 104991, stop := 105757 ), rec( content := "\n ", count := [ 3, 3, 38, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 38, 5 ], mathmode := "Text", name := "Description", next := 105775, root := ~, start := 104579, stop := 105774 ) ], count := [ 3, 3, 38, 1 ], mathmode := "Text", name := "ManSection", next := 105789, root := ~, start := 104428, stop := 105788 ), rec( content := "\n\n ", count := [ 3, 3, 38, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, i", Label := "for digraph an\ d int", Name := "DistanceDigraph" ), content := 0, count := [ 3, 3, 39, 2 ], mathmode := "Text", name := "Oper", next := 105893, root := ~, start := 105810, stop := 105892 ), rec( attributes := rec( Arg := "digraph, list", Label := "for digraph an\ d list", Name := "DistanceDigraph" ), content := 0, count := [ 3, 3, 39, 4 ], mathmode := "Text", name := "Oper", next := 105983, root := ~, start := 105896, stop := 105982 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "Returns", next := 106015, root := ~, start := 105986, stop := 106014 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ first argument is a digraph, the second argument is a non-negative\n integ\ er or a list of positive integers. This operation returns a digraph on\n th\ e same set of vertices as ", count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "A", next := 106233, root := ~, start := 106219, stop := 106232 ), rec( content := ", with t\ wo vertices being adjacent\n if and only if the distance between them in ", count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "A", next := 106330, root := ~, start := 106316, stop := 106329 ), rec( content := " equals \ ", count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "A", next := 106346, root := ~, start := 106338, stop := 106345 ), rec( content := "\n or\ is a number in ", count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "A", next := 106380, root := ~, start := 106369, stop := 106379 ), rec( content := ". See " , count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for a \ digraph and two vertices", Oper := "DigraphShortestDistance" ), content := 0, count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "Ref", next := 106467, root := ~, start := 106387, stop := 106466 ), rec( content := ". ", count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 39, 6 ], mathmode := "Text", name := "P", next := 106473, root := ~, start := 106469, stop := 106472 ), rec( content := "\n\n \ If ", count := [ 3, 3, 39, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 39, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 39, 6 ], mathmode := "Text", name := "A", next := 106496, root := ~, start := 106482, stop := 106495 ), rec( content := " is muta\ ble, then ", count := [ 3, 3, 39, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 39, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 39, 6 ], mathmode := "Text", name := "A", next := 106528, root := ~, start := 106514, stop := 106527 ), rec( content := " is modi\ fied in-place. If\n ", count := [ 3, 3, 39, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 39, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 39, 6 ], mathmode := "Text", name := "A", next := 106572, root := ~, start := 106558, stop := 106571 ), rec( content := " is immu\ table, then a new immutable digraph constructed as\n described above is ret\ urned.\n ", count := [ 3, 3, 39, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> digraph := DigraphFromSparse6String(\n> \":]n?AL`BC_DEbEF`GIaGHdIJeGKcKL\ _@McDHfILaBJfHMjKM\");\n\ngap> D\ istanceDigraph(digraph, 1);\n\ng\ ap> DistanceDigraph(digraph, [1, 2]);\n\n", count := [ 3, 3, 39, 7 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 39, 7 ], mathmode := "Text", name := "Example", next := 107012, root := ~, start := 106668, stop := 107011 ), rec( content := "\n ", count := [ 3, 3, 39, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "Description", next := 107029, root := ~, start := 106018, stop := 107028 ) ], count := [ 3, 3, 39, 1 ], mathmode := "Text", name := "ManSection", next := 107043, root := ~, start := 105795, stop := 107042 ), rec( content := "\n\n ", count := [ 3, 3, 39, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, k", Name := "DigraphClosure"\ ), content := 0, count := [ 3, 3, 40, 2 ], mathmode := "Text", name := "Oper", next := 107110, root := ~, start := 107064, stop := 107109 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "Returns", next := 107142, root := ~, start := 107113, stop := 107141 ), rec( attributes := rec( ), content := [ rec( content := "\n Giv\ en a symmetric loopless digraph with no multiple edges ", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "A", next := 107235, root := ~, start := 107221, stop := 107234 ), rec( content := ",\n t\ he ", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "k", count := [ 3, 3, 40, 3 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 40, 3 ], mathmode := \ "Text", name := "A", next := 107256, root := ~, start := 107248, stop := 10725\ 5 ), rec( content := "-closure of ", count := [ 3, 3, 40, 3 ], mathmode := "Te\ xt", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "digraph", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "A", next := 1072\ 82, root := ~, start := 107268, stop := 107281 ) ], count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "E", next := 107286, root := ~, start := 107245, stop := 107285 ), rec( content := " is defi\ ned to be the unique\n smallest symmetric loopless digraph ", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "C\ ", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "C", next := 107363, root := ~, start := 107355, stop := 107362 ), rec( content := " with no\ multiple edges on the\n vertices of ", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "A", next := 107424, root := ~, start := 107410, stop := 107423 ), rec( content := " that co\ ntains all the edges of ", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "A", next := 107470, root := ~, start := 107456, stop := 107469 ), rec( content := "\n an\ d satsifies the property that the sum of the degrees of every two\n non-adj\ acenct vertices in ", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "C\ ", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "C", next := 107581, root := ~, start := 107573, stop := 107580 ), rec( content := " is less\ than ", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "k\ ", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "A", next := 107603, root := ~, start := 107595, stop := 107602 ), rec( content := ". See ", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsSymme\ tricDigraph" ), content := 0, count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "Ref", next := 107645, root := ~, start := 107609, stop := 107644 ), rec( content := ", ", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "Digraph\ HasLoops" ), content := 0, count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "Ref", next := 107676, root := ~, start := 107647, stop := 107675 ), rec( content := ", ", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsMulti\ Digraph" ), content := 0, count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "Ref", next := 107710, root := ~, start := 107678, stop := 107709 ), rec( content := ", and ", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "OutDegr\ eeOfVertex" ), content := 0, count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "Ref", next := 107747, root := ~, start := 107716, stop := 107746 ), rec( content := ". ", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 40, 4 ], mathmode := "Text", name := "P", next := 107753, root := ~, start := 107749, stop := 107752 ), rec( content := "\n\n \ The operation ", count := [ 3, 3, 40, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphClosure", count := [ 3, 3, 40, 4 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 3, 3, 40, 4 ], mathmode := "Text", name := "C", next := 107794, root := ~, start := 107773, stop := 107793 ), rec( content := " returns\ the ", count := [ 3, 3, 40, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "k\ ", count := [ 3, 3, 40, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 40, 4 ], mathmode := "Text", name := "A", next := 107815, root := ~, start := 107807, stop := 107814 ), rec( content := "-closure\ of\n ", count := [ 3, 3, 40, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 40, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 40, 4 ], mathmode := "Text", name := "A", next := 107845, root := ~, start := 107831, stop := 107844 ), rec( content := ".\n " , count := [ 3, 3, 40, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CompleteDigraph(6);\n\n\ gap> D := DigraphRemoveEdges(D, [[1, 2], [2, 1]]);\n\ngap> closure := DigraphClosure(D, 6);\n\ngap> IsCompleteDigraph(closure);\ntrue\n", count := [ 3, 3, 40, 5 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 40, 5 ], mathmode := "Text", name := "Example", next := 108177, root := ~, start := 107851, stop := 108176 ), rec( content := "\n ", count := [ 3, 3, 40, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "Description", next := 108194, root := ~, start := 107145, stop := 108193 ) ], count := [ 3, 3, 40, 1 ], mathmode := "Text", name := "ManSection", next := 108208, root := ~, start := 107049, stop := 108207 ), rec( content := "\n\n ", count := [ 3, 3, 40, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphMycielsk\ ian" ), content := 0, count := [ 3, 3, 41, 2 ], mathmode := "Text", name := "Oper", next := 108276, root := ~, start := 108229, stop := 108275 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphMycielsk\ ianAttr" ), content := 0, count := [ 3, 3, 41, 4 ], mathmode := "Text", name := "Attr", next := 108330, root := ~, start := 108279, stop := 108329 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 3, 41, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 41, 5 ], mathmode := "Text", name := "Returns", next := 108362, root := ~, start := 108333, stop := 108361 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 3, 41, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 41, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 41, 5 ], mathmode := "Text", name := "A", next := 108400, root := ~, start := 108386, stop := 108399 ), rec( content := " is a sy\ mmetric digraph, then\n ", count := [ 3, 3, 41, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphMycielskian", count := [ 3, 3, 41, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 41, 5 ], mathmode := "Text", name := "C", next := 108459, root := ~, start := 108434, stop := 108458 ), rec( content := " returns\ the Mycielskian of ", count := [ 3, 3, 41, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 41, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 41, 5 ], mathmode := "Text", name := "A", next := 108501, root := ~, start := 108487, stop := 108500 ), rec( content := ".", count := [ 3, 3, 41, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 41, 6 ], mathmode := "Text", name := "P", next := 108506, root := ~, start := 108502, stop := 108505 ), rec( content := "\n \n\ The Mycielskian of a symmetric digraph is a larger symmetric digraph\n \ constructed from it, which has a larger chromatic number. For further\n inf\ ormation, see ", count := [ 3, 3, 41, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "h\ ttps://en.wikipedia.org/wiki/Mycielskian", count := [ 3, 3, 41, 6 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 41, 6 ], mathmode := "Text", name := "URL", next := 108732, root := ~, start := 108680, stop := 108731 ), rec( content := ".", count := [ 3, 3, 41, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 41, 7 ], mathmode := "Text", name := "P", next := 108737, root := ~, start := 108733, stop := 108736 ), rec( content := "\n\n \ If ", count := [ 3, 3, 41, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 41, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 41, 7 ], mathmode := "Text", name := "A", next := 108760, root := ~, start := 108746, stop := 108759 ), rec( content := " is immu\ table, then a new immutable digraph is returned.\n Otherwise, the mutable d\ igraph ", count := [ 3, 3, 41, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 3, 3, 41, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 41, 7 ], mathmode := "Text", name := "A", next := 108866, root := ~, start := 108852, stop := 108865 ), rec( content := " is chan\ ged in-place into\n its Mycielskian.", count := [ 3, 3, 41, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 41, 8 ], mathmode := "Text", name := "P", next := 108916, root := ~, start := 108912, stop := 108915 ), rec( content := "\n\n \ ", count := [ 3, 3, 41, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CycleDigraph(2);\n\ngap> C\ hromaticNumber(D);\n2\ngap> D := DigraphMycielskian(D);\n\ngap> ChromaticNumber(D);\n3\ngap> D := DigraphMyciel\ skian(D);\n\ngap> ChromaticNumbe\ r(D);\n4\ngap> D := CompleteBipartiteDigraph(IsMutable, 2, 3);\n\ngap> DigraphMycielskian(D);\n\ngap> D;\n\n", count := [ 3, 3, 41, 9 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 41, 9 ], mathmode := "Text", name := "Example", next := 109486, root := ~, start := 108922, stop := 109485 ), rec( content := "\n ", count := [ 3, 3, 41, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 41, 5 ], mathmode := "Text", name := "Description", next := 109503, root := ~, start := 108365, stop := 109502 ) ], count := [ 3, 3, 41, 1 ], mathmode := "Text", name := "ManSection", next := 109517, root := ~, start := 108214, stop := 109516 ), rec( content := "\n\n ", count := [ 3, 3, 41, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 0, 1 ], mathmode := "Text", name := "Section", next := 109531, root := ~, start := 43611, stop := 109530 ), rec( content := "\n\n ", count := [ 3, 3, 41, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Random digraphs", count := [ 3, 4, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 0, 2 ], mathmode := "Text", name := "Heading", next := 109578, root := ~, start := 109544, stop := 109577 ), rec( content := "\n ", count := [ 3, 4, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "[filt, ]n[, p]", Name := "RandomDigraph" ), content := 0, count := [ 3, 4, 1, 2 ], mathmode := "Text", name := "Oper", next := 109647, root := ~, start := 109598, stop := 109646 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "Returns", next := 109679, root := ~, start := 109650, stop := 109678 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ the optional first argument ", count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "A", next := 109742, root := ~, start := 109731, stop := 109741 ), rec( content := " is pres\ ent, then this should\n specify the category or representation the digraph \ being created will\n belong to. For example, if ", count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "A", next := 109888, root := ~, start := 109877, stop := 109887 ), rec( content := " is ", count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "Ref", next := 109922, root := ~, start := 109892, stop := 109921 ), rec( content := ",\n t\ hen the digraph being created will be mutable, if ", count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "A", next := 109990, root := ~, start := 109979, stop := 109989 ), rec( content := " is ", count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "Ref", next := 110030, root := ~, start := 109994, stop := 110029 ), rec( content := ", then t\ he digraph will be immutable. \n If the optional first argument ", count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "A", next := 110115, root := ~, start := 110104, stop := 110114 ), rec( content := " is not \ present, then ", count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "Ref", next := 110175, root := ~, start := 110137, stop := 110174 ), rec( content := " is used\ by default.", count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 4, 1, 4 ], mathmode := "Text", name := "P", next := 110199, root := ~, start := 110195, stop := 110198 ), rec( content := "\n\n \ If ", count := [ 3, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 1, 4 ], mathmode := "Text", name := "A", next := 110216, root := ~, start := 110208, stop := 110215 ), rec( content := " is a po\ sitive integer, then this function returns a random\n digraph with ", count := [ 3, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 1, 4 ], mathmode := "Text", name := "A", next := 110301, root := ~, start := 110293, stop := 110300 ), rec( content := " vertice\ s and without multiple edges. The result\n may or may not have loops.", count := [ 3, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "P", next := 110384, root := ~, start := 110380, stop := 110383 ), rec( content := "\n\n \ If the optional second argument ", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ ", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "A", next := 110430, root := ~, start := 110422, stop := 110429 ), rec( content := " is a fl\ oat with value\n ", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "0\ \\leq ", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "M", next := 110471, root := ~, start := 110457, stop := 110470 ), rec( content := " ", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := " \ p ", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "A", next := 110482, root := ~, start := 110472, stop := 110481 ), rec( content := " ", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := " \ \\leq 1", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "M", next := 110497, root := ~, start := 110483, stop := 110496 ), rec( content := ", then a\ n edge will exist between each\n pair of vertices with probability approxim\ ately ", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ ", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "A", next := 110596, root := ~, start := 110588, stop := 110595 ), rec( content := ".\n I\ f ", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ ", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "A", next := 110613, root := ~, start := 110605, stop := 110612 ), rec( content := " is not \ specified, then a random probability will be assumed\n (chosen with uniform\ probability).\n ", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> RandomDigraph(1000);\n\ngap> RandomDigraph(10000, 0.023);\n\ngap> RandomDigraph(IsMutableDigraph, 1000, 1 / 2);\n\n", count := [ 3, 4, 1, 6 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 4, 1, 6 ], mathmode := "Text", name := "Log", next := 111011, root := ~, start := 110717, stop := 111010 ), rec( content := "\n ", count := [ 3, 4, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "Description", next := 111028, root := ~, start := 109682, stop := 111027 ) ], count := [ 3, 4, 1, 1 ], mathmode := "Text", name := "ManSection", next := 111042, root := ~, start := 109583, stop := 111041 ), rec( content := "\n\n ", count := [ 3, 4, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "n[, m]", Name := "RandomMultiDigr\ aph" ), content := 0, count := [ 3, 4, 2, 2 ], mathmode := "Text", name := "Oper", next := 111109, root := ~, start := 111063, stop := 111108 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "Returns", next := 111141, root := ~, start := 111112, stop := 111140 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "A", next := 111173, root := ~, start := 111165, stop := 111172 ), rec( content := " is a po\ sitive integer, then this function returns a random\n digraph with ", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "A", next := 111258, root := ~, start := 111250, stop := 111257 ), rec( content := " vertice\ s. If the optional second argument\n ", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "A", next := 111313, root := ~, start := 111305, stop := 111312 ), rec( content := " is a po\ sitive integer, then the digraph will have ", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "A", next := 111372, root := ~, start := 111364, stop := 111371 ), rec( content := "\n ed\ ges. If ", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "A", next := 111395, root := ~, start := 111387, stop := 111394 ), rec( content := " is not \ specified, then the number of edges will be\n chosen randomly (with uniform\ probability) from the range\n ", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ 1 .. ", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "C", next := 111526, root := ~, start := 111513, stop := 111525 ), rec( attributes := rec( ), content := [ rec( content := "{\ n \\choose 2}", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "M", next := 111546, root := ~, start := 111526, stop := 111545 ), rec( attributes := rec( ), content := [ rec( content := "]\ ", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "C", next := 111554, root := ~, start := 111546, stop := 111553 ), rec( content := ".\n " , count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 4, 2, 4 ], mathmode := "Text", name := "P", next := 111564, root := ~, start := 111560, stop := 111563 ), rec( content := "\n\n \ The method used by this function chooses each edge from the set of\n all po\ ssible edges with uniform probability. No effort is made to avoid\n creatin\ g multiple edges, so it is possible (but not guaranteed) that the\n result \ will have multiple edges. The result may or may not have loops.", count := [ 3, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 4, 2, 5 ], mathmode := "Text", name := "P", next := 111868, root := ~, start := 111864, stop := 111867 ), rec( content := "\n ", count := [ 3, 4, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> RandomMultiDigraph(1000);\n\ngap> RandomMultiDigraph(1000, 950);\n\n", count := [ 3, 4, 2, 6 ], name := "PCDATA", root := ~ ) ], count := [ 3, 4, 2, 6 ], mathmode := "Text", name := "Log", next := 112077, root := ~, start := 111873, stop := 112076 ), rec( content := "\n ", count := [ 3, 4, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "Description", next := 112094, root := ~, start := 111144, stop := 112093 ) ], count := [ 3, 4, 2, 1 ], mathmode := "Text", name := "ManSection", next := 112108, root := ~, start := 111048, stop := 112107 ), rec( content := "\n\n ", count := [ 3, 4, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "[filt, ]n", Name := "RandomTournamen\ t" ), content := 0, count := [ 3, 4, 3, 2 ], mathmode := "Text", name := "Oper", next := 112176, root := ~, start := 112129, stop := 112175 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "Returns", next := 112208, root := ~, start := 112179, stop := 112207 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ the optional first argument ", count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "A", next := 112271, root := ~, start := 112260, stop := 112270 ), rec( content := " is pres\ ent, then this should\n specify the category or representation the digraph \ being created will\n belong to. For example, if ", count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "A", next := 112417, root := ~, start := 112406, stop := 112416 ), rec( content := " is ", count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "Ref", next := 112451, root := ~, start := 112421, stop := 112450 ), rec( content := ",\n t\ hen the digraph being created will be mutable, if ", count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "A", next := 112519, root := ~, start := 112508, stop := 112518 ), rec( content := " is ", count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "Ref", next := 112559, root := ~, start := 112523, stop := 112558 ), rec( content := ", then t\ he digraph will be immutable. \n If the optional first argument ", count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "A", next := 112644, root := ~, start := 112633, stop := 112643 ), rec( content := " is not \ present, then ", count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "Ref", next := 112704, root := ~, start := 112666, stop := 112703 ), rec( content := " is used\ by default.", count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 4, 3, 4 ], mathmode := "Text", name := "P", next := 112728, root := ~, start := 112724, stop := 112727 ), rec( content := "\n\n \ If ", count := [ 3, 4, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 4, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 3, 4 ], mathmode := "Text", name := "A", next := 112745, root := ~, start := 112737, stop := 112744 ), rec( content := " is a no\ n-negative integer, this function returns a random\n tournament with ", count := [ 3, 4, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 4, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 3, 4 ], mathmode := "Text", name := "A", next := 112832, root := ~, start := 112824, stop := 112831 ), rec( content := " vertice\ s. See ", count := [ 3, 4, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsTourn\ ament" ), content := 0, count := [ 3, 4, 3, 4 ], mathmode := "Text", name := "Ref", next := 112873, root := ~, start := 112847, stop := 112872 ), rec( content := ". ", count := [ 3, 4, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 4, 3, 5 ], mathmode := "Text", name := "P", next := 112879, root := ~, start := 112875, stop := 112878 ), rec( content := "\n ", count := [ 3, 4, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> RandomTournament(10);\n\ngap> Ran\ domTournament(IsMutableDigraph, 10);\n\n", count := [ 3, 4, 3, 6 ], name := "PCDATA", root := ~ ) ], count := [ 3, 4, 3, 6 ], mathmode := "Text", name := "Log", next := 113071, root := ~, start := 112884, stop := 113070 ), rec( content := "\n ", count := [ 3, 4, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "Description", next := 113088, root := ~, start := 112211, stop := 113087 ) ], count := [ 3, 4, 3, 1 ], mathmode := "Text", name := "ManSection", next := 113102, root := ~, start := 112114, stop := 113101 ), rec( content := "\n\n ", count := [ 3, 4, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "n", Name := "RandomLattice" ), content := 0, count := [ 3, 4, 4, 2 ], mathmode := "Text", name := "Oper", next := 113159, root := ~, start := 113123, stop := 113158 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "Returns", next := 113191, root := ~, start := 113162, stop := 113190 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ the optional first argument ", count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "A", next := 113254, root := ~, start := 113243, stop := 113253 ), rec( content := " is pres\ ent, then this should\n specify the category or representation the digraph \ being created will\n belong to. For example, if ", count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "A", next := 113400, root := ~, start := 113389, stop := 113399 ), rec( content := " is ", count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "Ref", next := 113434, root := ~, start := 113404, stop := 113433 ), rec( content := ",\n t\ hen the digraph being created will be mutable, if ", count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "A", next := 113502, root := ~, start := 113491, stop := 113501 ), rec( content := " is ", count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "Ref", next := 113542, root := ~, start := 113506, stop := 113541 ), rec( content := ", then t\ he digraph will be immutable. \n If the optional first argument ", count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "A", next := 113627, root := ~, start := 113616, stop := 113626 ), rec( content := " is not \ present, then ", count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "Ref", next := 113687, root := ~, start := 113649, stop := 113686 ), rec( content := " is used\ by default.", count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "P", next := 113711, root := ~, start := 113707, stop := 113710 ), rec( content := "\n\n \ If ", count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "A", next := 113728, root := ~, start := 113720, stop := 113727 ), rec( content := " is a po\ sitive integer, this function return a random lattice\n with ", count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "C", next := 113807, root := ~, start := 113799, stop := 113806 ), rec( content := " vertice\ s, where it is guaranteed that ", count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "C", next := 113854, root := ~, start := 113846, stop := 113853 ), rec( content := " is betw\ een\n ", count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "A", next := 113878, root := ~, start := 113870, stop := 113877 ), rec( content := " and ", count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "2\ * ", count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "n", count := [ 3, 4, 4, 4 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 4, 4 ], mathmode := \ "Text", name := "A", next := 113898, root := ~, start := 113890, stop := 11389\ 7 ) ], count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "C", next := 113902, root := ~, start := 113883, stop := 113901 ), rec( content := ". See ", count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsLatti\ ceDigraph" ), content := 0, count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "Ref", next := 113938, root := ~, start := 113908, stop := 113937 ), rec( content := ". ", count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 4, 4, 5 ], mathmode := "Text", name := "P", next := 113944, root := ~, start := 113940, stop := 113943 ), rec( content := "\n ", count := [ 3, 4, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> RandomLattice(10);\n\ngap> RandomLattice(IsMutableDigraph, 10);\n\n", count := [ 3, 4, 4, 6 ], name := "PCDATA", root := ~ ) ], count := [ 3, 4, 4, 6 ], mathmode := "Text", name := "Log", next := 114139, root := ~, start := 113949, stop := 114138 ), rec( content := "\n ", count := [ 3, 4, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "Description", next := 114156, root := ~, start := 113194, stop := 114155 ) ], count := [ 3, 4, 4, 1 ], mathmode := "Text", name := "ManSection", next := 114170, root := ~, start := 113108, stop := 114169 ), rec( content := "\n\n ", count := [ 3, 4, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 0, 1 ], mathmode := "Text", name := "Section", next := 114184, root := ~, start := 109535, stop := 114183 ) , rec( content := "\n\n ", count := [ 3, 4, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Standard examples\ ", count := [ 3, 5, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 0, 2 ], mathmode := "Text", name := "Heading", next := 114233, root := ~, start := 114197, stop := 114232 ), rec( content := "\n ", count := [ 3, 5, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "[filt, ]n", Name := "ChainDigraph" ) , content := 0, count := [ 3, 5, 1, 2 ], mathmode := "Text", name := "Oper", next := 114296, root := ~, start := 114253, stop := 114295 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "Returns", next := 114328, root := ~, start := 114299, stop := 114327 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "A", next := 114360, root := ~, start := 114352, stop := 114359 ), rec( content := " is a po\ sitive integer, this function returns a chain\n with ", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "A", next := 114431, root := ~, start := 114423, stop := 114430 ), rec( content := " vertice\ s and ", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "n", count := [ 3, 5, 1, 3 ], mathmode \ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 1, 3 ], mathmode := \ "Text", name := "A", next := 114456, root := ~, start := 114448, stop := 11445\ 5 ), rec( content := " - 1", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "C", next := 114464, root := ~, start := 114445, stop := 114463 ), rec( content := " edges.\\ n Specifically,\n for each vertex ", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "C", next := 114518, root := ~, start := 114510, stop := 114517 ), rec( content := " (with " , count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "C", next := 114533, root := ~, start := 114525, stop := 114532 ), rec( content := " < ", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "C", next := 114547, root := ~, start := 114539, stop := 114546 ), rec( content := "), there\ is a directed\n edge with source ", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "C", next := 114599, root := ~, start := 114591, stop := 114598 ), rec( content := " and ran\ ge ", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ + 1", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "C", next := 114622, root := ~, start := 114610, stop := 114621 ), rec( content := ". ", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "P", next := 114628, root := ~, start := 114624, stop := 114627 ), rec( content := "\n\n \ If the optional first argument ", count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "A", next := 114676, root := ~, start := 114665, stop := 114675 ), rec( content := " is pres\ ent, then this should\n specify the category or representation the digraph \ being created will\n belong to. For example, if ", count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "A", next := 114822, root := ~, start := 114811, stop := 114821 ), rec( content := " is ", count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "Ref", next := 114856, root := ~, start := 114826, stop := 114855 ), rec( content := ",\n t\ hen the digraph being created will be mutable, if ", count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "A", next := 114924, root := ~, start := 114913, stop := 114923 ), rec( content := " is ", count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "Ref", next := 114964, root := ~, start := 114928, stop := 114963 ), rec( content := ", then t\ he digraph will be immutable. \n If the optional first argument ", count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "A", next := 115049, root := ~, start := 115038, stop := 115048 ), rec( content := " is not \ present, then ", count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "Ref", next := 115109, root := ~, start := 115071, stop := 115108 ), rec( content := " is used\ by default.", count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 5, 1, 5 ], mathmode := "Text", name := "P", next := 115133, root := ~, start := 115129, stop := 115132 ), rec( content := "\n\n \ The ", count := [ 3, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ ReflexiveTransitiveClosure" ), content := 0, count := [ 3, 5, 1, 5 ], mathmode := "Text", name := "Ref", next := 115190, root := ~, start := 115143, stop := 115189 ), rec( content := " of a ch\ ain represents a\n total order.\n ", count := [ 3, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> ChainDigraph(42);\n\ngap> Chai\ nDigraph(IsMutableDigraph, 10);\n\n\ ", count := [ 3, 5, 1, 6 ], name := "PCDATA", root := ~ ) ], count := [ 3, 5, 1, 6 ], mathmode := "Text", name := "Example", next := 115419, root := ~, start := 115236, stop := 115418 ), rec( content := "\n ", count := [ 3, 5, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "Description", next := 115436, root := ~, start := 114331, stop := 115435 ) ], count := [ 3, 5, 1, 1 ], mathmode := "Text", name := "ManSection", next := 115450, root := ~, start := 114238, stop := 115449 ), rec( content := "\n\n ", count := [ 3, 5, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "[filt, ]n", Name := "CompleteDigraph\ " ), content := 0, count := [ 3, 5, 2, 2 ], mathmode := "Text", name := "Oper", next := 115517, root := ~, start := 115471, stop := 115516 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 2, 3 ], mathmode := "Text", name := "Returns", next := 115549, root := ~, start := 115520, stop := 115548 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 2, 3 ], mathmode := "Text", name := "A", next := 115581, root := ~, start := 115573, stop := 115580 ), rec( content := " is a no\ n-negative integer, this function returns the complete\n digraph with ", count := [ 3, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 2, 3 ], mathmode := "Text", name := "A", next := 115669, root := ~, start := 115661, stop := 115668 ), rec( content := " vertice\ s. See ", count := [ 3, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsCompl\ eteDigraph" ), content := 0, count := [ 3, 5, 2, 3 ], mathmode := "Text", name := "Ref", next := 115715, root := ~, start := 115684, stop := 115714 ), rec( content := ". ", count := [ 3, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "P", next := 115721, root := ~, start := 115717, stop := 115720 ), rec( content := "\n\n \ If the optional first argument ", count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "A", next := 115769, root := ~, start := 115758, stop := 115768 ), rec( content := " is pres\ ent, then this should\n specify the category or representation the digraph \ being created will\n belong to. For example, if ", count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "A", next := 115915, root := ~, start := 115904, stop := 115914 ), rec( content := " is ", count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "Ref", next := 115949, root := ~, start := 115919, stop := 115948 ), rec( content := ",\n t\ hen the digraph being created will be mutable, if ", count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "A", next := 116017, root := ~, start := 116006, stop := 116016 ), rec( content := " is ", count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "Ref", next := 116057, root := ~, start := 116021, stop := 116056 ), rec( content := ", then t\ he digraph will be immutable. \n If the optional first argument ", count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "A", next := 116142, root := ~, start := 116131, stop := 116141 ), rec( content := " is not \ present, then ", count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "Ref", next := 116202, root := ~, start := 116164, stop := 116201 ), rec( content := " is used\ by default.\n ", count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> CompleteDigraph(20);\n\ngap\ > CompleteDigraph(IsMutableDigraph, 10);\n\n", count := [ 3, 5, 2, 5 ], name := "PCDATA", root := ~ ) ], count := [ 3, 5, 2, 5 ], mathmode := "Text", name := "Example", next := 116420, root := ~, start := 116227, stop := 116419 ), rec( content := "\n ", count := [ 3, 5, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 2, 3 ], mathmode := "Text", name := "Description", next := 116437, root := ~, start := 115552, stop := 116436 ) ], count := [ 3, 5, 2, 1 ], mathmode := "Text", name := "ManSection", next := 116451, root := ~, start := 115456, stop := 116450 ), rec( content := "\n\n ", count := [ 3, 5, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "[filt, ]m, n", Name := "CompleteBiparti\ teDigraph" ), content := 0, count := [ 3, 5, 3, 2 ], mathmode := "Text", name := "Oper", next := 116530, root := ~, start := 116472, stop := 116529 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "Returns", next := 116562, root := ~, start := 116533, stop := 116561 ), rec( attributes := rec( ), content := [ rec( content := "\n A c\ omplete bipartite digraph is a digraph whose vertices\n can be partitioned \ into two non-empty vertex sets, such there exists\n a unique edge with sour\ ce ", count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "C", next := 116751, root := ~, start := 116743, stop := 116750 ), rec( content := " and ran\ ge ", count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "C", next := 116770, root := ~, start := 116762, stop := 116769 ), rec( content := " if and \ only if\n ", count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "C", next := 116798, root := ~, start := 116790, stop := 116797 ), rec( content := " and ", count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "C", next := 116811, root := ~, start := 116803, stop := 116810 ), rec( content := " lie in \ different vertex sets. ", count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "P", next := 116846, root := ~, start := 116842, stop := 116845 ), rec( content := "\n\n \ If ", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "A", next := 116863, root := ~, start := 116855, stop := 116862 ), rec( content := " and ", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "A", next := 116876, root := ~, start := 116868, stop := 116875 ), rec( content := " are pos\ itive integers, this function\n returns the complete bipartite digraph with\ vertex sets of sizes\n ", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "A", next := 116995, root := ~, start := 116987, stop := 116994 ), rec( content := " (contai\ ning the vertices ", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ 1 .. m]", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "C", next := 117036, root := ~, start := 117021, stop := 117035 ), rec( content := ") and\n \ ", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "A", next := 117054, root := ~, start := 117046, stop := 117053 ), rec( content := " (contai\ ning the vertices ", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ m + 1 .. m + n]", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "C", next := 117103, root := ~, start := 117080, stop := 117102 ), rec( content := ").\n \ ", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "P", next := 117114, root := ~, start := 117110, stop := 117113 ), rec( content := "\n\n \ If the optional first argument ", count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "A", next := 117162, root := ~, start := 117151, stop := 117161 ), rec( content := " is pres\ ent, then this should\n specify the category or representation the digraph \ being created will\n belong to. For example, if ", count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "A", next := 117308, root := ~, start := 117297, stop := 117307 ), rec( content := " is ", count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "Ref", next := 117342, root := ~, start := 117312, stop := 117341 ), rec( content := ",\n t\ hen the digraph being created will be mutable, if ", count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "A", next := 117410, root := ~, start := 117399, stop := 117409 ), rec( content := " is ", count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "Ref", next := 117450, root := ~, start := 117414, stop := 117449 ), rec( content := ", then t\ he digraph will be immutable. \n If the optional first argument ", count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "A", next := 117535, root := ~, start := 117524, stop := 117534 ), rec( content := " is not \ present, then ", count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "Ref", next := 117595, root := ~, start := 117557, stop := 117594 ), rec( content := " is used\ by default.\n\n ", count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> CompleteBipartiteDigraph(2, 3);\n\ngap> CompleteBipartiteDigraph(IsMutableDigraph\ , 3, 2);\n\n", count := [ 3, 5, 3, 6 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 5, 3, 6 ], mathmode := "Text", name := "Example", next := 117859, root := ~, start := 117621, stop := 117858 ), rec( content := "\n ", count := [ 3, 5, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "Description", next := 117876, root := ~, start := 116565, stop := 117875 ) ], count := [ 3, 5, 3, 1 ], mathmode := "Text", name := "ManSection", next := 117890, root := ~, start := 116457, stop := 117889 ), rec( content := "\n\n ", count := [ 3, 5, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "[filt, ]orders", Name := "CompleteMultipa\ rtiteDigraph" ), content := 0, count := [ 3, 5, 4, 2 ], mathmode := "Text", name := "Oper", next := 117980, root := ~, start := 117915, stop := 117979 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "Returns", next := 118014, root := ~, start := 117985, stop := 118013 ), rec( attributes := rec( ), content := [ rec( content := "\n F\ or a list ", count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ rders", count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "A", next := 118063, root := ~, start := 118050, stop := 118062 ), rec( content := " of ", count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "C", next := 118075, root := ~, start := 118067, stop := 118074 ), rec( content := " positiv\ e integers,\n this function returns the digraph containing ", count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "C", next := 118154, root := ~, start := 118146, stop := 118153 ), rec( content := " indepen\ dent sets\n of vertices of orders ", count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ ", count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "l", count := [ 3, 5, 4, 3 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 4, 3 ], mathmode := \ "Text", name := "A", next := 118212, root := ~, start := 118204, stop := 11821\ 1 ), rec( content := "[1] .. ", count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ", count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 4, 3 ], mathmode := \ "Text", name := "A", next := 118227, root := ~, start := 118219, stop := 11822\ 6 ), rec( content := "[n]]", count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "C", next := 118235, root := ~, start := 118200, stop := 118234 ), rec( content := ". Moreov\ er,\n each vertex is adjacent to every other not contained in the\n \ same independent set.\n ", count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "P", next := 118351, root := ~, start := 118347, stop := 118350 ), rec( content := "\n\n \ If the optional first argument ", count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "A", next := 118401, root := ~, start := 118390, stop := 118400 ), rec( content := " is pres\ ent, then this should\n specify the category or representation the digrap\ h being created will\n belong to. For example, if ", count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "A", next := 118551, root := ~, start := 118540, stop := 118550 ), rec( content := " is ", count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "Ref", next := 118585, root := ~, start := 118555, stop := 118584 ), rec( content := ",\n \ then the digraph being created will be mutable, if ", count := [ 3, 5, 4, 4 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "A", next := 118655, root := ~, start := 118644, stop := 118654 ), rec( content := " is ", count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "Ref", next := 118697, root := ~, start := 118659, stop := 118696 ), rec( content := ", then t\ he digraph will be immutable. \n If the optional first argument ", count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "A", next := 118784, root := ~, start := 118773, stop := 118783 ), rec( content := " is not \ present, then ", count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "Ref", next := 118846, root := ~, start := 118806, stop := 118845 ), rec( content := " is used\ by default.\n ", count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> CompleteMultipartiteDigraph([5, 4, 2]);\n\ngap> CompleteMultipartiteDigraph(IsMuta\ bleDigraph, [5, 4, 2]);\n\n", count := [ 3, 5, 4, 5 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 5, 4, 5 ], mathmode := "Text", name := "Example", next := 119127, root := ~, start := 118873, stop := 119126 ), rec( content := "\n ", count := [ 3, 5, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "Description", next := 119144, root := ~, start := 118019, stop := 119143 ) ], count := [ 3, 5, 4, 1 ], mathmode := "Text", name := "ManSection", next := 119158, root := ~, start := 117898, stop := 119157 ), rec( content := "\n\n ", count := [ 3, 5, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "[filt, ]n", Name := "CycleDigraph" ) , content := 0, count := [ 3, 5, 5, 2 ], mathmode := "Text", name := "Oper", next := 119222, root := ~, start := 119179, stop := 119221 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "Returns", next := 119254, root := ~, start := 119225, stop := 119253 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "A", next := 119286, root := ~, start := 119278, stop := 119285 ), rec( content := " is a po\ sitive integer, this function returns a ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ ycle", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "E", next := 119346, root := ~, start := 119334, stop := 119345 ), rec( content := "\n di\ graph with ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "A", next := 119372, root := ~, start := 119364, stop := 119371 ), rec( content := " vertice\ s and ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "A", next := 119394, root := ~, start := 119386, stop := 119393 ), rec( content := " edges. \ Specifically,\n for each vertex ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "C", next := 119444, root := ~, start := 119436, stop := 119443 ), rec( content := " (with " , count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "C", next := 119459, root := ~, start := 119451, stop := 119458 ), rec( content := " < ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "C", next := 119473, root := ~, start := 119465, stop := 119472 ), rec( content := "), there\ is a directed\n edge with source ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "C", next := 119525, root := ~, start := 119517, stop := 119524 ), rec( content := " and ran\ ge ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ + 1", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "C", next := 119548, root := ~, start := 119536, stop := 119547 ), rec( content := ". In add\ ition, there is\n an edge with source ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "C", next := 119604, root := ~, start := 119596, stop := 119603 ), rec( content := " and ran\ ge ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "1\ ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "C", next := 119623, root := ~, start := 119615, stop := 119622 ), rec( content := ". ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "P", next := 119629, root := ~, start := 119625, stop := 119628 ), rec( content := "\n\n \ If the optional first argument ", count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "A", next := 119677, root := ~, start := 119666, stop := 119676 ), rec( content := " is pres\ ent, then this should\n specify the category or representation the digraph \ being created will\n belong to. For example, if ", count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "A", next := 119823, root := ~, start := 119812, stop := 119822 ), rec( content := " is ", count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "Ref", next := 119857, root := ~, start := 119827, stop := 119856 ), rec( content := ",\n t\ hen the digraph being created will be mutable, if ", count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "A", next := 119925, root := ~, start := 119914, stop := 119924 ), rec( content := " is ", count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "Ref", next := 119965, root := ~, start := 119929, stop := 119964 ), rec( content := ", then t\ he digraph will be immutable. \n If the optional first argument ", count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "A", next := 120050, root := ~, start := 120039, stop := 120049 ), rec( content := " is not \ present, then ", count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "Ref", next := 120108, root := ~, start := 120072, stop := 120107 ), rec( content := " is used\ by default.\n ", count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> CycleDigraph(1);\n\ngap> CycleD\ igraph(123);\n\ngap> CycleDigraph(I\ sMutableDigraph, 10);\n\n", count := [ 3, 5, 5, 5 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 5, 5, 5 ], mathmode := "Text", name := "Example", next := 120381, root := ~, start := 120131, stop := 120380 ), rec( content := "\n ", count := [ 3, 5, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "Description", next := 120398, root := ~, start := 119257, stop := 120397 ) ], count := [ 3, 5, 5, 1 ], mathmode := "Text", name := "ManSection", next := 120412, root := ~, start := 119164, stop := 120411 ), rec( content := "\n\n ", count := [ 3, 5, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "[filt, ]n", Name := "EmptyDigraph" ) , content := 0, count := [ 3, 5, 6, 2 ], mathmode := "Text", name := "Oper", next := 120476, root := ~, start := 120433, stop := 120475 ), rec( attributes := rec( Arg := "[filt, ]n", Name := "NullDigraph" ), content := 0, count := [ 3, 5, 6, 4 ], mathmode := "Text", name := "Oper", next := 120521, root := ~, start := 120479, stop := 120520 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "Returns", next := 120553, root := ~, start := 120524, stop := 120552 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "A", next := 120585, root := ~, start := 120577, stop := 120584 ), rec( content := " is a no\ n-negative integer, this function returns the\n ", count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ mpty", count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "E", next := 120655, root := ~, start := 120643, stop := 120654 ), rec( content := " or ", count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ull", count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "E", next := 120670, root := ~, start := 120659, stop := 120669 ), rec( content := " digraph\ with ", count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "A", next := 120692, root := ~, start := 120684, stop := 120691 ), rec( content := " vertice\ s. An empty\n digraph is one with no edges.\n ", count := [ 3, 5, 6, 5 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "P", next := 120754, root := ~, start := 120750, stop := 120753 ), rec( content := "\n \ \n If the optional first argument ", count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "A", next := 120808, root := ~, start := 120797, stop := 120807 ), rec( content := " is pres\ ent, then this should\n specify the category or representation the digraph \ being created will\n belong to. For example, if ", count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "A", next := 120954, root := ~, start := 120943, stop := 120953 ), rec( content := " is ", count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "Ref", next := 120988, root := ~, start := 120958, stop := 120987 ), rec( content := ",\n t\ hen the digraph being created will be mutable, if ", count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "A", next := 121056, root := ~, start := 121045, stop := 121055 ), rec( content := " is ", count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "Ref", next := 121096, root := ~, start := 121060, stop := 121095 ), rec( content := ", then t\ he digraph will be immutable. \n If the optional first argument ", count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "A", next := 121181, root := ~, start := 121170, stop := 121180 ), rec( content := " is not \ present, then ", count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "Ref", next := 121241, root := ~, start := 121203, stop := 121240 ), rec( content := " is used\ by default.", count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 5, 6, 7 ], mathmode := "Text", name := "P", next := 121265, root := ~, start := 121261, stop := 121264 ), rec( content := "\n\n \ ", count := [ 3, 5, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "N\ ullDigraph", count := [ 3, 5, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 6, 7 ], mathmode := "Text", name := "C", next := 121289, root := ~, start := 121271, stop := 121288 ), rec( content := " is a sy\ nonym for ", count := [ 3, 5, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "E\ mptyDigraph", count := [ 3, 5, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 6, 7 ], mathmode := "Text", name := "C", next := 121326, root := ~, start := 121307, stop := 121325 ), rec( content := ".\n\n \ ", count := [ 3, 5, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> EmptyDigraph(20);\n\ngap> Null\ Digraph(10);\n\ngap> EmptyDigraph(Is\ MutableDigraph, 10);\n", count := [ 3, 5, 6, 8 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 5, 6, 8 ], mathmode := "Text", name := "Example", next := 121577, root := ~, start := 121333, stop := 121576 ), rec( content := "\n ", count := [ 3, 5, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "Description", next := 121594, root := ~, start := 120556, stop := 121593 ) ], count := [ 3, 5, 6, 1 ], mathmode := "Text", name := "ManSection", next := 121608, root := ~, start := 120418, stop := 121607 ), rec( content := "\n\n ", count := [ 3, 5, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "[filt, ]n, k", Name := "JohnsonDigraph"\ ), content := 0, count := [ 3, 5, 7, 2 ], mathmode := "Text", name := "Oper", next := 121677, root := ~, start := 121629, stop := 121676 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "Returns", next := 121709, root := ~, start := 121680, stop := 121708 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "A", next := 121741, root := ~, start := 121733, stop := 121740 ), rec( content := " and ", count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "k\ ", count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "A", next := 121754, root := ~, start := 121746, stop := 121753 ), rec( content := " are non\ -negative integers, then this operation\n returns a symmetric digraph which\ corresponds to the undirected ", count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "J\ ohnson\n graph", count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "E", next := 121894, root := ~, start := 121870, stop := 121893 ), rec( content := " ", count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "J\ (n, k)", count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "M", next := 121909, root := ~, start := 121895, stop := 121908 ), rec( content := ". ", count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "P", next := 121915, root := ~, start := 121911, stop := 121914 ), rec( content := "\n\n \ If the optional first argument ", count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "A", next := 121963, root := ~, start := 121952, stop := 121962 ), rec( content := " is pres\ ent, then this should\n specify the category or representation the digraph \ being created will\n belong to. For example, if ", count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "A", next := 122109, root := ~, start := 122098, stop := 122108 ), rec( content := " is ", count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "Ref", next := 122143, root := ~, start := 122113, stop := 122142 ), rec( content := ",\n t\ hen the digraph being created will be mutable, if ", count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "A", next := 122211, root := ~, start := 122200, stop := 122210 ), rec( content := " is ", count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "Ref", next := 122251, root := ~, start := 122215, stop := 122250 ), rec( content := ", then t\ he digraph will be immutable. \n If the optional first argument ", count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "A", next := 122336, root := ~, start := 122325, stop := 122335 ), rec( content := " is not \ present, then ", count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "Ref", next := 122396, root := ~, start := 122358, stop := 122395 ), rec( content := " is used\ by default.", count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "P", next := 122420, root := ~, start := 122416, stop := 122419 ), rec( content := "\n\n \ The ", count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "J\ ohnson graph", count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "E", next := 122450, root := ~, start := 122430, stop := 122449 ), rec( content := " ", count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "J\ (n, k)", count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "M", next := 122465, root := ~, start := 122451, stop := 122464 ), rec( content := " has ver\ tices given by all the\n ", count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "k\ ", count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "A", next := 122508, root := ~, start := 122500, stop := 122507 ), rec( content := "-subsets\ of the range ", count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ 1 .. ", count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "n", count := [ 3, 5, 7, 5 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 7, 5 ], mathmode := \ "Text", name := "A", next := 122547, root := ~, start := 122539, stop := 12254\ 6 ), rec( content := "]", count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "C", next := 122552, root := ~, start := 122530, stop := 122551 ), rec( content := ", and tw\ o vertices are\n connected by an edge iff their intersection has size ", count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "k", count := [ 3, 5, 7, 5 ], mathmode \ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 7, 5 ], mathmode := \ "Text", name := "A", next := 122645, root := ~, start := 122637, stop := 12264\ 4 ), rec( content := " - 1", count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "M", next := 122653, root := ~, start := 122634, stop := 122652 ), rec( content := ".\n\n \ ", count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := JohnsonDigraph(3, 1);\n\ngap> OutNeighbours(gr);\n[ [ 2, 3 ], [ 1, 3 ], [ 1, 2 ] ]\ngap> g\ r := JohnsonDigraph(4, 2);\n\ngap> OutNeighbours(gr);\n[ [ 2, 3, 4, 5 ], [ 1, 3, 4, 6 ], [ 1, 2, 5, 6\ ], [ 1, 2, 5, 6 ], \n [ 1, 3, 4, 6 ], [ 2, 3, 4, 5 ] ]\ngap> JohnsonDigraph(\ 1, 0);\n\ngap> JohnsonDigraph(IsMutable\ Digraph, 1, 0);\n\n", count := [ 3, 5, 7, 6 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 5, 7, 6 ], mathmode := "Text", name := "Example", next := 123202, root := ~, start := 122660, stop := 123201 ), rec( content := "\n ", count := [ 3, 5, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "Description", next := 123219, root := ~, start := 121712, stop := 123218 ) ], count := [ 3, 5, 7, 1 ], mathmode := "Text", name := "ManSection", next := 123233, root := ~, start := 121614, stop := 123232 ), rec( content := "\n\n ", count := [ 3, 5, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "[filt]", Name := "PetersenGraph" ), content := 0, count := [ 3, 5, 8, 2 ], mathmode := "Text", name := "Oper", next := 123295, root := ~, start := 123254, stop := 123294 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 5, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 8, 3 ], mathmode := "Text", name := "Returns", next := 123327, root := ~, start := 123298, stop := 123326 ), rec( attributes := rec( ), content := [ rec( content := "\n\n F\ rom ", count := [ 3, 5, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "h\ ttps://en.wikipedia.org/wiki/Petersen_graph", count := [ 3, 5, 8, 3 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 8, 3 ], mathmode := "Text", name := "URL", next := 123409, root := ~, start := 123354, stop := 123408 ), rec( content := ":", count := [ 3, 5, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 5, 8, 4 ], mathmode := "Text", name := "P", next := 123414, root := ~, start := 123410, stop := 123413 ), rec( content := "\n\n \ ", count := [ 3, 5, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "T\ he Petersen graph is an undirected graph with 10 vertices and 15 edges.\n I\ t is a small graph that serves as a useful example and counterexample for\n \ many problems in graph theory. The Petersen graph is named after Julius\n \ Petersen, who in 1898 constructed it to be the smallest bridgeless cubic\n \ graph with no three-edge-coloring.", count := [ 3, 5, 8, 4 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 8, 4 ], mathmode := "Text", name := "Q", next := 123770, root := ~, start := 123420, stop := 123769 ), rec( attributes := rec( ), content := 0, count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "P", next := 123774, root := ~, start := 123770, stop := 123773 ), rec( content := "\n \n\ If the optional first argument ", count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "A", next := 123826, root := ~, start := 123815, stop := 123825 ), rec( content := " is pres\ ent, then this should\n specify the category or representation the digraph \ being created will\n belong to. For example, if ", count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "A", next := 123972, root := ~, start := 123961, stop := 123971 ), rec( content := " is ", count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "Ref", next := 124006, root := ~, start := 123976, stop := 124005 ), rec( content := ",\n t\ hen the digraph being created will be mutable, if ", count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "A", next := 124074, root := ~, start := 124063, stop := 124073 ), rec( content := " is ", count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "Ref", next := 124114, root := ~, start := 124078, stop := 124113 ), rec( content := ", then t\ he digraph will be immutable. \n If the optional first argument ", count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "A", next := 124199, root := ~, start := 124188, stop := 124198 ), rec( content := " is not \ present, then ", count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "Ref", next := 124259, root := ~, start := 124221, stop := 124258 ), rec( content := " is used\ by default.", count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 5, 8, 6 ], mathmode := "Text", name := "P", next := 124283, root := ~, start := 124279, stop := 124282 ), rec( content := "\n\n \ See also ", count := [ 3, 5, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "General\ isedPetersenGraph" ), content := 0, count := [ 3, 5, 8, 6 ], mathmode := "Text", name := "Ref", next := 124336, root := ~, start := 124298, stop := 124335 ), rec( content := ".\n\n", count := [ 3, 5, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> ChromaticNumber(PetersenGraph());\n3\ngap> PetersenGraph(IsMutableDigrap\ h);\n\n", count := [ 3, 5, 8, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 5, 8, 7 ], mathmode := "Text", name := "Example", next := 124495, root := ~, start := 124339, stop := 124494 ), rec( content := "\n ", count := [ 3, 5, 8, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 8, 3 ], mathmode := "Text", name := "Description", next := 124512, root := ~, start := 123330, stop := 124511 ) ], count := [ 3, 5, 8, 1 ], mathmode := "Text", name := "ManSection", next := 124526, root := ~, start := 123239, stop := 124525 ), rec( content := "\n\n ", count := [ 3, 5, 8, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "[filt, ]n, k", Name := "GeneralisedPete\ rsenGraph" ), content := 0, count := [ 3, 5, 9, 2 ], mathmode := "Text", name := "Oper", next := 124605, root := ~, start := 124547, stop := 124604 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "Returns", next := 124637, root := ~, start := 124608, stop := 124636 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "A", next := 124669, root := ~, start := 124661, stop := 124668 ), rec( content := " is a po\ sitive integer and ", count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "k\ ", count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "A", next := 124704, root := ~, start := 124696, stop := 124703 ), rec( content := " is a no\ n-negative\n integer less than ", count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "n", count := [ 3, 5, 9, 3 ], mathmode \ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 9, 3 ], mathmode := \ "Text", name := "A", next := 124756, root := ~, start := 124748, stop := 12475\ 5 ), rec( content := " / 2", count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "C", next := 124764, root := ~, start := 124745, stop := 124763 ), rec( content := ", then t\ his operation returns\n the ", count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ eneralised Petersen graph", count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "E", next := 124835, root := ~, start := 124802, stop := 124834 ), rec( content := " ", count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ PG(", count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "n", count := [ 3, 5, 9, 3 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 9, 3 ], mathmode := \ "Text", name := "A", next := 124851, root := ~, start := 124843, stop := 12485\ 0 ), rec( content := ", k)", count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "M", next := 124859, root := ~, start := 124836, stop := 124858 ), rec( content := ". ", count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 5, 9, 4 ], mathmode := "Text", name := "P", next := 124865, root := ~, start := 124861, stop := 124864 ), rec( content := "\n\n \ From\n ", count := [ 3, 5, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "h\ ttps://en.wikipedia.org/wiki/Generalized_Petersen_graph", count := [ 3, 5, 9, 4 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 9, 4 ], mathmode := "Text", name := "URL", next := 124947, root := ~, start := 124880, stop := 124946 ), rec( content := ":\n " , count := [ 3, 5, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 5, 9, 5 ], mathmode := "Text", name := "P", next := 124957, root := ~, start := 124953, stop := 124956 ), rec( content := "\n\n \ ", count := [ 3, 5, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "T\ he generalized Petersen graphs are a family of cubic\n graphs formed by con\ necting the vertices of a regular polygon to the\n corresponding vertices o\ f a star polygon. They include the Petersen graph\n and generalize one of t\ he ways of constructing the Petersen graph. The\n generalized Petersen grap\ h family was introduced in 1950 by H. S. M.\n Coxeter and was given its nam\ e in 1969 by Mark Watkins.", count := [ 3, 5, 9, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 5, 9, 5 ], mathmode := "Text", name := "Q", next := 125382, root := ~, start := 124963, stop := 125381 ), rec( content := "\n ", count := [ 3, 5, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "P", next := 125391, root := ~, start := 125387, stop := 125390 ), rec( content := "\n\n \ If the optional first argument ", count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "A", next := 125439, root := ~, start := 125428, stop := 125438 ), rec( content := " is pres\ ent, then this should\n specify the category or representation the digraph \ being created will\n belong to. For example, if ", count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "A", next := 125585, root := ~, start := 125574, stop := 125584 ), rec( content := " is ", count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "Ref", next := 125619, root := ~, start := 125589, stop := 125618 ), rec( content := ",\n t\ hen the digraph being created will be mutable, if ", count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "A", next := 125687, root := ~, start := 125676, stop := 125686 ), rec( content := " is ", count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "Ref", next := 125727, root := ~, start := 125691, stop := 125726 ), rec( content := ", then t\ he digraph will be immutable. \n If the optional first argument ", count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "A", next := 125812, root := ~, start := 125801, stop := 125811 ), rec( content := " is not \ present, then ", count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "Ref", next := 125872, root := ~, start := 125834, stop := 125871 ), rec( content := " is used\ by default.", count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 5, 9, 7 ], mathmode := "Text", name := "P", next := 125896, root := ~, start := 125892, stop := 125895 ), rec( content := "\n\n \ See also ", count := [ 3, 5, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Peterse\ nGraph" ), content := 0, count := [ 3, 5, 9, 7 ], mathmode := "Text", name := "Ref", next := 125938, root := ~, start := 125911, stop := 125937 ), rec( content := ".\n\n", count := [ 3, 5, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> GeneralisedPetersenGraph(7, 2);\n\ngap> GeneralisedPetersenGraph(40, 1);\n\ngap> D := GeneralisedPetersenGraph(5, 2\ );\n\ngap> IsIsomorphi\ cDigraph(D, PetersenGraph());\ntrue\ngap> GeneralisedPetersenGraph(IsMutableDi\ graph, 9, 4);\n\n", count := [ 3, 5, 9, 8 ], name := "PCD\ ATA", root := ~ ) ], count := [ 3, 5, 9, 8 ], mathmode := "Text", name := "Example", next := 126413, root := ~, start := 125941, stop := 126412 ), rec( content := "\n ", count := [ 3, 5, 9, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "Description", next := 126430, root := ~, start := 124640, stop := 126429 ) ], count := [ 3, 5, 9, 1 ], mathmode := "Text", name := "ManSection", next := 126444, root := ~, start := 124532, stop := 126443 ), rec( content := "\n\n ", count := [ 3, 5, 9, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 0, 1 ], mathmode := "Text", name := "Section", next := 126458, root := ~, start := 114188, stop := 126457 ) , rec( content := "\n\n", count := [ 3, 5, 9, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 0, 0, 1 ], mathmode := "Text", name := "Chapter", next := 126470, root := ~, start := 19211, stop := 126469 ), rec( content := "\n ", count := [ 3, 5, 9, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := " creating ", count := [ 3, 5, 9, 9 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n ", count := [ 3, 5, 9, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "Operators" ), content := [ rec( attributes := rec( ), content := [ rec( content := "Operators", count := [ 4, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 0, 0, 2 ], mathmode := "Text", name := "Heading", next := 126547, root := ~, start := 126519, stop := 126546 ) , rec( content := "\n\n ", count := [ 4, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Operators for dig\ raphs", count := [ 4, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 2 ], mathmode := "Text", name := "Heading", next := 126601, root := ~, start := 126560, stop := 126600 ), rec( content := "\n ", count := [ 4, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "digraph1", count := [ 4, 1, 0, 4 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 4 ], mathmode := \ "Text", name := "A", next := 126642, root := ~, start := 126627, stop := 12664\ 1 ), rec( content := " = ", count := [ 4, 1, 0, 4 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 4, 1, 0, 4 ], mathmode := "Text", name := "PCDATA", root \ := ~ ) ], count := [ 4, 1, 0, 4 ], mathmode := "Text", name := "A", next := 1266\ 60, root := ~, start := 126645, stop := 126659 ) ], count := [ 4, 1, 0, 4 ], mathmode := "Text", name := "C", next := 126664, root := ~, start := 126624, stop := 126663 ) ], count := [ 4, 1, 0, 4 ], name := "Mark", next := 126671, root := ~, start := 126618, stop := 126670 ), rec( attributes := rec( ), content := [ rec( content := "\n \ ", count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "=" ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "=", count := [ 4, 1, 0, 5 ], mathmode \ := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 5 ], mathmode := \ "Text", name := "C", next := 126714, root := ~, start := 126706, stop := 12671\ 3 ), rec( content := " (for digraphs)", count := [ 4, 1, 0, 5 ], mathmode := "\ Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "Index", next := 126737, root := ~, start := 126691, stop := 126736 ), rec( content := "\n \ returns ", count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "K", next := 126764, root := ~, start := 126753, stop := 126763 ), rec( content := " if ", count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "A", next := 126783, root := ~, start := 126768, stop := 126782 ), rec( content := " and ", count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "A", next := 126803, root := ~, start := 126788, stop := 126802 ), rec( content := " have th\ e same\n vertices, and ", count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphEdges(", count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "digraph1", count := [ 4, 1, 0, 5 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 5 ], mathmode := \ "Text", name := "A", next := 126870, root := ~, start := 126855, stop := 12686\ 9 ), rec( content := ") =\n DigraphEdges(", count := [ 4, 1, 0, 5 ], mathmode := \ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( cont\ ent := "digraph2", count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "A", next := 1269\ 11, root := ~, start := 126896, stop := 126910 ), rec( content := ")", count := [ 4, 1, 0, 5 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "C", next := 126916, root := ~, start := 126839, stop := 126915 ), rec( content := ", up to \ some re-ordering of the edge\n lists. ", count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 4, 1, 0, 6 ], mathmode := "Text", name := "P", next := 126971, root := ~, start := 126967, stop := 126970 ), rec( content := "\n\n \ Note that this operator does not compare the vertex labels\n of ", count := [ 4, 1, 0, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 4, 1, 0, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 6 ], mathmode := "Text", name := "A", next := 127064, root := ~, start := 127049, stop := 127063 ), rec( content := " and ", count := [ 4, 1, 0, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 4, 1, 0, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 6 ], mathmode := "Text", name := "A", next := 127084, root := ~, start := 127069, stop := 127083 ), rec( content := ".\n \ ", count := [ 4, 1, 0, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 5 ], name := "Item", next := 127098, root := ~, start := 126677, stop := 127097 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "digraph1", count := [ 4, 1, 0, 7 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 7 ], mathmode := \ "Text", name := "A", next := 127129, root := ~, start := 127114, stop := 12712\ 8 ), rec( content := " < ", count := [ 4, 1, 0, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 4, 1, 0, 7 ], mathmode := "Text", name := "PCDATA", root \ := ~ ) ], count := [ 4, 1, 0, 7 ], mathmode := "Text", name := "A", next := 1271\ 50, root := ~, start := 127135, stop := 127149 ) ], count := [ 4, 1, 0, 7 ], mathmode := "Text", name := "C", next := 127154, root := ~, start := 127111, stop := 127153 ) ], count := [ 4, 1, 0, 7 ], name := "Mark", next := 127161, root := ~, start := 127105, stop := 127160 ), rec( attributes := rec( ), content := [ rec( content := "\n \ ", count := [ 4, 1, 0, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "<" ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "<", count := [ 4, 1, 0, 8 ], mathmode \ := "Text", name := "PCDATA", next := 6, root := ~ ) ], count := [ 4, 1, 0, 8 ] , mathmode := \ "Text", name := "C", next := 127210, root := ~, start := 127199, stop := 12720\ 9 ), rec( content := " (for digraphs)", count := [ 4, 1, 0, 8 ], mathmode := "\ Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 8 ], mathmode := "Text", name := "Index", next := 127233, root := ~, start := 127181, stop := 127232 ), rec( content := "\n\n \ This operator returns ", count := [ 4, 1, 0, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 4, 1, 0, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 8 ], mathmode := "Text", name := "K", next := 127275, root := ~, start := 127264, stop := 127274 ), rec( content := " if one \ of the following holds:\n\n ", count := [ 4, 1, 0, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "\n The number ", count := [ \ 4, 1, 0, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\ tes := rec( ), content := [ rec( content := "n_1", count := [ 4, 1, 0, 10 ], \ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 10 ], math\ mode := "Text", name := "M", next := 127370, root := ~, start := 127360, stop \ := 127369 ), rec( content := " of vertices in ", count := [ 4, 1, 0, 10 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "digraph1", count := [ 4, 1, 0, 10 ], mathmode := "Te\ xt", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 10 ], mathmode := "T\ ext", name := "A", next := 127401, root := ~, start := 127386, stop := 127400 ), rec( cont\ ent := " is less than\n the number ", count := [ 4, 1, 0, 10 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "n_2", count := [ 4, 1, 0, 10 ], mathmode := "Text", \ name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 10 ], mathmode := "Text", name\ := "M", next := 127447, root := ~, start := 127437, stop := 127446 ), rec( cont\ ent := " of vertices in ", count := [ 4, 1, 0, 10 ], mathmode := "Text", name \ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conten\ t := "digraph2", count := [ 4, 1, 0, 10 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 4, 1, 0, 10 ], mathmode := "Text", name := "A", next\ := 127478, root := ~, start := 127463, stop := 127477 ), rec( content := ";\n\ ", count := [ 4, 1, 0, 10 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 4, 1, 0, 10 ], name := "Item", next := 127496, root := ~, start := 127\ 331, stop := 127495 ), rec( attributes := rec( ), content := [ rec( content :\ = "\n ", count := [ 4, 1, 0, 12 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n_\ 1 = n_2", count := [ 4, 1, 0, 12 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 4, 1, 0, 12 ], mathmode := "Text", name := "M", next := \ 127540, root := ~, start := 127524, stop := 127539 ), rec( content := ", and t\ he number ", count := [ 4, 1, 0, 12 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "m_1", count\ := [ 4, 1, 0, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 4, 1, 0, 12 ], mathmode := "Text", name := "M", next := 127567, root :=\ ~, start := 127557, stop := 127566 ), rec( content := " of edges in\n \ ", count := [ 4, 1, 0, 12 ], mathmode := "Text", name := "PCDATA", root := \ ~ ), rec( attributes := rec( ), content := [ rec( content := "digraph1", coun\ t := [ 4, 1, 0, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 4, 1, 0, 12 ], mathmode := "Text", name := "A", next := 127606, root :=\ ~, start := 127591, stop := 127605 ), rec( content := " is less than the numb\ er ", count := [ 4, 1, 0, 12 ], mathmode := "Text", name := "PCDATA", root := \ ~ ), rec( attributes := rec( ), content := [ rec( content := "m_2", count := \ [ 4, 1, 0, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :=\ [ 4, 1, 0, 12 ], mathmode := "Text", name := "M", next := 127641, root := ~, star\ t := 127631, stop := 127640 ), rec( content := " of edges in\n ", coun\ t := [ 4, 1, 0, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "digraph2", count := [ 4, 1, 0\ , 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, \ 0, 12 ], mathmode := "Text", name := "A", next := 127680, root := ~, start := \ 127665, stop := 127679 ), rec( content := ";\n ", count := [ 4, 1, 0, \ 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 12 ], name := "Ite\ m", next := 127698, root := ~, start := 127506, stop := 127697 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n ", count := [ 4, 1, 0, 1\ 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec\ ( ), content := [ rec( content := "n_1 = n_2", count := [ 4, 1, 0, 14 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 14 ], math\ mode := "Text", name := "M", next := 127742, root := ~, start := 127726, stop \ := 127741 ), rec( content := ", ", count := [ 4, 1, 0, 14 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec\ ( content := "m_1 = m_2", count := [ 4, 1, 0, 14 ], mathmode := "Text", name :\ = "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 14 ], mathmode := "Text", name \ := "M", next := 127760, root := ~, start := 127744, stop := 127759 ), rec( cont\ ent := ", and\n ", count := [ 4, 1, 0, 14 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "DigraphEdges(", count := [ 4, 1, 0, 14 ], mathmode := "Text", name := "\ PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content :=\ "digraph1", count := [ 4, 1, 0, 14 ], mathmode := "Text", name := "PCDATA", r\ oot := ~ ) ], count := [ 4, 1, 0, 14 ], mathmode := "Text", name := "A", next \ := 127808, root := ~, start := 127793, stop := 127807 ), rec( content := ")", \ count := [ 4, 1, 0, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 4, 1, 0, 14 ], mathmode := "Text", name := "C", next := 127813, root :=\ ~, start := 127777, stop := 127812 ), rec( content := " is less than\n \ ", count := [ 4, 1, 0, 14 ], mathmode := "Text", name := "PCDATA", root :=\ ~ ), rec( attributes := rec( ), content := [ rec( content := "DigraphEdges("\ , count := [ 4, 1, 0, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ),\ rec( attributes := rec( ), content := [ rec( content := "digraph2", count :=\ [ 4, 1, 0, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :\ = [ 4, 1, 0, 14 ], mathmode := "Text", name := "A", next := 127869, root := ~,\ start := 127854, stop := 127868 ), rec( content := ")", count := [ 4, 1, 0, 1\ 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, \ 14 ], mathmode := "Text", name := "C", next := 127874, root := ~, start := 127\ 838, stop := 127873 ), rec( content := " after having both of these sets\n \ have been sorted with respect to the lexicographical order.\n " , coun\ t := [ 4, 1, 0, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 14 ], name := "Ite\ m", next := 127994, root := ~, start := 127708, stop := 127993 ) ], count := [ 4, 1, 0, 9 ], mathmode := "Text", name := "List", next := 128009, root := ~, start := 127315, stop := 128008 ), rec( content := "\n " , count := [ 4, 1, 0, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 8 ], name := "Item", next := 128022, root := ~, start := 127167, stop := 128021 ) ], count := [ 4, 1, 0, 4 ], mathmode := "Text", name := "List", next := 128033, root := ~, start := 126606, stop := 128032 ), rec( content := "\n\n ", count := [ 4, 1, 0, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "super, sub", Name := "IsSubdigraph" ) , content := 0, count := [ 4, 1, 1, 2 ], mathmode := "Text", name := "Oper", next := 128097, root := ~, start := 128053, stop := 128096 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "K", next := 128120, root := ~, start := 128109, stop := 128119 ), rec( content := " or ", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "K", next := 128136, root := ~, start := 128124, stop := 128135 ), rec( content := ".", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "Returns", next := 128147, root := ~, start := 128100, stop := 128146 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ uper", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "A", next := 128183, root := ~, start := 128171, stop := 128182 ), rec( content := " and ", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ub", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "A", next := 128198, root := ~, start := 128188, stop := 128197 ), rec( content := " are dig\ raphs, then this operation returns\n ", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "K", next := 128256, root := ~, start := 128245, stop := 128255 ), rec( content := " if ", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ub", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "A", next := 128270, root := ~, start := 128260, stop := 128269 ), rec( content := " is a su\ bdigraph of ", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ uper", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "A", next := 128302, root := ~, start := 128290, stop := 128301 ), rec( content := ", and ", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "K", next := 128320, root := ~, start := 128308, stop := 128319 ), rec( content := "\n if\ it is not. ", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "P", next := 128343, root := ~, start := 128339, stop := 128342 ), rec( content := "\n\n \ A digraph ", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ub", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "A", next := 128369, root := ~, start := 128359, stop := 128368 ), rec( content := " is a ", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ubdigraph", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "E", next := 128392, root := ~, start := 128375, stop := 128391 ), rec( content := " of a di\ graph ", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ uper", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "A", next := 128418, root := ~, start := 128406, stop := 128417 ), rec( content := " if\n \ ", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "s\ ub", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "A", next := 128436, root := ~, start := 128426, stop := 128435 ), rec( content := " and ", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ uper", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "A", next := 128453, root := ~, start := 128441, stop := 128452 ), rec( content := " share t\ he same number of vertices, and the\n collection of edges of ", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ uper", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "A", next := 128536, root := ~, start := 128524, stop := 128535 ), rec( content := " (includ\ ing repeats) contains the\n collection of edges of ", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ub", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "A", next := 128607, root := ~, start := 128597, stop := 128606 ), rec( content := " (includ\ ing repeats). ", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "P", next := 128634, root := ~, start := 128630, stop := 128633 ), rec( content := "\n\n \ In other words, ", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ub", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "A", next := 128666, root := ~, start := 128656, stop := 128665 ), rec( content := " is a su\ bdigraph of ", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ uper", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "A", next := 128698, root := ~, start := 128686, stop := 128697 ), rec( content := " if and \ only if\n ", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphNrVertices(", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "su\ b", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 5 ], mathmode := \ "Text", name := "A", next := 128749, root := ~, start := 128739, stop := 12874\ 8 ), rec( content := ") = DigraphNrVertices(", count := [ 4, 1, 1, 5 ], mathmode := \ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( cont\ ent := "super", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "A", next := 1287\ 83, root := ~, start := 128771, stop := 128782 ), rec( content := ")", count := [ 4, 1, 1, 5 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "C", next := 128788, root := ~, start := 128718, stop := 128787 ), rec( content := ", and\n \ for each pair of vertices ", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "C", next := 128832, root := ~, start := 128824, stop := 128831 ), rec( content := " and ", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "C", next := 128845, root := ~, start := 128837, stop := 128844 ), rec( content := ", there \ are at least as many\n edges of the form ", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ i, j]", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "C", next := 128909, root := ~, start := 128896, stop := 128908 ), rec( content := " in ", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ uper", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "A", next := 128925, root := ~, start := 128913, stop := 128924 ), rec( content := " as ther\ e are in ", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ub", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "A", next := 128952, root := ~, start := 128942, stop := 128951 ), rec( content := ".\n " , count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 4, 1, 1, 6 ], mathmode := "Text", name := "P", next := 128962, root := ~, start := 128958, stop := 128961 ), rec( content := "\n\n \ ", count := [ 4, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> g := Digraph([[2, 3], [1], [2, 3]]);\n\ngap> h := Digraph([[2, 3], [], [2]]);\n\ngap> IsSubdigraph(g, h);\ntrue\ngap> IsSubdigraph(h, g);\nf\ alse\ngap> IsSubdigraph(CompleteDigraph(4), CycleDigraph(4));\ntrue\ngap> IsSu\ bdigraph(CycleDigraph(4), ChainDigraph(4));\ntrue\ngap> g := Digraph([[2, 2], \ [1]]);\n\ngap> h := Digraph([\ [2], [1]]);\n\ngap> IsSubdigraph(g\ , h);\ntrue\ngap> IsSubdigraph(h, g);\nfalse", count := [ 4, 1, 1, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 4, 1, 1, 7 ], mathmode := "Text", name := "Example", next := 129570, root := ~, start := 128968, stop := 129569 ), rec( content := "\n ", count := [ 4, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "Description", next := 129587, root := ~, start := 128150, stop := 129586 ) ], count := [ 4, 1, 1, 1 ], mathmode := "Text", name := "ManSection", next := 129601, root := ~, start := 128038, stop := 129600 ), rec( content := "\n\n ", count := [ 4, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "super, sub", Name := "IsUndirectedSpa\ nningTree" ), content := 0, count := [ 4, 1, 2, 2 ], mathmode := "Text", name := "Oper", next := 129677, root := ~, start := 129621, stop := 129676 ), rec( attributes := rec( Arg := "super, sub", Name := "IsUndirectedSpa\ nningForest" ), content := 0, count := [ 4, 1, 2, 4 ], mathmode := "Text", name := "Oper", next := 129738, root := ~, start := 129680, stop := 129737 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "K", next := 129761, root := ~, start := 129750, stop := 129760 ), rec( content := " or ", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "K", next := 129777, root := ~, start := 129765, stop := 129776 ), rec( content := ".", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "Returns", next := 129788, root := ~, start := 129741, stop := 129787 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ operation ", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sUndirectedSpanningTree", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "C", next := 129854, root := ~, start := 129823, stop := 129853 ), rec( content := " returns\ ", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "K", next := 129874, root := ~, start := 129863, stop := 129873 ), rec( content := " if the\\ n digraph ", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ub", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "A", next := 129904, root := ~, start := 129894, stop := 129903 ), rec( content := " is an u\ ndirected spanning tree of the digraph\n ", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ uper", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "A", next := 129967, root := ~, start := 129955, stop := 129966 ), rec( content := ", and th\ e operation ", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sUndirectedSpanningForest", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "C", next := 130020, root := ~, start := 129987, stop := 130019 ), rec( content := " returns\ \n ", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "K", next := 130044, root := ~, start := 130033, stop := 130043 ), rec( content := " if the \ digraph ", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ub", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "A", next := 130070, root := ~, start := 130060, stop := 130069 ), rec( content := " is an u\ ndirected spanning forest of\n the digraph ", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ uper", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "A", next := 130135, root := ~, start := 130123, stop := 130134 ), rec( content := ". ", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "P", next := 130141, root := ~, start := 130137, stop := 130140 ), rec( content := "\n\n \ An ", count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ndirected spanning tree", count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "E", next := 130181, root := ~, start := 130150, stop := 130180 ), rec( content := " of a di\ graph ", count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ uper", count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "A", next := 130207, root := ~, start := 130195, stop := 130206 ), rec( content := " is a su\ bdigraph\n of ", count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ uper", count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "A", next := 130243, root := ~, start := 130231, stop := 130242 ), rec( content := " that is\ an undirected tree (see ", count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "IsSubdi\ graph" ), content := 0, count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "Ref", next := 130303, root := ~, start := 130276, stop := 130302 ), rec( content := "\n an\ d ", count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsUndir\ ectedTree" ), content := 0, count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "Ref", next := 130343, root := ~, start := 130312, stop := 130342 ), rec( content := "). Note \ that a digraph whose ", count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Maximal\ SymmetricSubdigraph" ), content := 0, count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "Ref", next := 130418, root := ~, start := 130372, stop := 130417 ), rec( content := " is not \ connected has no undirected\n spanning trees (see ", count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsConne\ ctedDigraph" ), content := 0, count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "Ref", next := 130510, root := ~, start := 130478, stop := 130509 ), rec( content := "). ", count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "P", next := 130517, root := ~, start := 130513, stop := 130516 ), rec( content := "\n\n \ An ", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ndirected spanning forest", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "E", next := 130559, root := ~, start := 130526, stop := 130558 ), rec( content := " of a di\ graph ", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ uper", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "A", next := 130585, root := ~, start := 130573, stop := 130584 ), rec( content := " is a\n \ subdigraph of ", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ uper", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "A", next := 130621, root := ~, start := 130609, stop := 130620 ), rec( content := " that is\ an undirected forest (see ", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "IsSubdi\ graph" ), content := 0, count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "Ref", next := 130688, root := ~, start := 130656, stop := 130687 ), rec( content := " and ", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsUndir\ ectedForest" ), content := 0, count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "Ref", next := 130725, root := ~, start := 130693, stop := 130724 ), rec( content := "), and i\ s not\n contained in any larger such subdigraph of ", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ uper", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "A", next := 130798, root := ~, start := 130786, stop := 130797 ), rec( content := ". Equiv\ alently, an\n undirected spanning forest is a subdigraph of ", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ uper", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "A", next := 130880, root := ~, start := 130868, stop := 130879 ), rec( content := " whose c\ onnected\n components coincide with those of the ", count := [ 4, 1, 2, 7 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Maximal\ SymmetricSubdigraph" ), content := 0, count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "Ref", next := 130985, root := ~, start := 130939, stop := 130984 ), rec( content := " of ", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ uper", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "A", next := 131001, root := ~, start := 130989, stop := 131000 ), rec( content := " (see ", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ ConnectedComponents" ), content := 0, count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "Ref", next := 131053, root := ~, start := 131007, stop := 131052 ), rec( content := "). ", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 4, 1, 2, 8 ], mathmode := "Text", name := "P", next := 131060, root := ~, start := 131056, stop := 131059 ), rec( content := "\n\n \ Note that an undirected spanning tree is an undirected spanning forest that\n \ is connected.\n\n ", count := [ 4, 1, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CompleteDigraph(4);\n\n\ gap> tree := Digraph([[3], [4], [1, 4], [2, 3]]);\n\ngap> IsSubdigraph(D, tree) and IsUndirectedTree(tree);\ntru\ e\ngap> IsUndirectedSpanningTree(D, tree);\ntrue\ngap> forest := EmptyDigraph(\ 4);\n\ngap> IsSubdigraph(D, forest) a\ nd IsUndirectedForest(forest);\ntrue\ngap> IsUndirectedSpanningForest(D, fores\ t);\nfalse\ngap> IsSubdigraph(tree, forest);\ntrue\ngap> D := DigraphDisjointU\ nion(CycleDigraph(2), CycleDigraph(2));\n\ngap> IsUndirectedTree(D);\nfalse\ngap> IsUndirectedForest(D) and IsUn\ directedSpanningForest(D, D);\ntrue", count := [ 4, 1, 2, 9 ], name := "PCDATA\ ", root := ~ ) ], count := [ 4, 1, 2, 9 ], mathmode := "Text", name := "Example", next := 131912, root := ~, start := 131165, stop := 131911 ), rec( content := "\n ", count := [ 4, 1, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "Description", next := 131929, root := ~, start := 129791, stop := 131928 ) ], count := [ 4, 1, 2, 1 ], mathmode := "Text", name := "ManSection", next := 131943, root := ~, start := 129606, stop := 131942 ), rec( content := "\n\n ", count := [ 4, 1, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 1 ], mathmode := "Text", name := "Section", next := 131957, root := ~, start := 126551, stop := 131956 ) , rec( content := "\n", count := [ 4, 1, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 0, 0, 1 ], mathmode := "Text", name := "Chapter", next := 131968, root := ~, start := 126492, stop := 131967 ), rec( content := "\n ", count := [ 4, 1, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := " operators/hashs ", count := [ 4, 1, 2, 10 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n ", count := [ 4, 1, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "Attributes and operations" ), content := [ rec( attributes := rec( ), content := [ rec( content := "Attributes and operations\ ", count := [ 5, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 0, 0, 2 ], mathmode := "Text", name := "Heading", next := 132084, root := ~, start := 132040, stop := 132083 ), rec( content := "\n ", count := [ 5, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Vertices and edge\ s", count := [ 5, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 0, 2 ], mathmode := "Text", name := "Heading", next := 132133, root := ~, start := 132096, stop := 132132 ), rec( content := "\n ", count := [ 5, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphVertices\ " ), content := 0, count := [ 5, 1, 1, 2 ], mathmode := "Text", name := "Attr", next := 132197, root := ~, start := 132153, stop := 132196 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ integers.", count := [ 5, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 1, 3 ], mathmode := "Text", name := "Returns", next := 132238, root := ~, start := 132200, stop := 132237 ), rec( attributes := rec( ), content := [ rec( content := "\n Ret\ urns the vertices of the digraph ", count := [ 5, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 1, 3 ], mathmode := "Text", name := "A", next := 132309, root := ~, start := 132295, stop := 132308 ), rec( content := ". ", count := [ 5, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 1, 4 ], mathmode := "Text", name := "P", next := 132315, root := ~, start := 132311, stop := 132314 ), rec( content := "\n\n \ Note that the vertices of a digraph are always a range of\n positive intege\ rs from ", count := [ 5, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "1\ ", count := [ 5, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 1, 4 ], mathmode := "Text", name := "C", next := 132414, root := ~, start := 132406, stop := 132413 ), rec( content := " to the \ number of vertices of the graph.\n ", count := [ 5, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := Digraph([\"a\", \"b\", \"c\"],\n> [\"a\", \"b\", \ \"b\"],\n> [\"b\", \"c\", \"a\"]);\n\ngap> DigraphVertices(gr);\n[ 1 .. 3 ]\ngap> gr := Digraph\ ([1, 2, 3, 4, 5, 7],\n> [1, 2, 2, 4, 4],\n> \ [2, 7, 5, 3, 7]);\n\ngap> DigraphV\ ertices(gr);\n[ 1 .. 6 ]\ngap> DigraphVertices(RandomDigraph(100));\n[ 1 .. 10\ 0 ]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n\ngap> DigraphVertices(D);\n[ 1 .. 3 ]\n", count := [ 5, 1, 1, 5 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 1, 1, 5 ], mathmode := "Text", name := "Example", next := 133055, root := ~, start := 132459, stop := 133054 ), rec( content := "\n ", count := [ 5, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 1, 3 ], mathmode := "Text", name := "Description", next := 133072, root := ~, start := 132241, stop := 133071 ) ], count := [ 5, 1, 1, 1 ], mathmode := "Text", name := "ManSection", next := 133086, root := ~, start := 132138, stop := 133085 ), rec( content := "\n\n ", count := [ 5, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphNrVertic\ es" ), content := 0, count := [ 5, 1, 2, 2 ], mathmode := "Text", name := "Attr", next := 133153, root := ~, start := 133107, stop := 133152 ), rec( attributes := rec( ), content := [ rec( content := "An intege\ r.", count := [ 5, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 2, 3 ], mathmode := "Text", name := "Returns", next := 133186, root := ~, start := 133156, stop := 133185 ), rec( attributes := rec( ), content := [ rec( content := "\n Ret\ urns the number of vertices of the digraph ", count := [ 5, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 2, 3 ], mathmode := "Text", name := "A", next := 133267, root := ~, start := 133253, stop := 133266 ), rec( content := ". ", count := [ 5, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 2, 4 ], mathmode := "Text", name := "P", next := 133273, root := ~, start := 133269, stop := 133272 ), rec( content := "\n\n \ ", count := [ 5, 1, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := Digraph([\"a\", \"b\", \"c\"],\n> [\"a\", \"b\", \ \"b\"],\n> [\"b\", \"c\", \"a\"]);\n\ngap> DigraphNrVertices(gr);\n3\ngap> gr := Digraph([1, 2,\ 3, 4, 5, 7],\n> [1, 2, 2, 4, 4],\n> [2, 7, \ 5, 3, 7]);\n\ngap> DigraphNrVertic\ es(gr);\n6\ngap> DigraphNrVertices(RandomDigraph(100));\n100\ngap> D := CycleD\ igraph(IsMutableDigraph, 3);\n\ngap>\ DigraphNrVertices(D);\n3\n", count := [ 5, 1, 2, 5 ], name := "PCDATA", root := ~ ) ], count := [ 5, 1, 2, 5 ], mathmode := "Text", name := "Example", next := 133847, root := ~, start := 133279, stop := 133846 ), rec( content := "\n ", count := [ 5, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 2, 3 ], mathmode := "Text", name := "Description", next := 133864, root := ~, start := 133189, stop := 133863 ) ], count := [ 5, 1, 2, 1 ], mathmode := "Text", name := "ManSection", next := 133878, root := ~, start := 133092, stop := 133877 ), rec( content := "\n\n ", count := [ 5, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphEdges" ) , content := 0, count := [ 5, 1, 3, 2 ], mathmode := "Text", name := "Attr", next := 133940, root := ~, start := 133899, stop := 133939 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ lists.", count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "Returns", next := 133978, root := ~, start := 133943, stop := 133977 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphEdges", count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "C", next := 134018, root := ~, start := 133999, stop := 134017 ), rec( content := " returns\ a list of edges of the digraph ", count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "A", next := 134072, root := ~, start := 134058, stop := 134071 ), rec( content := ",\n w\ here each edge is a pair of elements of ", count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Vertices" ), content := 0, count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "Ref", next := 134148, root := ~, start := 134119, stop := 134147 ), rec( content := " of\n \ the form ", count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ source,range]", count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "C", next := 134186, root := ~, start := 134165, stop := 134185 ), rec( content := ".\n " , count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "P", next := 134196, root := ~, start := 134192, stop := 134195 ), rec( content := "\n\n \ The entries of ", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphEdges(", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "C", next := 134237, root := ~, start := 134217, stop := 134236 ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "A", next := 134251, root := ~, start := 134237, stop := 134250 ), rec( attributes := rec( ), content := [ rec( content := ")\ ", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "C", next := 134259, root := ~, start := 134251, stop := 134258 ), rec( content := " are in \ one-to-one\n corresponence with the edges of ", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "A", next := 134328, root := ~, start := 134314, stop := 134327 ), rec( content := ". Hence\ \n ", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphEdges(", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "C", next := 134361, root := ~, start := 134341, stop := 134360 ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "A", next := 134375, root := ~, start := 134361, stop := 134374 ), rec( attributes := rec( ), content := [ rec( content := ")\ ", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "C", next := 134383, root := ~, start := 134375, stop := 134382 ), rec( content := " is dupl\ icate-free if and only if\n ", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "A", next := 134435, root := ~, start := 134421, stop := 134434 ), rec( content := " contain\ s no multiple edges. ", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 3, 5 ], mathmode := "Text", name := "P", next := 134468, root := ~, start := 134464, stop := 134467 ), rec( content := "\n\n \ The entries of ", count := [ 5, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphEdges", count := [ 5, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 3, 5 ], mathmode := "Text", name := "C", next := 134508, root := ~, start := 134489, stop := 134507 ), rec( content := " are gua\ ranteed to be sorted by their\n first component (i.e. by the source of each\ edge), but they are not\n necessarily then sorted by the second component.\ \n ", count := [ 5, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := DigraphFromDiSparse6String(\".DaXbOe?EAM@G~\");\n\ngap> edges := ShallowCopy(DigraphEdges(gr))\ ;; Sort(edges);\ngap> edges;\n[ [ 1, 1 ], [ 1, 3 ], [ 1, 3 ], [ 1, 4 ], [ 1, 5\ ], [ 2, 1 ], \n [ 2, 2 ], [ 2, 3 ], [ 2, 5 ], [ 3, 2 ], [ 3, 4 ], [ 3, 5 ], \ \n [ 4, 2 ], [ 4, 4 ], [ 4, 5 ], [ 5, 1 ] ]\ngap> D := CycleDigraph(IsMutable\ Digraph, 3);\n\ngap> DigraphEdges(D)\ ;\n[ [ 1, 2 ], [ 2, 3 ], [ 3, 1 ] ]\n", count := [ 5, 1, 3, 6 ], name := "PCDA\ TA", root := ~ ) ], count := [ 5, 1, 3, 6 ], mathmode := "Text", name := "Example", next := 135198, root := ~, start := 134675, stop := 135197 ), rec( content := "\n ", count := [ 5, 1, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "Description", next := 135215, root := ~, start := 133981, stop := 135214 ) ], count := [ 5, 1, 3, 1 ], mathmode := "Text", name := "ManSection", next := 135229, root := ~, start := 133884, stop := 135228 ), rec( content := "\n\n ", count := [ 5, 1, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphNrEdges"\ ), content := 0, count := [ 5, 1, 4, 2 ], mathmode := "Text", name := "Attr", next := 135293, root := ~, start := 135250, stop := 135292 ), rec( attributes := rec( ), content := [ rec( content := "An intege\ r.", count := [ 5, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 4, 3 ], mathmode := "Text", name := "Returns", next := 135326, root := ~, start := 135296, stop := 135325 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function returns the number of edges of the digraph ", count := [ 5, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 4, 3 ], mathmode := "Text", name := "A", next := 135418, root := ~, start := 135404, stop := 135417 ), rec( content := ".\n " , count := [ 5, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := Digraph([\n> [1, 3, 4, 5], [1, 2, 3, 5], [2, 4, 5], [2, 4, 5], [1]\ ]);;\ngap> DigraphNrEdges(gr);\n15\ngap> gr := Digraph([\"a\", \"b\", \"c\"],\ \n> [\"a\", \"b\", \"b\"],\n> [\"b\", \"a\",\ \"a\"]);\n\ngap> DigraphNrEd\ ges(gr);\n3\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n\ngap> DigraphNrEdges(D);\n3\n", count := [ 5, 1, 4, 4 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 1, 4, 4 ], mathmode := "Text", name := "Example", next := 135865, root := ~, start := 135424, stop := 135864 ), rec( content := "\n ", count := [ 5, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 4, 3 ], mathmode := "Text", name := "Description", next := 135882, root := ~, start := 135329, stop := 135881 ) ], count := [ 5, 1, 4, 1 ], mathmode := "Text", name := "ManSection", next := 135896, root := ~, start := 135235, stop := 135895 ), rec( content := "\n\n ", count := [ 5, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphSinks" ) , content := 0, count := [ 5, 1, 5, 2 ], mathmode := "Text", name := "Attr", next := 135958, root := ~, start := 135917, stop := 135957 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ vertices.", count := [ 5, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 5, 3 ], mathmode := "Text", name := "Returns", next := 135999, root := ~, start := 135961, stop := 135998 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function returns a list of the sinks of the digraph\n ", count := [ 5, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 5, 3 ], mathmode := "Text", name := "A", next := 136095, root := ~, start := 136081, stop := 136094 ), rec( content := ".\n A\ sink of a digraph is a vertex with out-degree zero.\n See ", count := [ 5, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "OutDegr\ eeOfVertex" ), content := 0, count := [ 5, 1, 5, 3 ], mathmode := "Text", name := "Ref", next := 136194, root := ~, start := 136163, stop := 136193 ), rec( content := ".\n " , count := [ 5, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := Digraph([[3, 5, 2, 2], [3], [], [5, 2, 5, 3], []]);\n\ngap> DigraphSinks(gr);\n[ 3, 5 ]\ngap> D\ := CycleDigraph(IsMutableDigraph, 3);\n\ngap> DigraphSinks(D);\n[ ]\n", count := [ 5, 1, 5, 4 ], name := "PCDATA\ ", root := ~ ) ], count := [ 5, 1, 5, 4 ], mathmode := "Text", name := "Example", next := 136492, root := ~, start := 136200, stop := 136491 ), rec( content := "\n ", count := [ 5, 1, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 5, 3 ], mathmode := "Text", name := "Description", next := 136509, root := ~, start := 136002, stop := 136508 ) ], count := [ 5, 1, 5, 1 ], mathmode := "Text", name := "ManSection", next := 136523, root := ~, start := 135902, stop := 136522 ), rec( content := "\n\n ", count := [ 5, 1, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphSources"\ ), content := 0, count := [ 5, 1, 6, 2 ], mathmode := "Text", name := "Attr", next := 136587, root := ~, start := 136544, stop := 136586 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ vertices.", count := [ 5, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 6, 3 ], mathmode := "Text", name := "Returns", next := 136628, root := ~, start := 136590, stop := 136627 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function returns an immutable list of the sources of the digraph\n ", count := [ 5, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 6, 3 ], mathmode := "Text", name := "A", next := 136737, root := ~, start := 136723, stop := 136736 ), rec( content := ".\n A\ source of a digraph is a vertex with in-degree zero.\n See ", count := [ 5, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "InDegre\ eOfVertex" ), content := 0, count := [ 5, 1, 6, 3 ], mathmode := "Text", name := "Ref", next := 136836, root := ~, start := 136806, stop := 136835 ), rec( content := ".\n " , count := [ 5, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := Digraph([[3, 5, 2, 2], [3], [], [5, 2, 5, 3], []]);\n\ngap> DigraphSources(gr);\n[ 1, 4 ]\ngap>\ D := CycleDigraph(IsMutableDigraph, 3);\n\ngap> DigraphSources(D);\n[ ]\n", count := [ 5, 1, 6, 4 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 1, 6, 4 ], mathmode := "Text", name := "Example", next := 137138, root := ~, start := 136842, stop := 137137 ), rec( content := "\n ", count := [ 5, 1, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 6, 3 ], mathmode := "Text", name := "Description", next := 137155, root := ~, start := 136631, stop := 137154 ) ], count := [ 5, 1, 6, 1 ], mathmode := "Text", name := "ManSection", next := 137169, root := ~, start := 136529, stop := 137168 ), rec( content := "\n\n ", count := [ 5, 1, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphTopologi\ calSort" ), content := 0, count := [ 5, 1, 7, 2 ], mathmode := "Text", name := "Attr", next := 137241, root := ~, start := 137190, stop := 137240 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ positive integers, or ", count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "K", next := 137296, root := ~, start := 137285, stop := 137295 ), rec( content := ".", count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "Returns", next := 137307, root := ~, start := 137244, stop := 137306 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "A", next := 137345, root := ~, start := 137331, stop := 137344 ), rec( content := " is a di\ graph whose only directed cycles are loops, then\n ", count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphTopologicalSort", count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "C", next := 137435, root := ~, start := 137406, stop := 137434 ), rec( content := " returns\ the vertices of ", count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "A", next := 137474, root := ~, start := 137460, stop := 137473 ), rec( content := " ordered\ \n so that every edge's source appears no earlier in the list than its rang\ e.\n If the digraph ", count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "A", next := 137595, root := ~, start := 137581, stop := 137594 ), rec( content := " contain\ s directed cycles of length greater\n than ", count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "1\ ", count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "M", next := 137656, root := ~, start := 137648, stop := 137655 ), rec( content := ", then t\ his operation returns ", count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "K", next := 137697, root := ~, start := 137686, stop := 137696 ), rec( content := ".\n " , count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 7, 4 ], mathmode := "Text", name := "P", next := 137707, root := ~, start := 137703, stop := 137706 ), rec( content := "\n\n \ See section ", count := [ 5, 1, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Style := "Number\ ", Subsect := "Definitions" ), content := 0, count := [ 5, 1, 7, 4 ], mathmode := "Text", name := "Ref", next := 137769, root := ~, start := 137725, stop := 137768 ), rec( content := " for the\ definition\n of a directed cycle, and the definition of a loop.\n\n ", count := [ 5, 1, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 7, 5 ], mathmode := "Text", name := "P", next := 137853, root := ~, start := 137849, stop := 137852 ), rec( content := "\n\n \ The method used for this attribute has complexity ", count := [ 5, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (m+n)", count := [ 5, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 7, 5 ], mathmode := "Text", name := "M", next := 137922, root := ~, start := 137909, stop := 137921 ), rec( content := " where\n\ ", count := [ 5, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 5, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 7, 5 ], mathmode := "Text", name := "M", next := 137941, root := ~, start := 137933, stop := 137940 ), rec( content := " is the \ number of edges (counting multiple edges as one) and\n ", count := [ 5, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 5, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 7, 5 ], mathmode := "Text", name := "M", next := 138014, root := ~, start := 138006, stop := 138013 ), rec( content := " is the \ number of vertices in the digraph. ", count := [ 5, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 7, 6 ], mathmode := "Text", name := "P", next := 138061, root := ~, start := 138057, stop := 138060 ), rec( content := "\n ", count := [ 5, 1, 7, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([\n> [2, 3], [], [4, 6], [5], [], [7, 8, 9], [], [], []]);\ \n\ngap> DigraphTopologicalSort(D)\ ;\n[ 2, 5, 4, 7, 8, 9, 6, 3, 1 ]\ngap> D := Digraph(IsMutableDigraph, [[2, 3],\ [3], [4], []]);\n\ngap> DigraphTopo\ logicalSort(D);\n[ 4, 3, 2, 1 ]\n", count := [ 5, 1, 7, 7 ], name := "PCDATA", root := ~ ) ], count := [ 5, 1, 7, 7 ], mathmode := "Text", name := "Example", next := 138432, root := ~, start := 138066, stop := 138431 ), rec( content := "\n ", count := [ 5, 1, 7, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "Description", next := 138449, root := ~, start := 137310, stop := 138448 ) ], count := [ 5, 1, 7, 1 ], mathmode := "Text", name := "ManSection", next := 138463, root := ~, start := 137175, stop := 138462 ), rec( content := "\n\n ", count := [ 5, 1, 7, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, i", Name := "DigraphVertexLa\ bel" ), content := 0, count := [ 5, 1, 8, 2 ], mathmode := "Text", name := "Oper", next := 138536, root := ~, start := 138484, stop := 138535 ), rec( attributes := rec( Arg := "digraph, i, obj" , Name := "SetDigraphVerte\ xLabel" ), content := 0, count := [ 5, 1, 8, 4 ], mathmode := "Text", name := "Oper", next := 138598, root := ~, start := 138539, stop := 138597 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "A", next := 138636, root := ~, start := 138622, stop := 138635 ), rec( content := " is a di\ graph, then the first operation returns the label\n of the vertex ", count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "A", next := 138720, root := ~, start := 138712, stop := 138719 ), rec( content := ". The se\ cond operation can be used to set the label\n of the vertex ", count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "A", next := 138798, root := ~, start := 138790, stop := 138797 ), rec( content := " in ", count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "A", next := 138816, root := ~, start := 138802, stop := 138815 ), rec( content := " to the \ arbitrary ", count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ AP", count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " object\\ n ", count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ bj", count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "A", next := 138861, root := ~, start := 138851, stop := 138860 ), rec( content := ". ", count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 8, 6 ], mathmode := "Text", name := "P", next := 138868, root := ~, start := 138864, stop := 138867 ), rec( content := "\n\n \ The label of a vertex can be changed an arbitrary number of times. If no\n \ label has been set for the vertex ", count := [ 5, 1, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 1, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 8, 6 ], mathmode := "Text", name := "A", next := 138993, root := ~, start := 138985, stop := 138992 ), rec( content := ", then t\ he default value is\n ", count := [ 5, 1, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 1, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 8, 6 ], mathmode := "Text", name := "A", next := 139033, root := ~, start := 139025, stop := 139032 ), rec( content := ". ", count := [ 5, 1, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 8, 7 ], mathmode := "Text", name := "P", next := 139039, root := ~, start := 139035, stop := 139038 ), rec( content := "\n\n \ If ", count := [ 5, 1, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 8, 7 ], mathmode := "Text", name := "A", next := 139062, root := ~, start := 139048, stop := 139061 ), rec( content := " is a di\ graph created from a record with a component\n ", count := [ 5, 1, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ertices", count := [ 5, 1, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 8, 7 ], mathmode := "Text", name := "C", next := 139134, root := ~, start := 139119, stop := 139133 ), rec( content := ", then t\ he labels of the vertices are set to the value of\n this component.", count := [ 5, 1, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 8, 8 ], mathmode := "Text", name := "P", next := 139215, root := ~, start := 139211, stop := 139214 ), rec( content := "\n\n \ Induced subdigraphs, and some other operations which create new digraphs from\ \n old ones, inherit their labels from their parents.\n\n ", count := [ 5, 1, 8, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := DigraphFromDigraph6String(\"&DHUEe_\");\n\ngap> DigraphVertexLabel(D, 3);\n3\ngap> D := Digraph([\"a\ \", \"b\", \"c\"], [], []);\n\ngap> D\ igraphVertexLabel(D, 2);\n\"b\"\ngap> SetDigraphVertexLabel(D, 2, \"d\");\ngap\ > DigraphVertexLabel(D, 2);\n\"d\"\ngap> D := InducedSubdigraph(D, [1, 2]);\n<\ immutable empty digraph with 2 vertices>\ngap> DigraphVertexLabel(D, 2);\n\"d\ \"\ngap> D := Digraph(IsMutableDigraph, [\"e\", \"f\", \"g\"], [], []);\n\ngap> DigraphVertexLabel(D, 1);\n\"e\"\ngap\ > SetDigraphVertexLabel(D, 1, \"h\");\ngap> DigraphVertexLabel(D, 1);\n\"h\"\n\ gap> InducedSubdigraph(D, [1, 2]);\n\ng\ ap> DigraphVertexLabel(D, 1);\n\"h\"\n", count := [ 5, 1, 8, 9 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 1, 8, 9 ], mathmode := "Text", name := "Example", next := 140151, root := ~, start := 139359, stop := 140150 ), rec( content := "\n ", count := [ 5, 1, 8, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "Description", next := 140168, root := ~, start := 138601, stop := 140167 ) ], count := [ 5, 1, 8, 1 ], mathmode := "Text", name := "ManSection", next := 140182, root := ~, start := 138469, stop := 140181 ), rec( content := "\n\n ", count := [ 5, 1, 8, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphVertexLa\ bels" ), content := 0, count := [ 5, 1, 9, 2 ], mathmode := "Text", name := "Oper", next := 140251, root := ~, start := 140203, stop := 140250 ), rec( attributes := rec( Arg := "digraph, list", Name := "SetDigraphVerte\ xLabels" ), content := 0, count := [ 5, 1, 9, 4 ], mathmode := "Text", name := "Oper", next := 140311, root := ~, start := 140254, stop := 140310 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "A", next := 140349, root := ~, start := 140335, stop := 140348 ), rec( content := " is a di\ graph, then ", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphVertexLabels", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "C", next := 140395, root := ~, start := 140369, stop := 140394 ), rec( content := " returns\ a\n copy of the labels of the vertices in ", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "A", next := 140462, root := ~, start := 140448, stop := 140461 ), rec( content := ".\n " , count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "S\ etDigraphVertexLabels", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "C", next := 140497, root := ~, start := 140468, stop := 140496 ), rec( content := " can be \ used to set the labels of the vertices\n in ", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "A", next := 140565, root := ~, start := 140551, stop := 140564 ), rec( content := " to the \ list of\n arbitrary ", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ AP", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " objects\ ", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "A", next := 140620, root := ~, start := 140609, stop := 140619 ), rec( content := ". ", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 9, 6 ], mathmode := "Text", name := "P", next := 140626, root := ~, start := 140622, stop := 140625 ), rec( content := "\n\n \ The label of a vertex can be changed an arbitrary number of times. If no\n \ label has been set for the vertex ", count := [ 5, 1, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 1, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 9, 6 ], mathmode := "Text", name := "A", next := 140751, root := ~, start := 140743, stop := 140750 ), rec( content := ", then t\ he default value is\n ", count := [ 5, 1, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 1, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 9, 6 ], mathmode := "Text", name := "A", next := 140791, root := ~, start := 140783, stop := 140790 ), rec( content := ". ", count := [ 5, 1, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 9, 7 ], mathmode := "Text", name := "P", next := 140797, root := ~, start := 140793, stop := 140796 ), rec( content := "\n\n \ If ", count := [ 5, 1, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 9, 7 ], mathmode := "Text", name := "A", next := 140820, root := ~, start := 140806, stop := 140819 ), rec( content := " is a di\ graph created from a record with a component\n ", count := [ 5, 1, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ertices", count := [ 5, 1, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 9, 7 ], mathmode := "Text", name := "C", next := 140892, root := ~, start := 140877, stop := 140891 ), rec( content := ", then t\ he labels of the vertices are set to the value of\n this component.", count := [ 5, 1, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 9, 8 ], mathmode := "Text", name := "P", next := 140973, root := ~, start := 140969, stop := 140972 ), rec( content := "\n\n \ Induced subdigraphs, and other operations which create new digraphs from\n \ old ones, inherit their labels from their parents.\n\n ", count := [ 5, 1, 9, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := DigraphFromDigraph6String(\"&DHUEe_\");\n\ngap> DigraphVertexLabels(D);\n[ 1 .. 5 ]\ngap> D := Digra\ ph([\"a\", \"b\", \"c\"], [], []);\n\ \ngap> DigraphVertexLabels(D);\n[ \"a\", \"b\", \"c\" ]\ngap> SetDigraphVertex\ Label(D, 2, \"d\");\ngap> DigraphVertexLabels(D);\n[ \"a\", \"d\", \"c\" ]\nga\ p> D := InducedSubdigraph(D, [1, 3]);\n\ngap> DigraphVertexLabels(D);\n[ \"a\", \"c\" ]\ngap> D := Digraph(IsMutabl\ eDigraph, [\"e\", \"f\", \"g\"], [], []);\n\ngap> SetDigraphVertexLabels(D, [\"h\", \"i\", \"j\"]);\ngap> DigraphVert\ exLabels(D);\n[ \"h\", \"i\", \"j\" ]\ngap> InducedSubdigraph(D, [1, 3]);\n\ngap> DigraphVertexLabels(D);\n[ \"h\", \ \"j\" ]\n", count := [ 5, 1, 9, 9 ], name := "PCDATA", root := ~ ) ], count := [ 5, 1, 9, 9 ], mathmode := "Text", name := "Example", next := 141936, root := ~, start := 141112, stop := 141935 ), rec( content := "\n ", count := [ 5, 1, 9, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "Description", next := 141953, root := ~, start := 140314, stop := 141952 ) ], count := [ 5, 1, 9, 1 ], mathmode := "Text", name := "ManSection", next := 141967, root := ~, start := 140188, stop := 141966 ), rec( content := "\n\n ", count := [ 5, 1, 9, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, i, j", Name := "DigraphEdgeLabe\ l" ), content := 0, count := [ 5, 1, 10, 2 ], mathmode := "Text", name := "Oper", next := 142041, root := ~, start := 141988, stop := 142040 ), rec( attributes := rec( Arg := "digraph, i, j, o\ bj", Name := "SetDigraphEdgeLabel" ), content := 0, count := [ 5, 1, 10, 4 ], mathmode := "Text", name := "Oper", next := 142105, root := ~, start := 142044, stop := 142104 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "A", next := 142143, root := ~, start := 142129, stop := 142142 ), rec( content := " is a di\ graph without multiple edges, then the first\n operation returns the label \ of the edge from vertex ", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "A", next := 142260, root := ~, start := 142252, stop := 142259 ), rec( content := " to vert\ ex\n ", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "A", next := 142283, root := ~, start := 142275, stop := 142282 ), rec( content := ". The s\ econd operation can be used to set the label of the edge\n between vertex " , count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "A", next := 142375, root := ~, start := 142367, stop := 142374 ), rec( content := " and ver\ tex ", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "A", next := 142395, root := ~, start := 142387, stop := 142394 ), rec( content := " to the \ arbitrary ", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ AP", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " object\\ n ", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ bj", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "A", next := 142440, root := ~, start := 142430, stop := 142439 ), rec( content := ". ", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 10, 6 ], mathmode := "Text", name := "P", next := 142446, root := ~, start := 142442, stop := 142445 ), rec( content := "\n\n \ The label of an edge can be changed an arbitrary number of times. If no\n l\ abel has been set for the edge, then the default value is ", count := [ 5, 1, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "1\ ", count := [ 5, 1, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 10, 6 ], mathmode := "Text", name := "A", next := 142595, root := ~, start := 142587, stop := 142594 ), rec( content := ". ", count := [ 5, 1, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 10, 7 ], mathmode := "Text", name := "P", next := 142601, root := ~, start := 142597, stop := 142600 ), rec( content := "\n\n \ Induced subdigraphs, and some other operations which create new digraphs from\ \n old ones, inherit their edge labels from their parents.\n\n See also \ ", count := [ 5, 1, 10, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( Oper := "Digraph\ EdgeLabels" ), content := 0, count := [ 5, 1, 10, 7 ], mathmode := "Text", name := "Ref", next := 142790, root := ~, start := 142759, stop := 142789 ), rec( content := ".\n\n \ ", count := [ 5, 1, 10, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := DigraphFromDigraph6String(\"&DHUEe_\");\n\ngap> DigraphEdgeLabel(D, 3, 1);\n1\ngap> SetDigraphEdgeLa\ bel(D, 2, 5, [42]);\ngap> DigraphEdgeLabel(D, 2, 5);\n[ 42 ]\ngap> D := Induce\ dSubdigraph(D, [2, 5]);\n\ngap> Di\ graphEdgeLabel(D, 1, 2);\n[ 42 ]\ngap> D := ChainDigraph(IsMutableDigraph, 5);\ \n\ngap> DigraphEdgeLabel(D, 2, 3);\ \n1\ngap> SetDigraphEdgeLabel(D, 4, 5, [1729]);\ngap> DigraphEdgeLabel(D, 4, 5\ );\n[ 1729 ]\ngap> InducedSubdigraph(D, [4, 5]);\n\ngap> DigraphEdgeLabel(D, 1, 2);\n[ 1729 ]\n", count := [ 5, 1, 10, 8 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 1, 10, 8 ], mathmode := "Text", name := "Example", next := 143485, root := ~, start := 142797, stop := 143484 ), rec( content := "\n ", count := [ 5, 1, 10, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "Description", next := 143502, root := ~, start := 142108, stop := 143501 ) ], count := [ 5, 1, 10, 1 ], mathmode := "Text", name := "ManSection", next := 143516, root := ~, start := 141973, stop := 143515 ), rec( content := "\n\n ", count := [ 5, 1, 10, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphEdgeLabe\ ls" ), content := 0, count := [ 5, 1, 11, 2 ], mathmode := "Text", name := "Oper", next := 143583, root := ~, start := 143537, stop := 143582 ), rec( attributes := rec( Arg := "digraph, labels" , Label := "for a digraph \ and a list of lists", Name := "SetDigraphEdgeLabels" ), content := 0, count := [ 5, 1, 11, 4 ], mathmode := "Text", name := "Oper", next := 143689, root := ~, start := 143586, stop := 143688 ), rec( attributes := rec( Arg := "digraph, func", Label := "for a digraph \ and a function", Name := "SetDigraphEdgeLabels" ), content := 0, count := [ 5, 1, 11, 6 ], mathmode := "Text", name := "Oper", next := 143788, root := ~, start := 143692, stop := 143787 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "A", next := 143826, root := ~, start := 143812, stop := 143825 ), rec( content := " is a di\ graph without multiple edges, then\n ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphEdgeLabels", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "C", next := 143897, root := ~, start := 143873, stop := 143896 ), rec( content := " returns\ a copy of the labels of the edges\n in ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "A", next := 143961, root := ~, start := 143947, stop := 143960 ), rec( content := " as a li\ st of lists ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ abels", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "C", next := 143994, root := ~, start := 143981, stop := 143993 ), rec( content := " such th\ at\n ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ abels[i][j]", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "C", next := 144028, root := ~, start := 144009, stop := 144027 ), rec( content := " is the \ label on the edge from vertex ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "C", next := 144074, root := ~, start := 144066, stop := 144073 ), rec( content := "\n to\ vertex ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ utNeighbours(digraph)[i][j]", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "C", next := 144124, root := ~, start := 144089, stop := 144123 ), rec( content := ".\n\n \ ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "S\ etDigraphEdgeLabels", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "C", next := 144158, root := ~, start := 144131, stop := 144157 ), rec( content := " can be \ used to set the labels of the edges in\n ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "A", next := 144223, root := ~, start := 144209, stop := 144222 ), rec( content := " without\ multiple edges to the list ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ abels", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "A", next := 144272, root := ~, start := 144259, stop := 144271 ), rec( content := " of list\ s of\n arbitrary ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ AP", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " objects\ such that ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist[i][j]", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "C", next := 144340, root := ~, start := 144323, stop := 144339 ), rec( content := " is the \ label on the edge\n from vertex ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "C", next := 144390, root := ~, start := 144382, stop := 144389 ), rec( content := " to the \ vertex ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ utNeighbours(digraph>[i][j]", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "C", next := 144440, root := ~, start := 144405, stop := 144439 ), rec( content := ".\n\n \ Alternatively ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "S\ etDigraphEdgeLabels", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "C", next := 144488, root := ~, start := 144461, stop := 144487 ), rec( content := " can be \ called with binary function\n ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ unc", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "A", next := 144539, root := ~, start := 144528, stop := 144538 ), rec( content := " that as\ its second argument that when passed two vertices ", count := [ 5, 1, 11, 7 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "C", next := 144606, root := ~, start := 144598, stop := 144605 ), rec( content := "\n an\ d ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "C", next := 144623, root := ~, start := 144615, stop := 144622 ), rec( content := " returns\ the label for the edge between vertex ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "C", next := 144678, root := ~, start := 144670, stop := 144677 ), rec( content := " and ver\ tex\n ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "C", next := 144702, root := ~, start := 144694, stop := 144701 ), rec( content := ". ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 11, 8 ], mathmode := "Text", name := "P", next := 144708, root := ~, start := 144704, stop := 144707 ), rec( content := "\n\n \ The label of an edge can be changed an arbitrary number of times. If no\n l\ abel has been set for an edge, then the default value is ", count := [ 5, 1, 11, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "1\ ", count := [ 5, 1, 11, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 11, 8 ], mathmode := "Text", name := "C", next := 144856, root := ~, start := 144848, stop := 144855 ), rec( content := ". ", count := [ 5, 1, 11, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 11, 9 ], mathmode := "Text", name := "P", next := 144862, root := ~, start := 144858, stop := 144861 ), rec( content := "\n\n \ Induced subdigraphs, and some other operations which create new digraphs\n \ from old ones, inherit their labels from their parents.\n\n ", count := [ 5, 1, 11, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := DigraphFromDigraph6String(\"&DHUEe_\");\n\ngap> DigraphEdgeLabels(D);\n[ [ 1 ], [ 1, 1, 1 ], [ 1 ], \ [ 1, 1, 1 ], [ 1, 1, 1 ] ]\ngap> SetDigraphEdgeLabel(D, 2, 1, \"d\");\ngap> Di\ graphEdgeLabels(D);\n[ [ 1 ], [ \"d\", 1, 1 ], [ 1 ], [ 1, 1, 1 ], [ 1, 1, 1 ]\ ]\ngap> D := InducedSubdigraph(D, [1, 2, 3]);\n\ngap> DigraphEdgeLabels(D);\n[ [ 1 ], [ \"d\", 1 ], [ 1 ] ]\nga\ p> OutNeighbours(D);\n[ [ 3 ], [ 1, 3 ], [ 1 ] ]\ngap> D := CompleteBipartiteD\ igraph(IsMutableDigraph, 2, 3);\n\n\ gap> DigraphEdgeLabels(D);\n[ [ 1, 1, 1 ], [ 1, 1, 1 ], [ 1, 1 ], [ 1, 1 ], [ \ 1, 1 ] ]\ngap> SetDigraphEdgeLabel(D, 2, 4, \"a\");\ngap> DigraphEdgeLabels(D)\ ;\n[ [ 1, 1, 1 ], [ 1, \"a\", 1 ], [ 1, 1 ], [ 1, 1 ], [ 1, 1 ] ]\ngap> Induce\ dSubdigraph(D, [1, 2, 3, 4]);\n\ngap\ > DigraphEdgeLabels(D);\n[ [ 1, 1 ], [ 1, \"a\" ], [ 1, 1 ], [ 1, 1 ] ]\ngap> \ OutNeighbors(D);\n[ [ 3, 4 ], [ 3, 4 ], [ 1, 2 ], [ 1, 2 ] ]\n", count := [ 5, 1, 11, 10 ] , name := "PCD\ ATA", root := ~ ) ], count := [ 5, 1, 11, 10 ], mathmode := "Text", name := "Example", next := 146073, root := ~, start := 145006, stop := 146072 ), rec( content := "\n ", count := [ 5, 1, 11, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "Description", next := 146090, root := ~, start := 143791, stop := 146089 ) ], count := [ 5, 1, 11, 1 ], mathmode := "Text", name := "ManSection", next := 146104, root := ~, start := 143522, stop := 146103 ), rec( content := "\n\n ", count := [ 5, 1, 11, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, vertex" , Name := "DigraphInEdges"\ ), content := 0, count := [ 5, 1, 12, 2 ], mathmode := "Text", name := "Oper", next := 146176, root := ~, start := 146125, stop := 146175 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ edges.", count := [ 5, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 12, 3 ], mathmode := "Text", name := "Returns", next := 146214, root := ~, start := 146179, stop := 146213 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 5, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphInEdges", count := [ 5, 1, 12, 3 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 5, 1, 12, 3 ], mathmode := "Text", name := "C", next := 146256, root := ~, start := 146235, stop := 146255 ), rec( content := " returns\ the list of all edges of ", count := [ 5, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 12, 3 ], mathmode := "Text", name := "A", next := 146304, root := ~, start := 146290, stop := 146303 ), rec( content := "\n wh\ ich have ", count := [ 5, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ertex", count := [ 5, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 12, 3 ], mathmode := "Text", name := "A", next := 146333, root := ~, start := 146320, stop := 146332 ), rec( content := " as thei\ r range.\n ", count := [ 5, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[2, 2], [3, 3], [4, 4], [1, 1]]);\n\ngap> DigraphInEdges(D, 2);\n[ [ 1, 2 ], [ 1, 2 ] ]\ \n", count := [ 5, 1, 12, 4 ], name := "PCDATA", root := ~ ) ], count := [ 5, 1, 12, 4 ], mathmode := "Text", name := "Example", next := 146539, root := ~, start := 146354, stop := 146538 ), rec( content := "\n ", count := [ 5, 1, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 12, 3 ], mathmode := "Text", name := "Description", next := 146556, root := ~, start := 146217, stop := 146555 ) ], count := [ 5, 1, 12, 1 ], mathmode := "Text", name := "ManSection", next := 146570, root := ~, start := 146110, stop := 146569 ), rec( content := "\n\n ", count := [ 5, 1, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, vertex" , Name := "DigraphOutEdges\ " ), content := 0, count := [ 5, 1, 13, 2 ], mathmode := "Text", name := "Oper", next := 146643, root := ~, start := 146591, stop := 146642 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ edges.", count := [ 5, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 13, 3 ], mathmode := "Text", name := "Returns", next := 146681, root := ~, start := 146646, stop := 146680 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 5, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphOutEdges", count := [ 5, 1, 13, 3 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 5, 1, 13, 3 ], mathmode := "Text", name := "C", next := 146724, root := ~, start := 146702, stop := 146723 ), rec( content := " returns\ the list of all edges of ", count := [ 5, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 13, 3 ], mathmode := "Text", name := "A", next := 146772, root := ~, start := 146758, stop := 146771 ), rec( content := "\n wh\ ich have ", count := [ 5, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ertex", count := [ 5, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 13, 3 ], mathmode := "Text", name := "A", next := 146801, root := ~, start := 146788, stop := 146800 ), rec( content := " as thei\ r source.\n ", count := [ 5, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[2, 2], [3, 3], [4, 4], [1, 1]]);\n\ngap> DigraphOutEdges(D, 2);\n[ [ 2, 3 ], [ 2, 3 ] \ ]\n", count := [ 5, 1, 13, 4 ], name := "PCDATA", root := ~ ) ], count := [ 5, 1, 13, 4 ], mathmode := "Text", name := "Example", next := 147009, root := ~, start := 146823, stop := 147008 ), rec( content := "\n ", count := [ 5, 1, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 13, 3 ], mathmode := "Text", name := "Description", next := 147026, root := ~, start := 146684, stop := 147025 ) ], count := [ 5, 1, 13, 1 ], mathmode := "Text", name := "ManSection", next := 147040, root := ~, start := 146576, stop := 147039 ), rec( content := "\n\n ", count := [ 5, 1, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, list", Label := "for digraph an\ d list", Name := "IsDigraphEdge" ), content := 0, count := [ 5, 1, 14, 2 ], mathmode := "Text", name := "Oper", next := 147146, root := ~, start := 147061, stop := 147145 ), rec( attributes := rec( Arg := "digraph, u, v", Label := "for digraph an\ d two pos ints", Name := "IsDigraphEdge" ), content := 0, count := [ 5, 1, 14, 4 ], mathmode := "Text", name := "Oper", next := 147242, root := ~, start := 147149, stop := 147241 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "K", next := 147265, root := ~, start := 147254, stop := 147264 ), rec( content := " or ", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "K", next := 147281, root := ~, start := 147269, stop := 147280 ), rec( content := ".", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "Returns", next := 147292, root := ~, start := 147245, stop := 147291 ), rec( attributes := rec( ), content := [ rec( content := "\n In \ the first form, this function returns ", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "K", next := 147365, root := ~, start := 147354, stop := 147364 ), rec( content := " if and \ only if the list\n ", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "A", next := 147405, root := ~, start := 147394, stop := 147404 ), rec( content := " specifi\ es an edge in the digraph ", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "A", next := 147453, root := ~, start := 147439, stop := 147452 ), rec( content := ". Speci\ fically,\n this operation returns ", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "K", next := 147508, root := ~, start := 147497, stop := 147507 ), rec( content := " if ", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "A", next := 147523, root := ~, start := 147512, stop := 147522 ), rec( content := " is a pa\ ir of positive\n integers where ", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "A", next := 147576, root := ~, start := 147565, stop := 147575 ), rec( attributes := rec( ), content := [ rec( content := "[\ 1]", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "C", next := 147586, root := ~, start := 147576, stop := 147585 ), rec( content := " is the \ source and ", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "A", next := 147616, root := ~, start := 147605, stop := 147615 ), rec( attributes := rec( ), content := [ rec( content := "[\ 2]", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "C", next := 147626, root := ~, start := 147616, stop := 147625 ), rec( content := "\n is\ the range of an edge in ", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "A", next := 147672, root := ~, start := 147658, stop := 147671 ), rec( content := ", and ", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "K", next := 147690, root := ~, start := 147678, stop := 147689 ), rec( content := " otherwi\ se. ", count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 14, 6 ], mathmode := "Text", name := "P", next := 147706, root := ~, start := 147702, stop := 147705 ), rec( content := "\n\n \ The second form simply returns ", count := [ 5, 1, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 5, 1, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 14, 6 ], mathmode := "Text", name := "K", next := 147754, root := ~, start := 147743, stop := 147753 ), rec( content := " if ", count := [ 5, 1, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ ", count := [ 5, 1, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes :\ = rec( ), content := [ rec( content := "u", count := [ 5, 1, 14, 6 ], mathmod\ e := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 14, 6 ], mathmode := \ "Text", name := "A", next := 147770, root := ~, start := 147762, stop := 14776\ 9 ), rec( content := ", ", count := [ 5, 1, 14, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 5, 1, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 14, 6 ], mathmode := \ "Text", name := "A", next := 147780, root := ~, start := 147772, stop := 14777\ 9 ), rec( content := "]", count := [ 5, 1, 14, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 1, 14, 6 ], mathmode := "Text", name := "C", next := 147785, root := ~, start := 147758, stop := 147784 ), rec( content := " is\n \ an edge in ", count := [ 5, 1, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 14, 6 ], mathmode := "Text", name := "A", next := 147818, root := ~, start := 147804, stop := 147817 ), rec( content := ", and ", count := [ 5, 1, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 5, 1, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 14, 6 ], mathmode := "Text", name := "K", next := 147836, root := ~, start := 147824, stop := 147835 ), rec( content := " otherwi\ se.\n\n", count := [ 5, 1, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[2, 2], [6], [], [3], [], [1]]);\n\ngap> IsDigraphEdge(D, [1, 1]);\nfalse\ngap> IsDigra\ phEdge(D, [1, 2]);\ntrue\ngap> IsDigraphEdge(D, [1, 8]);\nfalse\n", count := [ 5, 1, 14, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 1, 14, 7 ], mathmode := "Text", name := "Example", next := 148093, root := ~, start := 147849, stop := 148092 ), rec( content := "\n ", count := [ 5, 1, 14, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 14, 5 ], mathmode := "Text", name := "Description", next := 148110, root := ~, start := 147295, stop := 148109 ) ], count := [ 5, 1, 14, 1 ], mathmode := "Text", name := "ManSection", next := 148124, root := ~, start := 147046, stop := 148123 ), rec( content := "\n\n ", count := [ 5, 1, 14, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, list", Name := "IsMatching" ), content := 0, count := [ 5, 1, 15, 2 ], mathmode := "Text", name := "Oper", next := 148190, root := ~, start := 148145, stop := 148189 ), rec( attributes := rec( Arg := "digraph, list", Name := "IsMaximalMatchi\ ng" ), content := 0, count := [ 5, 1, 15, 4 ], mathmode := "Text", name := "Oper", next := 148245, root := ~, start := 148193, stop := 148244 ), rec( attributes := rec( Arg := "digraph, list", Name := "IsMaximumMatchi\ ng" ), content := 0, count := [ 5, 1, 15, 6 ], mathmode := "Text", name := "Oper", next := 148300, root := ~, start := 148248, stop := 148299 ), rec( attributes := rec( Arg := "digraph, list", Name := "IsPerfectMatchi\ ng" ), content := 0, count := [ 5, 1, 15, 8 ], mathmode := "Text", name := "Oper", next := 148355, root := ~, start := 148303, stop := 148354 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "K", next := 148378, root := ~, start := 148367, stop := 148377 ), rec( content := " or ", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "K", next := 148394, root := ~, start := 148382, stop := 148393 ), rec( content := ".", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "Returns", next := 148405, root := ~, start := 148358, stop := 148404 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "A", next := 148443, root := ~, start := 148429, stop := 148442 ), rec( content := " is a di\ graph and ", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "A", next := 148472, root := ~, start := 148461, stop := 148471 ), rec( content := " is a li\ st of pairs of\n vertices of ", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "A", next := 148525, root := ~, start := 148511, stop := 148524 ), rec( content := ", then " , count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sMatching", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "C", next := 148549, root := ~, start := 148532, stop := 148548 ), rec( content := " returns\ ", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "K", next := 148569, root := ~, start := 148558, stop := 148568 ), rec( content := " if\n \ ", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "A", next := 148588, root := ~, start := 148577, stop := 148587 ), rec( content := " is a ma\ tching of ", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "A", next := 148620, root := ~, start := 148606, stop := 148619 ), rec( content := ". The o\ peration\n ", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sMaximalMatching", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "C", next := 148665, root := ~, start := 148641, stop := 148664 ), rec( content := " returns\ ", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "K", next := 148685, root := ~, start := 148674, stop := 148684 ), rec( content := " if ", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "A", next := 148700, root := ~, start := 148689, stop := 148699 ), rec( content := " is a ma\ ximal \n matching, ", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sMaximumMatching", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "C", next := 148753, root := ~, start := 148729, stop := 148752 ), rec( content := " returns\ ", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "K", next := 148773, root := ~, start := 148762, stop := 148772 ), rec( content := " if ", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "A", next := 148788, root := ~, start := 148777, stop := 148787 ), rec( content := " is a\n \ maximum matching and ", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sPerfectMatching", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "C", next := 148843, root := ~, start := 148819, stop := 148842 ), rec( content := " returns\ ", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "K", next := 148863, root := ~, start := 148852, stop := 148862 ), rec( content := " if \n \ ", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "A", next := 148883, root := ~, start := 148872, stop := 148882 ), rec( content := " is a pe\ rfect, matching of ", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "A", next := 148924, root := ~, start := 148910, stop := 148923 ), rec( content := ", respec\ tively. \n Otherwise, each of these operations return ", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "K", next := 149001, root := ~, start := 148989, stop := 149000 ), rec( content := ".\n " , count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "P", next := 149011, root := ~, start := 149007, stop := 149010 ), rec( content := "\n\n \ A ", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ atching", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "E", next := 149034, root := ~, start := 149019, stop := 149033 ), rec( content := " ", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "M\ ", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "C", next := 149043, root := ~, start := 149035, stop := 149042 ), rec( content := " of a di\ graph ", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "A", next := 149071, root := ~, start := 149057, stop := 149070 ), rec( content := " is a su\ bset of the\n edges of ", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "A", next := 149118, root := ~, start := 149104, stop := 149117 ), rec( content := ", i.e. " , count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphEdges(", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA" , root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "digraph", count := [ 5, 1, 15, 10 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 10 ], mathmode := \ "Text", name := "A", next := 149155, root := ~, start := 149141, stop := 14915\ 4 ), rec( content := ")", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "C", next := 149160, root := ~, start := 149125, stop := 149159 ), rec( content := ", such\n\ that no pair of distinct edges in ", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "M\ ", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "C", next := 149213, root := ~, start := 149205, stop := 149212 ), rec( content := " are inc\ ident to the same vertex\n of ", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "A", next := 149267, root := ~, start := 149253, stop := 149266 ), rec( content := ". Note \ that this definition allows a matching to contain\n loops. See ", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "Digraph\ HasLoops" ), content := 0, count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "Ref", next := 149371, root := ~, start := 149341, stop := 149370 ), rec( content := ". The m\ atching ", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "M\ ", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "C", next := 149395, root := ~, start := 149387, stop := 149394 ), rec( content := " is\n \ ", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ aximal", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "E", next := 149417, root := ~, start := 149403, stop := 149416 ), rec( content := " if it i\ s contained in no larger matching of the digraph,\n is ", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ aximum", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "E", next := 149496, root := ~, start := 149482, stop := 149495 ), rec( content := " if it h\ as the greatest cardinality among all matchings and\n is ", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ erfect", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "E", next := 149577, root := ~, start := 149563, stop := 149576 ), rec( content := " if ever\ y vertex of the digraph is incident to an edge in\n the matching. Every ma\ ximum or perfect matching is maximal. Note, however,\n that not every perfe\ ct matching of digraphs with loops is maximum.\n\n ", count := [ 5, 1, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 2], [1, 2], [2, 3, 4], [3, 5], [1]]);\n\ngap> IsMatching(D, [[2, 1], [3, 2]]);\nfalse\n\ gap> edges := [[3, 2]];;\ngap> IsMatching(D, edges);\ntrue\ngap> IsMaximalMatc\ hing(D, edges);\nfalse\ngap> edges := [[2, 1], [3, 4]];;\ngap> IsMaximalMatchi\ ng(D, edges);\ntrue\ngap> IsPerfectMatching(D, edges);\nfalse\ngap> edges := [\ [1, 2], [3, 3], [4, 5]];;\ngap> IsPerfectMatching(D, edges);\ntrue\ngap> IsMax\ imumMatching(D, edges);\nfalse\ngap> edges := [[1, 1], [2, 2], [3, 3], [4, 5]]\ ;;\ngap> IsMaximumMatching(D, edges);\ntrue\n", count := [ 5, 1, 15, 11 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 1, 15, 11 ], mathmode := "Text", name := "Example", next := 150391, root := ~, start := 149791, stop := 150390 ), rec( content := "\n ", count := [ 5, 1, 15, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 9 ], mathmode := "Text", name := "Description", next := 150408, root := ~, start := 148408, stop := 150407 ) ], count := [ 5, 1, 15, 1 ], mathmode := "Text", name := "ManSection", next := 150422, root := ~, start := 148130, stop := 150421 ), rec( content := "\n\n ", count := [ 5, 1, 15, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphMaximalM\ atching" ), content := 0, count := [ 5, 1, 16, 2 ], mathmode := "Text", name := "Attr", next := 150494, root := ~, start := 150443, stop := 150493 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ pairs of vertices.", count := [ 5, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 16, 3 ], mathmode := "Text", name := "Returns", next := 150544, root := ~, start := 150497, stop := 150543 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function returns a maximal matching of the digraph ", count := [ 5, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 16, 3 ], mathmode := "Text", name := "A", next := 150635, root := ~, start := 150621, stop := 150634 ), rec( content := ".\n " , count := [ 5, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 16, 4 ], mathmode := "Text", name := "P", next := 150645, root := ~, start := 150641, stop := 150644 ), rec( content := "\n\n \ For the definition of a maximal matching, see ", count := [ 5, 1, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "IsMaxim\ alMatching" ), content := 0, count := [ 5, 1, 16, 4 ], mathmode := "Text", name := "Ref", next := 150728, root := ~, start := 150697, stop := 150727 ), rec( content := ". \n\n \ ", count := [ 5, 1, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := DigraphFromDiSparse6String(\".IeAoXCJU@|SHAe?d\");\n\ngap> M := DigraphMaximalMatching(D);; IsMaxim\ alMatching(D, M);\ntrue\ngap> D := RandomDigraph(100);;\ngap> IsMaximalMatchin\ g(D, DigraphMaximalMatching(D));\ntrue\ngap> D := GeneralisedPetersenGraph(IsM\ utableDigraph, 9, 2);\n\ngap> IsMa\ ximalMatching(D, DigraphMaximalMatching(D));\ntrue\n", count := [ 5, 1, 16, 5 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 1, 16, 5 ], mathmode := "Text", name := "Example", next := 151196, root := ~, start := 150736, stop := 151195 ), rec( content := "\n ", count := [ 5, 1, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 16, 3 ], mathmode := "Text", name := "Description", next := 151213, root := ~, start := 150547, stop := 151212 ) ], count := [ 5, 1, 16, 1 ], mathmode := "Text", name := "ManSection", next := 151227, root := ~, start := 150428, stop := 151226 ), rec( content := "\n\n ", count := [ 5, 1, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphMaximumM\ atching" ), content := 0, count := [ 5, 1, 17, 2 ], mathmode := "Text", name := "Attr", next := 151299, root := ~, start := 151248, stop := 151298 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ pairs of vertices.", count := [ 5, 1, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 17, 3 ], mathmode := "Text", name := "Returns", next := 151349, root := ~, start := 151302, stop := 151348 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function returns a maximum matching of the digraph ", count := [ 5, 1, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 17, 3 ], mathmode := "Text", name := "A", next := 151440, root := ~, start := 151426, stop := 151439 ), rec( content := ".\n " , count := [ 5, 1, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "P", next := 151450, root := ~, start := 151446, stop := 151449 ), rec( content := "\n\n \ For the definition of a maximum matching, see ", count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "IsMaxim\ umMatching" ), content := 0, count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "Ref", next := 151533, root := ~, start := 151502, stop := 151532 ), rec( content := ".\n I\ f ", count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "A", next := 151556, root := ~, start := 151542, stop := 151555 ), rec( content := " is bipa\ rtite (see ", count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "IsBipar\ titeDigraph" ), content := 0, count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "Ref", next := 151607, root := ~, start := 151575, stop := 151606 ), rec( content := "), then \ \n the algorithm used has complexity ", count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (m*sqrt(n))", count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "C", next := 151673, root := ~, start := 151654, stop := 151672 ), rec( content := ". Otherw\ ise for general \n graphs the complexity is ", count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (m*n*log(n))", count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "C", next := 151747, root := ~, start := 151727, stop := 151746 ), rec( content := ". Here " , count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "C", next := 151762, root := ~, start := 151754, stop := 151761 ), rec( content := " is the \ number of vertices \n and ", count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "C", next := 151806, root := ~, start := 151798, stop := 151805 ), rec( content := " is the \ number of edges.\n\n ", count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := DigraphFromDigraph6String(\"&I@EA_A?AdDp[_c??OO\");\n\ngap> M := DigraphMaximumMatching(D);; IsMaxi\ malMatching(D, M);\ntrue\ngap> Length(M);\n5\ngap> D := Digraph([[5, 6, 7, 8],\ [6, 7, 8], [7, 8], [8], \n> [], [], [], []]);;\ngap> M := Di\ graphMaximumMatching(D);\n[ [ 1, 5 ], [ 2, 6 ], [ 3, 7 ], [ 4, 8 ] ]\ngap> D :\ = GeneralisedPetersenGraph(IsMutableDigraph, 9, 2);\n\ngap> M := DigraphMaximumMatching(D);;\ngap> IsMaximalMatc\ hing(D, M);\ntrue\ngap> Length(M);\n9\n", count := [ 5, 1, 17, 5 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 1, 17, 5 ], mathmode := "Text", name := "Example", next := 152433, root := ~, start := 151836, stop := 152432 ), rec( content := "\n ", count := [ 5, 1, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 17, 3 ], mathmode := "Text", name := "Description", next := 152450, root := ~, start := 151352, stop := 152449 ) ], count := [ 5, 1, 17, 1 ], mathmode := "Text", name := "ManSection", next := 152464, root := ~, start := 151233, stop := 152463 ), rec( content := "\n\n ", count := [ 5, 1, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 0, 1 ], mathmode := "Text", name := "Section", next := 152478, root := ~, start := 132087, stop := 152477 ) , rec( content := "\n\n ", count := [ 5, 1, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Neighbours and de\ gree", count := [ 5, 2, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 0, 2 ], mathmode := "Text", name := "Heading", next := 152531, root := ~, start := 152491, stop := 152530 ), rec( content := "\n ", count := [ 5, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "AdjacencyMatrix\ " ), content := 0, count := [ 5, 2, 1, 2 ], mathmode := "Text", name := "Attr", next := 152595, root := ~, start := 152551, stop := 152594 ), rec( attributes := rec( Arg := "digraph", Name := "AdjacencyMatrix\ MutableCopy" ), content := 0, count := [ 5, 2, 1, 4 ], mathmode := "Text", name := "Oper", next := 152653, root := ~, start := 152598, stop := 152652 ), rec( attributes := rec( ), content := [ rec( content := "A square \ matrix of non-negative integers.", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "Returns", next := 152716, root := ~, start := 152656, stop := 152715 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function returns the adjacency matrix ", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ at", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "C", next := 152790, root := ~, start := 152780, stop := 152789 ), rec( content := " of the \ digraph\n ", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "A", next := 152824, root := ~, start := 152810, stop := 152823 ), rec( content := ".\n T\ he value of the matrix entry ", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ at[i][j]", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "C", next := 152876, root := ~, start := 152860, stop := 152875 ), rec( content := " is the \ number of edges\n in ", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "A", next := 152921, root := ~, start := 152907, stop := 152920 ), rec( content := " with so\ urce ", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "C", next := 152942, root := ~, start := 152934, stop := 152941 ), rec( content := " and ran\ ge ", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "C", next := 152961, root := ~, start := 152953, stop := 152960 ), rec( content := ". If ", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "A", next := 152980, root := ~, start := 152966, stop := 152979 ), rec( content := "\n ha\ s no vertices, then the empty list is returned. ", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 1, 6 ], mathmode := "Text", name := "P", next := 153039, root := ~, start := 153035, stop := 153038 ), rec( content := "\n\n \ The function ", count := [ 5, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A\ djacencyMatrix", count := [ 5, 2, 1, 6 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 5, 2, 1, 6 ], mathmode := "Text", name := "C", next := 153080, root := ~, start := 153058, stop := 153079 ), rec( content := " returns\ an immutable list of\n lists, whereas the function ", count := [ 5, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A\ djacencyMatrixMutableCopy", count := [ 5, 2, 1, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 2, 1, 6 ], mathmode := "Text", name := "C", next := 153175, root := ~, start := 153142, stop := 153174 ), rec( content := " returns\ a copy\n of ", count := [ 5, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A\ djacencyMatrix", count := [ 5, 2, 1, 6 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 5, 2, 1, 6 ], mathmode := "Text", name := "C", next := 153220, root := ~, start := 153198, stop := 153219 ), rec( content := " that is\ a mutable list of mutable lists. ", count := [ 5, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 1, 7 ], mathmode := "Text", name := "P", next := 153266, root := ~, start := 153262, stop := 153265 ), rec( content := "\n\n \ ", count := [ 5, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := Digraph([\n> [2, 2, 2], [1, 3, 6, 8, 9, 10], [4, 6, 8],\n> [1, 2, \ 3, 9], [3, 3], [3, 5, 6, 10], [1, 2, 7],\n> [1, 2, 3, 10, 5, 6, 10], [1, 3, 4,\ 5, 8, 10],\n> [2, 3, 4, 6, 7, 10]]);\n\ngap> mat := AdjacencyMatrix(gr);;\ngap> Display(mat);\n[ [ 0, \ 3, 0, 0, 0, 0, 0, 0, 0, 0 ],\n [ 1, 0, 1, 0, 0, 1, 0, 1, 1, \ 1 ],\n [ 0, 0, 0, 1, 0, 1, 0, 1, 0, 0 ],\n [ 1, 1, 1, 0, 0, \ 0, 0, 0, 1, 0 ],\n [ 0, 0, 2, 0, 0, 0, 0, 0, 0, 0 ],\n [ 0, \ 0, 1, 0, 1, 1, 0, 0, 0, 1 ],\n [ 1, 1, 0, 0, 0, 0, 1, 0, 0,\ 0 ],\n [ 1, 1, 1, 0, 1, 1, 0, 0, 0, 2 ],\n [ 1, 0, 1, 1, 1,\ 0, 0, 1, 0, 1 ],\n [ 0, 1, 1, 1, 0, 1, 1, 0, 0, 1 ] ]\ngap> D\ := CycleDigraph(IsMutableDigraph, 3);\n\ngap> Display(AdjacencyMatrix(D));\n[ [ 0, 1, 0 ],\n [ 0, 0, 1 ],\ \n [ 1, 0, 0 ] ]\n", count := [ 5, 2, 1, 8 ], name := "PCDATA", root := ~ ) ], count := [ 5, 2, 1, 8 ], mathmode := "Text", name := "Example", next := 154236, root := ~, start := 153272, stop := 154235 ), rec( content := "\n ", count := [ 5, 2, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "Description", next := 154253, root := ~, start := 152719, stop := 154252 ) ], count := [ 5, 2, 1, 1 ], mathmode := "Text", name := "ManSection", next := 154267, root := ~, start := 152536, stop := 154266 ), rec( content := "\n\n ", count := [ 5, 2, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "CharacteristicP\ olynomial" ), content := 0, count := [ 5, 2, 2, 2 ], mathmode := "Text", name := "Attr", next := 154341, root := ~, start := 154288, stop := 154340 ), rec( attributes := rec( ), content := [ rec( content := "A polynom\ ial with integer coefficients.", count := [ 5, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 2, 3 ], mathmode := "Text", name := "Returns", next := 154402, root := ~, start := 154344, stop := 154401 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function returns the characteristic polynomial of the digraph\n ", count := [ 5, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 2, 3 ], mathmode := "Text", name := "A", next := 154509, root := ~, start := 154495, stop := 154508 ), rec( content := ". That i\ s it returns the characteristic polynomial\n of the adjacency matrix of t\ he digraph ", count := [ 5, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 2, 3 ], mathmode := "Text", name := "A", next := 154619, root := ~, start := 154605, stop := 154618 ), rec( content := "\n ", count := [ 5, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([\n> [2, 2, 2], [1, 3, 6, 8, 9, 10], [4, 6, 8],\n> [1, 2, 3\ , 9], [3, 3], [3, 5, 6, 10], [1, 2, 7],\n> [1, 2, 3, 10, 5, 6, 10], [1, 3, 4, \ 5, 8, 10],\n> [2, 3, 4, 6, 7, 10]]);\n\ngap> CharacteristicPolynomial(D);\nx_1^10-3*x_1^9-7*x_1^8-x_1^7+1\ 4*x_1^6+x_1^5-26*x_1^4+51*x_1^3-10*x_1^2\\\n+18*x_1-30\ngap> D := CompleteDigr\ aph(5);\n\ngap> CharacteristicPoly\ nomial(D);\nx_1^5-10*x_1^3-20*x_1^2-15*x_1-4\ngap> D := CycleDigraph(IsMutable\ Digraph, 3);\n\ngap> CharacteristicP\ olynomial(D);\nx_1^3-1\n", count := [ 5, 2, 2, 4 ], name := "PCDATA", root := ~ ) ], count := [ 5, 2, 2, 4 ], mathmode := "Text", name := "Example", next := 155285, root := ~, start := 154624, stop := 155284 ), rec( content := "\n ", count := [ 5, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 2, 3 ], mathmode := "Text", name := "Description", next := 155302, root := ~, start := 154405, stop := 155301 ) ], count := [ 5, 2, 2, 1 ], mathmode := "Text", name := "ManSection", next := 155316, root := ~, start := 154273, stop := 155315 ), rec( content := "\n\n ", count := [ 5, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "BooleanAdjacenc\ yMatrix" ), content := 0, count := [ 5, 2, 3, 2 ], mathmode := "Text", name := "Attr", next := 155388, root := ~, start := 155337, stop := 155387 ), rec( attributes := rec( Arg := "digraph", Name := "BooleanAdjacenc\ yMatrixMutableCopy" ), content := 0, count := [ 5, 2, 3, 4 ], mathmode := "Text", name := "Oper", next := 155453, root := ~, start := 155391, stop := 155452 ), rec( attributes := rec( ), content := [ rec( content := "A square \ matrix of booleans.", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "Returns", next := 155503, root := ~, start := 155456, stop := 155502 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "A", next := 155541, root := ~, start := 155527, stop := 155540 ), rec( content := " is a di\ graph with a positive number of vertices\n ", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "C", next := 155602, root := ~, start := 155594, stop := 155601 ), rec( content := ", then " , count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "B\ ooleanAdjacencyMatrix(", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "C", next := 155639, root := ~, start := 155609, stop := 155638 ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "A", next := 155653, root := ~, start := 155639, stop := 155652 ), rec( attributes := rec( ), content := [ rec( content := ")\ ", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "C", next := 155661, root := ~, start := 155653, stop := 155660 ), rec( content := "\n re\ turns the boolean adjacency matrix ", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ at", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "C", next := 155713, root := ~, start := 155703, stop := 155712 ), rec( content := " of ", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "A", next := 155731, root := ~, start := 155717, stop := 155730 ), rec( content := ". The\n\ value of the matrix entry ", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ at[j][i]", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "C", next := 155784, root := ~, start := 155768, stop := 155783 ), rec( content := " is ", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "K", next := 155799, root := ~, start := 155788, stop := 155798 ), rec( content := " if and \ only if\n there exists an edge in ", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "A", next := 155857, root := ~, start := 155843, stop := 155856 ), rec( content := " with so\ urce ", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "C", next := 155878, root := ~, start := 155870, stop := 155877 ), rec( content := " and ran\ ge\n ", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "C", next := 155901, root := ~, start := 155893, stop := 155900 ), rec( content := ". If ", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "A", next := 155921, root := ~, start := 155907, stop := 155920 ), rec( content := " has no \ vertices, then the empty list is\n returned. ", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 3, 6 ], mathmode := "Text", name := "P", next := 155980, root := ~, start := 155976, stop := 155979 ), rec( content := "\n\n \ Note that the boolean adjacency matrix loses information about multiple\n e\ dges. ", count := [ 5, 2, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 3, 7 ], mathmode := "Text", name := "P", next := 156074, root := ~, start := 156070, stop := 156073 ), rec( content := "\n\n \ The attribute ", count := [ 5, 2, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "B\ ooleanAdjacencyMatrix", count := [ 5, 2, 3, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 2, 3, 7 ], mathmode := "Text", name := "C", next := 156123, root := ~, start := 156094, stop := 156122 ), rec( content := " returns\ an immutable list of\n immutable lists, whereas the function\n ", count := [ 5, 2, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "B\ ooleanAdjacencyMatrixMutableCopy", count := [ 5, 2, 3, 7 ], mathmode := "Text" , name := "PCD\ ATA", root := ~ ) ], count := [ 5, 2, 3, 7 ], mathmode := "Text", name := "C", next := 156239, root := ~, start := 156199, stop := 156238 ), rec( content := " returns\ a copy of the\n ", count := [ 5, 2, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "B\ ooleanAdjacencyMatrix", count := [ 5, 2, 3, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 2, 3, 7 ], mathmode := "Text", name := "C", next := 156295, root := ~, start := 156266, stop := 156294 ), rec( content := " that is\ a mutable list of mutable lists. ", count := [ 5, 2, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 3, 8 ], mathmode := "Text", name := "P", next := 156341, root := ~, start := 156337, stop := 156340 ), rec( content := "\n ", count := [ 5, 2, 3, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := Digraph([[3, 4], [2, 3], [1, 2, 4], [4]]);\n\ngap> PrintArray(BooleanAdjacencyMatrix(gr));\n[ [ fal\ se, false, true, true ],\n [ false, true, true, false ],\n [ tr\ ue, true, false, true ],\n [ false, false, false, true ] ]\ngap> gr\ := CycleDigraph(4);;\ngap> PrintArray(BooleanAdjacencyMatrix(gr));\n[ [ fals\ e, true, false, false ],\n [ false, false, true, false ],\n [ fals\ e, false, false, true ],\n [ true, false, false, false ] ]\ngap> Boo\ leanAdjacencyMatrix(EmptyDigraph(0));\n[ ]\ngap> D := CycleDigraph(IsMutableD\ igraph, 3);\n\ngap> PrintArray(Boole\ anAdjacencyMatrix(D));\n[ [ false, true, false ],\n [ false, false, t\ rue ],\n [ true, false, false ] ]\n", count := [ 5, 2, 3, 9 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 2, 3, 9 ], mathmode := "Text", name := "Example", next := 157176, root := ~, start := 156346, stop := 157175 ), rec( content := "\n ", count := [ 5, 2, 3, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "Description", next := 157193, root := ~, start := 155506, stop := 157192 ) ], count := [ 5, 2, 3, 1 ], mathmode := "Text", name := "ManSection", next := 157207, root := ~, start := 155322, stop := 157206 ), rec( content := "\n\n ", count := [ 5, 2, 3, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphAdjacenc\ yFunction" ), content := 0, count := [ 5, 2, 4, 2 ], mathmode := "Text", name := "Attr", next := 157281, root := ~, start := 157228, stop := 157280 ), rec( attributes := rec( ), content := [ rec( content := "A functio\ n.", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "Returns", next := 157314, root := ~, start := 157284, stop := 157313 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "A", next := 157352, root := ~, start := 157338, stop := 157351 ), rec( content := " is a di\ graph, then ", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphAdjacencyFunction", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "C", next := 157403, root := ~, start := 157372, stop := 157402 ), rec( content := " returns\ \n a function which takes two integer parameters ", count := [ 5, 2, 4, 3 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ , y", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "C", next := 157473, root := ~, start := 157462, stop := 157472 ), rec( content := " and ret\ urns\n ", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "K", next := 157501, root := ~, start := 157490, stop := 157500 ), rec( content := " if ther\ e exists an edge from vertex ", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "C", next := 157546, root := ~, start := 157538, stop := 157545 ), rec( content := " to vert\ ex ", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "y\ ", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "C", next := 157565, root := ~, start := 157557, stop := 157564 ), rec( content := "\n in\ ", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "A", next := 157587, root := ~, start := 157573, stop := 157586 ), rec( content := " and ", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "K", next := 157604, root := ~, start := 157592, stop := 157603 ), rec( content := " if not.\ \n\n ", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> digraph := Digraph([[1, 2], [3], []]);\n\ngap> foo := DigraphAdjacencyFunction(digraph);\nfunction( u, v )\ ... end\ngap> foo(1, 1);\ntrue\ngap> foo(1, 2);\ntrue\ngap> foo(1, 3);\nfalse\ \ngap> foo(3, 1);\nfalse\ngap> gr := Digraph([\"a\", \"b\", \"c\"],\n> \ [\"a\", \"b\", \"b\"],\n> [\"b\", \"a\", \"a\"]);\n\ \ngap> foo := DigraphAdjacenc\ yFunction(gr);\nfunction( u, v ) ... end\ngap> foo(1, 2);\ntrue\ngap> foo(3, 2\ );\nfalse\ngap> foo(3, 1);\nfalse\ngap> D := CycleDigraph(IsMutableDigraph, 3)\ ;\n\ngap> foo := DigraphAdjacencyFun\ ction(D);\nfunction( u, v ) ... end\ngap> foo(1, 2);\ntrue\ngap> foo(2, 1);\nf\ alse\n", count := [ 5, 2, 4, 4 ], name := "PCDATA", root := ~ ) ], count := [ 5, 2, 4, 4 ], mathmode := "Text", name := "Example", next := 158385, root := ~, start := 157618, stop := 158384 ), rec( content := "\n ", count := [ 5, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "Description", next := 158402, root := ~, start := 157317, stop := 158401 ) ], count := [ 5, 2, 4, 1 ], mathmode := "Text", name := "ManSection", next := 158416, root := ~, start := 157213, stop := 158415 ), rec( content := "\n\n ", count := [ 5, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphRange" ) , content := 0, count := [ 5, 2, 5, 2 ], mathmode := "Text", name := "Attr", next := 158478, root := ~, start := 158437, stop := 158477 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphSource" ), content := 0, count := [ 5, 2, 5, 4 ], mathmode := "Text", name := "Attr", next := 158523, root := ~, start := 158481, stop := 158522 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ positive integers.", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "Returns", next := 158573, root := ~, start := 158526, stop := 158572 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphRange", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "C", next := 158613, root := ~, start := 158594, stop := 158612 ), rec( content := " and ", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphSource", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "C", next := 158638, root := ~, start := 158618, stop := 158637 ), rec( content := " return \ the range and source of\n the digraph ", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "A", next := 158700, root := ~, start := 158686, stop := 158699 ), rec( content := ". More p\ recisely, position ", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "C", next := 158735, root := ~, start := 158727, stop := 158734 ), rec( content := " in\n \ ", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "D\ igraphRange(", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "digraph", count := [ 5, 2, 5, 5 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 5, 5 ], mathmode := \ "Text", name := "A", next := 158773, root := ~, start := 158759, stop := 15877\ 2 ), rec( content := ")", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "C", next := 158778, root := ~, start := 158743, stop := 158777 ), rec( content := " is the \ range of the ", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "C", next := 158807, root := ~, start := 158799, stop := 158806 ), rec( content := "th edge \ of\n ", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "A", next := 158836, root := ~, start := 158822, stop := 158835 ), rec( content := ".\n\n \ ", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := Digraph([\n> [2, 1, 3, 5], [1, 3, 4], [2, 3], [2], [1, 2, 3, 4]]);\ \n\ngap> DigraphRange(gr);\n[ 2, \ 1, 3, 5, 1, 3, 4, 2, 3, 2, 1, 2, 3, 4 ]\ngap> DigraphSource(gr);\n[ 1, 1, 1, 1\ , 2, 2, 2, 3, 3, 4, 5, 5, 5, 5 ]\ngap> DigraphEdges(gr);\n[ [ 1, 2 ], [ 1, 1 ]\ , [ 1, 3 ], [ 1, 5 ], [ 2, 1 ], [ 2, 3 ], \n [ 2, 4 ], [ 3, 2 ], [ 3, 3 ], [ \ 4, 2 ], [ 5, 1 ], [ 5, 2 ], \n [ 5, 3 ], [ 5, 4 ] ]\ngap> D := CycleDigraph(I\ sMutableDigraph, 3);\n\ngap> Digraph\ Range(D);\n[ 2, 3, 1 ]\ngap> DigraphSource(D);\n[ 1, 2, 3 ]\n", count := [ 5, 2, 5, 6 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 2, 5, 6 ], mathmode := "Text", name := "Example", next := 159464, root := ~, start := 158843, stop := 159463 ), rec( content := "\n ", count := [ 5, 2, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "Description", next := 159481, root := ~, start := 158576, stop := 159480 ) ], count := [ 5, 2, 5, 1 ], mathmode := "Text", name := "ManSection", next := 159495, root := ~, start := 158422, stop := 159494 ), rec( content := "\n\n ", count := [ 5, 2, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "OutNeighbours" ), content := 0, count := [ 5, 2, 6, 2 ], mathmode := "Text", name := "Attr", next := 159558, root := ~, start := 159516, stop := 159557 ), rec( attributes := rec( Arg := "digraph", Name := "OutNeighbors" ) , content := 0, count := [ 5, 2, 6, 4 ], mathmode := "Text", name := "Attr", next := 159602, root := ~, start := 159561, stop := 159601 ), rec( attributes := rec( Arg := "digraph", Name := "OutNeighboursMu\ tableCopy" ), content := 0, count := [ 5, 2, 6, 6 ], mathmode := "Text", name := "Oper", next := 159658, root := ~, start := 159605, stop := 159657 ), rec( attributes := rec( Arg := "digraph", Name := "OutNeighborsMut\ ableCopy" ), content := 0, count := [ 5, 2, 6, 8 ], mathmode := "Text", name := "Oper", next := 159713, root := ~, start := 159661, stop := 159712 ), rec( attributes := rec( ), content := [ rec( content := "The adjac\ encies of a digraph.", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "Returns", next := 159764, root := ~, start := 159716, stop := 159763 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function returns the list ", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ ut", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "C", next := 159826, root := ~, start := 159816, stop := 159825 ), rec( content := " of out-\ neighbours of each vertex\n of the digraph ", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "A", next := 159893, root := ~, start := 159879, stop := 159892 ), rec( content := ".\n M\ ore specifically, a vertex ", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "C", next := 159935, root := ~, start := 159927, stop := 159934 ), rec( content := " appears\ in ", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ ut[i]", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "C", next := 159960, root := ~, start := 159947, stop := 159959 ), rec( content := " each ti\ me\n there exists an edge with source ", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "C", next := 160016, root := ~, start := 160008, stop := 160015 ), rec( content := " and ran\ ge ", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "C", next := 160035, root := ~, start := 160027, stop := 160034 ), rec( content := " in\n \ ", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "A", next := 160057, root := ~, start := 160043, stop := 160056 ), rec( content := ". ", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 6, 10 ], mathmode := "Text", name := "P", next := 160063, root := ~, start := 160059, stop := 160062 ), rec( content := "\n\n \ The function ", count := [ 5, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ utNeighbours", count := [ 5, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 6, 10 ], mathmode := "Text", name := "C", next := 160102, root := ~, start := 160082, stop := 160101 ), rec( content := " returns\ an immutable list of\n lists, whereas the function ", count := [ 5, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ utNeighboursMutableCopy", count := [ 5, 2, 6, 10 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 2, 6, 10 ], mathmode := "Text", name := "C", next := 160195, root := ~, start := 160164, stop := 160194 ), rec( content := " returns\ a copy\n of ", count := [ 5, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ utNeighbours", count := [ 5, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 6, 10 ], mathmode := "Text", name := "C", next := 160238, root := ~, start := 160218, stop := 160237 ), rec( content := " which i\ s a mutable list of mutable lists. ", count := [ 5, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 6, 11 ], mathmode := "Text", name := "P", next := 160285, root := ~, start := 160281, stop := 160284 ), rec( content := "\n\n \ ", count := [ 5, 2, 6, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := Digraph([\"a\", \"b\", \"c\"],\n> [\"a\", \"b\", \ \"b\"],\n> [\"b\", \"a\", \"c\"]);\n\ngap> OutNeighbours(gr);\n[ [ 2 ], [ 1, 3 ], [ ] ]\ngap> \ gr := Digraph([[1, 2, 3], [2, 1], [3]]);\n\ngap> OutNeighbours(gr);\n[ [ 1, 2, 3 ], [ 2, 1 ], [ 3 ] ]\ngap> gr :\ = DigraphByAdjacencyMatrix([\n> [1, 2, 1],\n> [1, 1, 0],\n> [0, 0, 1]]);\n<\ immutable multidigraph with 3 vertices, 7 edges>\ngap> OutNeighbours(gr);\n[ [\ 1, 2, 2, 3 ], [ 1, 2 ], [ 3 ] ]\ngap> OutNeighboursMutableCopy(gr);\n[ [ 1, 2\ , 2, 3 ], [ 1, 2 ], [ 3 ] ]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n\ngap> OutNeighbours(D);\n[ [ 2 ], [ 3 \ ], [ 1 ] ]\n", count := [ 5, 2, 6, 12 ], name := "PCDATA", root := ~ ) ], count := [ 5, 2, 6, 12 ], mathmode := "Text", name := "Example", next := 161073, root := ~, start := 160291, stop := 161072 ), rec( content := "\n ", count := [ 5, 2, 6, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "Description", next := 161090, root := ~, start := 159767, stop := 161089 ) ], count := [ 5, 2, 6, 1 ], mathmode := "Text", name := "ManSection", next := 161104, root := ~, start := 159501, stop := 161103 ), rec( content := "\n\n ", count := [ 5, 2, 6, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "InNeighbours" ) , content := 0, count := [ 5, 2, 7, 2 ], mathmode := "Text", name := "Attr", next := 161166, root := ~, start := 161125, stop := 161165 ), rec( attributes := rec( Arg := "digraph", Name := "InNeighbors" ), content := 0, count := [ 5, 2, 7, 4 ], mathmode := "Text", name := "Attr", next := 161209, root := ~, start := 161169, stop := 161208 ), rec( attributes := rec( Arg := "digraph", Name := "InNeighboursMut\ ableCopy" ), content := 0, count := [ 5, 2, 7, 6 ], mathmode := "Text", name := "Oper", next := 161264, root := ~, start := 161212, stop := 161263 ), rec( attributes := rec( Arg := "digraph", Name := "InNeighborsMuta\ bleCopy" ), content := 0, count := [ 5, 2, 7, 8 ], mathmode := "Text", name := "Oper", next := 161318, root := ~, start := 161267, stop := 161317 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ lists of vertices.", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "Returns", next := 161368, root := ~, start := 161321, stop := 161367 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function returns the list ", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nn", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "C", next := 161430, root := ~, start := 161420, stop := 161429 ), rec( content := " of in-n\ eighbours of each vertex\n of the digraph ", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "A", next := 161496, root := ~, start := 161482, stop := 161495 ), rec( content := ".\n M\ ore specifically, a vertex ", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "C", next := 161538, root := ~, start := 161530, stop := 161537 ), rec( content := " appears\ in ", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nn[i]", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "C", next := 161563, root := ~, start := 161550, stop := 161562 ), rec( content := " each ti\ me\n there exists an edge with source ", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "C", next := 161619, root := ~, start := 161611, stop := 161618 ), rec( content := " and ran\ ge ", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "C", next := 161638, root := ~, start := 161630, stop := 161637 ), rec( content := " in\n \ ", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "A", next := 161660, root := ~, start := 161646, stop := 161659 ), rec( content := ". ", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 7, 10 ], mathmode := "Text", name := "P", next := 161666, root := ~, start := 161662, stop := 161665 ), rec( content := "\n\n \ The function ", count := [ 5, 2, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ nNeighbours", count := [ 5, 2, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 7, 10 ], mathmode := "Text", name := "C", next := 161704, root := ~, start := 161685, stop := 161703 ), rec( content := " returns\ an immutable list of\n lists, whereas the function ", count := [ 5, 2, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ nNeighboursMutableCopy", count := [ 5, 2, 7, 10 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 2, 7, 10 ], mathmode := "Text", name := "C", next := 161796, root := ~, start := 161766, stop := 161795 ), rec( content := " returns\ a copy\n of ", count := [ 5, 2, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ nNeighbours", count := [ 5, 2, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 7, 10 ], mathmode := "Text", name := "C", next := 161838, root := ~, start := 161819, stop := 161837 ), rec( content := " which i\ s a mutable list of mutable lists. ", count := [ 5, 2, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 7, 11 ], mathmode := "Text", name := "P", next := 161885, root := ~, start := 161881, stop := 161884 ), rec( content := "\n\n \ Note that each entry of ", count := [ 5, 2, 7, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nn", count := [ 5, 2, 7, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 7, 11 ], mathmode := "Text", name := "C", next := 161925, root := ~, start := 161915, stop := 161924 ), rec( content := " is sort\ ed into ascending order. ", count := [ 5, 2, 7, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 7, 12 ], mathmode := "Text", name := "P", next := 161962, root := ~, start := 161958, stop := 161961 ), rec( content := "\n\n \ ", count := [ 5, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := Digraph([\"a\", \"b\", \"c\"],\n> [\"a\", \"b\", \ \"b\"],\n> [\"b\", \"a\", \"c\"]);\n\ngap> InNeighbours(gr);\n[ [ 2 ], [ 1 ], [ 2 ] ]\ngap> gr \ := Digraph([[1, 2, 3], [2, 1], [3]]);\n\ngap> InNeighbours(gr);\n[ [ 1, 2 ], [ 1, 2 ], [ 1, 3 ] ]\ngap> gr := Di\ graphByAdjacencyMatrix([\n> [1, 2, 1],\n> [1, 1, 0],\n> [0, 0, 1]]);\n\ngap> InNeighbours(gr);\n[ [ 1, 2\ ], [ 1, 1, 2 ], [ 1, 3 ] ]\ngap> InNeighboursMutableCopy(gr);\n[ [ 1, 2 ], [ \ 1, 1, 2 ], [ 1, 3 ] ]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n\ngap> InNeighbours(D);\n[ [ 3 ], [ 1 ], [ 2 \ ] ]\n", count := [ 5, 2, 7, 13 ], name := "PCDATA", root := ~ ) ], count := [ 5, 2, 7, 13 ], mathmode := "Text", name := "Example", next := 162743, root := ~, start := 161968, stop := 162742 ), rec( content := "\n ", count := [ 5, 2, 7, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "Description", next := 162760, root := ~, start := 161371, stop := 162759 ) ], count := [ 5, 2, 7, 1 ], mathmode := "Text", name := "ManSection", next := 162774, root := ~, start := 161110, stop := 162773 ), rec( content := "\n\n ", count := [ 5, 2, 7, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "OutDegrees" ), content := 0, count := [ 5, 2, 8, 2 ], mathmode := "Text", name := "Attr", next := 162834, root := ~, start := 162795, stop := 162833 ), rec( attributes := rec( Arg := "digraph", Name := "OutDegreeSequen\ ce" ), content := 0, count := [ 5, 2, 8, 4 ], mathmode := "Text", name := "Attr", next := 162883, root := ~, start := 162837, stop := 162882 ), rec( attributes := rec( Arg := "digraph", Name := "OutDegreeSet" ) , content := 0, count := [ 5, 2, 8, 6 ], mathmode := "Text", name := "Attr", next := 162927, root := ~, start := 162886, stop := 162926 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ non-negative integers.", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "Returns", next := 162981, root := ~, start := 162930, stop := 162980 ), rec( attributes := rec( ), content := [ rec( content := "\n\n G\ iven a digraph ", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "A", next := 163033, root := ~, start := 163019, stop := 163032 ), rec( content := " with ", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "M", next := 163047, root := ~, start := 163039, stop := 163046 ), rec( content := " vertice\ s, the function\n ", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ utDegrees", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "C", next := 163092, root := ~, start := 163075, stop := 163091 ), rec( content := " returns\ an immutable list ", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ ut", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "C", next := 163129, root := ~, start := 163119, stop := 163128 ), rec( content := " of leng\ th ", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "M", next := 163148, root := ~, start := 163140, stop := 163147 ), rec( content := ", such t\ hat\n for a vertex ", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "C", next := 163185, root := ~, start := 163177, stop := 163184 ), rec( content := " in ", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "A", next := 163203, root := ~, start := 163189, stop := 163202 ), rec( content := ", the va\ lue of ", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ ut[i]", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "C", next := 163231, root := ~, start := 163218, stop := 163230 ), rec( content := " is the\\ n out-degree of vertex ", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "C", next := 163272, root := ~, start := 163264, stop := 163271 ), rec( content := ".\n S\ ee ", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "OutDegr\ eeOfVertex" ), content := 0, count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "Ref", next := 163313, root := ~, start := 163282, stop := 163312 ), rec( content := ". ", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 8, 8 ], mathmode := "Text", name := "P", next := 163319, root := ~, start := 163315, stop := 163318 ), rec( content := "\n\n \ The function ", count := [ 5, 2, 8, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ utDegreeSequence", count := [ 5, 2, 8, 8 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 5, 2, 8, 8 ], mathmode := "Text", name := "C", next := 163362, root := ~, start := 163338, stop := 163361 ), rec( content := " returns\ the same list,\n after it has been sorted into non-increasing order. ", count := [ 5, 2, 8, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 8, 9 ], mathmode := "Text", name := "P", next := 163446, root := ~, start := 163442, stop := 163445 ), rec( content := "\n\n \ The function ", count := [ 5, 2, 8, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ utDegreeSet", count := [ 5, 2, 8, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 8, 9 ], mathmode := "Text", name := "C", next := 163484, root := ~, start := 163465, stop := 163483 ), rec( content := " returns\ the same list, sorted into\n increasing order with duplicate entries remov\ ed. ", count := [ 5, 2, 8, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 8, 10 ], mathmode := "Text", name := "P", next := 163577, root := ~, start := 163573, stop := 163576 ), rec( content := "\n\n \ ", count := [ 5, 2, 8, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 3, 2, 2], [], [2, 1], []]);\n\ngap> OutDegrees(D);\n[ 4, 0, 2, 0 ]\ngap> OutDegreeS\ equence(D);\n[ 4, 2, 0, 0 ]\ngap> OutDegreeSet(D);\n[ 0, 2, 4 ]\ngap> D := Cyc\ leDigraph(IsMutableDigraph, 3);\n\ng\ ap> OutDegrees(D);\n[ 1, 1, 1 ]\n", count := [ 5, 2, 8, 11 ], name := "PCDATA" , root := ~ ) ], count := [ 5, 2, 8, 11 ], mathmode := "Text", name := "Example", next := 163947, root := ~, start := 163583, stop := 163946 ), rec( content := "\n ", count := [ 5, 2, 8, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "Description", next := 163964, root := ~, start := 162984, stop := 163963 ) ], count := [ 5, 2, 8, 1 ], mathmode := "Text", name := "ManSection", next := 163978, root := ~, start := 162780, stop := 163977 ), rec( content := "\n\n ", count := [ 5, 2, 8, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "InDegrees" ), content := 0, count := [ 5, 2, 9, 2 ], mathmode := "Text", name := "Attr", next := 164037, root := ~, start := 163999, stop := 164036 ), rec( attributes := rec( Arg := "digraph", Name := "InDegreeSequenc\ e" ), content := 0, count := [ 5, 2, 9, 4 ], mathmode := "Text", name := "Attr", next := 164085, root := ~, start := 164040, stop := 164084 ), rec( attributes := rec( Arg := "digraph", Name := "InDegreeSet" ), content := 0, count := [ 5, 2, 9, 6 ], mathmode := "Text", name := "Attr", next := 164128, root := ~, start := 164088, stop := 164127 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ non-negative integers.", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "Returns", next := 164182, root := ~, start := 164131, stop := 164181 ), rec( attributes := rec( ), content := [ rec( content := "\n\n G\ iven a digraph ", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "A", next := 164234, root := ~, start := 164220, stop := 164233 ), rec( content := " with ", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "M", next := 164248, root := ~, start := 164240, stop := 164247 ), rec( content := " vertice\ s, the function\n ", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ nDegrees", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "C", next := 164292, root := ~, start := 164276, stop := 164291 ), rec( content := " returns\ an immutable list ", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nn", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "C", next := 164329, root := ~, start := 164319, stop := 164328 ), rec( content := " of leng\ th ", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "M", next := 164348, root := ~, start := 164340, stop := 164347 ), rec( content := ", such t\ hat\n for a vertex ", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "C", next := 164385, root := ~, start := 164377, stop := 164384 ), rec( content := " in ", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "A", next := 164403, root := ~, start := 164389, stop := 164402 ), rec( content := ", the va\ lue of ", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nn[i]", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "C", next := 164431, root := ~, start := 164418, stop := 164430 ), rec( content := " is\n \ the in-degree of vertex ", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "C", next := 164471, root := ~, start := 164463, stop := 164470 ), rec( content := ".\n S\ ee ", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "InDegre\ eOfVertex" ), content := 0, count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "Ref", next := 164511, root := ~, start := 164481, stop := 164510 ), rec( content := ". ", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 9, 8 ], mathmode := "Text", name := "P", next := 164517, root := ~, start := 164513, stop := 164516 ), rec( content := "\n\n \ The function ", count := [ 5, 2, 9, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ nDegreeSequence", count := [ 5, 2, 9, 8 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 5, 2, 9, 8 ], mathmode := "Text", name := "C", next := 164559, root := ~, start := 164536, stop := 164558 ), rec( content := " returns\ the same list,\n after it has been sorted into non-increasing order. ", count := [ 5, 2, 9, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 9, 9 ], mathmode := "Text", name := "P", next := 164643, root := ~, start := 164639, stop := 164642 ), rec( content := "\n\n \ The function ", count := [ 5, 2, 9, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ nDegreeSet", count := [ 5, 2, 9, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 9, 9 ], mathmode := "Text", name := "C", next := 164680, root := ~, start := 164662, stop := 164679 ), rec( content := " returns\ the same list, sorted into\n increasing order with duplicate entries remov\ ed. ", count := [ 5, 2, 9, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 9, 10 ], mathmode := "Text", name := "P", next := 164773, root := ~, start := 164769, stop := 164772 ), rec( content := "\n\n \ ", count := [ 5, 2, 9, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 3, 2, 2, 4], [], [2, 1, 4], []]);\n\ngap> InDegrees(D);\n[ 2, 3, 1, 2 ]\ngap> InDeg\ reeSequence(D);\n[ 3, 2, 2, 1 ]\ngap> InDegreeSet(D);\n[ 1, 2, 3 ]\ngap> D := \ CycleDigraph(IsMutableDigraph, 3);\n\ \ngap> InDegrees(D);\n[ 1, 1, 1 ]\n", count := [ 5, 2, 9, 11 ], name := "PCDAT\ A", root := ~ ) ], count := [ 5, 2, 9, 11 ], mathmode := "Text", name := "Example", next := 165145, root := ~, start := 164779, stop := 165144 ), rec( content := "\n ", count := [ 5, 2, 9, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "Description", next := 165162, root := ~, start := 164185, stop := 165161 ) ], count := [ 5, 2, 9, 1 ], mathmode := "Text", name := "ManSection", next := 165176, root := ~, start := 163984, stop := 165175 ), rec( content := "\n\n ", count := [ 5, 2, 9, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, vertex" , Name := "OutDegreeOfVert\ ex" ), content := 0, count := [ 5, 2, 10, 2 ], mathmode := "Text", name := "Oper", next := 165251, root := ~, start := 165197, stop := 165250 ), rec( attributes := rec( ), content := [ rec( content := "The non-n\ egative integer.", count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "Returns", next := 165298, root := ~, start := 165254, stop := 165297 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s operation returns the out-degree of the vertex ", count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ertex", count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "A", next := 165384, root := ~, start := 165371, stop := 165383 ), rec( content := " in the\\ n digraph ", count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "A", next := 165418, root := ~, start := 165404, stop := 165417 ), rec( content := ".\n T\ he out-degree of ", count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ertex", count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "A", next := 165455, root := ~, start := 165442, stop := 165454 ), rec( content := " is the \ number of edges in ", count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "A", next := 165496, root := ~, start := 165482, stop := 165495 ), rec( content := "\n wh\ ose source is ", count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ertex", count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "A", next := 165530, root := ~, start := 165517, stop := 165529 ), rec( content := ".\n " , count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 10, 4 ], mathmode := "Text", name := "P", next := 165540, root := ~, start := 165536, stop := 165539 ), rec( content := "\n ", count := [ 5, 2, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([\n> [2, 2, 1], [1, 4], [2, 2, 4, 2], [1, 1, 2, 2, 1, 2, 2]\ ]);\n\ngap> OutDegreeOfVerte\ x(D, 1);\n3\ngap> OutDegreeOfVertex(D, 2);\n2\ngap> OutDegreeOfVertex(D, 3);\n\ 4\ngap> OutDegreeOfVertex(D, 4);\n7\n", count := [ 5, 2, 10, 5 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 2, 10, 5 ], mathmode := "Text", name := "Example", next := 165836, root := ~, start := 165545, stop := 165835 ), rec( content := "\n ", count := [ 5, 2, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "Description", next := 165853, root := ~, start := 165301, stop := 165852 ) ], count := [ 5, 2, 10, 1 ], mathmode := "Text", name := "ManSection", next := 165867, root := ~, start := 165182, stop := 165866 ), rec( content := "\n\n ", count := [ 5, 2, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, vertex" , Name := "OutNeighboursOf\ Vertex" ), content := 0, count := [ 5, 2, 11, 2 ], mathmode := "Text", name := "Oper", next := 165946, root := ~, start := 165888, stop := 165945 ), rec( attributes := rec( Arg := "digraph, vertex" , Name := "OutNeighborsOfV\ ertex" ), content := 0, count := [ 5, 2, 11, 4 ], mathmode := "Text", name := "Oper", next := 166006, root := ~, start := 165949, stop := 166005 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ vertices.", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "Returns", next := 166047, root := ~, start := 166009, stop := 166046 ), rec( attributes := rec( ), content := [ rec( content := "\n\n T\ his operation returns the list ", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ ut", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "C", next := 166111, root := ~, start := 166101, stop := 166110 ), rec( content := " of vert\ ices of the digraph\n ", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "A", next := 166157, root := ~, start := 166143, stop := 166156 ), rec( content := ".\n A\ vertex ", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "C", next := 166180, root := ~, start := 166172, stop := 166179 ), rec( content := " appears\ in the list ", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ ut", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "C", next := 166211, root := ~, start := 166201, stop := 166210 ), rec( content := " each ti\ me there exists an\n edge with source ", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ertex", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "A", next := 166273, root := ~, start := 166260, stop := 166272 ), rec( content := " and ran\ ge ", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "C", next := 166292, root := ~, start := 166284, stop := 166291 ), rec( content := " in ", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "A", next := 166310, root := ~, start := 166296, stop := 166309 ), rec( content := "; in\n \ particular, this means that ", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ ut", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "C", next := 166357, root := ~, start := 166347, stop := 166356 ), rec( content := " may con\ tain duplicates.", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 11, 6 ], mathmode := "Text", name := "P", next := 166385, root := ~, start := 166381, stop := 166384 ), rec( content := "\n ", count := [ 5, 2, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([\n> [2, 2, 3], [1, 3, 4], [2, 2, 3], [1, 1, 2, 2, 1, 2, 2]\ ]);\n\ngap> OutNeighboursOfV\ ertex(D, 1);\n[ 2, 2, 3 ]\ngap> OutNeighboursOfVertex(D, 3);\n[ 2, 2, 3 ]\n", count := [ 5, 2, 11, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 2, 11, 7 ], mathmode := "Text", name := "Example", next := 166645, root := ~, start := 166390, stop := 166644 ), rec( content := "\n ", count := [ 5, 2, 11, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "Description", next := 166662, root := ~, start := 166050, stop := 166661 ) ], count := [ 5, 2, 11, 1 ], mathmode := "Text", name := "ManSection", next := 166676, root := ~, start := 165873, stop := 166675 ), rec( content := "\n\n ", count := [ 5, 2, 11, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, vertex" , Name := "InDegreeOfVerte\ x" ), content := 0, count := [ 5, 2, 12, 2 ], mathmode := "Text", name := "Oper", next := 166750, root := ~, start := 166697, stop := 166749 ), rec( attributes := rec( ), content := [ rec( content := "A non-neg\ ative integer.", count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "Returns", next := 166795, root := ~, start := 166753, stop := 166794 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s operation returns the in-degree of the vertex ", count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ertex", count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "A", next := 166880, root := ~, start := 166867, stop := 166879 ), rec( content := " in the\\ n digraph ", count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "A", next := 166914, root := ~, start := 166900, stop := 166913 ), rec( content := ".\n T\ he in-degree of ", count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ertex", count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "A", next := 166950, root := ~, start := 166937, stop := 166949 ), rec( content := " is the \ number of edges in ", count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "A", next := 166991, root := ~, start := 166977, stop := 166990 ), rec( content := "\n wh\ ose range is ", count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ertex", count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "A", next := 167024, root := ~, start := 167011, stop := 167023 ), rec( content := ".\n " , count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([\n> [2, 2, 1], [1, 4], [2, 2, 4, 2], [1, 1, 2, 2, 1, 2, 2]\ ]);\n\ngap> InDegreeOfVertex\ (D, 1);\n5\ngap> InDegreeOfVertex(D, 2);\n9\ngap> InDegreeOfVertex(D, 3);\n0\n\ gap> InDegreeOfVertex(D, 4);\n2\n", count := [ 5, 2, 12, 4 ], name := "PCDATA" , root := ~ ) ], count := [ 5, 2, 12, 4 ], mathmode := "Text", name := "Example", next := 167317, root := ~, start := 167030, stop := 167316 ), rec( content := "\n ", count := [ 5, 2, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "Description", next := 167334, root := ~, start := 166798, stop := 167333 ) ], count := [ 5, 2, 12, 1 ], mathmode := "Text", name := "ManSection", next := 167348, root := ~, start := 166682, stop := 167347 ), rec( content := "\n\n ", count := [ 5, 2, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, vertex" , Name := "InNeighboursOfV\ ertex" ), content := 0, count := [ 5, 2, 13, 2 ], mathmode := "Text", name := "Oper", next := 167426, root := ~, start := 167369, stop := 167425 ), rec( attributes := rec( Arg := "digraph, vertex" , Name := "InNeighborsOfVe\ rtex" ), content := 0, count := [ 5, 2, 13, 4 ], mathmode := "Text", name := "Oper", next := 167485, root := ~, start := 167429, stop := 167484 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ postitive vertices.", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "Returns", next := 167536, root := ~, start := 167488, stop := 167535 ), rec( attributes := rec( ), content := [ rec( content := "\n\n T\ his operation returns the list ", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nn", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "C", next := 167600, root := ~, start := 167590, stop := 167599 ), rec( content := " of vert\ ices of the digraph\n ", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "A", next := 167646, root := ~, start := 167632, stop := 167645 ), rec( content := ".\n A\ vertex ", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "C", next := 167669, root := ~, start := 167661, stop := 167668 ), rec( content := " appears\ in the list ", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nn", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "C", next := 167700, root := ~, start := 167690, stop := 167699 ), rec( content := " each ti\ me there exists an\n edge with source ", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "C", next := 167757, root := ~, start := 167749, stop := 167756 ), rec( content := " and ran\ ge ", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ertex", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "A", next := 167781, root := ~, start := 167768, stop := 167780 ), rec( content := " in ", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "A", next := 167799, root := ~, start := 167785, stop := 167798 ), rec( content := "; in\n \ particular, this means that ", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nn", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "C", next := 167846, root := ~, start := 167836, stop := 167845 ), rec( content := " may con\ tain duplicates. ", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 13, 6 ], mathmode := "Text", name := "P", next := 167875, root := ~, start := 167871, stop := 167874 ), rec( content := "\n\n \ ", count := [ 5, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([\n> [2, 2, 3], [1, 3, 4], [2, 2, 3], [1, 1, 2, 2, 1, 2, 2]\ ]);\n\ngap> InNeighboursOfVe\ rtex(D, 1);\n[ 2, 4, 4, 4 ]\ngap> InNeighboursOfVertex(D, 2);\n[ 1, 1, 3, 3, 4\ , 4, 4, 4 ]\n", count := [ 5, 2, 13, 7 ], name := "PCDATA", root := ~ ) ], count := [ 5, 2, 13, 7 ], mathmode := "Text", name := "Example", next := 168152, root := ~, start := 167881, stop := 168151 ), rec( content := "\n ", count := [ 5, 2, 13, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "Description", next := 168169, root := ~, start := 167539, stop := 168168 ) ], count := [ 5, 2, 13, 1 ], mathmode := "Text", name := "ManSection", next := 168183, root := ~, start := 167354, stop := 168182 ), rec( content := "\n\n ", count := [ 5, 2, 13, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphLoops" ) , content := 0, count := [ 5, 2, 14, 2 ], mathmode := "Text", name := "Attr", next := 168245, root := ~, start := 168204, stop := 168244 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ vertices.", count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "Returns", next := 168286, root := ~, start := 168248, stop := 168285 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "A", next := 168324, root := ~, start := 168310, stop := 168323 ), rec( content := " is a di\ graph, then ", count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphLoops", count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "C", next := 168363, root := ~, start := 168344, stop := 168362 ), rec( content := " returns\ the list\n consisting of the ", count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Vertices" ), content := 0, count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "Ref", next := 168432, root := ~, start := 168403, stop := 168431 ), rec( content := " of ", count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "A", next := 168450, root := ~, start := 168436, stop := 168449 ), rec( content := "\n at\ which there is a loop. See ", count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "Digraph\ HasLoops" ), content := 0, count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "Ref", next := 168514, root := ~, start := 168485, stop := 168513 ), rec( content := ". ", count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 14, 4 ], mathmode := "Text", name := "P", next := 168520, root := ~, start := 168516, stop := 168519 ), rec( content := "\n\n \ ", count := [ 5, 2, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[2], [3], []]);\n\ngap> DigraphHasLoops(D);\nfalse\ngap> DigraphLoops(D);\n[ ]\ngap> D := D\ igraph([[3, 5], [1], [2, 4, 3], [4], [2, 1]]);\n\ngap> DigraphLoops(D);\n[ 3, 4 ]\ngap> D := Digraph(IsMutableDi\ graph, [[1], [1]]);\n\ngap> DigraphL\ oops(D);\n[ 1 ]\n", count := [ 5, 2, 14, 5 ], name := "PCDATA", root := ~ ) ], count := [ 5, 2, 14, 5 ], mathmode := "Text", name := "Example", next := 168950, root := ~, start := 168526, stop := 168949 ), rec( content := "\n ", count := [ 5, 2, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "Description", next := 168967, root := ~, start := 168289, stop := 168966 ) ], count := [ 5, 2, 14, 1 ], mathmode := "Text", name := "ManSection", next := 168981, root := ~, start := 168189, stop := 168980 ), rec( content := "\n\n ", count := [ 5, 2, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, u, v", Name := "PartialOrderDig\ raphMeetOfVertices" ), content := 0, count := [ 5, 2, 15, 2 ], mathmode := "Text", name := "Oper", next := 169074, root := ~, start := 169002, stop := 169073 ), rec( attributes := rec( Arg := "digraph, u, v", Name := "PartialOrderDig\ raphJoinOfVertices" ), content := 0, count := [ 5, 2, 15, 4 ], mathmode := "Text", name := "Oper", next := 169149, root := ~, start := 169077, stop := 169148 ), rec( attributes := rec( ), content := [ rec( content := "A positiv\ e integer or ", count := [ 5, 2, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 2, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 15, 5 ], mathmode := "Text", name := "K", next := 169194, root := ~, start := 169183, stop := 169193 ) ], count := [ 5, 2, 15, 5 ], mathmode := "Text", name := "Returns", next := 169204, root := ~, start := 169152, stop := 169203 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ the first argument is a partial order digraph ", count := [ 5, 2, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsParti\ alOrderDigraph" ), content := 0, count := [ 5, 2, 15, 5 ], mathmode := "Text", name := "Ref", next := 169315, root := ~, start := 169276, stop := 169314 ), rec( content := " then th\ ese operations return the meet, or\n the join, of the two input vertices. I\ f the meet (or join) is does not\n exist then ", count := [ 5, 2, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 2, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 15, 5 ], mathmode := "Text", name := "K", next := 169459, root := ~, start := 169448, stop := 169458 ), rec( content := " is retu\ rned. The meet (or join) is guaranteed to\n exist when the first argument s\ atisfies\n ", count := [ 5, 2, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsMeetS\ emilatticeDigraph" ), content := 0, count := [ 5, 2, 15, 5 ], mathmode := "Text", name := "Ref", next := 169595, root := ~, start := 169557, stop := 169594 ), rec( content := " (or\n \ ", count := [ 5, 2, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsJoinS\ emilatticeDigraph" ), content := 0, count := [ 5, 2, 15, 5 ], mathmode := "Text", name := "Ref", next := 169643, root := ~, start := 169605, stop := 169642 ), rec( content := ") - see \ the documentation for these\n properties for the definition of the meet (or\ the join).\n\n ", count := [ 5, 2, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1], [1, 2], [1, 3], [1, 2, 3, 4]]);\n\ngap> PartialOrderDigraphMeetOfVertices(D, 2, 3);\n4\ \ngap> PartialOrderDigraphJoinOfVertices(D, 2, 3);\n1\ngap> PartialOrderDigrap\ hMeetOfVertices(D, 1, 2);\n2\ngap> PartialOrderDigraphJoinOfVertices(D, 3, 4);\ \n3\ngap> D := Digraph([[1], [2], [1, 2, 3], [1, 2, 4]]);\n\ngap> PartialOrderDigraphMeetOfVertices(D, 3, 4);\nf\ ail\ngap> PartialOrderDigraphJoinOfVertices(D, 3, 4);\nfail\ngap> PartialOrder\ DigraphMeetOfVertices(D, 1, 2);\nfail\ngap> PartialOrderDigraphJoinOfVertices(\ D, 1, 2);\nfail\n", count := [ 5, 2, 15, 6 ], name := "PCDATA", root := ~ ) ], count := [ 5, 2, 15, 6 ], mathmode := "Text", name := "Example", next := 170396, root := ~, start := 169745, stop := 170395 ), rec( content := "\n ", count := [ 5, 2, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 15, 5 ], mathmode := "Text", name := "Description", next := 170413, root := ~, start := 169209, stop := 170412 ) ], count := [ 5, 2, 15, 1 ], mathmode := "Text", name := "ManSection", next := 170427, root := ~, start := 168987, stop := 170426 ), rec( content := "\n\n ", count := [ 5, 2, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DegreeMatrix" ) , content := 0, count := [ 5, 2, 16, 2 ], mathmode := "Text", name := "Attr", next := 170489, root := ~, start := 170448, stop := 170488 ), rec( attributes := rec( ), content := [ rec( content := "A square \ matrix of non-negative integers.", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "Returns", next := 170552, root := ~, start := 170492, stop := 170551 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function returns the outdegree matrix ", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ at", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "C", next := 170626, root := ~, start := 170616, stop := 170625 ), rec( content := " of the \ digraph\n ", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "A", next := 170660, root := ~, start := 170646, stop := 170659 ), rec( content := ". The va\ lue of the ", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "C", next := 170687, root := ~, start := 170679, stop := 170686 ), rec( content := "th diago\ nal matrix entry is the\n outdegree of the vertex ", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "C", next := 170755, root := ~, start := 170747, stop := 170754 ), rec( content := " in ", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "A", next := 170773, root := ~, start := 170759, stop := 170772 ), rec( content := ". All of\ f-diagonal entries \n are ", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "0\ ", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "C", next := 170817, root := ~, start := 170809, stop := 170816 ), rec( content := ".\n I\ f ", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "A", next := 170840, root := ~, start := 170826, stop := 170839 ), rec( content := " has no \ vertices, then the empty list is returned. ", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 16, 4 ], mathmode := "Text", name := "P", next := 170895, root := ~, start := 170891, stop := 170894 ), rec( content := "\n\n \ See ", count := [ 5, 2, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "OutDegr\ ees" ), content := 0, count := [ 5, 2, 16, 4 ], mathmode := "Text", name := "Ref", next := 170929, root := ~, start := 170905, stop := 170928 ), rec( content := " for mor\ e information.\n ", count := [ 5, 2, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 2, 3], [4], [1, 3, 4], []]);\n\ngap> PrintArray(DegreeMatrix(D));\n[ [ 3, 0, 0, 0 ],\ \n [ 0, 1, 0, 0 ],\n [ 0, 0, 3, 0 ],\n [ 0, 0, 0, 0 ] ]\ngap> D\ := CycleDigraph(5);;\ngap> PrintArray(DegreeMatrix(D));\n[ [ 1, 0, 0, 0, \ 0 ],\n [ 0, 1, 0, 0, 0 ],\n [ 0, 0, 1, 0, 0 ],\n [ 0, 0, 0, \ 1, 0 ],\n [ 0, 0, 0, 0, 1 ] ]\ngap> DegreeMatrix(EmptyDigraph(0));\n[ \ ]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n\ngap> Display(DegreeMatrix(D));\n[ [ 1, 0, 0 ],\n [ 0, 1, \ 0 ],\n [ 0, 0, 1 ] ]\n", count := [ 5, 2, 16, 5 ], name := "PCDATA", root := ~ ) ], count := [ 5, 2, 16, 5 ], mathmode := "Text", name := "Example", next := 171616, root := ~, start := 170956, stop := 171615 ), rec( content := "\n ", count := [ 5, 2, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "Description", next := 171633, root := ~, start := 170555, stop := 171632 ) ], count := [ 5, 2, 16, 1 ], mathmode := "Text", name := "ManSection", next := 171647, root := ~, start := 170433, stop := 171646 ), rec( content := "\n\n ", count := [ 5, 2, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "LaplacianMatrix\ " ), content := 0, count := [ 5, 2, 17, 2 ], mathmode := "Text", name := "Attr", next := 171712, root := ~, start := 171668, stop := 171711 ), rec( attributes := rec( ), content := [ rec( content := "A square \ matrix of integers.", count := [ 5, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 17, 3 ], mathmode := "Text", name := "Returns", next := 171762, root := ~, start := 171715, stop := 171761 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function returns the outdegree Laplacian matrix ", count := [ 5, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ at", count := [ 5, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 17, 3 ], mathmode := "Text", name := "C", next := 171846, root := ~, start := 171836, stop := 171845 ), rec( content := " of the\\ n digraph ", count := [ 5, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 17, 3 ], mathmode := "Text", name := "A", next := 171880, root := ~, start := 171866, stop := 171879 ), rec( content := ". The ou\ tdegree Laplacian matrix is defined as\n ", count := [ 5, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ egreeMatrix(digraph) - AdjacencyMatrix(digraph)", count := [ 5, 2, 17, 3 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 17, 3 ], mathmode := "Text", name := "C", next := 171986, root := ~, start := 171931, stop := 171985 ), rec( content := ". If\n \ ", count := [ 5, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 17, 3 ], mathmode := "Text", name := "A", next := 172010, root := ~, start := 171996, stop := 172009 ), rec( content := " has no \ vertices, then the empty list is returned. ", count := [ 5, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 2, 17, 4 ], mathmode := "Text", name := "P", next := 172065, root := ~, start := 172061, stop := 172064 ), rec( content := "\n\n \ See ", count := [ 5, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "DegreeM\ atrix" ), content := 0, count := [ 5, 2, 17, 4 ], mathmode := "Text", name := "Ref", next := 172101, root := ~, start := 172075, stop := 172100 ), rec( content := " and ", count := [ 5, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Adjacen\ cyMatrix" ), content := 0, count := [ 5, 2, 17, 4 ], mathmode := "Text", name := "Ref", next := 172135, root := ~, start := 172106, stop := 172134 ), rec( content := " for mor\ e\n information.\n ", count := [ 5, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := Digraph([[1, 2, 3], [4], [1, 3, 4], []]);\n\ngap> PrintArray(LaplacianMatrix(gr));\n[ [ 2, -1, -\ 1, 0 ],\n [ 0, 1, 0, -1 ],\n [ -1, 0, 2, -1 ],\n [ 0, 0,\ 0, 0 ] ]\ngap> LaplacianMatrix(EmptyDigraph(0));\n[ ]\ngap> D := CycleDi\ graph(IsMutableDigraph, 3);\n\ngap> \ Display(LaplacianMatrix(D));\n[ [ 1, -1, 0 ],\n [ 0, 1, -1 ],\n [ \ -1, 0, 1 ] ]\n", count := [ 5, 2, 17, 5 ], name := "PCDATA", root := ~ ) ], count := [ 5, 2, 17, 5 ], mathmode := "Text", name := "Example", next := 172669, root := ~, start := 172166, stop := 172668 ), rec( content := "\n ", count := [ 5, 2, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 17, 3 ], mathmode := "Text", name := "Description", next := 172686, root := ~, start := 171765, stop := 172685 ) ], count := [ 5, 2, 17, 1 ], mathmode := "Text", name := "ManSection", next := 172700, root := ~, start := 171653, stop := 172699 ), rec( content := "\n\n ", count := [ 5, 2, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 0, 1 ], mathmode := "Text", name := "Section", next := 172714, root := ~, start := 152482, stop := 172713 ) , rec( content := "\n\n ", count := [ 5, 2, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Reachability and \ connectivity", count := [ 5, 3, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 0, 2 ], mathmode := "Text", name := "Heading", next := 172775, root := ~, start := 172727, stop := 172774 ), rec( content := "\n ", count := [ 5, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphDiameter\ " ), content := 0, count := [ 5, 3, 1, 2 ], mathmode := "Text", name := "Attr", next := 172839, root := ~, start := 172795, stop := 172838 ), rec( attributes := rec( ), content := [ rec( content := "An intege\ r or ", count := [ 5, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 1, 3 ], mathmode := "Text", name := "C", next := 172876, root := ~, start := 172865, stop := 172875 ), rec( content := ".", count := [ 5, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 1, 3 ], mathmode := "Text", name := "Returns", next := 172887, root := ~, start := 172842, stop := 172886 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function returns the diameter of the digraph ", count := [ 5, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 1, 3 ], mathmode := "Text", name := "A", next := 172972, root := ~, start := 172958, stop := 172971 ), rec( content := ".\n " , count := [ 5, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 1, 4 ], mathmode := "Text", name := "P", next := 172982, root := ~, start := 172978, stop := 172981 ), rec( content := "\n\n \ If a digraph ", count := [ 5, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 1, 4 ], mathmode := "Text", name := "A", next := 173015, root := ~, start := 173001, stop := 173014 ), rec( content := " is stro\ ngly connected and has at least 1\n vertex, then the ", count := [ 5, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ iameter", count := [ 5, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 1, 4 ], mathmode := "Text", name := "E", next := 173093, root := ~, start := 173078, stop := 173092 ), rec( content := " is the \ maximum shortest distance between\n any pair of distinct vertices. Otherwis\ e then the diameter of\n ", count := [ 5, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 1, 4 ], mathmode := "Text", name := "A", next := 173219, root := ~, start := 173205, stop := 173218 ), rec( content := " is unde\ fined, and this function returns the value\n ", count := [ 5, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 1, 4 ], mathmode := "Text", name := "C", next := 173285, root := ~, start := 173274, stop := 173284 ), rec( content := ". ", count := [ 5, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 1, 5 ], mathmode := "Text", name := "P", next := 173291, root := ~, start := 173287, stop := 173290 ), rec( content := "\n\n \ See ", count := [ 5, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ ShortestDistances" ), content := 0, count := [ 5, 3, 1, 5 ], mathmode := "Text", name := "Ref", next := 173339, root := ~, start := 173301, stop := 173338 ), rec( content := ". ", count := [ 5, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 1, 6 ], mathmode := "Text", name := "P", next := 173345, root := ~, start := 173341, stop := 173344 ), rec( content := "\n ", count := [ 5, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[2], [3], [4, 5], [5], [1, 2, 3, 4, 5]]);\n\ngap> DigraphDiameter(D);\n3\ngap> D := ChainDi\ graph(2);\n\ngap> DigraphDiameter(D);\ \nfail\ngap> IsStronglyConnectedDigraph(D);\nfalse\ngap> D := GeneralisedPeter\ senGraph(IsMutableDigraph, 6, 2);\n\ngap> DigraphDiameter(D);\n4\n", count := [ 5, 3, 1, 7 ], name := "PCDATA", root := ~ ) ], count := [ 5, 3, 1, 7 ], mathmode := "Text", name := "Example", next := 173789, root := ~, start := 173350, stop := 173788 ), rec( content := "\n ", count := [ 5, 3, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 1, 3 ], mathmode := "Text", name := "Description", next := 173806, root := ~, start := 172890, stop := 173805 ) ], count := [ 5, 3, 1, 1 ], mathmode := "Text", name := "ManSection", next := 173820, root := ~, start := 172780, stop := 173819 ), rec( content := "\n\n ", count := [ 5, 3, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, u, v", Label := "for a digraph \ and two vertices", Name := "DigraphShortestDistance" ), content := 0, count := [ 5, 3, 2, 2 ], mathmode := "Text", name := "Oper", next := 173946, root := ~, start := 173841, stop := 173945 ), rec( attributes := rec( Arg := "digraph, list", Label := "for a digraph \ and a list", Name := "DigraphShortestDistance" ), content := 0, count := [ 5, 3, 2, 4 ], mathmode := "Text", name := "Oper", next := 174048, root := ~, start := 173949, stop := 174047 ), rec( attributes := rec( Arg := "digraph, list1, \ list2", Label := "for a digraph, a list, and a list", Name := "DigraphShortest\ Distance" ), content := 0, count := [ 5, 3, 2, 6 ], mathmode := "Text", name := "Oper", next := 174167, root := ~, start := 174051, stop := 174166 ), rec( attributes := rec( ), content := [ rec( content := "An intege\ r or ", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "K", next := 174204, root := ~, start := 174193, stop := 174203 ) ], count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "Returns", next := 174214, root := ~, start := 174170, stop := 174213 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ there is a directed path in the digraph ", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "A", next := 174292, root := ~, start := 174278, stop := 174291 ), rec( content := " between\ vertex\n ", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "A", next := 174320, root := ~, start := 174312, stop := 174319 ), rec( content := " and ver\ tex ", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "A", next := 174340, root := ~, start := 174332, stop := 174339 ), rec( content := ", then t\ his operation returns the length of the\n shortest such directed path. If \ no such directed path exists, then this\n operation returns ", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "K", next := 174498, root := ~, start := 174487, stop := 174497 ), rec( content := ". See se\ ction ", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Style := "Number\ ", Subsect := "Definitions" ), content := 0, count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "Ref", next := 174562, root := ~, start := 174512, stop := 174561 ), rec( content := " for the\ definition of a directed path. ", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 2, 8 ], mathmode := "Text", name := "P", next := 174606, root := ~, start := 174602, stop := 174605 ), rec( content := "\n\n \ If the second form is used, then ", count := [ 5, 3, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 5, 3, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 2, 8 ], mathmode := "Text", name := "A", next := 174656, root := ~, start := 174645, stop := 174655 ), rec( content := " should \ be a list of length two,\n containing two positive integers which correspon\ d to the vertices ", count := [ 5, 3, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 5, 3, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 2, 8 ], mathmode := "Text", name := "A", next := 174767, root := ~, start := 174759, stop := 174766 ), rec( content := "\n an\ d ", count := [ 5, 3, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 5, 3, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 2, 8 ], mathmode := "Text", name := "A", next := 174784, root := ~, start := 174776, stop := 174783 ), rec( content := ". ", count := [ 5, 3, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 2, 9 ], mathmode := "Text", name := "P", next := 174790, root := ~, start := 174786, stop := 174789 ), rec( content := "\n\n \ Note that as usual, a vertex is considered to be at distance 0 from\n itsel\ f .", count := [ 5, 3, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "P", next := 174880, root := ~, start := 174876, stop := 174879 ), rec( content := "\n\n \ If the third form is used, then ", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist1", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "A", next := 174930, root := ~, start := 174918, stop := 174929 ), rec( content := " and ", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist2", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "A", next := 174947, root := ~, start := 174935, stop := 174946 ), rec( content := " are bot\ h lists\n of vertices. The shortest directed path between ", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist1", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "A", next := 175027, root := ~, start := 175015, stop := 175026 ), rec( content := " and\n \ ", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist2", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "A", next := 175048, root := ~, start := 175036, stop := 175047 ), rec( content := " is then\ the length of the shortest directed path which starts\n with a vertex in " , count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist1", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "A", next := 175144, root := ~, start := 175132, stop := 175143 ), rec( content := " and ter\ minates at a vertex in ", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist2", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "A", next := 175187, root := ~, start := 175175, stop := 175186 ), rec( content := ", if\n \ such directed path exists. If ", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist1", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "A", next := 175238, root := ~, start := 175226, stop := 175237 ), rec( content := " and ", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist2", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "A", next := 175255, root := ~, start := 175243, stop := 175254 ), rec( content := " have no\ n-empty\n intersection, the operation returns ", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "0\ ", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "C", next := 175319, root := ~, start := 175311, stop := 175318 ), rec( content := ".", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 2, 11 ], mathmode := "Text", name := "P", next := 175324, root := ~, start := 175320, stop := 175323 ), rec( content := "\n ", count := [ 5, 3, 2, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[2], [3], [1, 4], [1, 3], [5]]);\n\ngap> DigraphShortestDistance(D, 1, 3);\n2\ngap> DigraphS\ hortestDistance(D, [3, 3]);\n0\ngap> DigraphShortestDistance(D, 5, 2);\nfail\n\ gap> DigraphShortestDistance(D, [1, 2], [4, 5]);\n2\ngap> DigraphShortestDista\ nce(D, [1, 3], [3, 5]);\n0\n", count := [ 5, 3, 2, 12 ], name := "PCDATA", root := ~ ) ], count := [ 5, 3, 2, 12 ], mathmode := "Text", name := "Example", next := 175688, root := ~, start := 175329, stop := 175687 ), rec( content := "\n ", count := [ 5, 3, 2, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "Description", next := 175705, root := ~, start := 174217, stop := 175704 ) ], count := [ 5, 3, 2, 1 ], mathmode := "Text", name := "ManSection", next := 175719, root := ~, start := 173826, stop := 175718 ), rec( content := "\n\n ", count := [ 5, 3, 2, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphShortest\ Distances" ), content := 0, count := [ 5, 3, 3, 2 ], mathmode := "Text", name := "Attr", next := 175793, root := ~, start := 175740, stop := 175792 ), rec( attributes := rec( ), content := [ rec( content := "A square \ matrix.", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "Returns", next := 175831, root := ~, start := 175796, stop := 175830 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "A", next := 175869, root := ~, start := 175855, stop := 175868 ), rec( content := " is a di\ graph with ", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "M", next := 175896, root := ~, start := 175888, stop := 175895 ), rec( content := " vertice\ s, then this\n function returns an ", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ \\times n", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "M", next := 175958, root := ~, start := 175941, stop := 175957 ), rec( content := " matrix \ ", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ at", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "C", next := 175976, root := ~, start := 175966, stop := 175975 ), rec( content := ", where \ each entry is\n either a non-negative integer, or ", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "K", next := 176047, root := ~, start := 176036, stop := 176046 ), rec( content := ". If ", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ = 0", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "M", next := 176065, root := ~, start := 176053, stop := 176064 ), rec( content := ", then a\ n\n empty list is returned. ", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "P", next := 176107, root := ~, start := 176103, stop := 176106 ), rec( content := "\n\n \ If there is a directed path from vertex ", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "C", next := 176161, root := ~, start := 176153, stop := 176160 ), rec( content := " to vert\ ex ", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "C", next := 176180, root := ~, start := 176172, stop := 176179 ), rec( content := ", then\n\ the value of ", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ at[i][j]", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "C", next := 176220, root := ~, start := 176204, stop := 176219 ), rec( content := " is the \ length of the shortest such directed\n path. If no such directed path exist\ s, then the value of ", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ at[i][j]", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "C", next := 176342, root := ~, start := 176326, stop := 176341 ), rec( content := " is\n \ ", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "C", next := 176361, root := ~, start := 176350, stop := 176360 ), rec( content := ". We us\ e the convention that the distance from every vertex to\n itself is ", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "0\ ", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "C", next := 176447, root := ~, start := 176439, stop := 176446 ), rec( content := ", i.e. " , count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ at[i][i] = 0", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "C", next := 176474, root := ~, start := 176454, stop := 176473 ), rec( content := " for all\ vertices ", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "C", next := 176500, root := ~, start := 176492, stop := 176499 ), rec( content := ".\n " , count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 3, 5 ], mathmode := "Text", name := "P", next := 176510, root := ~, start := 176506, stop := 176509 ), rec( content := "\n\n \ The method used in this function is a version of the Floyd-Warshall\n algor\ ithm, and has complexity ", count := [ 5, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (n^3)", count := [ 5, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 3, 5 ], mathmode := "Text", name := "M", next := 176631, root := ~, start := 176618, stop := 176630 ), rec( content := ".\n\n \ ", count := [ 5, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 2], [3], [1, 2], [4]]);\n\ngap> mat := DigraphShortestDistances(D);;\ngap> PrintArray(ma\ t);\n[ [ 0, 1, 2, fail ],\n [ 2, 0, 1, fail ],\n [\ 1, 1, 0, fail ],\n [ fail, fail, fail, 0 ] ]\ngap> D := \ CycleDigraph(IsMutableDigraph, 3);\n\ \ngap> DigraphShortestDistances(D);\n[ [ 0, 1, 2 ], [ 2, 0, 1 ], [ 1, 2, 0 ] ]\ \n", count := [ 5, 3, 3, 6 ], name := "PCDATA", root := ~ ) ], count := [ 5, 3, 3, 6 ], mathmode := "Text", name := "Example", next := 177127, root := ~, start := 176638, stop := 177126 ), rec( content := "\n ", count := [ 5, 3, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "Description", next := 177144, root := ~, start := 175834, stop := 177143 ) ], count := [ 5, 3, 3, 1 ], mathmode := "Text", name := "ManSection", next := 177158, root := ~, start := 175725, stop := 177157 ), rec( content := "\n\n ", count := [ 5, 3, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, v", Name := "DigraphLongestD\ istanceFromVertex" ), content := 0, count := [ 5, 3, 4, 2 ], mathmode := "Text", name := "Oper", next := 177243, root := ~, start := 177179, stop := 177242 ), rec( attributes := rec( ), content := [ rec( content := "An intege\ r, or ", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nfinity", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "K", next := 177285, root := ~, start := 177270, stop := 177284 ), rec( content := ".", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "Returns", next := 177296, root := ~, start := 177246, stop := 177295 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "A", next := 177334, root := ~, start := 177320, stop := 177333 ), rec( content := " is a di\ graph and ", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "A", next := 177360, root := ~, start := 177352, stop := 177359 ), rec( content := " is a ve\ rtex in ", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "A", next := 177390, root := ~, start := 177376, stop := 177389 ), rec( content := ",\n t\ hen this operation returns the length of the longest directed walk in\n ", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "A", next := 177485, root := ~, start := 177471, stop := 177484 ), rec( content := " which b\ egins at vertex ", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "A", next := 177517, root := ~, start := 177509, stop := 177516 ), rec( content := ". See s\ ection ", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Style := "Number\ ", Subsect := "Definitions" ), content := 0, count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "Ref", next := 177582, root := ~, start := 177532, stop := 177581 ), rec( content := " for the\ definitions of directed\n walk, directed cycle, and loop.\n ", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 4, 4 ], mathmode := "Text", name := "P", next := 177659, root := ~, start := 177655, stop := 177658 ), rec( content := "\n\n \ ", count := [ 5, 3, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "\n If there exists a directed w\ alk starting at vertex ", count := [ 5, 3, 4, 6 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content \ := "v", count := [ 5, 3, 4, 6 ], mathmode := "Text", name := "PCDATA", root :=\ ~ ) ], count := [ 5, 3, 4, 6 ], mathmode := "Text", name := "A", next := 1777\ 52, root := ~, start := 177744, stop := 177751 ), rec( content := "\n w\ hich traverses a loop or a directed cycle,\n then we consider there to \ be a walk of infinite length from ", count := [ 5, 3, 4, 6 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ re\ c( content := "v", count := [ 5, 3, 4, 6 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 5, 3, 4, 6 ], mathmode := "Text", name := "A", next\ := 177881, root := ~, start := 177873, stop := 177880 ), rec( content := "\n \ (realised by repeatedly traversing the loop/directed cycle),\n a\ nd so the result is ", count := [ 5, 3, 4, 6 ], mathmode := "Text", name := "P\ CDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := \ "infinity", count := [ 5, 3, 4, 6 ], mathmode := "Text", name := "PCDATA", roo\ t := ~ ) ], count := [ 5, 3, 4, 6 ], mathmode := "Text", name := "K", next := \ 177995, root := ~, start := 177980, stop := 177994 ), rec( content := ".\n \ To disallow walks using loops, try using\n ", count := [ 5, 3, 4, 6\ ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(\ Oper := "DigraphRemoveLoops" ), content := 0, count := [ 5, 3, 4, 6 ], mathmo\ de := "Text", name := "Ref", next := 178086, root := ~, start := 178054, stop \ := 178085 ), rec( content := ":", count := [ 5, 3, 4, 6 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ \ 5, 3, 4, 7 ], mathmode := "Text", name := "P", next := 178091, root := ~, star\ t := 178087, stop := 178090 ), rec( content := "\n\n ", count := [ 5, 3\ , 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "DigraphLongestDistanceFromVertex(Digr\ aphRemoveLoops(", count := [ 5, 3, 4, 7 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "digr\ aph", count := [ 5, 3, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~\ ) ], count := [ 5, 3, 4, 7 ], mathmode := "Text", name := "A", next := 178170\ , root := ~, start := 178156, stop := 178169 ), rec( content := ",", count := \ [ 5, 3, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attrib\ utes := rec( ), content := [ rec( content := "v", count := [ 5, 3, 4, 7 ], ma\ thmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 4, 7 ], ma\ thmode := "Text", name := "A", next := 178179, root := ~, start := 178171, sto\ p := 178178 ), rec( content := "))", count := [ 5, 3, 4, 7 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 4, 7 ], mathmode := "Tex\ t", name := "C", next := 178185, root := ~, start := 178101, stop := 178184 ), rec( cont\ ent := ".\n ", count := [ 5, 3, 4, 7 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 5, 3, 4, 6 ], name := "Item", next := 178200, root := ~, start := 177\ 678, stop := 178199 ), rec( attributes := rec( ), content := [ rec( content :\ = "\n Otherwise, if all directed walks\n starting at vertex ", coun\ t := [ 5, 3, 4, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "v", count := [ 5, 3, 4, 9 ], \ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 4, 9 ], math\ mode := "Text", name := "A", next := 178291, root := ~, start := 178283, stop \ := 178290 ), rec( content := " have finite length,\n then the length of\ the longest such walk is returned.\n ", count := [ 5, 3, 4, 9 ], mathmod\ e := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 4, 9 ], name := "Ite\ m", next := 178387, root := ~, start := 178208, stop := 178386 ) ], count := [ 5, 3, 4, 5 ], mathmode := "Text", name := "List", next := 178399, root := ~, start := 177665, stop := 178398 ), rec( content := "\n\n \ Note that the result is ", count := [ 5, 3, 4, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "0\ ", count := [ 5, 3, 4, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 4, 11 ], mathmode := "Text", name := "C", next := 178437, root := ~, start := 178429, stop := 178436 ), rec( content := " if and \ only if ", count := [ 5, 3, 4, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 5, 3, 4, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 4, 11 ], mathmode := "Text", name := "A", next := 178461, root := ~, start := 178453, stop := 178460 ), rec( content := " is a si\ nk of\n ", count := [ 5, 3, 4, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 4, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 4, 11 ], mathmode := "Text", name := "A", next := 178493, root := ~, start := 178479, stop := 178492 ), rec( content := ". See " , count := [ 5, 3, 4, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Sinks" ), content := 0, count := [ 5, 3, 4, 11 ], mathmode := "Text", name := "Ref", next := 178526, root := ~, start := 178500, stop := 178525 ), rec( content := ".\n\n", count := [ 5, 3, 4, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[2], [3, 4], [], [5], [], [6]]);\n\ngap> DigraphLongestDistanceFromVertex(D, 1);\n3\ngap> Di\ graphLongestDistanceFromVertex(D, 3);\n0\ngap> 3 in DigraphSinks(D);\ntrue\nga\ p> DigraphLongestDistanceFromVertex(D, 6);\ninfinity\n", count := [ 5, 3, 4, 12 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 4, 12 ], mathmode := "Text", name := "Example", next := 178838, root := ~, start := 178529, stop := 178837 ), rec( content := "\n ", count := [ 5, 3, 4, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "Description", next := 178855, root := ~, start := 177299, stop := 178854 ) ], count := [ 5, 3, 4, 1 ], mathmode := "Text", name := "ManSection", next := 178869, root := ~, start := 177164, stop := 178868 ), rec( content := "\n\n ", count := [ 5, 3, 4, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, vertex,\ distance", Label := "for a digraph, a pos int, and an int", Name := "DigraphDistance\ Set" ), content := 0, count := [ 5, 3, 5, 2 ], mathmode := "Text", name := "Oper", next := 179000, root := ~, start := 178890, stop := 178999 ), rec( attributes := rec( Arg := "digraph, vertex,\ distances", Label := "for a digraph, a pos int, and a list", Name := "DigraphDistance\ Set" ), content := 0, count := [ 5, 3, 5, 4 ], mathmode := "Text", name := "Oper", next := 179114, root := ~, start := 179003, stop := 179113 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ vertices", count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "Returns", next := 179154, root := ~, start := 179117, stop := 179153 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s operation returns the list of all vertices in digraph ", count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "A", next := 179248, root := ~, start := 179234, stop := 179247 ), rec( content := "\n su\ ch that the shortest distance to a vertex ", count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ertex", count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "A", next := 179310, root := ~, start := 179297, stop := 179309 ), rec( content := " is\n \ ", count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ istance", count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "A", next := 179333, root := ~, start := 179318, stop := 179332 ), rec( content := " or is i\ n the list ", count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ istances", count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "A", next := 179368, root := ~, start := 179352, stop := 179367 ), rec( content := ". ", count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 5, 6 ], mathmode := "Text", name := "P", next := 179374, root := ~, start := 179370, stop := 179373 ), rec( content := "\n\n \ ", count := [ 5, 3, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 5, 6 ], mathmode := "Text", name := "A", next := 179394, root := ~, start := 179380, stop := 179393 ), rec( content := " should \ be a digraph, ", count := [ 5, 3, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ertex", count := [ 5, 3, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 5, 6 ], mathmode := "Text", name := "A", next := 179429, root := ~, start := 179416, stop := 179428 ), rec( content := " should \ be a positive\n integer, ", count := [ 5, 3, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ istance", count := [ 5, 3, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 5, 6 ], mathmode := "Text", name := "A", next := 179479, root := ~, start := 179464, stop := 179478 ), rec( content := " should \ be a non-negative integer, and\n ", count := [ 5, 3, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ istances", count := [ 5, 3, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 5, 6 ], mathmode := "Text", name := "A", next := 179538, root := ~, start := 179522, stop := 179537 ), rec( content := " should \ be a list of non-negative integers.\n\n ", count := [ 5, 3, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[2], [3], [1, 4], [1, 3]]);\n\ngap> DigraphDistanceSet(D, 2, [1, 2]);\n[ 3, 1, 4 ]\ngap> Dig\ raphDistanceSet(D, 3, 1);\n[ 1, 4 ]\ngap> DigraphDistanceSet(D, 2, 0);\n[ 2 ]\ \n", count := [ 5, 3, 5, 7 ], name := "PCDATA", root := ~ ) ], count := [ 5, 3, 5, 7 ], mathmode := "Text", name := "Example", next := 179845, root := ~, start := 179587, stop := 179844 ), rec( content := "\n ", count := [ 5, 3, 5, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "Description", next := 179862, root := ~, start := 179157, stop := 179861 ) ], count := [ 5, 3, 5, 1 ], mathmode := "Text", name := "ManSection", next := 179876, root := ~, start := 178875, stop := 179875 ), rec( content := "\n\n ", count := [ 5, 3, 5, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphGirth" ) , content := 0, count := [ 5, 3, 6, 2 ], mathmode := "Text", name := "Attr", next := 179938, root := ~, start := 179897, stop := 179937 ), rec( attributes := rec( ), content := [ rec( content := "An intege\ r, or ", count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nfinity", count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "K", next := 179980, root := ~, start := 179965, stop := 179979 ), rec( content := ".", count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "Returns", next := 179991, root := ~, start := 179941, stop := 179990 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s attribute returns the ", count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ irth", count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "E", next := 180051, root := ~, start := 180039, stop := 180050 ), rec( content := " of the \ digraph ", count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "A", next := 180081, root := ~, start := 180067, stop := 180080 ), rec( content := ".\n T\ he ", count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ irth", count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "E", next := 180103, root := ~, start := 180091, stop := 180102 ), rec( content := " of a di\ graph is the length of its shortest simple circuit.\n See section ", count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Style := "Number\ ", Subsect := "Definitions" ), content := 0, count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "Ref", next := 180223, root := ~, start := 180179, stop := 180222 ), rec( content := " for the\ definitions\n of simple circuit, directed cycle, and loop.\n ", count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 6, 4 ], mathmode := "Text", name := "P", next := 180301, root := ~, start := 180297, stop := 180300 ), rec( content := "\n\n \ If ", count := [ 5, 3, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 6, 4 ], mathmode := "Text", name := "A", next := 180324, root := ~, start := 180310, stop := 180323 ), rec( content := " has no \ directed cycles, then this function will return\n ", count := [ 5, 3, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nfinity", count := [ 5, 3, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 6, 4 ], mathmode := "Text", name := "K", next := 180399, root := ~, start := 180384, stop := 180398 ), rec( content := ". If ", count := [ 5, 3, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 6, 4 ], mathmode := "Text", name := "A", next := 180419, root := ~, start := 180405, stop := 180418 ), rec( content := " contain\ s a loop, then this function will\n return ", count := [ 5, 3, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "1\ ", count := [ 5, 3, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 6, 4 ], mathmode := "Text", name := "C", next := 180480, root := ~, start := 180472, stop := 180479 ), rec( content := ".\n " , count := [ 5, 3, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 6, 5 ], mathmode := "Text", name := "P", next := 180490, root := ~, start := 180486, stop := 180489 ), rec( content := "\n\n \ In the worst case, the method used in this function is a version of the\n F\ loyd-Warshall algorithm, and has complexity ", count := [ 5, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (", count := [ 5, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes :\ = rec( ), content := [ rec( content := "n", count := [ 5, 3, 6, 5 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 6, 5 ], mathmode := \ "Text", name := "A", next := 180630, root := ~, start := 180622, stop := 18062\ 9 ), rec( content := " ^ 3)", count := [ 5, 3, 6, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 6, 5 ], mathmode := "Text", name := "C", next := 180639, root := ~, start := 180617, stop := 180638 ), rec( content := ", where\\ n ", count := [ 5, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 5, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 6, 5 ], mathmode := "Text", name := "A", next := 180659, root := ~, start := 180651, stop := 180658 ), rec( content := " is the \ number of vertices in ", count := [ 5, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 6, 5 ], mathmode := "Text", name := "A", next := 180703, root := ~, start := 180689, stop := 180702 ), rec( content := ". If th\ e digraph has\n known automorphisms [see ", count := [ 5, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Group" ), content := 0, count := [ 5, 3, 6, 5 ], mathmode := "Text", name := "Ref", next := 180780, root := ~, start := 180754, stop := 180779 ), rec( content := "], then \ the performance\n is likely to be better.\n ", count := [ 5, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 6, 6 ], mathmode := "Text", name := "P", next := 180840, root := ~, start := 180836, stop := 180839 ), rec( content := "\n\n \ For symmetric digraphs, see also ", count := [ 5, 3, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ UndirectedGirth" ), content := 0, count := [ 5, 3, 6, 6 ], mathmode := "Text", name := "Ref", next := 180915, root := ~, start := 180879, stop := 180914 ), rec( content := ". ", count := [ 5, 3, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 6, 7 ], mathmode := "Text", name := "P", next := 180921, root := ~, start := 180917, stop := 180920 ), rec( content := "\n ", count := [ 5, 3, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1], [1]]);\n\ \ngap> DigraphGirth(D);\n1\ngap> D := Digraph([[2, 3], [3], [4], []]);\n\ngap> DigraphGirth(D);\ninfinity\ngap> \ D := Digraph([[2, 3], [3], [4], [1]]);\n\ngap> DigraphGirth(D);\n3\ngap> D := GeneralisedPetersenGraph(IsMutable\ Digraph, 6, 2);\n\ngap> DigraphGir\ th(D);\n2\n", count := [ 5, 3, 6, 8 ], name := "PCDATA", root := ~ ) ], count := [ 5, 3, 6, 8 ], mathmode := "Text", name := "Example", next := 181419, root := ~, start := 180926, stop := 181418 ), rec( content := "\n ", count := [ 5, 3, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "Description", next := 181436, root := ~, start := 179994, stop := 181435 ) ], count := [ 5, 3, 6, 1 ], mathmode := "Text", name := "ManSection", next := 181450, root := ~, start := 179882, stop := 181449 ), rec( content := "\n\n ", count := [ 5, 3, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphOddGirth\ " ), content := 0, count := [ 5, 3, 7, 2 ], mathmode := "Text", name := "Attr", next := 181515, root := ~, start := 181471, stop := 181514 ), rec( attributes := rec( ), content := [ rec( content := "An intege\ r, or ", count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nfinity", count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "K", next := 181557, root := ~, start := 181542, stop := 181556 ), rec( content := ".", count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "Returns", next := 181568, root := ~, start := 181518, stop := 181567 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s attribute returns the ", count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ dd girth", count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "E", next := 181632, root := ~, start := 181616, stop := 181631 ), rec( content := " of the \ digraph ", count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "A", next := 181662, root := ~, start := 181648, stop := 181661 ), rec( content := ".\n T\ he ", count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ dd girth", count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "E", next := 181688, root := ~, start := 181672, stop := 181687 ), rec( content := " of a di\ graph is the length of its shortest simple\n circuit of odd length. See Se\ ction ", count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Style := "Number\ ", Subsect := "Definitions" ), content := 0, count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "Ref", next := 181827, root := ~, start := 181779, stop := 181826 ), rec( content := " for the\ definitions of simple circuit, directed\n cycle, and loop.\n ", count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "P", next := 181905, root := ~, start := 181901, stop := 181904 ), rec( content := "\n\n \ If ", count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "A", next := 181928, root := ~, start := 181914, stop := 181927 ), rec( content := " has no \ directed cycles of odd length, then this function\n will return ", count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nfinity", count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "K", next := 182017, root := ~, start := 182002, stop := 182016 ), rec( content := ", even i\ f ", count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "A", next := 182041, root := ~, start := 182027, stop := 182040 ), rec( content := " has a d\ irected cycle\n of even length. If ", count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "A", next := 182101, root := ~, start := 182087, stop := 182100 ), rec( content := " contain\ s a loop, then this function\n will return ", count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "1\ ", count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "C", next := 182162, root := ~, start := 182154, stop := 182161 ), rec( content := ".\n " , count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 7, 5 ], mathmode := "Text", name := "P", next := 182172, root := ~, start := 182168, stop := 182171 ), rec( content := "\n\n \ See also ", count := [ 5, 3, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Girth" ), content := 0, count := [ 5, 3, 7, 5 ], mathmode := "Text", name := "Ref", next := 182213, root := ~, start := 182187, stop := 182212 ), rec( content := ". ", count := [ 5, 3, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 7, 6 ], mathmode := "Text", name := "P", next := 182219, root := ~, start := 182215, stop := 182218 ), rec( content := "\n ", count := [ 5, 3, 7, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[2], [3, 1], [1]]);\n\ngap> DigraphOddGirth(D);\n3\ngap> D := CycleDigraph(4);\n\ngap> DigraphOddGirth(D);\ninfinity\ngap> D := D\ igraph([[2], [3], [], [3], [4]]);\n\ngap> DigraphOddGirth(D);\ninfinity\ngap> D := CycleDigraph(IsMutableDigraph\ , 4);\n\ngap> DigraphDisjointUnion(D\ , CycleDigraph(5));\n\ngap> DigraphO\ ddGirth(D);\n5\n", count := [ 5, 3, 7, 7 ], name := "PCDATA", root := ~ ) ], count := [ 5, 3, 7, 7 ], mathmode := "Text", name := "Example", next := 182799, root := ~, start := 182224, stop := 182798 ), rec( content := "\n ", count := [ 5, 3, 7, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "Description", next := 182816, root := ~, start := 181571, stop := 182815 ) ], count := [ 5, 3, 7, 1 ], mathmode := "Text", name := "ManSection", next := 182830, root := ~, start := 181456, stop := 182829 ), rec( content := "\n\n ", count := [ 5, 3, 7, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphUndirect\ edGirth" ), content := 0, count := [ 5, 3, 8, 2 ], mathmode := "Text", name := "Attr", next := 182902, root := ~, start := 182851, stop := 182901 ), rec( attributes := rec( ), content := [ rec( content := "An intege\ r or ", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nfinity", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "K", next := 182943, root := ~, start := 182928, stop := 182942 ), rec( content := ".", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "Returns", next := 182954, root := ~, start := 182905, stop := 182953 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "A", next := 182992, root := ~, start := 182978, stop := 182991 ), rec( content := " is a sy\ mmetric digraph, then this function returns the\n girth of ", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "A", next := 183075, root := ~, start := 183061, stop := 183074 ), rec( content := " when tr\ eated as an undirected graph (i.e. each pair\n of edges ", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ i, j]", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "M", next := 183154, root := ~, start := 183141, stop := 183153 ), rec( content := " and ", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ j, i]", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "M", next := 183172, root := ~, start := 183159, stop := 183171 ), rec( content := " is trea\ ted as a single edge between\n ", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "M", next := 183221, root := ~, start := 183213, stop := 183220 ), rec( content := " and ", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "M", next := 183234, root := ~, start := 183226, stop := 183233 ), rec( content := "). ", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 8, 4 ], mathmode := "Text", name := "P", next := 183241, root := ~, start := 183237, stop := 183240 ), rec( content := "\n\n \ The ", count := [ 5, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ irth", count := [ 5, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 8, 4 ], mathmode := "Text", name := "E", next := 183263, root := ~, start := 183251, stop := 183262 ), rec( content := " of an u\ ndirected graph is the length of its shortest simple\n cycle, i.e. the shor\ test non-trivial path starting and ending at the same\n vertex and passing \ through no vertex or edge more than once. ", count := [ 5, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 8, 5 ], mathmode := "Text", name := "P", next := 183471, root := ~, start := 183467, stop := 183470 ), rec( content := "\n\n \ If ", count := [ 5, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 8, 5 ], mathmode := "Text", name := "A", next := 183494, root := ~, start := 183480, stop := 183493 ), rec( content := " has no \ cycles, then this function will return\n ", count := [ 5, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nfinity", count := [ 5, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 8, 5 ], mathmode := "Text", name := "K", next := 183560, root := ~, start := 183545, stop := 183559 ), rec( content := ". ", count := [ 5, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 8, 6 ], mathmode := "Text", name := "P", next := 183566, root := ~, start := 183562, stop := 183565 ), rec( content := "\n ", count := [ 5, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[2, 4], [1, 3], [2, 4], [1, 3]]);\n\ngap> DigraphUndirectedGirth(D);\n4\ngap> D := Digraph([\ [2], [1, 3], [2]]);\n\ngap> Digrap\ hUndirectedGirth(D);\ninfinity\ngap> D := Digraph([[1], [], [4], [3]]);\n\ngap> DigraphUndirectedGirth(D);\n1\ng\ ap> D := GeneralisedPetersenGraph(IsMutableDigraph, 9, 2);\n\ngap> DigraphUndirectedGirth(D);\n5\n", count := [ 5, 3, 8, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 8, 7 ], mathmode := "Text", name := "Example", next := 184118, root := ~, start := 183571, stop := 184117 ), rec( content := "\n ", count := [ 5, 3, 8, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "Description", next := 184135, root := ~, start := 182957, stop := 184134 ) ], count := [ 5, 3, 8, 1 ], mathmode := "Text", name := "ManSection", next := 184149, root := ~, start := 182836, stop := 184148 ), rec( content := "\n\n ", count := [ 5, 3, 8, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphConnecte\ dComponents" ), content := 0, count := [ 5, 3, 9, 2 ], mathmode := "Text", name := "Attr", next := 184225, root := ~, start := 184170, stop := 184224 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphNrConnec\ tedComponents" ), content := 0, count := [ 5, 3, 9, 4 ], mathmode := "Text", name := "Attr", next := 184285, root := ~, start := 184228, stop := 184284 ), rec( attributes := rec( ), content := [ rec( content := "A record.\ ", count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "Returns", next := 184316, root := ~, start := 184288, stop := 184315 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function returns the record ", count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "w\ cc", count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "C", next := 184380, root := ~, start := 184370, stop := 184379 ), rec( content := " corresp\ onding to the weakly\n connected components of the digraph ", count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "A", next := 184463, root := ~, start := 184449, stop := 184462 ), rec( content := ". Two v\ ertices of\n ", count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "A", next := 184500, root := ~, start := 184486, stop := 184499 ), rec( content := " are in \ the same weakly connected component whenever they are\n equal, or there exi\ sts a directed path (ignoring the orientation of edges)\n between them. Mo\ re formally, two vertices are in the same weakly connected\n component of " , count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "A", next := 184752, root := ~, start := 184738, stop := 184751 ), rec( content := " if and \ only if they are in the same strongly\n connected component (see ", count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ StronglyConnectedComponents" ), content := 0, count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "Ref", next := 184875, root := ~, start := 184827, stop := 184874 ), rec( content := ")\n o\ f the ", count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ SymmetricClosure" ), content := 0, count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "Ref", next := 184925, root := ~, start := 184888, stop := 184924 ), rec( content := " of ", count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "A", next := 184943, root := ~, start := 184929, stop := 184942 ), rec( content := ". ", count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 9, 6 ], mathmode := "Text", name := "P", next := 184950, root := ~, start := 184946, stop := 184949 ), rec( content := "\n\n \ The set of weakly connected components is a partition of\n the vertex set o\ f ", count := [ 5, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 6 ], mathmode := "Text", name := "A", next := 185049, root := ~, start := 185035, stop := 185048 ), rec( content := ". ", count := [ 5, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "P", next := 185055, root := ~, start := 185051, stop := 185054 ), rec( content := "\n\n \ The record ", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "w\ cc", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "C", next := 185082, root := ~, start := 185072, stop := 185081 ), rec( content := " has 2 c\ omponents: ", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ omps", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "C", next := 185113, root := ~, start := 185101, stop := 185112 ), rec( content := " and ", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ d", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "C", next := 185127, root := ~, start := 185118, stop := 185126 ), rec( content := ".\n T\ he component ", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ omps", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "C", next := 185159, root := ~, start := 185147, stop := 185158 ), rec( content := " is a li\ st of the weakly connected components\n of ", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "A", next := 185227, root := ~, start := 185213, stop := 185226 ), rec( content := " (each o\ f which is a list of vertices).\n The component ", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ d", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "C", next := 185294, root := ~, start := 185285, stop := 185293 ), rec( content := " is a li\ st such that the vertex ", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "C", next := 185334, root := ~, start := 185326, stop := 185333 ), rec( content := " is an\n\ element of the weakly connected component ", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ omps[id[i]]", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "C", next := 185406, root := ~, start := 185387, stop := 185405 ), rec( content := ". ", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 9, 8 ], mathmode := "Text", name := "P", next := 185412, root := ~, start := 185408, stop := 185411 ), rec( content := "\n\n \ The method used in this function has complexity ", count := [ 5, 3, 9, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (m+n)", count := [ 5, 3, 9, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 8 ], mathmode := "Text", name := "M", next := 185480, root := ~, start := 185467, stop := 185479 ), rec( content := ", where\\ n ", count := [ 5, 3, 9, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 5, 3, 9, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 8 ], mathmode := "Text", name := "M", next := 185500, root := ~, start := 185492, stop := 185499 ), rec( content := " is the \ number of edges and\n ", count := [ 5, 3, 9, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 5, 3, 9, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 8 ], mathmode := "Text", name := "M", next := 185540, root := ~, start := 185532, stop := 185539 ), rec( content := " is the \ number of vertices in the digraph. ", count := [ 5, 3, 9, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 9, 9 ], mathmode := "Text", name := "P", next := 185587, root := ~, start := 185583, stop := 185586 ), rec( content := "\n\n \ ", count := [ 5, 3, 9, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphNrConnectedComponents(", count := [ 5, 3, 9, 9 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 9, 9 ], mathmode := "Text", name := "PCDATA", root :\ = ~ ) ], count := [ 5, 3, 9, 9 ], mathmode := "Text", name := "A", next := 1856\ 39, root := ~, start := 185625, stop := 185638 ), rec( content := ")", count := [ 5, 3, 9, 9 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 9 ], mathmode := "Text", name := "C", next := 185644, root := ~, start := 185593, stop := 185643 ), rec( content := " is simp\ ly a shortcut\n for ", count := [ 5, 3, 9, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "L\ ength(DigraphConnectedComponents(", count := [ 5, 3, 9, 9 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "digraph", count := [ 5, 3, 9, 9 ], mathmode := "Text", name := "PCDATA" , root\ := ~ ) ], count := [ 5, 3, 9, 9 ], mathmode := "Text", name := "A", next := 1857\ 25, root := ~, start := 185711, stop := 185724 ), rec( content := ").comps)", count := [ 5, 3, 9, 9 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 9 ], mathmode := "Text", name := "C", next := 185737, root := ~, start := 185674, stop := 185736 ), rec( content := ",\n a\ nd is no more efficient.\n\n ", count := [ 5, 3, 9, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := Digraph([[2], [3, 1], []]);\n\ngap> DigraphConnectedComponents(gr);\nrec( comps := [ [ 1, 2, 3 ] ], \ id := [ 1, 1, 1 ] )\ngap> gr := Digraph([[1], [1, 2], []]);\n\ngap> DigraphConnectedComponents(gr);\nrec( comps \ := [ [ 1, 2 ], [ 3 ] ], id := [ 1, 1, 2 ] )\ngap> DigraphNrConnectedComponents\ (gr);\n2\ngap> gr := EmptyDigraph(0);\n\ngap> DigraphConnectedComponents(gr);\nrec( comps := [ ], id := [ ] )\nga\ p> D := CycleDigraph(IsMutableDigraph, 2);\n\ngap> G := CycleDigraph(3);\n\ngap> DigraphDisjointUnion(D, G);\n\ngap> DigraphConnectedComponents(D);\nrec( comps := [ [ 1, 2 ], [ 3, 4, 5 ] \ ], id := [ 1, 1, 2, 2, 2 ] )\n", count := [ 5, 3, 9, 10 ], name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 10 ], mathmode := "Text", name := "Example", next := 186671, root := ~, start := 185774, stop := 186670 ), rec( content := "\n ", count := [ 5, 3, 9, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "Description", next := 186688, root := ~, start := 184319, stop := 186687 ) ], count := [ 5, 3, 9, 1 ], mathmode := "Text", name := "ManSection", next := 186702, root := ~, start := 184155, stop := 186701 ), rec( content := "\n\n ", count := [ 5, 3, 9, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, vertex" , Name := "DigraphConnecte\ dComponent" ), content := 0, count := [ 5, 3, 10, 2 ], mathmode := "Text", name := "Oper", next := 186785, root := ~, start := 186723, stop := 186784 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ vertices.", count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "Returns", next := 186826, root := ~, start := 186788, stop := 186825 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "v\ ertex", count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "A", next := 186863, root := ~, start := 186850, stop := 186862 ), rec( content := " is a ve\ rtex in the digraph ", count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "A", next := 186905, root := ~, start := 186891, stop := 186904 ), rec( content := ", then\n\ this operation returns the connected component of ", count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ertex", count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "A", next := 186979, root := ~, start := 186966, stop := 186978 ), rec( content := "\n in\ ", count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "A", next := 187001, root := ~, start := 186987, stop := 187000 ), rec( content := ".\n S\ ee ", count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ ConnectedComponents" ), content := 0, count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "Ref", next := 187051, root := ~, start := 187011, stop := 187050 ), rec( content := " for mor\ e information.\n ", count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[3], [2], [1, 2], [4]]);\n\ngap> DigraphConnectedComponent(D, 3);\n[ 1, 2, 3 ]\ngap> Digraph\ ConnectedComponent(D, 2);\n[ 1, 2, 3 ]\ngap> DigraphConnectedComponent(D, 4);\ \n[ 4 ]\n", count := [ 5, 3, 10, 4 ], name := "PCDATA", root := ~ ) ], count := [ 5, 3, 10, 4 ], mathmode := "Text", name := "Example", next := 187343, root := ~, start := 187078, stop := 187342 ), rec( content := "\n ", count := [ 5, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "Description", next := 187360, root := ~, start := 186829, stop := 187359 ) ], count := [ 5, 3, 10, 1 ], mathmode := "Text", name := "ManSection", next := 187374, root := ~, start := 186708, stop := 187373 ), rec( content := "\n\n ", count := [ 5, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphStrongly\ ConnectedComponents" ), content := 0, count := [ 5, 3, 11, 2 ], mathmode := "Text", name := "Attr", next := 187458, root := ~, start := 187395, stop := 187457 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphNrStrong\ lyConnectedComponents" ), content := 0, count := [ 5, 3, 11, 4 ], mathmode := "Text", name := "Attr", next := 187526, root := ~, start := 187461, stop := 187525 ), rec( attributes := rec( ), content := [ rec( content := "A record.\ ", count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "Returns", next := 187557, root := ~, start := 187529, stop := 187556 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function returns the record ", count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ cc", count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "C", next := 187621, root := ~, start := 187611, stop := 187620 ), rec( content := " corresp\ onding to the strongly\n connected components of the digraph ", count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "A", next := 187706, root := ~, start := 187692, stop := 187705 ), rec( content := ". Two v\ ertices of\n ", count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "A", next := 187743, root := ~, start := 187729, stop := 187742 ), rec( content := " are in \ the same strongly connected component whenever they\n are equal, or there i\ s a directed path from each vertex to the other. The\n set of strongly con\ nected components is a partition of the vertex set of\n ", count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "A", next := 187977, root := ~, start := 187963, stop := 187976 ), rec( content := ".\n " , count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "P", next := 187987, root := ~, start := 187983, stop := 187986 ), rec( content := "\n\n \ The record ", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ cc", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "C", next := 188014, root := ~, start := 188004, stop := 188013 ), rec( content := " has 2 c\ omponents: ", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ omps", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "C", next := 188045, root := ~, start := 188033, stop := 188044 ), rec( content := " and ", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ d", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "C", next := 188059, root := ~, start := 188050, stop := 188058 ), rec( content := ".\n T\ he component ", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ omps", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "C", next := 188091, root := ~, start := 188079, stop := 188090 ), rec( content := " is a li\ st of the strongly connected components\n of ", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "A", next := 188160, root := ~, start := 188146, stop := 188159 ), rec( content := " (each o\ f which is a list of vertices).\n The component ", count := [ 5, 3, 11, 6 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ d", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "C", next := 188227, root := ~, start := 188218, stop := 188226 ), rec( content := " is a li\ st such that the vertex ", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "C", next := 188267, root := ~, start := 188259, stop := 188266 ), rec( content := " is an\n\ element of the strongly connected component ", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ omps[id[i]]", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "C", next := 188341, root := ~, start := 188322, stop := 188340 ), rec( content := ". ", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 11, 7 ], mathmode := "Text", name := "P", next := 188347, root := ~, start := 188343, stop := 188346 ), rec( content := "\n\n \ The method used in this function is a non-recursive version of Gabow's\n Al\ gorithm ", count := [ 5, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "Gab00" ) , content := 0, count := [ 5, 3, 11, 7 ], mathmode := "Text", name := "Cite", next := 188457, root := ~, start := 188438, stop := 188456 ), rec( content := " and has\ complexity ", count := [ 5, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (m+n)", count := [ 5, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 7 ], mathmode := "Text", name := "M", next := 188490, root := ~, start := 188477, stop := 188489 ), rec( content := " where\n\ ", count := [ 5, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 5, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 7 ], mathmode := "Text", name := "M", next := 188509, root := ~, start := 188501, stop := 188508 ), rec( content := " is the \ number of edges (counting multiple edges as one) and\n ", count := [ 5, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 5, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 7 ], mathmode := "Text", name := "M", next := 188582, root := ~, start := 188574, stop := 188581 ), rec( content := " is the \ number of vertices in the digraph. ", count := [ 5, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 11, 8 ], mathmode := "Text", name := "P", next := 188629, root := ~, start := 188625, stop := 188628 ), rec( content := "\n\n \ ", count := [ 5, 3, 11, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "D\ igraphNrStronglyConnectedComponents(", count := [ 5, 3, 11, 8 ], mathmode := "\ Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( cont\ ent := "digraph", count := [ 5, 3, 11, 8 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 5, 3, 11, 8 ], mathmode := "Text", name := "A", next := 1886\ 89, root := ~, start := 188675, stop := 188688 ), rec( content := ")", count := [ 5, 3, 11, 8 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 8 ], mathmode := "Text", name := "C", next := 188694, root := ~, start := 188635, stop := 188693 ), rec( content := " is simp\ ly a\n shortcut for\n ", count := [ 5, 3, 11, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "L\ ength(DigraphStronglyConnectedComponents(", count := [ 5, 3, 11, 8 ], mathmode := \ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( cont\ ent := "digraph", count := [ 5, 3, 11, 8 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 5, 3, 11, 8 ], mathmode := "Text", name := "A", next := 1887\ 87, root := ~, start := 188773, stop := 188786 ), rec( content := ").comps)", count := [ 5, 3, 11, 8 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 8 ], mathmode := "Text", name := "C", next := 188799, root := ~, start := 188728, stop := 188798 ), rec( content := ",\n a\ nd is no more efficient.\n\n ", count := [ 5, 3, 11, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := Digraph([[2], [3, 1], []]);\n\ngap> DigraphStronglyConnectedComponents(gr);\nrec( comps := [ [ 3 ], \ [ 1, 2 ] ], id := [ 2, 2, 1 ] )\ngap> DigraphNrStronglyConnectedComponents(gr)\ ;\n2\ngap> D := DigraphDisjointUnion(CycleDigraph(4), CycleDigraph(5));\n\ngap> DigraphStronglyConnectedComponen\ ts(D);\nrec( comps := [ [ 1, 2, 3, 4 ], [ 5, 6, 7, 8, 9 ] ], \n id := [ 1, 1,\ 1, 1, 2, 2, 2, 2, 2 ] )\ngap> DigraphNrStronglyConnectedComponents(D);\n2\nga\ p> D := CycleDigraph(IsMutableDigraph, 2);\n\ngap> G := CycleDigraph(3);\n\ngap> DigraphDisjointUnion(D, G);\n\ngap> DigraphStronglyConnectedComponents(D);\nrec( comps := [ [ 1, 2 ], [ 3,\ 4, 5 ] ], id := [ 1, 1, 2, 2, 2 ] )\n", count := [ 5, 3, 11, 9 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 11, 9 ], mathmode := "Text", name := "Example", next := 189742, root := ~, start := 188836, stop := 189741 ), rec( content := "\n ", count := [ 5, 3, 11, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "Description", next := 189759, root := ~, start := 187560, stop := 189758 ) ], count := [ 5, 3, 11, 1 ], mathmode := "Text", name := "ManSection", next := 189773, root := ~, start := 187380, stop := 189772 ), rec( content := "\n\n ", count := [ 5, 3, 11, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, vertex" , Name := "DigraphStrongly\ ConnectedComponent" ), content := 0, count := [ 5, 3, 12, 2 ], mathmode := "Text", name := "Oper", next := 189864, root := ~, start := 189794, stop := 189863 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ vertices.", count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "Returns", next := 189905, root := ~, start := 189867, stop := 189904 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "v\ ertex", count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "A", next := 189942, root := ~, start := 189929, stop := 189941 ), rec( content := " is a ve\ rtex in the digraph ", count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "A", next := 189984, root := ~, start := 189970, stop := 189983 ), rec( content := ", then\n\ this operation returns the strongly connected component of ", count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ertex", count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "A", next := 190067, root := ~, start := 190054, stop := 190066 ), rec( content := "\n in\ ", count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "A", next := 190089, root := ~, start := 190075, stop := 190088 ), rec( content := ".\n S\ ee ", count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ StronglyConnectedComponents" ), content := 0, count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "Ref", next := 190147, root := ~, start := 190099, stop := 190146 ), rec( content := " for mor\ e information.\n ", count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[3], [2], [1, 2], [3]]);\n\ngap> DigraphStronglyConnectedComponent(D, 3);\n[ 1, 3 ]\ngap> Di\ graphStronglyConnectedComponent(D, 2);\n[ 2 ]\ngap> DigraphStronglyConnectedCo\ mponent(D, 4);\n[ 4 ]\n", count := [ 5, 3, 12, 4 ], name := "PCDATA", root := ~ ) ], count := [ 5, 3, 12, 4 ], mathmode := "Text", name := "Example", next := 190454, root := ~, start := 190174, stop := 190453 ), rec( content := "\n ", count := [ 5, 3, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "Description", next := 190471, root := ~, start := 189908, stop := 190470 ) ], count := [ 5, 3, 12, 1 ], mathmode := "Text", name := "ManSection", next := 190485, root := ~, start := 189779, stop := 190484 ), rec( content := "\n\n ", count := [ 5, 3, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphBicompon\ ents" ), content := 0, count := [ 5, 3, 13, 2 ], mathmode := "Text", name := "Attr", next := 190554, root := ~, start := 190506, stop := 190553 ), rec( attributes := rec( ), content := [ rec( content := "A pair of\ lists of vertices, or ", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "K", next := 190609, root := ~, start := 190598, stop := 190608 ), rec( content := ".", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "Returns", next := 190620, root := ~, start := 190557, stop := 190619 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "A", next := 190658, root := ~, start := 190644, stop := 190657 ), rec( content := " is a bi\ partite digraph, i.e. if it satisfies ", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsBipar\ titeDigraph" ), content := 0, count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "Ref", next := 190742, root := ~, start := 190704, stop := 190741 ), rec( content := ", then " , count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphBicomponents", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "C", next := 190775, root := ~, start := 190749, stop := 190774 ), rec( content := " returns\ a\n pair of bicomponents of ", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "A", next := 190828, root := ~, start := 190814, stop := 190827 ), rec( content := ". Otherw\ ise,\n ", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphBicomponents", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "C", next := 190871, root := ~, start := 190845, stop := 190870 ), rec( content := " returns\ ", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "K", next := 190891, root := ~, start := 190880, stop := 190890 ), rec( content := ".", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 13, 4 ], mathmode := "Text", name := "P", next := 190896, root := ~, start := 190892, stop := 190895 ), rec( content := "\n\n \ For a bipartite digraph, the vertices can be partitioned into two non-empty\n \ sets such that the source and range of any edge are in distinct sets. The\n\ parts of this partition are called ", count := [ 5, 3, 13, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "b\ icomponents", count := [ 5, 3, 13, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 13, 4 ], mathmode := "Text", name := "E", next := 191114, root := ~, start := 191095, stop := 191113 ), rec( content := " of ", count := [ 5, 3, 13, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 13, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 13, 4 ], mathmode := "Text", name := "A", next := 191132, root := ~, start := 191118, stop := 191131 ), rec( content := ".\n E\ quivalently, a pair of bicomponents of ", count := [ 5, 3, 13, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 13, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 13, 4 ], mathmode := "Text", name := "A", next := 191192, root := ~, start := 191178, stop := 191191 ), rec( content := " consist\ s of the\n color-classes of a 2-coloring of ", count := [ 5, 3, 13, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 13, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 13, 4 ], mathmode := "Text", name := "A", next := 191260, root := ~, start := 191246, stop := 191259 ), rec( content := ". ", count := [ 5, 3, 13, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 13, 5 ], mathmode := "Text", name := "P", next := 191266, root := ~, start := 191262, stop := 191265 ), rec( content := "\n\n \ For a bipartite digraph with at least 3 vertices, there is a unique pair of\n \ bicomponents of bipartite if and only if the digraph is connected. See ", count := [ 5, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsConne\ ctedDigraph" ), content := 0, count := [ 5, 3, 13, 5 ], mathmode := "Text", name := "Ref", next := 191461, root := ~, start := 191423, stop := 191460 ), rec( content := " for mor\ e information.\n ", count := [ 5, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CycleDigraph(3);\n\ngap> D\ igraphBicomponents(D);\nfail\ngap> D := ChainDigraph(5);\n\ngap> DigraphBicomponents(D);\n[ [ 1, 3, 5 ], [ 2, 4 ] ]\ \ngap> D := Digraph([[5], [1, 4], [5], [5], []]);\n\ngap> DigraphBicomponents(D);\n[ [ 1, 3, 4 ], [ 2, 5 ] ]\nga\ p> D := CompleteBipartiteDigraph(IsMutableDigraph, 2, 3);\n\ngap> DigraphBicomponents(D);\n[ [ 1, 2 ], [ 3, 4, 5 \ ] ]\n", count := [ 5, 3, 13, 6 ], name := "PCDATA", root := ~ ) ], count := [ 5, 3, 13, 6 ], mathmode := "Text", name := "Example", next := 192054, root := ~, start := 191488, stop := 192053 ), rec( content := "\n ", count := [ 5, 3, 13, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "Description", next := 192071, root := ~, start := 190623, stop := 192070 ) ], count := [ 5, 3, 13, 1 ], mathmode := "Text", name := "ManSection", next := 192085, root := ~, start := 190491, stop := 192084 ), rec( content := "\n\n ", count := [ 5, 3, 13, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "ArticulationPoi\ nts" ), content := 0, count := [ 5, 3, 14, 2 ], mathmode := "Text", name := "Attr", next := 192153, root := ~, start := 192106, stop := 192152 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ vertices.", count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "Returns", next := 192194, root := ~, start := 192156, stop := 192193 ), rec( attributes := rec( ), content := [ rec( content := "\n\n A\ connected digraph is ", count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "b\ iconnected", count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "E", next := 192257, root := ~, start := 192239, stop := 192256 ), rec( content := " if it i\ s still connected (in the\n sense of ", count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsConne\ ctedDigraph" ), content := 0, count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "Ref", next := 192336, root := ~, start := 192304, stop := 192335 ), rec( content := ") when a\ ny vertex is removed. \n If the digraph ", count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "A", next := 192400, root := ~, start := 192386, stop := 192399 ), rec( content := " is not \ biconnected but is connected, then any\n vertex ", count := [ 5, 3, 14, 3 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "C", next := 192466, root := ~, start := 192458, stop := 192465 ), rec( content := " of ", count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "A", next := 192484, root := ~, start := 192470, stop := 192483 ), rec( content := " whose r\ emoval makes the resulting digraph\n disconnected is called an ", count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "a\ rticulation point", count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "E", next := 192582, root := ~, start := 192557, stop := 192581 ), rec( content := ".", count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 14, 4 ], mathmode := "Text", name := "P", next := 192587, root := ~, start := 192583, stop := 192586 ), rec( content := "\n\n \ ", count := [ 5, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "A\ rticulationPoints", count := [ 5, 3, 14, 4 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 14, 4 ], mathmode := "Text", name := "C", next := 192618, root := ~, start := 192593, stop := 192617 ), rec( content := " returns\ a list of the articulation points of\n ", count := [ 5, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 14, 4 ], mathmode := "Text", name := "A", next := 192682, root := ~, start := 192668, stop := 192681 ), rec( content := ", if any\ , and, in particular, returns the empty list if\n ", count := [ 5, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 14, 4 ], mathmode := "Text", name := "A", next := 192756, root := ~, start := 192742, stop := 192755 ), rec( content := " is not \ connected. ", count := [ 5, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 14, 5 ], mathmode := "Text", name := "P", next := 192779, root := ~, start := 192775, stop := 192778 ), rec( content := "\n\n \ Multiple edges and loops are ignored by this method. ", count := [ 5, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 14, 6 ], mathmode := "Text", name := "P", next := 192842, root := ~, start := 192838, stop := 192841 ), rec( content := "\n\n \ The method used in this operation has complexity ", count := [ 5, 3, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (m+n)", count := [ 5, 3, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 14, 6 ], mathmode := "Text", name := "M", next := 192910, root := ~, start := 192897, stop := 192909 ), rec( content := " where\n\ ", count := [ 5, 3, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 5, 3, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 14, 6 ], mathmode := "Text", name := "M", next := 192929, root := ~, start := 192921, stop := 192928 ), rec( content := " is the \ number of edges (counting multiple edges as one, and not\n counting loops) \ and ", count := [ 5, 3, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 5, 3, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 14, 6 ], mathmode := "Text", name := "M", next := 193026, root := ~, start := 193018, stop := 193025 ), rec( content := " is the \ number of vertices in the digraph.\n\n See also ", count := [ 5, 3, 14, 6 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsBicon\ nectedDigraph" ), content := 0, count := [ 5, 3, 14, 6 ], mathmode := "Text", name := "Ref", next := 193117, root := ~, start := 193083, stop := 193116 ), rec( content := ".\n", count := [ 5, 3, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> ArticulationPoints(CycleDigraph(5));\n[ ]\ngap> D := Digraph([[2, 7], [\ 3, 5], [4], [2], [6], [1], []]);;\ngap> ArticulationPoints(D);\n[ 2, 1 ]\ngap>\ ArticulationPoints(ChainDigraph(5));\n[ 4, 3, 2 ]\ngap> ArticulationPoints(Nu\ llDigraph(5));\n[ ]\ngap> D := ChainDigraph(IsMutableDigraph, 4);\n\ngap> ArticulationPoints(D);\n[ 3, 2 ]\n", count := [ 5, 3, 14, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 14, 7 ], mathmode := "Text", name := "Example", next := 193522, root := ~, start := 193119, stop := 193521 ), rec( content := "\n ", count := [ 5, 3, 14, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "Description", next := 193539, root := ~, start := 192197, stop := 193538 ) ], count := [ 5, 3, 14, 1 ], mathmode := "Text", name := "ManSection", next := 193553, root := ~, start := 192091, stop := 193552 ), rec( content := "\n\n ", count := [ 5, 3, 14, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphPeriod" ), content := 0, count := [ 5, 3, 15, 2 ], mathmode := "Text", name := "Attr", next := 193616, root := ~, start := 193574, stop := 193615 ), rec( attributes := rec( ), content := [ rec( content := "An intege\ r.", count := [ 5, 3, 15, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 15, 3 ], mathmode := "Text", name := "Returns", next := 193649, root := ~, start := 193619, stop := 193648 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function returns the period of the digraph ", count := [ 5, 3, 15, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 15, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 15, 3 ], mathmode := "Text", name := "A", next := 193732, root := ~, start := 193718, stop := 193731 ), rec( content := ".", count := [ 5, 3, 15, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "P", next := 193737, root := ~, start := 193733, stop := 193736 ), rec( content := "\n\n \ If a digraph ", count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "A", next := 193770, root := ~, start := 193756, stop := 193769 ), rec( content := " has at \ least one directed cycle, then the period\n is the greatest positive intege\ r which divides the lengths of all directed\n cycles of ", count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "A", next := 193927, root := ~, start := 193913, stop := 193926 ), rec( content := ". If ", count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "A", next := 193947, root := ~, start := 193933, stop := 193946 ), rec( content := " has no \ directed cycles, then\n this function returns ", count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "0\ ", count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "M", next := 194011, root := ~, start := 194003, stop := 194010 ), rec( content := ". See s\ ection ", count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Style := "Number\ ", Subsect := "Definitions" ), content := 0, count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "Ref", next := 194076, root := ~, start := 194026, stop := 194075 ), rec( content := " for the\ definition of a directed cycle. ", count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 15, 5 ], mathmode := "Text", name := "P", next := 194121, root := ~, start := 194117, stop := 194120 ), rec( content := "\n\n \ A digraph with a period of ", count := [ 5, 3, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "1\ ", count := [ 5, 3, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 15, 5 ], mathmode := "Text", name := "M", next := 194162, root := ~, start := 194154, stop := 194161 ), rec( content := " is said\ to be ", count := [ 5, 3, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "a\ periodic", count := [ 5, 3, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 15, 5 ], mathmode := "Text", name := "E", next := 194193, root := ~, start := 194177, stop := 194192 ), rec( content := ". See\n\ ", count := [ 5, 3, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsAperi\ odicDigraph" ), content := 0, count := [ 5, 3, 15, 5 ], mathmode := "Text", name := "Ref", next := 194236, root := ~, start := 194204, stop := 194235 ), rec( content := ". ", count := [ 5, 3, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 15, 6 ], mathmode := "Text", name := "P", next := 194242, root := ~, start := 194238, stop := 194241 ), rec( content := "\n ", count := [ 5, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[6], [1], [2], [3], [4, 4], [5]]);\n\ngap> DigraphPeriod(D);\n6\ngap> D := Digraph([[2]\ , [3, 5], [4], [5], [1, 2]]);\n\ng\ ap> DigraphPeriod(D);\n1\ngap> D := ChainDigraph(2);\n\ngap> DigraphPeriod(D);\n0\ngap> IsAcyclicDigraph(D);\ntrue\ \ngap> D := GeneralisedPetersenGraph(IsMutableDigraph, 5, 2);\n\ngap> DigraphPeriod(D);\n1\n", count := [ 5, 3, 15, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 15, 7 ], mathmode := "Text", name := "Example", next := 194785, root := ~, start := 194247, stop := 194784 ), rec( content := "\n ", count := [ 5, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 15, 3 ], mathmode := "Text", name := "Description", next := 194802, root := ~, start := 193652, stop := 194801 ) ], count := [ 5, 3, 15, 1 ], mathmode := "Text", name := "ManSection", next := 194816, root := ~, start := 193559, stop := 194815 ), rec( content := "\n\n ", count := [ 5, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, func, n\ opath, edge", Name := "DigraphFloydWarshall" ), content := 0, count := [ 5, 3, 16, 2 ], mathmode := "Text", name := "Oper", next := 194906, root := ~, start := 194837, stop := 194905 ), rec( attributes := rec( ), content := [ rec( content := "A matrix.\ ", count := [ 5, 3, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 3 ], mathmode := "Text", name := "Returns", next := 194937, root := ~, start := 194909, stop := 194936 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 3, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 3 ], mathmode := "Text", name := "A", next := 194975, root := ~, start := 194961, stop := 194974 ), rec( content := " is a di\ graph with ", count := [ 5, 3, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 5, 3, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 3 ], mathmode := "Text", name := "M", next := 195002, root := ~, start := 194994, stop := 195001 ), rec( content := " vertice\ s, then\n this operation returns an ", count := [ 5, 3, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ \\times n", count := [ 5, 3, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 3 ], mathmode := "Text", name := "M", next := 195065, root := ~, start := 195048, stop := 195064 ), rec( content := " matrix \ ", count := [ 5, 3, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "m\ at", count := [ 5, 3, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 3 ], mathmode := "Text", name := "C", next := 195083, root := ~, start := 195073, stop := 195082 ), rec( content := " contain\ ing\n the output of a generalised version of the Floyd-Warshall algorithm,\ \n applied to ", count := [ 5, 3, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 3 ], mathmode := "Text", name := "A", next := 195197, root := ~, start := 195183, stop := 195196 ), rec( content := ". ", count := [ 5, 3, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "P", next := 195203, root := ~, start := 195199, stop := 195202 ), rec( content := "\n\n \ The operation ", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphFloydWarshall", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "C", next := 195250, root := ~, start := 195223, stop := 195249 ), rec( content := " is cust\ omised by the arguments\n ", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ unc", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "A", next := 195297, root := ~, start := 195286, stop := 195296 ), rec( content := ", ", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ opath", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "A", next := 195312, root := ~, start := 195299, stop := 195311 ), rec( content := ", and ", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dge", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "A", next := 195329, root := ~, start := 195318, stop := 195328 ), rec( content := ".\n T\ he arguments ", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ opath", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "A", next := 195362, root := ~, start := 195349, stop := 195361 ), rec( content := " and ", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dge", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "A", next := 195378, root := ~, start := 195367, stop := 195377 ), rec( content := " can be \ arbitrary ", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ AP", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " objects\ .\n The argument ", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ unc", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "A", next := 195439, root := ~, start := 195428, stop := 195438 ), rec( content := " must be\ a function which accepts 4 arguments:\n the matrix ", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ at", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "C", next := 195511, root := ~, start := 195501, stop := 195510 ), rec( content := ", follow\ ed by 3 postive integers. The function\n ", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ unc", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "A", next := 195573, root := ~, start := 195562, stop := 195572 ), rec( content := " is wher\ e the work to calculate the desired outcome must be\n performed. ", count := [ 5, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "P", next := 195652, root := ~, start := 195648, stop := 195651 ), rec( content := "\n\n \ This method initialises the matrix ", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ at", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "C", next := 195703, root := ~, start := 195693, stop := 195702 ), rec( content := " by sett\ ing entry\n ", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ at[i][j]", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "C", next := 195741, root := ~, start := 195725, stop := 195740 ), rec( content := " to equa\ l ", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dge", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "A", next := 195762, root := ~, start := 195751, stop := 195761 ), rec( content := " if ther\ e is an edge with source\n ", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "C", next := 195807, root := ~, start := 195799, stop := 195806 ), rec( content := " and ran\ ge ", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "C", next := 195826, root := ~, start := 195818, stop := 195825 ), rec( content := ", and by\ setting entry ", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ at[i][j]", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "C", next := 195865, root := ~, start := 195849, stop := 195864 ), rec( content := " to equa\ l\n ", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ opath", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "A", next := 195892, root := ~, start := 195879, stop := 195891 ), rec( content := " otherwi\ se.\n The final part of ", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphFloydWarshall", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "C", next := 195953, root := ~, start := 195926, stop := 195952 ), rec( content := " then ca\ lls the function\n ", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ unc", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "A", next := 195993, root := ~, start := 195982, stop := 195992 ), rec( content := " inside \ three nested for loops, over the vertices of\n ", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "A", next := 196064, root := ~, start := 196050, stop := 196063 ), rec( content := ": ", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 16, 6 ], mathmode := "Text", name := "P", next := 196070, root := ~, start := 196066, stop := 196069 ), rec( content := "\n\n", count := [ 5, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ nfor i in DigraphsVertices(digraph) do\n for j in DigraphsVertices(digraph) d\ o\n for k in DigraphsVertices(digraph) do\n func(mat, i, j, k);\n o\ d;\n od;\nod;\n", count := [ 5, 3, 16, 7 ], name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 7 ], mathmode := "Text", name := "Listing", next := 196268, root := ~, start := 196072, stop := 196267 ), rec( content := "\n\n \ The matrix ", count := [ 5, 3, 16, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ at", count := [ 5, 3, 16, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 8 ], mathmode := "Text", name := "C", next := 196295, root := ~, start := 196285, stop := 196294 ), rec( content := " is then\ returned as the result. An example of using\n ", count := [ 5, 3, 16, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphFloydWarshall", count := [ 5, 3, 16, 8 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 16, 8 ], mathmode := "Text", name := "C", next := 196379, root := ~, start := 196352, stop := 196378 ), rec( content := " to calc\ ulate the shortest (non-zero) distances\n between the vertices of a digraph\ is shown below: ", count := [ 5, 3, 16, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 16, 9 ], mathmode := "Text", name := "P", next := 196485, root := ~, start := 196481, stop := 196484 ), rec( content := "\n\n \ ", count := [ 5, 3, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := DigraphFromDigraph6String(\"&EAHQeDB\");\n\ngap> func := function(mat, i, j, k)\n> if mat[i][k] <>\ -1 and mat[k][j] <> -1 then\n> if (mat[i][j] = -1) or (mat[i][j] > mat[i]\ [k] + mat[k][j]) then\n> mat[i][j] := mat[i][k] + mat[k][j];\n> fi;\ \n> fi;\n> end;\nfunction( mat, i, j, k ) ... end\ngap> shortest_distances :\ = DigraphFloydWarshall(D, func, -1, 1);;\ngap> Display(shortest_distances);\n[\ [ 3, -1, -1, 2, 1, 2 ],\n [ 4, 2, 1, 3, 2, 1 ],\n [ \ 3, 1, 2, 2, 1, 2 ],\n [ 1, -1, -1, 1, 1, 2 ],\n [ 2, \ -1, -1, 1, 2, 1 ],\n [ 3, -1, -1, 2, 1, 1 ] ]\n", count := [ 5, 3, 16, 10 ] , name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 16, 10 ], mathmode := "Text", name := "Example", next := 197191, root := ~, start := 196491, stop := 197190 ), rec( content := "\n ", count := [ 5, 3, 16, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 16, 3 ], mathmode := "Text", name := "Description", next := 197208, root := ~, start := 194940, stop := 197207 ) ], count := [ 5, 3, 16, 1 ], mathmode := "Text", name := "ManSection", next := 197222, root := ~, start := 194822, stop := 197221 ), rec( content := "\n\n ", count := [ 5, 3, 16, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, u, v", Name := "IsReachable" ), content := 0, count := [ 5, 3, 17, 2 ], mathmode := "Text", name := "Oper", next := 197289, root := ~, start := 197243, stop := 197288 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "K", next := 197312, root := ~, start := 197301, stop := 197311 ), rec( content := " or ", count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "K", next := 197328, root := ~, start := 197316, stop := 197327 ), rec( content := ".", count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "Returns", next := 197339, root := ~, start := 197292, stop := 197338 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s operation returns ", count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "K", next := 197394, root := ~, start := 197383, stop := 197393 ), rec( content := " if ther\ e exists a non-trivial directed\n walk from vertex ", count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "A", next := 197463, root := ~, start := 197455, stop := 197462 ), rec( content := " to vert\ ex ", count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "A", next := 197482, root := ~, start := 197474, stop := 197481 ), rec( content := " in the \ digraph ", count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "A", next := 197512, root := ~, start := 197498, stop := 197511 ), rec( content := ",\n a\ nd ", count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "K", next := 197534, root := ~, start := 197522, stop := 197533 ), rec( content := " if ther\ e does not exist such a directed walk. See section\n ", count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Style := "Number\ ", Subsect := "Definitions" ), content := 0, count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "Ref", next := 197642, root := ~, start := 197598, stop := 197641 ), rec( content := " for the\ definition of a\n non-trivial directed walk.\n ", count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "P", next := 197706, root := ~, start := 197702, stop := 197705 ), rec( content := "\n\n \ The method for ", count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sReachable", count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "C", next := 197745, root := ~, start := 197727, stop := 197744 ), rec( content := " has wor\ st case complexity of ", count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (m +\n n)", count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "M", next := 197796, root := ~, start := 197775, stop := 197795 ), rec( content := " where " , count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "M", next := 197811, root := ~, start := 197803, stop := 197810 ), rec( content := " is the \ number of edges and ", count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "M", next := 197847, root := ~, start := 197839, stop := 197846 ), rec( content := " the num\ ber of\n vertices in ", count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "A", next := 197892, root := ~, start := 197878, stop := 197891 ), rec( content := ".\n\n", count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[2], [3], [2, 3]]);\n\ngap> IsReachable(D, 1, 3);\ntrue\ngap> IsReachable(D, 2, 1);\nfalse\n\ gap> IsReachable(D, 3, 3);\ntrue\ngap> IsReachable(D, 1, 1);\nfalse\n", count := [ 5, 3, 17, 5 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 17, 5 ], mathmode := "Text", name := "Example", next := 198141, root := ~, start := 197895, stop := 198140 ), rec( content := "\n ", count := [ 5, 3, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "Description", next := 198158, root := ~, start := 197342, stop := 198157 ) ], count := [ 5, 3, 17, 1 ], mathmode := "Text", name := "ManSection", next := 198172, root := ~, start := 197228, stop := 198171 ), rec( content := "\n\n ", count := [ 5, 3, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, u, v", Name := "DigraphPath" ), content := 0, count := [ 5, 3, 18, 2 ], mathmode := "Text", name := "Oper", next := 198239, root := ~, start := 198193, stop := 198238 ), rec( attributes := rec( ), content := [ rec( content := "A pair of\ lists, or ", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "K", next := 198282, root := ~, start := 198271, stop := 198281 ), rec( content := ".", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "Returns", next := 198293, root := ~, start := 198242, stop := 198292 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ there exists a non-trivial directed path (or a non-trivial cycle, in the\n \ case that ", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "A", next := 198412, root := ~, start := 198404, stop := 198411 ), rec( content := " ", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "=\ ", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "C", next := 198421, root := ~, start := 198413, stop := 198420 ), rec( content := " ", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "A", next := 198430, root := ~, start := 198422, stop := 198429 ), rec( content := ") from v\ ertex ", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "A", next := 198452, root := ~, start := 198444, stop := 198451 ), rec( content := " to vert\ ex\n ", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "A", next := 198475, root := ~, start := 198467, stop := 198474 ), rec( content := " in the \ digraph ", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "A", next := 198505, root := ~, start := 198491, stop := 198504 ), rec( content := ", then t\ his operation returns such a\n directed path (or directed cycle). Otherwise\ , this operation returns\n ", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "K", next := 198630, root := ~, start := 198619, stop := 198629 ), rec( content := ". See S\ ection ", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Style := "Text", Subsect := "Defi\ nitions" ), content := 0, count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "Ref", next := 198686, root := ~, start := 198645, stop := 198685 ), rec( content := " for the\ \n definition of a directed path and a directed cycle.\n ", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 18, 4 ], mathmode := "Text", name := "P", next := 198759, root := ~, start := 198755, stop := 198758 ), rec( content := "\n\n \ A directed path (or directed cycle) of non-zero length ", count := [ 5, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ -1", count := [ 5, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 4 ], mathmode := "Text", name := "C", next := 198830, root := ~, start := 198820, stop := 198829 ), rec( content := ",\n " , count := [ 5, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "(\ v_1, e_1, v_2, e_2, ..., e_{n-1}, v_n)", count := [ 5, 3, 18, 4 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 4 ], mathmode := "Text", name := "M", next := 198882, root := ~, start := 198836, stop := 198881 ), rec( content := ",\n i\ s represented by a pair of lists ", count := [ 5, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ v,a]", count := [ 5, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 4 ], mathmode := "Text", name := "C", next := 198934, root := ~, start := 198922, stop := 198933 ), rec( content := " as foll\ ows:\n\n ", count := [ 5, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "\n ", count := [ 5, 3, 18, 6 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "v", count := [ 5, 3, 18, 6 ], mathmode := "Text", na\ me := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 6 ], mathmode := "Text", name\ := "C", next := 198988, root := ~, start := 198980, stop := 198987 ), rec( cont\ ent := " is the list ", count := [ 5, 3, 18, 6 ], mathmode := "Text", name := \ "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content :\ = "[v_1, v_2, ..., v_n]", count := [ 5, 3, 18, 6 ], mathmode := "Text", name :\ = "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 6 ], mathmode := "Text", name \ := "M", next := 199028, root := ~, start := 199001, stop := 199027 ), rec( cont\ ent := ".\n ", count := [ 5, 3, 18, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 18, 6 ], name := "Item", next := 199043, root := ~, start := 198\ 965, stop := 199042 ), rec( attributes := rec( ), content := [ rec( content :\ = "\n ", count := [ 5, 3, 18, 8 ], mathmode := "Text", name := "PCDATA" , root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "a", count :\ = [ 5, 3, 18, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count \ := [ 5, 3, 18, 8 ], mathmode := "Text", name := "C", next := 199073, root := ~ , star\ t := 199065, stop := 199072 ), rec( content := " is the list of positive integ\ ers ", count := [ 5, 3, 18, 8 ], mathmode := "Text", name := "PCDATA", root :=\ ~ ), rec( attributes := rec( ), content := [ rec( content := "[a_1, a_2, ...\ , a_{n-1}]", count := [ 5, 3, 18, 8 ], mathmode := "Text", name := "PCDATA", r\ oot := ~ ) ], count := [ 5, 3, 18, 8 ], mathmode := "Text", name := "M", next \ := 199138, root := ~, start := 199107, stop := 199137 ), rec( content := "\n \ where for each each ", count := [ 5, 3, 18, 8 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "i < n", count := [ 5, 3, 18, 8 ], mathmode := "Text", name := "PCDATA",\ root := ~ ) ], count := [ 5, 3, 18, 8 ], mathmode := "Text", name := "M", next\ := 199182, root := ~, start := 199167, stop := 199181 ), rec( content := ", " , coun\ t := [ 5, 3, 18, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "a_i", count := [ 5, 3, 18, 8 \ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 8\ ], mathmode := "Text", name := "M", next := 199194, root := ~, start := 19918\ 4, stop := 199193 ), rec( content := " is the position of\n ", count :=\ [ 5, 3, 18, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "v_{i+1}", count := [ 5, 3, 18\ , 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 1\ 8, 8 ], mathmode := "Text", name := "M", next := 199236, root := ~, start := 1\ 99222, stop := 199235 ), rec( content := " in\n ", count := [ 5, 3, 18,\ 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\ c( ), content := [ rec( content := "OutNeighboursOfVertex(", count := [ 5, 3,\ 18, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3\ , 18, 8 ], mathmode := "Text", name := "C", next := 199277, root := ~, start :\ = 199248, stop := 199276 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "digraph", count := [ 5, 3, 18, 8 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 5, 3, 18, 8 ], mathmode := "Text", name := "A", next\ := 199291, root := ~, start := 199277, stop := 199290 ), rec( attributes := re\ c( ), content := [ rec( content := ",", count := [ 5, 3, 18, 8 ], mathmode :=\ "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 8 ], mathmode :\ = "Text", name := "C", next := 199299, root := ~, start := 199291, stop := 199\ 298 ), rec( attributes := rec( ), content := [ rec( content := "v_i", count :\ = [ 5, 3, 18, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count \ := [ 5, 3, 18, 8 ], mathmode := "Text", name := "M", next := 199309, root := ~ , star\ t := 199299, stop := 199308 ), rec( attributes := rec( ), content := [ rec( c\ ontent := ")", count := [ 5, 3, 18, 8 ], mathmode := "Text", name := "PCDATA",\ root := ~ ) ], count := [ 5, 3, 18, 8 ], mathmode := "Text", name := "C", next\ := 199317, root := ~, start := 199309, stop := 199316 ), rec( content := "\n \ corresponding to the edge ", count := [ 5, 3, 18, 8 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ re\ c( content := "e_i", count := [ 5, 3, 18, 8 ], mathmode := "Text", name := "PC\ DATA", root := ~ ) ], count := [ 5, 3, 18, 8 ], mathmode := "Text", name := "M\ ", next := 199362, root := ~, start := 199352, stop := 199361 ), rec( content \ := ". This is can be useful if the\n position of a vertex in a list of\ out-neighours is significant, for\n example in orbit digraphs.\n \ ", count := [ 5, 3, 18, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 8 ], name := "Ite\ m", next := 199518, root := ~, start := 199050, stop := 199517 ) ], count := [ 5, 3, 18, 5 ], mathmode := "Text", name := "List", next := 199530, root := ~, start := 198952, stop := 199529 ), rec( content := "\n\n \ The method for ", count := [ 5, 3, 18, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphPath", count := [ 5, 3, 18, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 10 ], mathmode := "Text", name := "C", next := 199569, root := ~, start := 199551, stop := 199568 ), rec( content := " has wor\ st case complexity of ", count := [ 5, 3, 18, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (m +\n n)", count := [ 5, 3, 18, 10 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 5, 3, 18, 10 ], mathmode := "Text", name := "M", next := 199620, root := ~, start := 199599, stop := 199619 ), rec( content := " where " , count := [ 5, 3, 18, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 5, 3, 18, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 10 ], mathmode := "Text", name := "M", next := 199635, root := ~, start := 199627, stop := 199634 ), rec( content := " is the \ number of edges and ", count := [ 5, 3, 18, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 5, 3, 18, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 10 ], mathmode := "Text", name := "M", next := 199671, root := ~, start := 199663, stop := 199670 ), rec( content := " the num\ ber of\n vertices in ", count := [ 5, 3, 18, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 18, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 10 ], mathmode := "Text", name := "A", next := 199716, root := ~, start := 199702, stop := 199715 ), rec( content := ".\n\n", count := [ 5, 3, 18, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[2], [3], [2, 3]]);\n\ngap> DigraphPath(D, 1, 3);\n[ [ 1, 2, 3 ], [ 1, 1 ] ]\ngap> DigraphPa\ th(D, 2, 1);\nfail\ngap> DigraphPath(D, 3, 3);\n[ [ 3, 3 ], [ 2 ] ]\ngap> Digr\ aphPath(D, 1, 1);\nfail\n", count := [ 5, 3, 18, 11 ], name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 11 ], mathmode := "Text", name := "Example", next := 199999, root := ~, start := 199719, stop := 199998 ), rec( content := "\n ", count := [ 5, 3, 18, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "Description", next := 200016, root := ~, start := 198296, stop := 200015 ) ], count := [ 5, 3, 18, 1 ], mathmode := "Text", name := "ManSection", next := 200030, root := ~, start := 198178, stop := 200029 ), rec( content := "\n\n ", count := [ 5, 3, 18, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, u, v", Name := "DigraphShortest\ Path" ), content := 0, count := [ 5, 3, 19, 2 ], mathmode := "Text", name := "Oper", next := 200105, root := ~, start := 200051, stop := 200104 ), rec( attributes := rec( ), content := [ rec( content := "A pair of\ lists, or ", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "K", next := 200148, root := ~, start := 200137, stop := 200147 ), rec( content := ".", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "Returns", next := 200159, root := ~, start := 200108, stop := 200158 ), rec( attributes := rec( ), content := [ rec( content := "\n Ret\ urns the shortest directed path in the digraph digraph from the vertex\n ", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "A", next := 200266, root := ~, start := 200258, stop := 200265 ), rec( content := " to the \ vertex ", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "A", next := 200289, root := ~, start := 200281, stop := 200288 ), rec( content := ", if suc\ h a path exists. If ", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "u", count := [ 5, 3, 19, 3 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 19, 3 ], mathmode := \ "Text", name := "A", next := 200328, root := ~, start := 200320, stop := 20032\ 7 ), rec( content := " =\n ", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 19, 3 ], mathmode := \ "Text", name := "A", next := 200343, root := ~, start := 200335, stop := 20034\ 2 ) ], count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "C", next := 200347, root := ~, start := 200317, stop := 200346 ), rec( content := ", then t\ he shortest non-trivial cycle is returned, again, if it\n exists. Otherwise\ , this operation returns ", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "K", next := 200468, root := ~, start := 200457, stop := 200467 ), rec( content := ". See S\ ection\n ", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Style := "Text", Subsect := "Defi\ nitions" ), content := 0, count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "Ref", next := 200528, root := ~, start := 200487, stop := 200527 ), rec( content := " for the\ definition of a directed\n path and a directed cycle.\n ", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "P", next := 200601, root := ~, start := 200597, stop := 200600 ), rec( content := "\n\n \ See ", count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ Path" ), content := 0, count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "Ref", next := 200636, root := ~, start := 200611, stop := 200635 ), rec( content := " for det\ ails on the output.\n\n The method for ", count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphShortestPath", count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "C", next := 200710, root := ~, start := 200684, stop := 200709 ), rec( content := " has wor\ st case complexity of\n ", count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (m + n)", count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "M", next := 200759, root := ~, start := 200744, stop := 200758 ), rec( content := " where " , count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "M", next := 200774, root := ~, start := 200766, stop := 200773 ), rec( content := " is the \ number of edges and ", count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "M", next := 200810, root := ~, start := 200802, stop := 200809 ), rec( content := " the\n \ number of vertices in ", count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "A", next := 200855, root := ~, start := 200841, stop := 200854 ), rec( content := ".\n\n", count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 2], [3], [2, 4], [1], [2, 4]]);\n\ngap> DigraphShortestPath(D, 5, 1);\n[ [ 5, 4, 1 ], [ \ 2, 1 ] ]\ngap> DigraphShortestPath(D, 3, 3);\n[ [ 3, 2, 3 ], [ 1, 1 ] ]\ngap> \ DigraphShortestPath(D, 5, 5);\nfail\ngap> DigraphShortestPath(D, 1, 1);\n[ [ 1\ , 1 ], [ 1 ] ]\n", count := [ 5, 3, 19, 5 ], name := "PCDATA", root := ~ ) ], count := [ 5, 3, 19, 5 ], mathmode := "Text", name := "Example", next := 201207, root := ~, start := 200858, stop := 201206 ), rec( content := "\n ", count := [ 5, 3, 19, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "Description", next := 201224, root := ~, start := 200162, stop := 201223 ) ], count := [ 5, 3, 19, 1 ], mathmode := "Text", name := "ManSection", next := 201238, root := ~, start := 200036, stop := 201237 ), rec( content := "\n\n ", count := [ 5, 3, 19, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, u, v", Name := "IteratorOfPaths\ " ), content := 0, count := [ 5, 3, 20, 2 ], mathmode := "Text", name := "Oper", next := 201309, root := ~, start := 201259, stop := 201308 ), rec( attributes := rec( ), content := [ rec( content := "An iterat\ or.", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "Returns", next := 201343, root := ~, start := 201312, stop := 201342 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "A", next := 201381, root := ~, start := 201367, stop := 201380 ), rec( content := " is a di\ graph or a list of adjacencies which defines a\n digraph - see ", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "OutNeig\ hbours" ), content := 0, count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "Ref", next := 201481, root := ~, start := 201454, stop := 201480 ), rec( content := " - then \ this operation returns an\n iterator of the non-trivial directed paths (or \ directed cycles, in the case\n that ", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "A", next := 201612, root := ~, start := 201604, stop := 201611 ), rec( content := " ", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "=\ ", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "C", next := 201621, root := ~, start := 201613, stop := 201620 ), rec( content := " ", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "A", next := 201630, root := ~, start := 201622, stop := 201629 ), rec( content := ") in ", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "A", next := 201649, root := ~, start := 201635, stop := 201648 ), rec( content := " from th\ e vertex ", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "A", next := 201674, root := ~, start := 201666, stop := 201673 ), rec( content := "\n to\ the vertex ", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "A", next := 201701, root := ~, start := 201693, stop := 201700 ), rec( content := ".\n " , count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 20, 4 ], mathmode := "Text", name := "P", next := 201711, root := ~, start := 201707, stop := 201710 ), rec( content := "\n\n \ See ", count := [ 5, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ Path" ), content := 0, count := [ 5, 3, 20, 4 ], mathmode := "Text", name := "Ref", next := 201746, root := ~, start := 201721, stop := 201745 ), rec( content := " for mor\ e information about the repesentation\n of a directed path or directed cycl\ e which is used, and see ", count := [ 5, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "ref\ ", Sect := "Iterators" ), content := 0, count := [ 5, 3, 20, 4 ], mathmode := "Text", name := "Ref", next := 201900, root := ~, start := 201856, stop := 201899 ), rec( content := " for mor\ e information about iterators.\n See Section ", count := [ 5, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Style := "Text", Subsect := "Defi\ nitions" ), content := 0, count := [ 5, 3, 20, 4 ], mathmode := "Text", name := "Ref", next := 201996, root := ~, start := 201955, stop := 201995 ), rec( content := " for the\ definition of\n a directed path and a directed cycle.\n ", count := [ 5, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 20, 5 ], mathmode := "Text", name := "P", next := 202069, root := ~, start := 202065, stop := 202068 ), rec( content := "\n\n", count := [ 5, 3, 20, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 4, 4, 2], [3, 5], [2, 3], [1, 2], [4]]);\n\ngap> iter := IteratorOfPaths(D, 1, 4);\ \n\ngap> NextIterator(iter);\n[ [ 1, 4 ], [ 2 ] ]\ngap> NextIterator\ (iter);\n[ [ 1, 4 ], [ 3 ] ]\ngap> NextIterator(iter);\n[ [ 1, 2, 5, 4 ], [ 4,\ 2, 1 ] ]\ngap> IsDoneIterator(iter);\ntrue\ngap> iter := IteratorOfPaths(D, 4\ , 3);\n\ngap> NextIterator(iter);\n[ [ 4, 1, 2, 3 ], [ 1, 4, 1 ] ]\n\ ", count := [ 5, 3, 20, 6 ], name := "PCDATA", root := ~ ) ], count := [ 5, 3, 20, 6 ], mathmode := "Text", name := "Example", next := 202554, root := ~, start := 202071, stop := 202553 ), rec( content := "\n ", count := [ 5, 3, 20, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "Description", next := 202571, root := ~, start := 201346, stop := 202570 ) ], count := [ 5, 3, 20, 1 ], mathmode := "Text", name := "ManSection", next := 202585, root := ~, start := 201244, stop := 202584 ), rec( content := "\n\n ", count := [ 5, 3, 20, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphAllSimpl\ eCircuits" ), content := 0, count := [ 5, 3, 21, 2 ], mathmode := "Text", name := "Attr", next := 202659, root := ~, start := 202606, stop := 202658 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ lists of vertices.", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "Returns", next := 202709, root := ~, start := 202662, stop := 202708 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "A", next := 202747, root := ~, start := 202733, stop := 202746 ), rec( content := " is a di\ graph, then ", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphAllSimpleCircuits", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "C", next := 202798, root := ~, start := 202767, stop := 202797 ), rec( content := "\n re\ turns a list of the ", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ imple circuits", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "E", next := 202847, root := ~, start := 202825, stop := 202846 ), rec( content := " in ", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "A", next := 202865, root := ~, start := 202851, stop := 202864 ), rec( content := ". ", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 21, 4 ], mathmode := "Text", name := "P", next := 202871, root := ~, start := 202867, stop := 202870 ), rec( content := "\n\n \ See section ", count := [ 5, 3, 21, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Style := "Number\ ", Subsect := "Definitions" ), content := 0, count := [ 5, 3, 21, 4 ], mathmode := "Text", name := "Ref", next := 202933, root := ~, start := 202889, stop := 202932 ), rec( content := " for the\ definition\n of a simple circuit, and related notions. Note that a loop is\ a simple\n circuit. ", count := [ 5, 3, 21, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 21, 5 ], mathmode := "Text", name := "P", next := 203045, root := ~, start := 203041, stop := 203044 ), rec( content := "\n\n \ For a digraph without multiple edges, a simple circuit is uniquely\n determ\ ined by its subsequence of vertices. However this is not the case for\n a m\ ultidigraph. The attribute ", count := [ 5, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphAllSimpleCircuits", count := [ 5, 3, 21, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 21, 5 ], mathmode := "Text", name := "C", next := 203264, root := ~, start := 203233, stop := 203263 ), rec( content := " ignores\ \n multiple edges, and identifies a simple circuit using only its subsequen\ ce\n of vertices. For example, although the simple circuits ", count := [ 5, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "(\ v, e, v)", count := [ 5, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 21, 5 ], mathmode := "Text", name := "M", next := 203427, root := ~, start := 203411, stop := 203426 ), rec( content := " and\n \ ", count := [ 5, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "(\ v, e', v)", count := [ 5, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 21, 5 ], mathmode := "Text", name := "M", next := 203453, root := ~, start := 203436, stop := 203452 ), rec( content := " (for di\ stinct edges ", count := [ 5, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ ", count := [ 5, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 21, 5 ], mathmode := "Text", name := "M", next := 203482, root := ~, start := 203474, stop := 203481 ), rec( content := " and ", count := [ 5, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ '", count := [ 5, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 21, 5 ], mathmode := "Text", name := "M", next := 203496, root := ~, start := 203487, stop := 203495 ), rec( content := ") are\n \ mathematically distinct, ", count := [ 5, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphAllSimpleCircuits", count := [ 5, 3, 21, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 21, 5 ], mathmode := "Text", name := "C", next := 203562, root := ~, start := 203531, stop := 203561 ), rec( content := " conside\ rs them to\n be the same. ", count := [ 5, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "P", next := 203602, root := ~, start := 203598, stop := 203601 ), rec( content := "\n\n \ With this approach, a directed circuit of length ", count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "C", next := 203665, root := ~, start := 203657, stop := 203664 ), rec( content := " can be \ determined\n by a list of its first ", count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "C", next := 203719, root := ~, start := 203711, stop := 203718 ), rec( content := " vertice\ s. Thus a simple circuit ", count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "(\ v_1,\n e_1, v_2, e_2, ..., e_{n-1}, v_n, e_{n+1}, v_1)", count := [ 5, 3, 21, 6 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "M", next := 203818, root := ~, start := 203752, stop := 203817 ), rec( content := " can be \ represented as\n the list ", count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ v_1, \\ldots, v_n]", count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "M", next := 203879, root := ~, start := 203854, stop := 203878 ), rec( content := ", or any\ cyclic permutation thereof. For\n each simple circuit of ", count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "A", next := 203962, root := ~, start := 203948, stop := 203961 ), rec( content := ",\n " , count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphAllSimpleCircuits(", count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root \ := ~ ) ], count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "A", next := 2040\ 10, root := ~, start := 203996, stop := 204009 ), rec( content := ")", count := [ 5, 3, 21, 6 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "C", next := 204015, root := ~, start := 203968, stop := 204014 ), rec( content := " include\ s precisely one such\n list to represent the circuit. ", count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 21, 7 ], mathmode := "Text", name := "P", next := 204084, root := ~, start := 204080, stop := 204083 ), rec( content := "\n\n \ ", count := [ 5, 3, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[], [3], [2, 4], [5, 4], [4]]);\n\ngap> DigraphAllSimpleCircuits(D);\n[ [ 4 ], [ 4, 5 ], [ 2\ , 3 ] ]\ngap> D := ChainDigraph(10);;\ngap> DigraphAllSimpleCircuits(D);\n[ ]\ \ngap> D := Digraph([[3], [1], [1]]);\n\ngap> DigraphAllSimpleCircuits(D);\n[ [ 1, 3 ] ]\ngap> D := Digraph([[1,\ 1]]);\n\ngap> DigraphAllSimple\ Circuits(D);\n[ [ 1 ] ]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n\ngap> DigraphAllSimpleCircuits(D);\n[ [ 1,\ 2, 3 ] ]\n", count := [ 5, 3, 21, 8 ], name := "PCDATA", root := ~ ) ], count := [ 5, 3, 21, 8 ], mathmode := "Text", name := "Example", next := 204737, root := ~, start := 204090, stop := 204736 ), rec( content := "\n ", count := [ 5, 3, 21, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "Description", next := 204754, root := ~, start := 202712, stop := 204753 ) ], count := [ 5, 3, 21, 1 ], mathmode := "Text", name := "ManSection", next := 204768, root := ~, start := 202591, stop := 204767 ), rec( content := "\n\n ", count := [ 5, 3, 21, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphLongestS\ impleCircuit" ), content := 0, count := [ 5, 3, 22, 2 ], mathmode := "Text", name := "Attr", next := 204845, root := ~, start := 204789, stop := 204844 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ vertices, or ", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "K", next := 204891, root := ~, start := 204880, stop := 204890 ), rec( content := ".", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "Returns", next := 204902, root := ~, start := 204848, stop := 204901 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "A", next := 204940, root := ~, start := 204926, stop := 204939 ), rec( content := " is a di\ graph, then ", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphLongestSimpleCircuit", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "C", next := 204994, root := ~, start := 204960, stop := 204993 ), rec( content := "\n re\ turns the longest ", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ imple circuit", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "E", next := 205040, root := ~, start := 205019, stop := 205039 ), rec( content := " in ", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "A", next := 205058, root := ~, start := 205044, stop := 205057 ), rec( content := ". See se\ ction\n ", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Style := "Number\ ", Subsect := "Definitions" ), content := 0, count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "Ref", next := 205120, root := ~, start := 205076, stop := 205119 ), rec( content := " for the\ definition of simple\n circuit, and the definition of length for a simple \ circuit.", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 22, 4 ], mathmode := "Text", name := "P", next := 205217, root := ~, start := 205213, stop := 205216 ), rec( content := "\n\n \ This attribute computes\n ", count := [ 5, 3, 22, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphAllSimpleCircuits(", count := [ 5, 3, 22, 4 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 22, 4 ], mathmode := "Text", name := "C", next := 205283, root := ~, start := 205251, stop := 205282 ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 22, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 22, 4 ], mathmode := "Text", name := "A", next := 205297, root := ~, start := 205283, stop := 205296 ), rec( attributes := rec( ), content := [ rec( content := ")\ ", count := [ 5, 3, 22, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 22, 4 ], mathmode := "Text", name := "C", next := 205305, root := ~, start := 205297, stop := 205304 ), rec( content := " to find\ all the\n simple circuits of ", count := [ 5, 3, 22, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 22, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 22, 4 ], mathmode := "Text", name := "A", next := 205359, root := ~, start := 205345, stop := 205358 ), rec( content := ", and re\ turns one of maximal length. A\n simple circuit is represented as a list o\ f vertices, in the same way as\n described in ", count := [ 5, 3, 22, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ AllSimpleCircuits" ), content := 0, count := [ 5, 3, 22, 4 ], mathmode := "Text", name := "Ref", next := 205530, root := ~, start := 205492, stop := 205529 ), rec( content := ".", count := [ 5, 3, 22, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 22, 5 ], mathmode := "Text", name := "P", next := 205535, root := ~, start := 205531, stop := 205534 ), rec( content := "\n\n \ If ", count := [ 5, 3, 22, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 22, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 22, 5 ], mathmode := "Text", name := "A", next := 205558, root := ~, start := 205544, stop := 205557 ), rec( content := " has no \ simple circuits, then this attribute returns\n ", count := [ 5, 3, 22, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 22, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 22, 5 ], mathmode := "Text", name := "K", next := 205626, root := ~, start := 205615, stop := 205625 ), rec( content := ". If ", count := [ 5, 3, 22, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 22, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 22, 5 ], mathmode := "Text", name := "A", next := 205646, root := ~, start := 205632, stop := 205645 ), rec( content := " has mul\ tiple simple circuits of maximal\n length, then this attribute returns one \ of them.", count := [ 5, 3, 22, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 22, 6 ], mathmode := "Text", name := "P", next := 205743, root := ~, start := 205739, stop := 205742 ), rec( content := "\n\n \ ", count := [ 5, 3, 22, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[], [3], [2, 4], [5, 4], [4]]);;\ngap> DigraphLongestSimpl\ eCircuit(D);\n[ 4, 5 ]\ngap> D := ChainDigraph(10);;\ngap> DigraphLongestSimpl\ eCircuit(D);\nfail\ngap> D := Digraph([[3], [1], [1, 4], [1, 1]]);;\ngap> Digr\ aphLongestSimpleCircuit(D);\n[ 1, 3, 4 ]\ngap> D := GeneralisedPetersenGraph(I\ sMutableDigraph, 4, 1);\n\ngap> Dig\ raphLongestSimpleCircuit(D);\n[ 1, 2, 3, 4, 8, 7, 6, 5 ]\n", count := [ 5, 3, 22, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 22, 7 ], mathmode := "Text", name := "Example", next := 206215, root := ~, start := 205749, stop := 206214 ), rec( content := "\n ", count := [ 5, 3, 22, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "Description", next := 206232, root := ~, start := 204905, stop := 206231 ) ], count := [ 5, 3, 22, 1 ], mathmode := "Text", name := "ManSection", next := 206246, root := ~, start := 204774, stop := 206245 ), rec( content := "\n\n ", count := [ 5, 3, 22, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, vertex" , Name := "DigraphLayers" ), content := 0, count := [ 5, 3, 23, 2 ], mathmode := "Text", name := "Oper", next := 206317, root := ~, start := 206267, stop := 206316 ), rec( attributes := rec( ), content := [ rec( content := "A list.", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "Returns", next := 206346, root := ~, start := 206320, stop := 206345 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s operation returns a list ", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "K", next := 206408, root := ~, start := 206397, stop := 206407 ), rec( content := " such th\ at ", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist[i]", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "K", next := 206433, root := ~, start := 206419, stop := 206432 ), rec( content := " is the\\ n list of vertices whose minimum distance from the vertex ", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ertex", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "A", next := 206514, root := ~, start := 206501, stop := 206513 ), rec( content := " in\n \ ", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "A", next := 206536, root := ~, start := 206522, stop := 206535 ), rec( content := " is ", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ - 1", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "K", next := 206552, root := ~, start := 206540, stop := 206551 ), rec( content := ". Vertex\ ", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ertex", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "A", next := 206574, root := ~, start := 206561, stop := 206573 ), rec( content := " is\n \ assumed to be at distance ", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "0\ ", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "K", next := 206616, root := ~, start := 206608, stop := 206615 ), rec( content := " from it\ self.\n ", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CompleteDigraph(4);;\ngap> DigraphLayers(D, 1);\n[ [ 1 ], [ 2, 3, 4\ ] ]\n", count := [ 5, 3, 23, 4 ], name := "PCDATA", root := ~ ) ], count := [ 5, 3, 23, 4 ], mathmode := "Text", name := "Example", next := 206746, root := ~, start := 206634, stop := 206745 ), rec( content := "\n ", count := [ 5, 3, 23, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "Description", next := 206763, root := ~, start := 206349, stop := 206762 ) ], count := [ 5, 3, 23, 1 ], mathmode := "Text", name := "ManSection", next := 206777, root := ~, start := 206252, stop := 206776 ), rec( content := "\n\n ", count := [ 5, 3, 23, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphDegenera\ cy" ), content := 0, count := [ 5, 3, 24, 2 ], mathmode := "Text", name := "Attr", next := 206844, root := ~, start := 206798, stop := 206843 ), rec( attributes := rec( ), content := [ rec( content := "A non-neg\ ative integer, or ", count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "K", next := 206894, root := ~, start := 206883, stop := 206893 ), rec( content := ".", count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "Returns", next := 206905, root := ~, start := 206847, stop := 206904 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "A", next := 206943, root := ~, start := 206929, stop := 206942 ), rec( content := " is a sy\ mmetric digraph without multiple edges - see\n ", count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsSymme\ tricDigraph" ), content := 0, count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "Ref", next := 207032, root := ~, start := 207000, stop := 207031 ), rec( content := " and ", count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsMulti\ Digraph" ), content := 0, count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "Ref", next := 207065, root := ~, start := 207037, stop := 207064 ), rec( content := " - then\\ n this attribute returns the degeneracy of ", count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "A", next := 207132, root := ~, start := 207118, stop := 207131 ), rec( content := ". ", count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 24, 4 ], mathmode := "Text", name := "P", next := 207138, root := ~, start := 207134, stop := 207137 ), rec( content := "\n\n \ The degeneracy of a digraph is the least integer ", count := [ 5, 3, 24, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "k\ ", count := [ 5, 3, 24, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 24, 4 ], mathmode := "Text", name := "C", next := 207201, root := ~, start := 207193, stop := 207200 ), rec( content := " such\n \ that every induced of ", count := [ 5, 3, 24, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 24, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 24, 4 ], mathmode := "Text", name := "A", next := 207247, root := ~, start := 207233, stop := 207246 ), rec( content := " contain\ s a vertex whose number of\n neighbours (excluding itself) is at most ", count := [ 5, 3, 24, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "k\ ", count := [ 5, 3, 24, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 24, 4 ], mathmode := "Text", name := "C", next := 207335, root := ~, start := 207327, stop := 207334 ), rec( content := ". Note t\ hat this means\n that loops are ignored.", count := [ 5, 3, 24, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 24, 5 ], mathmode := "Text", name := "P", next := 207389, root := ~, start := 207385, stop := 207388 ), rec( content := "\n\n \ If ", count := [ 5, 3, 24, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 24, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 24, 5 ], mathmode := "Text", name := "A", next := 207412, root := ~, start := 207398, stop := 207411 ), rec( content := " is not \ symmetric or has multiple edges then this\n attribute returns ", count := [ 5, 3, 24, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 24, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 24, 5 ], mathmode := "Text", name := "K", next := 207495, root := ~, start := 207484, stop := 207494 ), rec( content := ".\n " , count := [ 5, 3, 24, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := DigraphSymmetricClosure(ChainDigraph(5));;\ngap> DigraphDegeneracy(\ D);\n1\ngap> D := CompleteDigraph(5);;\ngap> DigraphDegeneracy(D);\n4\ngap> D \ := Digraph([[1], [2, 4, 5], [3, 4], [2, 3, 4], [2], []]);\n\ngap> DigraphDegeneracy(D);\n1\ngap> D := Generalis\ edPetersenGraph(IsMutableDigraph, 10, 3);\n\ngap> DigraphDegeneracy(D);\n3\n", count := [ 5, 3, 24, 6 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 24, 6 ], mathmode := "Text", name := "Example", next := 207950, root := ~, start := 207501, stop := 207949 ), rec( content := "\n ", count := [ 5, 3, 24, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "Description", next := 207967, root := ~, start := 206908, stop := 207966 ) ], count := [ 5, 3, 24, 1 ], mathmode := "Text", name := "ManSection", next := 207981, root := ~, start := 206783, stop := 207980 ), rec( content := "\n\n ", count := [ 5, 3, 24, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphDegenera\ cyOrdering" ), content := 0, count := [ 5, 3, 25, 2 ], mathmode := "Text", name := "Attr", next := 208056, root := ~, start := 208002, stop := 208055 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ integers, or ", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "K", next := 208102, root := ~, start := 208091, stop := 208101 ), rec( content := ".", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "Returns", next := 208113, root := ~, start := 208059, stop := 208112 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "A", next := 208151, root := ~, start := 208137, stop := 208150 ), rec( content := " is a di\ graph for which\n ", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphDegeneracy(", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "C", next := 208204, root := ~, start := 208179, stop := 208203 ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "A", next := 208218, root := ~, start := 208204, stop := 208217 ), rec( attributes := rec( ), content := [ rec( content := ")\ ", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "C", next := 208226, root := ~, start := 208218, stop := 208225 ), rec( content := " is a no\ n-negative integer\n ", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "k\ ", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "C", next := 208265, root := ~, start := 208257, stop := 208264 ), rec( content := " - see " , count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Degeneracy" ), content := 0, count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "Ref", next := 208303, root := ~, start := 208272, stop := 208302 ), rec( content := " - then \ this attribute\n returns a degeneracy ordering of the vertices of the verti\ ces of\n ", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "A", next := 208413, root := ~, start := 208399, stop := 208412 ), rec( content := ".", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "P", next := 208418, root := ~, start := 208414, stop := 208417 ), rec( content := "\n\n \ A degeneracy ordering of ", count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "A", next := 208463, root := ~, start := 208449, stop := 208462 ), rec( content := " is a li\ st ", count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ rdering", count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "C", next := 208489, root := ~, start := 208474, stop := 208488 ), rec( content := " of the\\ n vertices of ", count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "A", next := 208527, root := ~, start := 208513, stop := 208526 ), rec( content := " ordered\ such that for any\n position ", count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "C", next := 208575, root := ~, start := 208567, stop := 208574 ), rec( content := " of the \ list, the vertex ", count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ rdering[i]", count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "C", next := 208618, root := ~, start := 208600, stop := 208617 ), rec( content := " has at \ most\n ", count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "k\ ", count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "C", next := 208643, root := ~, start := 208635, stop := 208642 ), rec( content := " neighbo\ urs in later position of the list.", count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 25, 5 ], mathmode := "Text", name := "P", next := 208689, root := ~, start := 208685, stop := 208688 ), rec( content := "\n\n \ If ", count := [ 5, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphDegeneracy(", count := [ 5, 3, 25, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 25, 5 ], mathmode := "Text", name := "C", next := 208723, root := ~, start := 208698, stop := 208722 ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 25, 5 ], mathmode := "Text", name := "A", next := 208737, root := ~, start := 208723, stop := 208736 ), rec( attributes := rec( ), content := [ rec( content := ")\ ", count := [ 5, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 25, 5 ], mathmode := "Text", name := "C", next := 208745, root := ~, start := 208737, stop := 208744 ), rec( content := " returns\ ", count := [ 5, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 25, 5 ], mathmode := "Text", name := "K", next := 208765, root := ~, start := 208754, stop := 208764 ), rec( content := ",\n t\ hen this attribute returns ", count := [ 5, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 25, 5 ], mathmode := "Text", name := "K", next := 208810, root := ~, start := 208799, stop := 208809 ), rec( content := ".\n " , count := [ 5, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := DigraphSymmetricClosure(ChainDigraph(5));;\ngap> DigraphDegeneracyO\ rdering(D);\n[ 5, 4, 3, 2, 1 ]\ngap> D := CompleteDigraph(5);;\ngap> DigraphDe\ generacyOrdering(D);\n[ 5, 4, 3, 2, 1 ]\ngap> D := Digraph([[1], [2, 4, 5], [3\ , 4], [2, 3, 4], [2], []]);\n\nga\ p> DigraphDegeneracyOrdering(D);\n[ 1, 6, 5, 2, 4, 3 ]\ngap> D := GeneralisedP\ etersenGraph(IsMutableDigraph, 3, 1);\n\ngap> DigraphDegeneracyOrdering(D);\n[ 6, 5, 4, 1, 3, 2 ]\n", count := [ 5, 3, 25, 6 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 25, 6 ], mathmode := "Text", name := "Example", next := 209365, root := ~, start := 208816, stop := 209364 ), rec( content := "\n ", count := [ 5, 3, 25, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "Description", next := 209382, root := ~, start := 208116, stop := 209381 ) ], count := [ 5, 3, 25, 1 ], mathmode := "Text", name := "ManSection", next := 209396, root := ~, start := 207987, stop := 209395 ), rec( content := "\n\n ", count := [ 5, 3, 25, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "HamiltonianPath\ " ), content := 0, count := [ 5, 3, 26, 2 ], mathmode := "Text", name := "Attr", next := 209461, root := ~, start := 209417, stop := 209460 ), rec( attributes := rec( ), content := [ rec( content := "A list or\ ", count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "K", next := 209494, root := ~, start := 209483, stop := 209493 ), rec( content := ".", count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "Returns", next := 209505, root := ~, start := 209464, stop := 209504 ), rec( attributes := rec( ), content := [ rec( content := "\n Ret\ urns a Hamiltonian path if one exists, ", count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "K", next := 209579, root := ~, start := 209568, stop := 209578 ), rec( content := " if not.\ ", count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := 0, count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "P", next := 209591, root := ~, start := 209587, stop := 209590 ), rec( content := "\n\n \ A ", count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "H\ amiltonian path", count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "E", next := 209622, root := ~, start := 209599, stop := 209621 ), rec( content := " of a di\ graph with ", count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "C", next := 209649, root := ~, start := 209641, stop := 209648 ), rec( content := " vertice\ s is directed\n cycle of length ", count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "C", next := 209699, root := ~, start := 209691, stop := 209698 ), rec( content := ". If ", count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "A", next := 209718, root := ~, start := 209704, stop := 209717 ), rec( content := " is a di\ graph that contains a\n Hamiltonian path, then this function returns one, d\ escribed in the form\n used by ", count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ AllSimpleCircuits" ), content := 0, count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "Ref", next := 209874, root := ~, start := 209836, stop := 209873 ), rec( content := ". Note i\ f ", count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "A", next := 209898, root := ~, start := 209884, stop := 209897 ), rec( content := " has\n \ 0 or 1 vertices, then ", count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "H\ amiltonianPath", count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "C", next := 209951, root := ~, start := 209929, stop := 209950 ), rec( content := " returns\ ", count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ ]", count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "C", next := 209969, root := ~, start := 209960, stop := 209968 ), rec( content := " or\n \ ", count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ 1]", count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "C", next := 209987, root := ~, start := 209977, stop := 209986 ), rec( content := ", respec\ tively.", count := [ 5, 3, 26, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 26, 5 ], mathmode := "Text", name := "P", next := 210006, root := ~, start := 210002, stop := 210005 ), rec( content := "\n\n \ The method used in this attribute has the same worst case complexity as\n " , count := [ 5, 3, 26, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ Monomorphism" ), content := 0, count := [ 5, 3, 26, 5 ], mathmode := "Text", name := "Ref", next := 210121, root := ~, start := 210088, stop := 210120 ), rec( content := ".\n\n \ ", count := [ 5, 3, 26, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[]]);\n\ngap> Hamil\ tonianPath(D);\n[ 1 ]\ngap> D := Digraph([[2], [1]]);\n\ngap> HamiltonianPath(D);\n[ 1, 2 ]\ngap> D := Digraph([\ [3], [], [2]]);\n\ngap> Hamiltonia\ nPath(D);\nfail\ngap> D := Digraph([[2], [3], [1]]);\n\ngap> HamiltonianPath(D);\n[ 1, 2, 3 ]\ngap> D := General\ isedPetersenGraph(IsMutableDigraph, 5, 2);\n\ngap> HamiltonianPath(D);\nfail\n", count := [ 5, 3, 26, 6 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 26, 6 ], mathmode := "Text", name := "Example", next := 210729, root := ~, start := 210128, stop := 210728 ), rec( content := "\n ", count := [ 5, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "Description", next := 210746, root := ~, start := 209508, stop := 210745 ) ], count := [ 5, 3, 26, 1 ], mathmode := "Text", name := "ManSection", next := 210760, root := ~, start := 209402, stop := 210759 ), rec( content := "\n\n ", count := [ 5, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "NrSpanningTrees\ " ), content := 0, count := [ 5, 3, 27, 2 ], mathmode := "Text", name := "Attr", next := 210825, root := ~, start := 210781, stop := 210824 ), rec( attributes := rec( ), content := [ rec( content := "An intege\ r.", count := [ 5, 3, 27, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 27, 3 ], mathmode := "Text", name := "Returns", next := 210858, root := ~, start := 210828, stop := 210857 ), rec( attributes := rec( ), content := [ rec( content := "\n Ret\ urns the number of spanning trees of the symmetric digraph\n ", count := [ 5, 3, 27, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 27, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 27, 3 ], mathmode := "Text", name := "A", next := 210959, root := ~, start := 210945, stop := 210958 ), rec( content := ".\n " , count := [ 5, 3, 27, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "N\ rSpanningTrees", count := [ 5, 3, 27, 3 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 5, 3, 27, 3 ], mathmode := "Text", name := "C", next := 210987, root := ~, start := 210965, stop := 210986 ), rec( content := " will re\ turn an error if ", count := [ 5, 3, 27, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 27, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 27, 3 ], mathmode := "Text", name := "A", next := 211026, root := ~, start := 211012, stop := 211025 ), rec( content := " is not \ a\n symmetric digraph. ", count := [ 5, 3, 27, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 27, 4 ], mathmode := "Text", name := "P", next := 211063, root := ~, start := 211059, stop := 211062 ), rec( content := " \n\n \ See ", count := [ 5, 3, 27, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsSymme\ tricDigraph" ), content := 0, count := [ 5, 3, 27, 4 ], mathmode := "Text", name := "Ref", next := 211106, root := ~, start := 211074, stop := 211105 ), rec( content := " and\n \ ", count := [ 5, 3, 27, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "IsUndir\ ectedSpanningTree" ), content := 0, count := [ 5, 3, 27, 4 ], mathmode := "Text", name := "Ref", next := 211154, root := ~, start := 211115, stop := 211153 ), rec( content := " for mor\ e information. \n\n ", count := [ 5, 3, 27, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CompleteDigraph(5);\n\n\ gap> NrSpanningTrees(D);\n125\ngap> D := DigraphSymmetricClosure(CycleDigraph(\ 24));;\ngap> NrSpanningTrees(D);\n24\ngap> NrSpanningTrees(EmptyDigraph(0));\n\ 0\ngap> D := GeneralisedPetersenGraph(IsMutableDigraph, 9, 2);\n\ngap> NrSpanningTrees(D);\n1134225\n", count := [ 5, 3, 27, 5 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 27, 5 ], mathmode := "Text", name := "Example", next := 211580, root := ~, start := 211183, stop := 211579 ), rec( content := "\n ", count := [ 5, 3, 27, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 27, 3 ], mathmode := "Text", name := "Description", next := 211597, root := ~, start := 210861, stop := 211596 ) ], count := [ 5, 3, 27, 1 ], mathmode := "Text", name := "ManSection", next := 211611, root := ~, start := 210766, stop := 211610 ), rec( content := "\n\n ", count := [ 5, 3, 27, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, source,\ target", Label := "for a source and target", Name := "DigraphDijkstra" ), content := 0, count := [ 5, 3, 28, 2 ], mathmode := "Text", name := "Oper", next := 211724, root := ~, start := 211632, stop := 211723 ), rec( attributes := rec( Arg := "digraph, source" , Label := "for a source", Name := "DigraphDijkstra\ " ), content := 0, count := [ 5, 3, 28, 4 ], mathmode := "Text", name := "Oper", next := 211800, root := ~, start := 211727, stop := 211799 ), rec( attributes := rec( ), content := [ rec( content := "Two lists\ .", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "Returns", next := 211832, root := ~, start := 211803, stop := 211831 ), rec( attributes := rec( ), content := [ rec( content := "\n If ", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "A", next := 211868, root := ~, start := 211854, stop := 211867 ), rec( content := " is a di\ graph and ", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ource", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "A", next := 211899, root := ~, start := 211886, stop := 211898 ), rec( content := " and ", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ arget", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "A", next := 211917, root := ~, start := 211904, stop := 211916 ), rec( content := " are\n \ vertices of ", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "A", next := 211951, root := ~, start := 211937, stop := 211950 ), rec( content := ", then " , count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphDijkstra", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "C", next := 211980, root := ~, start := 211958, stop := 211979 ), rec( content := " calcula\ tes the\n length of the shortest path from ", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ource", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "A", next := 212044, root := ~, start := 212031, stop := 212043 ), rec( content := " to ", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ arget", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "A", next := 212061, root := ~, start := 212048, stop := 212060 ), rec( content := " and ret\ urns\n two lists. Each element of the first list is the distance of the\n co\ rresponding element from ", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ource", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "A", next := 212183, root := ~, start := 212170, stop := 212182 ), rec( content := ". If a \ vertex was not visited in\n the process of calculating the shortest distance \ to ", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ arget", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "A", next := 212284, root := ~, start := 212271, stop := 212283 ), rec( content := " or if\n\ there is no path connecting that vertex with ", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ource", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "A", next := 212351, root := ~, start := 212338, stop := 212350 ), rec( content := ", then\n\ the corresponding distance is ", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nfinity", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "K", next := 212405, root := ~, start := 212390, stop := 212404 ), rec( content := ". Each \ element of the\n second list gives the previous vertex in the shortest path\n\ from ", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ource", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "A", next := 212509, root := ~, start := 212496, stop := 212508 ), rec( content := " to the \ corresponding vertex. For\n ", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ource", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "A", next := 212559, root := ~, start := 212546, stop := 212558 ), rec( content := " and for\ any vertices that remained unvisited this\n will be ", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "-\ 1", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "C", next := 212631, root := ~, start := 212622, stop := 212630 ), rec( content := ".", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 3, 28, 6 ], mathmode := "Text", name := "P", next := 212636, root := ~, start := 212632, stop := 212635 ), rec( content := "\n\n \ If the optional second argument ", count := [ 5, 3, 28, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ arget", count := [ 5, 3, 28, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 28, 6 ], mathmode := "Text", name := "A", next := 212687, root := ~, start := 212674, stop := 212686 ), rec( content := " is not \ present, then\n ", count := [ 5, 3, 28, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphDijkstra", count := [ 5, 3, 28, 6 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 5, 3, 28, 6 ], mathmode := "Text", name := "C", next := 212735, root := ~, start := 212713, stop := 212734 ), rec( content := " returns\ the shortest path from ", count := [ 5, 3, 28, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ource", count := [ 5, 3, 28, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 28, 6 ], mathmode := "Text", name := "A", next := 212780, root := ~, start := 212767, stop := 212779 ), rec( content := " to\n \ every vertex that is reachable from ", count := [ 5, 3, 28, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ource", count := [ 5, 3, 28, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 28, 6 ], mathmode := "Text", name := "A", next := 212837, root := ~, start := 212824, stop := 212836 ), rec( content := ".\n\n " , count := [ 5, 3, 28, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> mat := [[0, 1, 1], [0, 0, 1], [0, 0, 0]];\n[ [ 0, 1, 1 ], [ 0, 0, 1 ], [\ 0, 0, 0 ] ]\ngap> D := DigraphByAdjacencyMatrix(mat);\n\ngap> DigraphDijkstra(D, 2, 3);\n[ [ infinity, 0, 1 ], \ [ -1, -1, 2 ] ]\ngap> DigraphDijkstra(D, 1, 3);\n[ [ 0, 1, 1 ], [ -1, 1, 1 ] ]\ \ngap> DigraphDijkstra(D, 1, 2);\n[ [ 0, 1, 1 ], [ -1, 1, 1 ] ]\n", count := [ 5, 3, 28, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 3, 28, 7 ], mathmode := "Text", name := "Example", next := 213240, root := ~, start := 212842, stop := 213239 ), rec( content := "\n", count := [ 5, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "Description", next := 213255, root := ~, start := 211835, stop := 213254 ) ], count := [ 5, 3, 28, 1 ], mathmode := "Text", name := "ManSection", next := 213269, root := ~, start := 211617, stop := 213268 ), rec( content := "\n\n ", count := [ 5, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 0, 1 ], mathmode := "Text", name := "Section", next := 213283, root := ~, start := 172718, stop := 213282 ) , rec( content := "\n\n ", count := [ 5, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Cayley graphs of \ groups", count := [ 5, 4, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 4, 0, 2 ], mathmode := "Text", name := "Heading", next := 213338, root := ~, start := 213296, stop := 213337 ), rec( content := "\n ", count := [ 5, 4, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "GroupOfCayleyDi\ graph" ), content := 0, count := [ 5, 4, 1, 2 ], mathmode := "Text", name := "Attr", next := 213407, root := ~, start := 213358, stop := 213406 ), rec( attributes := rec( Arg := "digraph", Name := "SemigroupOfCayl\ eyDigraph" ), content := 0, count := [ 5, 4, 1, 4 ], mathmode := "Text", name := "Attr", next := 213463, root := ~, start := 213410, stop := 213462 ), rec( attributes := rec( ), content := [ rec( content := "A group o\ r semigroup.", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "Returns", next := 213506, root := ~, start := 213466, stop := 213505 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "A", next := 213544, root := ~, start := 213530, stop := 213543 ), rec( content := " is an i\ mmutable Cayley graph of a group ", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "C", next := 213593, root := ~, start := 213585, stop := 213592 ), rec( content := " and\n \ ", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "A", next := 213616, root := ~, start := 213602, stop := 213615 ), rec( content := " belongs\ to the category ", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsCayle\ yDigraph" ), content := 0, count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "Ref", next := 213670, root := ~, start := 213641, stop := 213669 ), rec( content := ", then\n\ ", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ roupOfCayleyDigraph", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "C", next := 213708, root := ~, start := 213681, stop := 213707 ), rec( content := " returns\ ", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "C", next := 213725, root := ~, start := 213717, stop := 213724 ), rec( content := ".\n " , count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "P", next := 213735, root := ~, start := 213731, stop := 213734 ), rec( content := "\n\n \ If ", count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "A", next := 213758, root := ~, start := 213744, stop := 213757 ), rec( content := " is a Ca\ yley graph of a semigroup ", count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "S\ ", count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "C", next := 213800, root := ~, start := 213792, stop := 213799 ), rec( content := " and\n \ ", count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "A", next := 213823, root := ~, start := 213809, stop := 213822 ), rec( content := " belongs\ to the category ", count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsCayle\ yDigraph" ), content := 0, count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "Ref", next := 213877, root := ~, start := 213848, stop := 213876 ), rec( content := ", then\n\ ", count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "S\ emigroupOfCayleyDigraph", count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "C", next := 213919, root := ~, start := 213888, stop := 213918 ), rec( content := " returns\ ", count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "S\ ", count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "C", next := 213936, root := ~, start := 213928, stop := 213935 ), rec( content := ".\n " , count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 4, 1, 7 ], mathmode := "Text", name := "P", next := 213946, root := ~, start := 213942, stop := 213945 ), rec( content := "\n\n \ See also ", count := [ 5, 4, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Generat\ orsOfCayleyDigraph" ), content := 0, count := [ 5, 4, 1, 7 ], mathmode := "Text", name := "Ref", next := 214000, root := ~, start := 213961, stop := 213999 ), rec( content := ".\n " , count := [ 5, 4, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> G := DihedralGroup(IsPermGroup, 8);\nGroup([ (1,2,3,4), (2,4) ])\ngap> d\ igraph := CayleyDigraph(G);\n\nga\ p> GroupOfCayleyDigraph(digraph) = G;\ntrue\n", count := [ 5, 4, 1, 8 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 4, 1, 8 ], mathmode := "Text", name := "Example", next := 214232, root := ~, start := 214006, stop := 214231 ), rec( content := "\n ", count := [ 5, 4, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "Description", next := 214249, root := ~, start := 213509, stop := 214248 ) ], count := [ 5, 4, 1, 1 ], mathmode := "Text", name := "ManSection", next := 214263, root := ~, start := 213343, stop := 214262 ), rec( content := "\n\n ", count := [ 5, 4, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "GeneratorsOfCay\ leyDigraph" ), content := 0, count := [ 5, 4, 2, 2 ], mathmode := "Text", name := "Attr", next := 214338, root := ~, start := 214284, stop := 214337 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ generators.", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "Returns", next := 214381, root := ~, start := 214341, stop := 214380 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "A", next := 214419, root := ~, start := 214405, stop := 214418 ), rec( content := " is an i\ mmutable Cayley graph of a group or semigroup with\n respect to a set of ge\ nerators ", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ ens", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "C", next := 214524, root := ~, start := 214513, stop := 214523 ), rec( content := " and ", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "A", next := 214543, root := ~, start := 214529, stop := 214542 ), rec( content := " belongs\ to\n the category ", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsCayle\ yDigraph" ), content := 0, count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "Ref", next := 214601, root := ~, start := 214572, stop := 214600 ), rec( content := ", then\n\ ", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ eneratorsOfCayleyDigraph", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "C", next := 214644, root := ~, start := 214612, stop := 214643 ), rec( content := " return \ the list of generators ", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ ens", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "C", next := 214686, root := ~, start := 214675, stop := 214685 ), rec( content := "\n ov\ er which ", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "A", next := 214716, root := ~, start := 214702, stop := 214715 ), rec( content := " is defi\ ned.\n ", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 4, 2, 4 ], mathmode := "Text", name := "P", next := 214737, root := ~, start := 214733, stop := 214736 ), rec( content := "\n\n \ See also ", count := [ 5, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "GroupOf\ CayleyDigraph" ), content := 0, count := [ 5, 4, 2, 4 ], mathmode := "Text", name := "Ref", next := 214786, root := ~, start := 214752, stop := 214785 ), rec( content := " \n o\ r ", count := [ 5, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Semigro\ upOfCayleyDigraph" ), content := 0, count := [ 5, 4, 2, 4 ], mathmode := "Text", name := "Ref", next := 214833, root := ~, start := 214795, stop := 214832 ), rec( content := ".\n " , count := [ 5, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> G := DihedralGroup(IsPermGroup, 8);\nGroup([ (1,2,3,4), (2,4) ])\ngap> d\ igraph := CayleyDigraph(G);\n\nga\ p> GeneratorsOfCayleyDigraph(digraph) = GeneratorsOfGroup(G);\ntrue\ngap> digr\ aph := CayleyDigraph(G, [()]);\n\n\ gap> GeneratorsOfCayleyDigraph(digraph) = [()];\ntrue", count := [ 5, 4, 2, 5 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 4, 2, 5 ], mathmode := "Text", name := "Example", next := 215226, root := ~, start := 214839, stop := 215225 ), rec( content := "\n ", count := [ 5, 4, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "Description", next := 215243, root := ~, start := 214384, stop := 215242 ) ], count := [ 5, 4, 2, 1 ], mathmode := "Text", name := "ManSection", next := 215257, root := ~, start := 214269, stop := 215256 ), rec( content := "\n\n ", count := [ 5, 4, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 4, 0, 1 ], mathmode := "Text", name := "Section", next := 215271, root := ~, start := 213287, stop := 215270 ) , rec( content := "\n\n ", count := [ 5, 4, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Associated semigr\ oups", count := [ 5, 5, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 0, 2 ], mathmode := "Text", name := "Heading", next := 215324, root := ~, start := 215284, stop := 215323 ), rec( content := "\n ", count := [ 5, 5, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "filt, digraph", Label := "for a filter a\ nd a digraph", Name := "AsSemigroup" ), content := 0, count := [ 5, 5, 1, 2 ], mathmode := "Text", name := "Oper", next := 215435, root := ~, start := 215348, stop := 215434 ), rec( attributes := rec( Arg := "filt, digraph", Name := "AsMonoid" ), content := 0, count := [ 5, 5, 1, 4 ], mathmode := "Text", name := "Oper", next := 215483, root := ~, start := 215440, stop := 215482 ), rec( attributes := rec( ), content := [ rec( content := "A semilat\ tice of partial perms.", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "Returns", next := 215538, root := ~, start := 215488, stop := 215537 ), rec( attributes := rec( ), content := [ rec( content := "\n T\ he operation ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A\ sSemigroup", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "C", next := 215595, root := ~, start := 215577, stop := 215594 ), rec( content := " require\ s that ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "A", next := 215621, root := ~, start := 215610, stop := 215620 ), rec( content := " be equa\ l to\n ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "ref\ ", Filt := "IsPartialPermSemigroup" ), content := 0, count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "Ref", next := 215691, root := ~, start := 215640, stop := 215690 ), rec( content := ".\n \ If ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "A", next := 215716, root := ~, start := 215702, stop := 215715 ), rec( content := " is a\n \ ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsJoinS\ emilatticeDigraph" ), content := 0, count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "Ref", next := 215766, root := ~, start := 215728, stop := 215765 ), rec( content := " or ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsLatti\ ceDigraph" ), content := 0, count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "Ref", next := 215800, root := ~, start := 215770, stop := 215799 ), rec( content := "\n \ then ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A\ sSemigroup", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "C", next := 215830, root := ~, start := 215812, stop := 215829 ), rec( content := " returns\ a semigroup of partial perms which is\n isomorphic to the semigroup whos\ e elements are the vertices of\n ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "A", next := 215966, root := ~, start := 215952, stop := 215965 ), rec( content := " with th\ e binary operation\n ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Partial\ OrderDigraphJoinOfVertices" ), content := 0, count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "Ref", next := 216046, root := ~, start := 215999, stop := 216045 ), rec( content := ".\n \ If ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "A", next := 216071, root := ~, start := 216057, stop := 216070 ), rec( content := "\n \ satisfies ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsMeetS\ emilatticeDigraph" ), content := 0, count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "Ref", next := 216127, root := ~, start := 216089, stop := 216126 ), rec( content := " but not\ \n ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsJoinS\ emilatticeDigraph" ), content := 0, count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "Ref", next := 216180, root := ~, start := 216142, stop := 216179 ), rec( content := " then\n \ ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A\ sSemigroup", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "C", next := 216210, root := ~, start := 216192, stop := 216209 ), rec( content := " returns\ a semigroup of partial perms which is\n isomorphic to the semigroup whos\ e elements are the vertices of\n ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "A", next := 216346, root := ~, start := 216332, stop := 216345 ), rec( content := " with th\ e binary operation\n ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Partial\ OrderDigraphMeetOfVertices" ), content := 0, count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "Ref", next := 216426, root := ~, start := 216379, stop := 216425 ), rec( content := ".\n \ ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := 0, count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "P", next := 216438, root := ~, start := 216434, stop := 216437 ), rec( content := "\n\n \ The operation ", count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A\ sMonoid", count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "C", next := 216475, root := ~, start := 216460, stop := 216474 ), rec( content := " behaves\ similarly to ", count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A\ sSemigroup", count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "C", next := 216515, root := ~, start := 216497, stop := 216514 ), rec( content := "\n \ except that ", count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "A", next := 216545, root := ~, start := 216534, stop := 216544 ), rec( content := " may als\ o be equal to\n ", count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "ref\ ", Filt := "IsPartialPermMonoid" ), content := 0, count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "Ref", next := 216621, root := ~, start := 216573, stop := 216620 ), rec( content := ",\n \ ", count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "A", next := 216643, root := ~, start := 216629, stop := 216642 ), rec( content := " must sa\ tisfy ", count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsLatti\ ceDigraph" ), content := 0, count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "Ref", next := 216687, root := ~, start := 216657, stop := 216686 ), rec( content := ", and th\ e\n output satisfies ", count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "ref\ ", Filt := "IsMonoid" ), content := 0, count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "Ref", next := 216757, root := ~, start := 216720, stop := 216756 ), rec( content := ". ", count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 5, 1, 7 ], mathmode := "Text", name := "P", next := 216763, root := ~, start := 216759, stop := 216762 ), rec( content := "\n\n \ The output of both of these operations is guaranteed to be of minimal\n \ degree (see ", count := [ 5, 5, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "DegreeO\ fPartialPermSemigroup", BookName := "ref" ), content := 0, count := [ 5, 5, 1, 7 ], mathmode := "Text", name := "Ref", next := 216916, root := ~, start := 216859, stop := 216915 ), rec( content := ").\n \ Furthermore the ", count := [ 5, 5, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Generat\ orsOfSemigroup", BookName := "ref" ), content := 0, count := [ 5, 5, 1, 7 ], mathmode := "Text", name := "Ref", next := 216991, root := ~, start := 216941, stop := 216990 ), rec( content := " of\n \ the output is guaranteed to be the unique generating set of minimal size.\n\ ", count := [ 5, 5, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> di := Digraph([[1], [1, 2], [1, 3], [1, 4], [1, 2, 3, 5]]);\n\ngap> S := AsSemigroup(IsPartialPermSemigro\ up, di);\n\ngap> ForAll(El\ ements(S), IsIdempotent);\ntrue\ngap> IsInverseSemigroup(S);\ntrue\ngap> Size(\ S);\n5\ngap> di := Digraph([[1], [1, 2], [1, 2, 3]]);\n\ngap> M := AsMonoid(IsPartialPermMonoid, di);\n\ngap> Size(M);\n3", count := [ 5, 5, 1, 8 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 5, 1, 8 ], mathmode := "Text", name := "Example", next := 217623, root := ~, start := 217081, stop := 217622 ), rec( content := "\n ", count := [ 5, 5, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "Description", next := 217642, root := ~, start := 215543, stop := 217641 ) ], count := [ 5, 5, 1, 1 ], mathmode := "Text", name := "ManSection", next := 217658, root := ~, start := 215331, stop := 217657 ), rec( content := "\n\n ", count := [ 5, 5, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "filt, Y, gps, ho\ ms", Label := "for a filter, semilattice digraph, and two lists", Name := "AsSemigroup" ), content := 0, count := [ 5, 5, 2, 2 ], mathmode := "Text", name := "Oper", next := 217797, root := ~, start := 217683, stop := 217796 ), rec( attributes := rec( ), content := [ rec( content := " A Cliffo\ rd semigroup of partial perms. ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "Returns", next := 217861, root := ~, start := 217802, stop := 217860 ), rec( attributes := rec( ), content := [ rec( content := "\n T\ he operation ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A\ sSemigroup", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "C", next := 217918, root := ~, start := 217900, stop := 217917 ), rec( content := " require\ s that ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "A", next := 217944, root := ~, start := 217933, stop := 217943 ), rec( content := " be equa\ l to\n ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "ref\ ", Filt := "IsPartialPermSemigroup" ), content := 0, count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "Ref", next := 218014, root := ~, start := 217963, stop := 218013 ), rec( content := ".\n \ If ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Y\ ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "A", next := 218033, root := ~, start := 218025, stop := 218032 ), rec( content := " is a ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsJoinS\ emilatticeDigraph" ), content := 0, count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "Ref", next := 218077, root := ~, start := 218039, stop := 218076 ), rec( content := " or\n \ ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsMeetS\ emilatticeDigraph" ), content := 0, count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "Ref", next := 218125, root := ~, start := 218087, stop := 218124 ), rec( content := ",\n \ ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "g\ ps", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "A", next := 218143, root := ~, start := 218133, stop := 218142 ), rec( content := " is a li\ st of groups corresponding to each vertex, and\n ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "h\ oms", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "A", next := 218215, root := ~, start := 218204, stop := 218214 ), rec( content := " is a li\ st containing for each edge ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "(\ i, j)", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "C", next := 218264, root := ~, start := 218251, stop := 218263 ), rec( content := " in\n \ the transitive reduction of ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "A", next := 218316, root := ~, start := 218302, stop := 218315 ), rec( content := " a tripl\ e ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ i, j, hom]", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "C", next := 218344, root := ~, start := 218326, stop := 218343 ), rec( content := "\n \ where ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "h\ om", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "C", next := 218367, root := ~, start := 218357, stop := 218366 ), rec( content := " is a gr\ oup homomorphism from ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ ps[i]", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "C", next := 218410, root := ~, start := 218397, stop := 218409 ), rec( content := " to\n \ ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ ps[j]", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "C", next := 218433, root := ~, start := 218420, stop := 218432 ), rec( content := ", and th\ e diagram of homomorphisms commutes, then\n ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A\ sSemigroup", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "C", next := 218507, root := ~, start := 218489, stop := 218506 ), rec( content := " returns\ a semigroup of partial perms which is\n isomorphic to the strong semilat\ tice of groups ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "S\ [Y; gps; homs]", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "M", next := 218629, root := ~, start := 218607, stop := 218628 ), rec( content := ".\n \ ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> G1 := AlternatingGroup(4);;\ngap> G2 := SymmetricGroup(2);;\ngap> G3 := \ SymmetricGroup(3);;\ngap> gr := Digraph([[1, 3], [2, 3], [3]]);;\ngap> sgn := \ function(x)\n> if SignPerm(x) = 1 then\n> return ();\n> fi;\n> return (1, 2);\ \n> end;;\ngap> hom13 := GroupHomomorphismByFunction(G1, G3, sgn);;\ngap> hom2\ 3 := GroupHomomorphismByFunction(G2, G3, sgn);;\ngap> T := AsSemigroup(IsParti\ alPermSemigroup,\n> gr,\n> [G1, G2, G3], [[1, 3, hom13], [2, 3, hom23]]);;\nga\ p> Size(T);\n20\ngap> D := GreensDClasses(T);;\ngap> List(D, x -> Size(x));\n[\ 6, 12, 2 ]\n", count := [ 5, 5, 2, 4 ], name := "PCDATA", root := ~ ) ], count := [ 5, 5, 2, 4 ], mathmode := "Text", name := "Example", next := 219206, root := ~, start := 218637, stop := 219205 ), rec( content := "\n ", count := [ 5, 5, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "Description", next := 219225, root := ~, start := 217866, stop := 219224 ) ], count := [ 5, 5, 2, 1 ], mathmode := "Text", name := "ManSection", next := 219241, root := ~, start := 217666, stop := 219240 ), rec( content := "\n\n ", count := [ 5, 5, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 5, 0, 1 ], mathmode := "Text", name := "Section", next := 219255, root := ~, start := 215275, stop := 219254 ) , rec( content := "\n\n ", count := [ 5, 5, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Planarity", count := [ 5, 6, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 0, 2 ], mathmode := "Text", name := "Heading", next := 219296, root := ~, start := 219268, stop := 219295 ), rec( content := "\n ", count := [ 5, 6, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "KuratowskiPlana\ rSubdigraph" ), content := 0, count := [ 5, 6, 1, 2 ], mathmode := "Text", name := "Attr", next := 219371, root := ~, start := 219316, stop := 219370 ), rec( attributes := rec( ), content := [ rec( content := "A list or\ ", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "K", next := 219404, root := ~, start := 219393, stop := 219403 ), rec( content := ".", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "Returns", next := 219415, root := ~, start := 219374, stop := 219414 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "K\ uratowskiPlanarSubdigraph", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "C", next := 219469, root := ~, start := 219436, stop := 219468 ), rec( content := " returns\ the immutable list of\n lists of out-neighbours of a (not necessarily indu\ ced) subdigraph of the\n digraph ", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "A", next := 219603, root := ~, start := 219589, stop := 219602 ), rec( content := " that wi\ tnesses the fact that ", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "A", next := 219647, root := ~, start := 219633, stop := 219646 ), rec( content := " is not\\ n planar, or ", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "K", next := 219681, root := ~, start := 219670, stop := 219680 ), rec( content := " if ", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "A", next := 219699, root := ~, start := 219685, stop := 219698 ), rec( content := " is plan\ ar. In other words,\n ", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "K\ uratowskiPlanarSubdigraph", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "C", next := 219765, root := ~, start := 219732, stop := 219764 ), rec( content := " returns\ the out-neighbours of a\n subdigraph of ", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "A", next := 219830, root := ~, start := 219816, stop := 219829 ), rec( content := " that is\ homeomorphic to the complete graph\n with ", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "5\ ", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "C", next := 219891, root := ~, start := 219883, stop := 219890 ), rec( content := " vertice\ s, or to the complete bipartite graph with vertex sets\n of sizes ", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "3\ ", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "C", next := 219975, root := ~, start := 219967, stop := 219974 ), rec( content := " and ", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "3\ ", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "C", next := 219988, root := ~, start := 219980, stop := 219987 ), rec( content := ". ", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 6, 1, 4 ], mathmode := "Text", name := "P", next := 219994, root := ~, start := 219990, stop := 219993 ), rec( content := "\n \n\ The directions and multiplicities of any edges in ", count := [ 5, 6, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 1, 4 ], mathmode := "Text", name := "A", next := 220068, root := ~, start := 220054, stop := 220067 ), rec( content := " are\n \ ignored when considering whether or not ", count := [ 5, 6, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 1, 4 ], mathmode := "Text", name := "A", next := 220131, root := ~, start := 220117, stop := 220130 ), rec( content := " is plan\ ar. ", count := [ 5, 6, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 6, 1, 5 ], mathmode := "Text", name := "P", next := 220147, root := ~, start := 220143, stop := 220146 ), rec( content := "\n\n \ See also ", count := [ 5, 6, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsPlana\ rDigraph" ), content := 0, count := [ 5, 6, 1, 5 ], mathmode := "Text", name := "Ref", next := 220191, root := ~, start := 220162, stop := 220190 ), rec( content := "\n an\ d ", count := [ 5, 6, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Subdigr\ aphHomeomorphicToK33" ), content := 0, count := [ 5, 6, 1, 5 ], mathmode := "Text", name := "Ref", next := 220241, root := ~, start := 220200, stop := 220240 ), rec( content := ".\n " , count := [ 5, 6, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 6, 1, 6 ], mathmode := "Text", name := "P", next := 220251, root := ~, start := 220247, stop := 220250 ), rec( content := "\n \n\ This method uses the reference implementation in\n ", count := [ 5, 6, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "edge-addition-planarity-suite" ), content := [ rec( content := \ "https://github.com/graph-algorithms/edge-addition-planarity-suite", count := [ \ 5, 6, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 1, 6 ], mathmode := \ "Text", name := "URL", next := 140, root := ~, start := 17, stop := 139 ) ], count := [ 5, 6, 1, 6 ], name := "Alt", next := 146, root := ~, start := 1, stop := 145 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "edge-addition-planarity-suite", count \ := [ 5, 6, 1, 6 ], name := "PCDATA", root := ~ ) ], count := [ 5, 6, 1, 6 ], name := "Pac\ kage", next := 218, root := ~, start := 170, stop := 217 ) ], count := [ 5, 6, 1, 6 ], mathmode := "Text", name := "Alt", next := 224, root := ~, start := 146, stop := 223 ), rec( content := " by John\ Boyer of the algorithms described\n in ", count := [ 5, 6, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "BM06" ), content := 0, count := [ 5, 6, 1, 6 ], mathmode := "Text", name := "Cite", next := 220413, root := ~, start := 220395, stop := 220412 ), rec( content := ".\n\n", count := [ 5, 6, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], \n> [1, 7, 11], [4\ , 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n\ngap> KuratowskiPlanarSubdigraph(D);\nfail\ngap> D := Digra\ ph([[2, 4, 7, 9, 10], [1, 3, 4, 6, 9, 10], [6, 10], \n> [2, 5, 8, 9], [1, 2, 3\ , 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10], \n> [3, 4, 5, 6, 9, 10], [3, 4, 5, 7, \ 9], [2, 3, 5, 6, 7, 8], [3, 5]]);\n\ngap> IsPlanarDigraph(D);\nfalse\ngap> KuratowskiPlanarSubdigraph(D);\n[ [\ 2, 9, 7 ], [ 3 ], [ 6 ], [ 5, 9 ], [ 6 ], [ ], [ 4 ], \n [ 7, 9, 3 ], [ ],\ [ ] ]\ngap> D := Digraph(IsMutableDigraph, [[3, 5, 10], [8, 9, 10], [1, 4],\ \n> [3, 6], [1, 7, 11], [4, 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n\ngap> KuratowskiPlanarSubdigraph(D)\ ;\nfail\ngap> D := Digraph(IsMutableDigraph, [[2, 4, 7, 9, 10],\n> [1, 3, 4, 6\ , 9, 10], [6, 10], [2, 5, 8, 9],\n> [1, 2, 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9,\ 10],\n> [3, 4, 5, 6, 9, 10], [3, 4, 5, 7, 9], [2, 3, 5, 6, 7, 8], [3, 5]]);\n\ \ngap> IsPlanarDigraph(D);\nfalse\ \ngap> KuratowskiPlanarSubdigraph(D);\n[ [ 2, 9, 7 ], [ 3 ], [ 6 ], [ 5, 9 ], \ [ 6 ], [ ], [ 4 ], \n [ 7, 9, 3 ], [ ], [ ] ]\n", count := [ 5, 6, 1, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 6, 1, 7 ], mathmode := "Text", name := "Example", next := 221715, root := ~, start := 220416, stop := 221714 ), rec( content := "\n ", count := [ 5, 6, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "Description", next := 221732, root := ~, start := 219418, stop := 221731 ) ], count := [ 5, 6, 1, 1 ], mathmode := "Text", name := "ManSection", next := 221746, root := ~, start := 219301, stop := 221745 ), rec( content := "\n\n ", count := [ 5, 6, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "KuratowskiOuter\ PlanarSubdigraph" ), content := 0, count := [ 5, 6, 2, 2 ], mathmode := "Text", name := "Attr", next := 221827, root := ~, start := 221767, stop := 221826 ), rec( attributes := rec( ), content := [ rec( content := "A list or\ ", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "K", next := 221860, root := ~, start := 221849, stop := 221859 ), rec( content := ".", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "Returns", next := 221871, root := ~, start := 221830, stop := 221870 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "K\ uratowskiOuterPlanarSubdigraph", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "C", next := 221930, root := ~, start := 221892, stop := 221929 ), rec( content := " returns\ the immutable list of\n immutable lists of out-neighbours of a (not necess\ arily induced)\n subdigraph of the digraph ", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "A", next := 222074, root := ~, start := 222060, stop := 222073 ), rec( content := " that wi\ tnesses the fact\n that ", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "A", next := 222122, root := ~, start := 222108, stop := 222121 ), rec( content := " is not \ outer planar, or ", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "K", next := 222158, root := ~, start := 222147, stop := 222157 ), rec( content := " if\n \ ", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "A", next := 222180, root := ~, start := 222166, stop := 222179 ), rec( content := " is oute\ r planar. In other words,\n ", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "K\ uratowskiOuterPlanarSubdigraph", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "C", next := 222257, root := ~, start := 222219, stop := 222256 ), rec( content := " returns\ the out-neighbours of a\n subdigraph of ", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "A", next := 222322, root := ~, start := 222308, stop := 222321 ), rec( content := " that is\ homeomorphic to the complete graph\n with ", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "4\ ", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "C", next := 222383, root := ~, start := 222375, stop := 222382 ), rec( content := " vertice\ s, or to the complete bipartite graph with vertex sets\n of sizes ", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "2\ ", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "C", next := 222467, root := ~, start := 222459, stop := 222466 ), rec( content := " and ", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "3\ ", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "C", next := 222480, root := ~, start := 222472, stop := 222479 ), rec( content := ". ", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 6, 2, 4 ], mathmode := "Text", name := "P", next := 222486, root := ~, start := 222482, stop := 222485 ), rec( content := "\n \n\ The directions and multiplicities of any edges in ", count := [ 5, 6, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 2, 4 ], mathmode := "Text", name := "A", next := 222560, root := ~, start := 222546, stop := 222559 ), rec( content := " are\n \ ignored when considering whether or not ", count := [ 5, 6, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 2, 4 ], mathmode := "Text", name := "A", next := 222623, root := ~, start := 222609, stop := 222622 ), rec( content := " is oute\ r planar. \n ", count := [ 5, 6, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 6, 2, 5 ], mathmode := "Text", name := "P", next := 222650, root := ~, start := 222646, stop := 222649 ), rec( content := "\n\n \ See also \n ", count := [ 5, 6, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsOuter\ PlanarDigraph" ), content := 0, count := [ 5, 6, 2, 5 ], mathmode := "Text", name := "Ref", next := 222704, root := ~, start := 222670, stop := 222703 ), rec( content := ",\n " , count := [ 5, 6, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Subdigr\ aphHomeomorphicToK4" ), content := 0, count := [ 5, 6, 2, 5 ], mathmode := "Text", name := "Ref", next := 222750, root := ~, start := 222710, stop := 222749 ), rec( content := ", and \n\ ", count := [ 5, 6, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Subdigr\ aphHomeomorphicToK23" ), content := 0, count := [ 5, 6, 2, 5 ], mathmode := "Text", name := "Ref", next := 222802, root := ~, start := 222761, stop := 222801 ), rec( content := ".\n " , count := [ 5, 6, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 6, 2, 6 ], mathmode := "Text", name := "P", next := 222812, root := ~, start := 222808, stop := 222811 ), rec( content := "\n\n \ This method uses the reference implementation in\n ", count := [ 5, 6, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "edge-addition-planarity-suite" ), content := [ rec( content := \ "https://github.com/graph-algorithms/edge-addition-planarity-suite", count := [ \ 5, 6, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 2, 6 ], mathmode := \ "Text", name := "URL", next := 140, root := ~, start := 17, stop := 139 ) ], count := [ 5, 6, 2, 6 ], name := "Alt", next := 146, root := ~, start := 1, stop := 145 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "edge-addition-planarity-suite", count \ := [ 5, 6, 2, 6 ], name := "PCDATA", root := ~ ) ], count := [ 5, 6, 2, 6 ], name := "Pac\ kage", next := 218, root := ~, start := 170, stop := 217 ) ], count := [ 5, 6, 2, 6 ], mathmode := "Text", name := "Alt", next := 224, root := ~, start := 146, stop := 223 ), rec( content := " by John\ Boyer of the algorithms described\n in ", count := [ 5, 6, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "BM06" ), content := 0, count := [ 5, 6, 2, 6 ], mathmode := "Text", name := "Cite", next := 222970, root := ~, start := 222952, stop := 222969 ), rec( content := ".\n\n", count := [ 5, 6, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], \n> [1, 7, 11], [4\ , 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n\ngap> KuratowskiOuterPlanarSubdigraph(D);\n[ [ 3, 5, 10 ], \ [ 9, 8, 10 ], [ 4 ], [ 6 ], [ 11 ], [ 7 ], [ 8 ], \n [ ], [ 11 ], [ ], [ ]\ ]\ngap> D := Digraph([[2, 4, 7, 9, 10], [1, 3, 4, 6, 9, 10], [6, 10], \n> [2,\ 5, 8, 9], [1, 2, 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10], \n> [3, 4, 5, 6, 9,\ 10], [3, 4, 5, 7, 9], [2, 3, 5, 6, 7, 8], [3, 5]]);\n\ngap> IsOuterPlanarDigraph(D);\nfalse\ngap> KuratowskiO\ uterPlanarSubdigraph(D);\n[ [ ], [ ], [ ], [ 8, 9 ], [ ], [ ], [ 9, 4 ], \ [ 7, 9 ], [ ], \n [ ] ]\ngap> D := Digraph(IsMutableDigraph, [[3, 5, 10], [\ 8, 9, 10], [1, 4],\n> [3, 6], [1, 7, 11], [4, 7], [6, 8], [2, 7], [2, 11], [1,\ 2], [5, 9]]);\n\ngap> KuratowskiO\ uterPlanarSubdigraph(D);\n[ [ 3, 5, 10 ], [ 9, 8, 10 ], [ 4 ], [ 6 ], [ 11 ], \ [ 7 ], [ 8 ], \n [ ], [ 11 ], [ ], [ ] ]\ngap> D := Digraph(IsMutableDigra\ ph, [[2, 4, 7, 9, 10],\n> [1, 3, 4, 6, 9, 10], [6, 10], [2, 5, 8, 9],\n> [1, 2\ , 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10],\n> [3, 4, 5, 6, 9, 10], [3, 4, 5, 7\ , 9], [2, 3, 5, 6, 7, 8], [3, 5]]);\n\ngap> IsOuterPlanarDigraph(D);\nfalse\ngap> KuratowskiOuterPlanarSubdigrap\ h(D);\n[ [ ], [ ], [ ], [ 8, 9 ], [ ], [ ], [ 9, 4 ], [ 7, 9 ], [ ], \n \ [ ] ]", count := [ 5, 6, 2, 7 ], name := "PCDATA", root := ~ ) ], count := [ 5, 6, 2, 7 ], mathmode := "Text", name := "Example", next := 224463, root := ~, start := 222973, stop := 224462 ), rec( content := "\n ", count := [ 5, 6, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "Description", next := 224480, root := ~, start := 221874, stop := 224479 ) ], count := [ 5, 6, 2, 1 ], mathmode := "Text", name := "ManSection", next := 224494, root := ~, start := 221752, stop := 224493 ), rec( content := "\n\n ", count := [ 5, 6, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "PlanarEmbedding\ " ), content := 0, count := [ 5, 6, 3, 2 ], mathmode := "Text", name := "Attr", next := 224559, root := ~, start := 224515, stop := 224558 ), rec( attributes := rec( ), content := [ rec( content := "A list or\ ", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "K", next := 224592, root := ~, start := 224581, stop := 224591 ), rec( content := ".", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "Returns", next := 224603, root := ~, start := 224562, stop := 224602 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "A", next := 224641, root := ~, start := 224627, stop := 224640 ), rec( content := " is a pl\ anar digraph, then \n ", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "P\ lanarEmbedding", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "C", next := 224695, root := ~, start := 224673, stop := 224694 ), rec( content := " returns\ the immutable list of lists of\n out-neighbours of a subdigraph of ", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "A", next := 224787, root := ~, start := 224773, stop := 224786 ), rec( content := " such th\ at each vertex's\n neighbours are given in clockwise order. If ", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "A", next := 224874, root := ~, start := 224860, stop := 224873 ), rec( content := " is not \ planar,\n then ", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "K", next := 224910, root := ~, start := 224899, stop := 224909 ), rec( content := " is retu\ rned. ", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 6, 3, 4 ], mathmode := "Text", name := "P", next := 224928, root := ~, start := 224924, stop := 224927 ), rec( content := "\n \n\ The directions and multiplicities of any edges in ", count := [ 5, 6, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 3, 4 ], mathmode := "Text", name := "A", next := 225002, root := ~, start := 224988, stop := 225001 ), rec( content := " are\n \ ignored by ", count := [ 5, 6, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "P\ lanarEmbedding", count := [ 5, 6, 3, 4 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 5, 6, 3, 4 ], mathmode := "Text", name := "C", next := 225044, root := ~, start := 225022, stop := 225043 ), rec( content := ".\n " , count := [ 5, 6, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 6, 3, 5 ], mathmode := "Text", name := "P", next := 225054, root := ~, start := 225050, stop := 225053 ), rec( content := "\n\n \ See also \n ", count := [ 5, 6, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsPlana\ rDigraph" ), content := 0, count := [ 5, 6, 3, 5 ], mathmode := "Text", name := "Ref", next := 225103, root := ~, start := 225074, stop := 225102 ), rec( content := ".\n " , count := [ 5, 6, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 6, 3, 6 ], mathmode := "Text", name := "P", next := 225113, root := ~, start := 225109, stop := 225112 ), rec( content := "\n\n \ This method uses the reference implementation in\n ", count := [ 5, 6, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "edge-addition-planarity-suite" ), content := [ rec( content := \ "https://github.com/graph-algorithms/edge-addition-planarity-suite", count := [ \ 5, 6, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 3, 6 ], mathmode := \ "Text", name := "URL", next := 140, root := ~, start := 17, stop := 139 ) ], count := [ 5, 6, 3, 6 ], name := "Alt", next := 146, root := ~, start := 1, stop := 145 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "edge-addition-planarity-suite", count \ := [ 5, 6, 3, 6 ], name := "PCDATA", root := ~ ) ], count := [ 5, 6, 3, 6 ], name := "Pac\ kage", next := 218, root := ~, start := 170, stop := 217 ) ], count := [ 5, 6, 3, 6 ], mathmode := "Text", name := "Alt", next := 224, root := ~, start := 146, stop := 223 ), rec( content := " by John\ Boyer of the algorithms described\n in ", count := [ 5, 6, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "BM06" ), content := 0, count := [ 5, 6, 3, 6 ], mathmode := "Text", name := "Cite", next := 225271, root := ~, start := 225253, stop := 225270 ), rec( content := ".\n\n", count := [ 5, 6, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], \n> [1, 7, 11], [4\ , 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n\ngap> PlanarEmbedding(D);\n[ [ 3, 10, 5 ], [ 10, 8, 9 ], [ \ 4 ], [ 6 ], [ 11, 7 ], [ 7 ], [ 8 ], \n [ ], [ 11 ], [ ], [ ] ]\ngap> D :=\ Digraph([[2, 4, 7, 9, 10], [1, 3, 4, 6, 9, 10], [6, 10], \n> [2, 5, 8, 9], [1\ , 2, 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10], \n> [3, 4, 5, 6, 9, 10], [3, 4, \ 5, 7, 9], [2, 3, 5, 6, 7, 8], [3, 5]]);\n\ngap> PlanarEmbedding(D);\nfail\ngap> D := Digraph(IsMutableDigraph,\ [[3, 5, 10], [8, 9, 10], [1, 4],\n> [3, 6], [1, 7, 11], [4, 7], [6, 8], [2, 7\ ], [2, 11], [1, 2], [5, 9]]);\n\ng\ ap> PlanarEmbedding(D);\n[ [ 3, 10, 5 ], [ 10, 8, 9 ], [ 4 ], [ 6 ], [ 11, 7 ]\ , [ 7 ], [ 8 ], \n [ ], [ 11 ], [ ], [ ] ]\ngap> D := Digraph(IsMutableDig\ raph, [[2, 4, 7, 9, 10],\n> [1, 3, 4, 6, 9, 10], [6, 10], [2, 5, 8, 9],\n> [1,\ 2, 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10],\n> [3, 4, 5, 6, 9, 10], [3, 4, 5,\ 7, 9], [2, 3, 5, 6, 7, 8], [3, 5]]);\n\ngap> PlanarEmbedding(D);\nfail\n", count := [ 5, 6, 3, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 6, 3, 7 ], mathmode := "Text", name := "Example", next := 226489, root := ~, start := 225274, stop := 226488 ), rec( content := "\n ", count := [ 5, 6, 3, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "Description", next := 226506, root := ~, start := 224606, stop := 226505 ) ], count := [ 5, 6, 3, 1 ], mathmode := "Text", name := "ManSection", next := 226520, root := ~, start := 224500, stop := 226519 ), rec( content := "\n\n ", count := [ 5, 6, 3, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "OuterPlanarEmbe\ dding" ), content := 0, count := [ 5, 6, 4, 2 ], mathmode := "Text", name := "Attr", next := 226590, root := ~, start := 226541, stop := 226589 ), rec( attributes := rec( ), content := [ rec( content := "A list or\ ", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "K", next := 226623, root := ~, start := 226612, stop := 226622 ), rec( content := ".", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "Returns", next := 226634, root := ~, start := 226593, stop := 226633 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "A", next := 226672, root := ~, start := 226658, stop := 226671 ), rec( content := " is an o\ uter planar digraph, then\n ", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ uterPlanarEmbedding", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "C", next := 226737, root := ~, start := 226710, stop := 226736 ), rec( content := " returns\ the immutable list of lists\n of out-neighbours of a subdigraph of ", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "A", next := 226829, root := ~, start := 226815, stop := 226828 ), rec( content := " such th\ at each\n vertex's neighbours are given in clockwise order. If ", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "A", next := 226916, root := ~, start := 226902, stop := 226915 ), rec( content := " is not\\ n outer planar, then ", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "K", next := 226958, root := ~, start := 226947, stop := 226957 ), rec( content := " is retu\ rned. ", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 6, 4, 4 ], mathmode := "Text", name := "P", next := 226976, root := ~, start := 226972, stop := 226975 ), rec( content := "\n \n\ The directions and multiplicities of any edges in ", count := [ 5, 6, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 4, 4 ], mathmode := "Text", name := "A", next := 227050, root := ~, start := 227036, stop := 227049 ), rec( content := " are\n \ ignored by ", count := [ 5, 6, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ uterPlanarEmbedding", count := [ 5, 6, 4, 4 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 5, 6, 4, 4 ], mathmode := "Text", name := "C", next := 227097, root := ~, start := 227070, stop := 227096 ), rec( content := ".\n " , count := [ 5, 6, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 6, 4, 5 ], mathmode := "Text", name := "P", next := 227107, root := ~, start := 227103, stop := 227106 ), rec( content := "\n\n \ See also ", count := [ 5, 6, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsOuter\ PlanarDigraph" ), content := 0, count := [ 5, 6, 4, 5 ], mathmode := "Text", name := "Ref", next := 227156, root := ~, start := 227122, stop := 227155 ), rec( content := ".\n " , count := [ 5, 6, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 6, 4, 6 ], mathmode := "Text", name := "P", next := 227166, root := ~, start := 227162, stop := 227165 ), rec( content := "\n\n \ This method uses the reference implementation in\n ", count := [ 5, 6, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "edge-addition-planarity-suite" ), content := [ rec( content := \ "https://github.com/graph-algorithms/edge-addition-planarity-suite", count := [ \ 5, 6, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 4, 6 ], mathmode := \ "Text", name := "URL", next := 140, root := ~, start := 17, stop := 139 ) ], count := [ 5, 6, 4, 6 ], name := "Alt", next := 146, root := ~, start := 1, stop := 145 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "edge-addition-planarity-suite", count \ := [ 5, 6, 4, 6 ], name := "PCDATA", root := ~ ) ], count := [ 5, 6, 4, 6 ], name := "Pac\ kage", next := 218, root := ~, start := 170, stop := 217 ) ], count := [ 5, 6, 4, 6 ], mathmode := "Text", name := "Alt", next := 224, root := ~, start := 146, stop := 223 ), rec( content := " by John\ Boyer of the algorithms described\n in ", count := [ 5, 6, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "BM06" ), content := 0, count := [ 5, 6, 4, 6 ], mathmode := "Text", name := "Cite", next := 227324, root := ~, start := 227306, stop := 227323 ), rec( content := ".\n\n", count := [ 5, 6, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], \n> [1, 7, 11], [4\ , 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n\ngap> OuterPlanarEmbedding(D);\nfail\ngap> D := Digraph([[2\ , 4, 7, 9, 10], [1, 3, 4, 6, 9, 10], [6, 10], \n> [2, 5, 8, 9], [1, 2, 3, 4, 6\ , 7, 9, 10], [3, 4, 5, 7, 9, 10], \n> [3, 4, 5, 6, 9, 10], [3, 4, 5, 7, 9], [2\ , 3, 5, 6, 7, 8], [3, 5]]);\n\ng\ ap> OuterPlanarEmbedding(D);\nfail\ngap> OuterPlanarEmbedding(CompleteBipartit\ eDigraph(2, 2));\n[ [ 3, 4 ], [ 4, 3 ], [ ], [ ] ]\ngap> D := Digraph(IsMuta\ bleDigraph, [[3, 5, 10], [8, 9, 10], [1, 4],\n> [3, 6], [1, 7, 11], [4, 7], [6\ , 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n\ngap> OuterPlanarEmbedding(D);\nfail\ngap> D := Digraph(IsMutableDigr\ aph, [[2, 4, 7, 9, 10],\n> [1, 3, 4, 6, 9, 10], [6, 10], [2, 5, 8, 9],\n> [1, \ 2, 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10],\n> [3, 4, 5, 6, 9, 10], [3, 4, 5, \ 7, 9], [2, 3, 5, 6, 7, 8], [3, 5]]);\n\ngap> OuterPlanarEmbedding(D);\nfail\ngap> OuterPlanarEmbedding(CompleteB\ ipartiteDigraph(2, 2));\n[ [ 3, 4 ], [ 4, 3 ], [ ], [ ] ]\n", count := [ 5, 6, 4, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 6, 4, 7 ], mathmode := "Text", name := "Example", next := 228562, root := ~, start := 227327, stop := 228561 ), rec( content := "\n ", count := [ 5, 6, 4, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "Description", next := 228579, root := ~, start := 226637, stop := 228578 ) ], count := [ 5, 6, 4, 1 ], mathmode := "Text", name := "ManSection", next := 228593, root := ~, start := 226526, stop := 228592 ), rec( content := "\n\n ", count := [ 5, 6, 4, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "SubdigraphHomeo\ morphicToK23" ), content := 0, count := [ 5, 6, 5, 2 ], mathmode := "Text", name := "Attr", next := 228670, root := ~, start := 228614, stop := 228669 ), rec( attributes := rec( Arg := "digraph", Name := "SubdigraphHomeo\ morphicToK33" ), content := 0, count := [ 5, 6, 5, 4 ], mathmode := "Text", name := "Attr", next := 228729, root := ~, start := 228673, stop := 228728 ), rec( attributes := rec( Arg := "digraph", Name := "SubdigraphHomeo\ morphicToK4" ), content := 0, count := [ 5, 6, 5, 6 ], mathmode := "Text", name := "Attr", next := 228787, root := ~, start := 228732, stop := 228786 ), rec( attributes := rec( ), content := [ rec( content := "A list or\ ", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "K", next := 228820, root := ~, start := 228809, stop := 228819 ), rec( content := ".", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "Returns", next := 228831, root := ~, start := 228790, stop := 228830 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ se attributes return the immutable list of lists of\n out-neighbours of a s\ ubdigraph of the digraph ", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "A", next := 228971, root := ~, start := 228957, stop := 228970 ), rec( content := " which i\ s\n homeomorphic to one of the following:\n the complete bipartite graph\ with vertex sets of sizes ", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "2\ ", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "C", next := 229090, root := ~, start := 229082, stop := 229089 ), rec( content := " and\n \ ", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "3\ ", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "C", next := 229107, root := ~, start := 229099, stop := 229106 ), rec( content := "; the co\ mplete bipartite graph with vertex sets of sizes ", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "3\ ", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "C", next := 229172, root := ~, start := 229164, stop := 229171 ), rec( content := "\n an\ d ", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "3\ ", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "C", next := 229189, root := ~, start := 229181, stop := 229188 ), rec( content := "; or the\ complete graph with ", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "4\ ", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "C", next := 229226, root := ~, start := 229218, stop := 229225 ), rec( content := " vertice\ s. If\n ", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "A", next := 229258, root := ~, start := 229244, stop := 229257 ), rec( content := " has no \ such subdigraphs, then ", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "K", next := 229300, root := ~, start := 229289, stop := 229299 ), rec( content := " is retu\ rned. \n ", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 6, 5, 8 ], mathmode := "Text", name := "P", next := 229323, root := ~, start := 229319, stop := 229322 ), rec( content := "\n\n \ See also ", count := [ 5, 6, 5, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsPlana\ rDigraph" ), content := 0, count := [ 5, 6, 5, 8 ], mathmode := "Text", name := "Ref", next := 229367, root := ~, start := 229338, stop := 229366 ), rec( content := " and ", count := [ 5, 6, 5, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsOuter\ PlanarDigraph" ), content := 0, count := [ 5, 6, 5, 8 ], mathmode := "Text", name := "Ref", next := 229412, root := ~, start := 229372, stop := 229411 ), rec( content := " for mor\ e details.", count := [ 5, 6, 5, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 5, 6, 5, 9 ], mathmode := "Text", name := "P", next := 229434, root := ~, start := 229430, stop := 229433 ), rec( content := "\n\n \ This method uses the reference implementation in\n ", count := [ 5, 6, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "edge-addition-planarity-suite" ), content := [ rec( content := \ "https://github.com/graph-algorithms/edge-addition-planarity-suite", count := [ \ 5, 6, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 5, 9 ], mathmode := \ "Text", name := "URL", next := 140, root := ~, start := 17, stop := 139 ) ], count := [ 5, 6, 5, 9 ], name := "Alt", next := 146, root := ~, start := 1, stop := 145 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "edge-addition-planarity-suite", count \ := [ 5, 6, 5, 9 ], name := "PCDATA", root := ~ ) ], count := [ 5, 6, 5, 9 ], name := "Pac\ kage", next := 218, root := ~, start := 170, stop := 217 ) ], count := [ 5, 6, 5, 9 ], mathmode := "Text", name := "Alt", next := 224, root := ~, start := 146, stop := 223 ), rec( content := " by John\ Boyer of the algorithms described\n in ", count := [ 5, 6, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "BM06" ), content := 0, count := [ 5, 6, 5, 9 ], mathmode := "Text", name := "Cite", next := 229592, root := ~, start := 229574, stop := 229591 ), rec( content := ".\n\n", count := [ 5, 6, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], [1, 7, 11], \n> [4\ , 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n\ngap> SubdigraphHomeomorphicToK4(D);\n[ [ 3, 5, 10 ], [ 9, \ 8, 10 ], [ 4 ], [ 6 ], [ 7, 11 ], [ 7 ], [ 8 ], \n [ ], [ 11 ], [ ], [ ] ]\ \ngap> SubdigraphHomeomorphicToK23(D);\n[ [ 3, 5, 10 ], [ 9, 8, 10 ], [ 4 ], [\ 6 ], [ 11 ], [ 7 ], [ 8 ], \n [ ], [ 11 ], [ ], [ ] ]\ngap> D := Digraph(\ [[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], [1, 11], \n> [4, 7], [6, 8], [2, 7],\ [2, 11], [1, 2], [5, 9]]);\n\ng\ ap> SubdigraphHomeomorphicToK4(D);\nfail\ngap> SubdigraphHomeomorphicToK23(D);\ \n[ [ 3, 10, 5 ], [ 10, 8, 9 ], [ 4 ], [ 6 ], [ 11 ], [ 7 ], [ 8 ], \n [ ], \ [ 11 ], [ ], [ ] ]\ngap> SubdigraphHomeomorphicToK33(D);\nfail\ngap> Subdigr\ aphHomeomorphicToK23(NullDigraph(0));\nfail\ngap> SubdigraphHomeomorphicToK33(\ CompleteDigraph(5));\nfail\ngap> SubdigraphHomeomorphicToK33(CompleteBipartite\ Digraph(3, 3));\n[ [ 4, 6, 5 ], [ 4, 5, 6 ], [ 6, 5, 4 ], [ ], [ ], [ ] ]\n\ gap> SubdigraphHomeomorphicToK4(CompleteDigraph(3));\nfail\ngap> D := Digraph(\ IsMutableDigraph, [[3, 5, 10], [8, 9, 10], [1, 4],\n> [3, 6], [1, 7, 11], [4, \ 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n\ngap> SubdigraphHomeomorphicToK4(D);\n[ [ 3, 5, 10 ], [ 9, 8, 1\ 0 ], [ 4 ], [ 6 ], [ 7, 11 ], [ 7 ], [ 8 ], \n [ ], [ 11 ], [ ], [ ] ]\nga\ p> SubdigraphHomeomorphicToK23(D);\n[ [ 3, 5, 10 ], [ 9, 8, 10 ], [ 4 ], [ 6 ]\ , [ 11 ], [ 7 ], [ 8 ], \n [ ], [ 11 ], [ ], [ ] ]\ngap> D := Digraph(IsMu\ tableDigraph, [[3, 5, 10], [8, 9, 10], [1, 4],\n> [3, 6], [1, 11], [4, 7], [6,\ 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n\ngap> SubdigraphHomeomorphicToK4(D);\nfail\ngap> SubdigraphHomeomorphi\ cToK23(D);\n[ [ 3, 10, 5 ], [ 10, 8, 9 ], [ 4 ], [ 6 ], [ 11 ], [ 7 ], [ 8 ], \ \n [ ], [ 11 ], [ ], [ ] ]\ngap> SubdigraphHomeomorphicToK33(D);\nfail\nga\ p> SubdigraphHomeomorphicToK23(NullDigraph(0));\nfail\ngap> SubdigraphHomeomor\ phicToK33(CompleteDigraph(5));\nfail\ngap> SubdigraphHomeomorphicToK33(Complet\ eBipartiteDigraph(3, 3));\n[ [ 4, 6, 5 ], [ 4, 5, 6 ], [ 6, 5, 4 ], [ ], [ ]\ , [ ] ]\ngap> SubdigraphHomeomorphicToK4(CompleteDigraph(3));\nfail\n", count := [ 5, 6, 5, 10 ], name := "PCD\ ATA", root := ~ ) ], count := [ 5, 6, 5, 10 ], mathmode := "Text", name := "Example", next := 231904, root := ~, start := 229595, stop := 231903 ), rec( content := "\n ", count := [ 5, 6, 5, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "Description", next := 231921, root := ~, start := 228834, stop := 231920 ) ], count := [ 5, 6, 5, 1 ], mathmode := "Text", name := "ManSection", next := 231935, root := ~, start := 228599, stop := 231934 ), rec( content := "\n\n ", count := [ 5, 6, 5, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 6, 0, 1 ], mathmode := "Text", name := "Section", next := 231949, root := ~, start := 219259, stop := 231948 ) , rec( content := "\n\n", count := [ 5, 6, 5, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 0, 0, 1 ], mathmode := "Text", name := "Chapter", next := 231961, root := ~, start := 131997, stop := 231960 ), rec( content := "\n ", count := [ 5, 6, 5, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := " attributes, operations ", count := [ 5, 6, 5, 11 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n ", count := [ 5, 6, 5, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "Properties of digraphs" ), content := [ rec( attributes := rec( ), content := [ rec( content := "Properties of digraphs", count := [ 6, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 0, 0, 2 ], mathmode := "Text", name := "Heading", next := 232078, root := ~, start := 232037, stop := 232077 ) , rec( content := "\n\n ", count := [ 6, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Edge properties", count := [ 6, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 0, 2 ], mathmode := "Text", name := "Heading", next := 232125, root := ~, start := 232091, stop := 232124 ), rec( content := "\n ", count := [ 6, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphHasLoops\ " ), content := 0, count := [ 6, 1, 1, 2 ], mathmode := "Text", name := "Prop", next := 232189, root := ~, start := 232145, stop := 232188 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "K", next := 232212, root := ~, start := 232201, stop := 232211 ), rec( content := " or ", count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "K", next := 232228, root := ~, start := 232216, stop := 232227 ), rec( content := ".", count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "Returns", next := 232239, root := ~, start := 232192, stop := 232238 ), rec( attributes := rec( ), content := [ rec( content := "\n Ret\ urns ", count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "K", next := 232279, root := ~, start := 232268, stop := 232278 ), rec( content := " if the \ digraph ", count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "A", next := 232309, root := ~, start := 232295, stop := 232308 ), rec( content := " has loo\ ps, and\n ", count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "K", next := 232341, root := ~, start := 232329, stop := 232340 ), rec( content := " if it d\ oes not. A loop is an edge with equal source and range.\n ", count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 1, 4 ], mathmode := "Text", name := "P", next := 232413, root := ~, start := 232409, stop := 232412 ), rec( content := "\n \ \n If the argument ", count := [ 6, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 1, 4 ], mathmode := "Text", name := "A", next := 232455, root := ~, start := 232441, stop := 232454 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n", count := [ 6, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 2], [2]]);\n\ngap> DigraphEdges(D);\n[ [ 1, 1 ], [ 1, 2 ], [ 2, 2 ] ]\ngap> DigraphHasLo\ ops(D);\ntrue\ngap> D := Digraph([[2, 3], [1], [2]]);\n\ngap> DigraphEdges(D);\n[ [ 1, 2 ], [ 1, 3 ], [ 2, 1 ], \ [ 3, 2 ] ]\ngap> DigraphHasLoops(D);\nfalse\ngap> D := CompleteDigraph(IsMutab\ leDigraph, 4);\n\ngap> DigraphHasLo\ ops(D);\nfalse", count := [ 6, 1, 1, 5 ], name := "PCDATA", root := ~ ) ], count := [ 6, 1, 1, 5 ], mathmode := "Text", name := "Example", next := 233050, root := ~, start := 232552, stop := 233049 ), rec( content := "\n ", count := [ 6, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "Description", next := 233067, root := ~, start := 232242, stop := 233066 ) ], count := [ 6, 1, 1, 1 ], mathmode := "Text", name := "ManSection", next := 233081, root := ~, start := 232130, stop := 233080 ), rec( content := "\n\n ", count := [ 6, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsAntiSymmetric\ Digraph" ), content := 0, count := [ 6, 1, 2, 2 ], mathmode := "Text", name := "Prop", next := 233153, root := ~, start := 233102, stop := 233152 ), rec( attributes := rec( Arg := "digraph", Name := "IsAntisymmetric\ Digraph" ), content := 0, count := [ 6, 1, 2, 4 ], mathmode := "Text", name := "Prop", next := 233207, root := ~, start := 233156, stop := 233206 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "K", next := 233230, root := ~, start := 233219, stop := 233229 ), rec( content := " or ", count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "K", next := 233246, root := ~, start := 233234, stop := 233245 ), rec( content := ".", count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "Returns", next := 233257, root := ~, start := 233210, stop := 233256 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s property is ", count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "K", next := 233306, root := ~, start := 233295, stop := 233305 ), rec( content := " if the \ digraph ", count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "A", next := 233336, root := ~, start := 233322, stop := 233335 ), rec( content := "\n is\ antisymmetric, and ", count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "K", next := 233375, root := ~, start := 233363, stop := 233374 ), rec( content := " if it i\ s not.\n ", count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "P", next := 233398, root := ~, start := 233394, stop := 233397 ), rec( content := "\n\n \ A digraph is ", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "a\ ntisymmetric", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "E", next := 233437, root := ~, start := 233417, stop := 233436 ), rec( content := " if when\ ever there is an edge with source\n ", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "C", next := 233491, root := ~, start := 233483, stop := 233490 ), rec( content := " and ran\ ge ", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "C", next := 233510, root := ~, start := 233502, stop := 233509 ), rec( content := ", and an\ edge with source ", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "C", next := 233544, root := ~, start := 233536, stop := 233543 ), rec( content := " and ran\ ge\n ", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "C", next := 233567, root := ~, start := 233559, stop := 233566 ), rec( content := ", then t\ he vertices ", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "C", next := 233595, root := ~, start := 233587, stop := 233594 ), rec( content := " and ", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "C", next := 233608, root := ~, start := 233600, stop := 233607 ), rec( content := " are equ\ al.\n ", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 2, 7 ], mathmode := "Text", name := "P", next := 233628, root := ~, start := 233624, stop := 233627 ), rec( content := "\n \ \n If the argument ", count := [ 6, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 2, 7 ], mathmode := "Text", name := "A", next := 233670, root := ~, start := 233656, stop := 233669 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n ", count := [ 6, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr1 := Digraph([[2], [1, 3], [2, 3]]);\n\ngap> IsAntisymmetricDigraph(gr1);\nfalse\ngap> DigraphEdges(gr1)\ {[1, 2]};\n[ [ 1, 2 ], [ 2, 1 ] ]\ngap> gr2 := Digraph([[1, 2], [3, 3], [1]]);\ \n\ngap> IsAntisymmetricDigra\ ph(gr2);\ntrue\ngap> DigraphEdges(gr2);\n[ [ 1, 1 ], [ 1, 2 ], [ 2, 3 ], [ 2, \ 3 ], [ 3, 1 ] ]\n", count := [ 6, 1, 2, 8 ], name := "PCDATA", root := ~ ) ], count := [ 6, 1, 2, 8 ], mathmode := "Text", name := "Example", next := 234197, root := ~, start := 233771, stop := 234196 ), rec( content := "\n ", count := [ 6, 1, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "Description", next := 234214, root := ~, start := 233260, stop := 234213 ) ], count := [ 6, 1, 2, 1 ], mathmode := "Text", name := "ManSection", next := 234228, root := ~, start := 233087, stop := 234227 ), rec( content := "\n\n ", count := [ 6, 1, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsBipartiteDigr\ aph" ), content := 0, count := [ 6, 1, 3, 2 ], mathmode := "Text", name := "Prop", next := 234296, root := ~, start := 234249, stop := 234295 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "K", next := 234319, root := ~, start := 234308, stop := 234318 ), rec( content := " or ", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "K", next := 234335, root := ~, start := 234323, stop := 234334 ), rec( content := ".", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "Returns", next := 234346, root := ~, start := 234299, stop := 234345 ), rec( attributes := rec( ), content := [ rec( content := "\n This \ property is ", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "K", next := 234393, root := ~, start := 234382, stop := 234392 ), rec( content := " if the \ digraph ", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "A", next := 234423, root := ~, start := 234409, stop := 234422 ), rec( content := " is bipa\ rtite, and\n ", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "K", next := 234456, root := ~, start := 234444, stop := 234455 ), rec( content := " if it i\ s not. A digraph is bipartite if and only if the\n vertices of ", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "A", next := 234542, root := ~, start := 234528, stop := 234541 ), rec( content := " can be \ partitioned into two non-empty sets such\n that the source and range of any e\ dge of ", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "A", next := 234648, root := ~, start := 234634, stop := 234647 ), rec( content := " lie in \ distinct sets.\n Equivalently, a digraph is bipartite if and only if it is 2-\ colorable; see\n ", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ GreedyColouring", Label := "for a digraph" ), content := 0, count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "Ref", next := 234808, root := ~, start := 234750, stop := 234807 ), rec( content := ". ", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 3, 4 ], mathmode := "Text", name := "P", next := 234814, root := ~, start := 234810, stop := 234813 ), rec( content := "\n\n Se\ e also ", count := [ 6, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Bicomponents" ), content := 0, count := [ 6, 1, 3, 4 ], mathmode := "Text", name := "Ref", next := 234860, root := ~, start := 234827, stop := 234859 ), rec( content := ".\n " , count := [ 6, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 3, 5 ], mathmode := "Text", name := "P", next := 234870, root := ~, start := 234866, stop := 234869 ), rec( content := "\n \ \n If the argument ", count := [ 6, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 3, 5 ], mathmode := "Text", name := "A", next := 234912, root := ~, start := 234898, stop := 234911 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n ", count := [ 6, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := ChainDigraph(4);\n\ngap> I\ sBipartiteDigraph(D);\ntrue\ngap> D := CycleDigraph(3);\n\ngap> IsBipartiteDigraph(D);\nfalse\ngap> D := CompleteBi\ partiteDigraph(IsMutableDigraph, 5, 4);\n\ngap> IsBipartiteDigraph(D);\ntrue", count := [ 6, 1, 3, 6 ], name := "PCD\ ATA", root := ~ ) ], count := [ 6, 1, 3, 6 ], mathmode := "Text", name := "Example", next := 235385, root := ~, start := 235012, stop := 235384 ), rec( content := "\n ", count := [ 6, 1, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "Description", next := 235402, root := ~, start := 234349, stop := 235401 ) ], count := [ 6, 1, 3, 1 ], mathmode := "Text", name := "ManSection", next := 235416, root := ~, start := 234234, stop := 235415 ), rec( content := "\n\n ", count := [ 6, 1, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsCompleteBipar\ titeDigraph" ), content := 0, count := [ 6, 1, 4, 2 ], mathmode := "Text", name := "Prop", next := 235492, root := ~, start := 235437, stop := 235491 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "K", next := 235515, root := ~, start := 235504, stop := 235514 ), rec( content := " or ", count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "K", next := 235531, root := ~, start := 235519, stop := 235530 ), rec( content := ".", count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "Returns", next := 235542, root := ~, start := 235495, stop := 235541 ), rec( attributes := rec( ), content := [ rec( content := "\n Ret\ urns ", count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "K", next := 235582, root := ~, start := 235571, stop := 235581 ), rec( content := " if the \ digraph ", count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "A", next := 235612, root := ~, start := 235598, stop := 235611 ), rec( content := " is a co\ mplete bipartite\n digraph, and ", count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "K", next := 235666, root := ~, start := 235654, stop := 235665 ), rec( content := " if it i\ s not. ", count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "P", next := 235685, root := ~, start := 235681, stop := 235684 ), rec( content := "\n\n \ A digraph is a ", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ omplete bipartite digraph", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "E", next := 235739, root := ~, start := 235706, stop := 235738 ), rec( content := " if it i\ s bipartite, see\n ", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsBipar\ titeDigraph" ), content := 0, count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "Ref", next := 235800, root := ~, start := 235768, stop := 235799 ), rec( content := ", and th\ ere exists a unique edge with\n source ", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "C", next := 235857, root := ~, start := 235849, stop := 235856 ), rec( content := " and ran\ ge ", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "C", next := 235876, root := ~, start := 235868, stop := 235875 ), rec( content := " if and \ only if ", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "C", next := 235900, root := ~, start := 235892, stop := 235899 ), rec( content := " and ", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "C", next := 235913, root := ~, start := 235905, stop := 235912 ), rec( content := " lie\n \ in different bicomponents of ", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "A", next := 235965, root := ~, start := 235951, stop := 235964 ), rec( content := ", see ", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Bicomponents" ), content := 0, count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "Ref", next := 236010, root := ~, start := 235971, stop := 236009 ), rec( content := ". ", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 4, 5 ], mathmode := "Text", name := "P", next := 236016, root := ~, start := 236012, stop := 236015 ), rec( content := "\n\n \ Equivalently, a bipartite digraph with bicomponents of size ", count := [ 6, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 6, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 4, 5 ], mathmode := "Text", name := "M", next := 236090, root := ~, start := 236082, stop := 236089 ), rec( content := " and\n \ ", count := [ 6, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 6, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 4, 5 ], mathmode := "Text", name := "M", next := 236107, root := ~, start := 236099, stop := 236106 ), rec( content := " is comp\ lete precisely when it has ", count := [ 6, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "2\ mn", count := [ 6, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 4, 5 ], mathmode := "Text", name := "M", next := 236152, root := ~, start := 236142, stop := 236151 ), rec( content := " edges, \ none of which\n are multiple edges. ", count := [ 6, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 4, 6 ], mathmode := "Text", name := "P", next := 236202, root := ~, start := 236198, stop := 236201 ), rec( content := "\n\n \ See also ", count := [ 6, 1, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Complet\ eBipartiteDigraph" ), content := 0, count := [ 6, 1, 4, 6 ], mathmode := "Text", name := "Ref", next := 236255, root := ~, start := 236217, stop := 236254 ), rec( content := ".\n " , count := [ 6, 1, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 4, 7 ], mathmode := "Text", name := "P", next := 236265, root := ~, start := 236261, stop := 236264 ), rec( content := "\n \ \n If the argument ", count := [ 6, 1, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 4, 7 ], mathmode := "Text", name := "A", next := 236307, root := ~, start := 236293, stop := 236306 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n ", count := [ 6, 1, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CycleDigraph(2);\n\ngap> I\ sCompleteBipartiteDigraph(D);\ntrue\ngap> D := CycleDigraph(4);\n\ngap> IsBipartiteDigraph(D);\ntrue\ngap> IsComple\ teBipartiteDigraph(D);\nfalse\ngap> D := CompleteBipartiteDigraph(IsMutableDig\ raph, 5, 4);\n\ngap> IsCompleteBipa\ rtiteDigraph(D);\ntrue", count := [ 6, 1, 4, 8 ], name := "PCDATA", root := ~ ) ], count := [ 6, 1, 4, 8 ], mathmode := "Text", name := "Example", next := 236838, root := ~, start := 236408, stop := 236837 ), rec( content := "\n ", count := [ 6, 1, 4, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "Description", next := 236855, root := ~, start := 235545, stop := 236854 ) ], count := [ 6, 1, 4, 1 ], mathmode := "Text", name := "ManSection", next := 236869, root := ~, start := 235422, stop := 236868 ), rec( content := "\n\n ", count := [ 6, 1, 4, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsCompleteDigra\ ph" ), content := 0, count := [ 6, 1, 5, 2 ], mathmode := "Text", name := "Prop", next := 236936, root := ~, start := 236890, stop := 236935 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "K", next := 236959, root := ~, start := 236948, stop := 236958 ), rec( content := " or ", count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "K", next := 236975, root := ~, start := 236963, stop := 236974 ), rec( content := ".", count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "Returns", next := 236986, root := ~, start := 236939, stop := 236985 ), rec( attributes := rec( ), content := [ rec( content := "\n Ret\ urns ", count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "K", next := 237026, root := ~, start := 237015, stop := 237025 ), rec( content := " if the \ digraph ", count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "A", next := 237056, root := ~, start := 237042, stop := 237055 ), rec( content := " is comp\ lete, and\n ", count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "K", next := 237090, root := ~, start := 237078, stop := 237089 ), rec( content := " if it i\ s not. ", count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "P", next := 237109, root := ~, start := 237105, stop := 237108 ), rec( content := "\n\n \ A digraph is ", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ omplete", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "E", next := 237143, root := ~, start := 237128, stop := 237142 ), rec( content := " if it h\ as no loops, and for all\n ", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ istinct", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "E", next := 237195, root := ~, start := 237180, stop := 237194 ), rec( content := " vertice\ s ", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "C", next := 237213, root := ~, start := 237205, stop := 237212 ), rec( content := " and ", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "C", next := 237226, root := ~, start := 237218, stop := 237225 ), rec( content := ",\n t\ here is exactly one edge with source ", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "C", next := 237278, root := ~, start := 237270, stop := 237277 ), rec( content := " and ran\ ge ", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "C", next := 237297, root := ~, start := 237289, stop := 237296 ), rec( content := ".\n\n \ Equivalently, a digraph with ", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "M", next := 237341, root := ~, start := 237333, stop := 237340 ), rec( content := " vertice\ s is complete precisely when\n it has ", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ (n - 1)", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "M", next := 237404, root := ~, start := 237389, stop := 237403 ), rec( content := " edges, \ no loops, and no multiple edges.\n ", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 5, 5 ], mathmode := "Text", name := "P", next := 237453, root := ~, start := 237449, stop := 237452 ), rec( content := "\n \ \n If the argument ", count := [ 6, 1, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 5, 5 ], mathmode := "Text", name := "A", next := 237495, root := ~, start := 237481, stop := 237494 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n ", count := [ 6, 1, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[2, 3], [1, 3], [1, 2]]);\n\ngap> IsCompleteDigraph(D);\ntrue\ngap> D := Digraph([[2, 2], [1\ ]]);\n\ngap> IsCompleteDigrap\ h(D);\nfalse\ngap> D := CompleteBipartiteDigraph(IsMutableDigraph, 5, 4);\n\ngap> IsCompleteDigraph(D);\nfalse", count := [ 6, 1, 5, 6 ], name := "PCD\ ATA", root := ~ ) ], count := [ 6, 1, 5, 6 ], mathmode := "Text", name := "Example", next := 238003, root := ~, start := 237596, stop := 238002 ), rec( content := "\n ", count := [ 6, 1, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "Description", next := 238020, root := ~, start := 236989, stop := 238019 ) ], count := [ 6, 1, 5, 1 ], mathmode := "Text", name := "ManSection", next := 238034, root := ~, start := 236875, stop := 238033 ), rec( content := "\n\n ", count := [ 6, 1, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsCompleteMulti\ partiteDigraph" ), content := 0, count := [ 6, 1, 6, 2 ], mathmode := "Text", name := "Prop", next := 238113, root := ~, start := 238055, stop := 238112 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "K", next := 238136, root := ~, start := 238125, stop := 238135 ), rec( content := " or ", count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "K", next := 238152, root := ~, start := 238140, stop := 238151 ), rec( content := ".", count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "Returns", next := 238163, root := ~, start := 238116, stop := 238162 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s property returns ", count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "K", next := 238217, root := ~, start := 238206, stop := 238216 ), rec( content := " if ", count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "A", next := 238235, root := ~, start := 238221, stop := 238234 ), rec( content := " is a co\ mplete\n multipartite digraph, and ", count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "K", next := 238292, root := ~, start := 238280, stop := 238291 ), rec( content := " if not.\ ", count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := 0, count := [ 6, 1, 6, 4 ], mathmode := "Text", name := "P", next := 238305, root := ~, start := 238301, stop := 238304 ), rec( content := "\n\n \ A digraph is a ", count := [ 6, 1, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ omplete multipartite digraph", count := [ 6, 1, 6, 4 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 6, 1, 6, 4 ], mathmode := "Text", name := "E", next := 238362, root := ~, start := 238326, stop := 238361 ), rec( content := " if and \ only if\n its vertices can be partitioned into at least two maximal indepen\ dent sets,\n where every possible edge between these independent sets occur\ s in the\n digraph exactly once.\n ", count := [ 6, 1, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 6, 5 ], mathmode := "Text", name := "P", next := 238567, root := ~, start := 238563, stop := 238566 ), rec( content := "\n \ \n If the argument ", count := [ 6, 1, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 6, 5 ], mathmode := "Text", name := "A", next := 238609, root := ~, start := 238595, stop := 238608 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n ", count := [ 6, 1, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CompleteMultipartiteDigraph([2, 4, 6]);\n\ngap> IsCompleteMultipartiteDigraph\ (D);\ntrue\ngap> D := CompleteBipartiteDigraph(IsMutableDigraph, 5, 4);\n\ngap> IsCompleteMultipartiteDigraph(D);\ \ntrue", count := [ 6, 1, 6, 6 ], name := "PCDATA", root := ~ ) ], count := [ 6, 1, 6, 6 ], mathmode := "Text", name := "Example", next := 239052, root := ~, start := 238710, stop := 239051 ), rec( content := "\n ", count := [ 6, 1, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "Description", next := 239069, root := ~, start := 238166, stop := 239068 ) ], count := [ 6, 1, 6, 1 ], mathmode := "Text", name := "ManSection", next := 239083, root := ~, start := 238040, stop := 239082 ), rec( content := "\n\n ", count := [ 6, 1, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsEmptyDigraph"\ ), content := 0, count := [ 6, 1, 7, 2 ], mathmode := "Text", name := "Prop", next := 239147, root := ~, start := 239104, stop := 239146 ), rec( attributes := rec( Arg := "digraph", Name := "IsNullDigraph" ), content := 0, count := [ 6, 1, 7, 4 ], mathmode := "Text", name := "Prop", next := 239192, root := ~, start := 239150, stop := 239191 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "K", next := 239215, root := ~, start := 239204, stop := 239214 ), rec( content := " or ", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "K", next := 239231, root := ~, start := 239219, stop := 239230 ), rec( content := ".", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "Returns", next := 239242, root := ~, start := 239195, stop := 239241 ), rec( attributes := rec( ), content := [ rec( content := "\n Ret\ urns ", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "K", next := 239282, root := ~, start := 239271, stop := 239281 ), rec( content := " if the \ digraph ", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "A", next := 239312, root := ~, start := 239298, stop := 239311 ), rec( content := " is empt\ y, and\n ", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "K", next := 239343, root := ~, start := 239331, stop := 239342 ), rec( content := " if it i\ s not. A digraph is ", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ mpty", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "E", next := 239383, root := ~, start := 239371, stop := 239382 ), rec( content := " if it h\ as no\n edges.", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 7, 6 ], mathmode := "Text", name := "P", next := 239411, root := ~, start := 239407, stop := 239410 ), rec( content := "\n\n \ ", count := [ 6, 1, 7, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sNullDigraph", count := [ 6, 1, 7, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 7, 6 ], mathmode := "Text", name := "C", next := 239437, root := ~, start := 239417, stop := 239436 ), rec( content := " is a sy\ nonym for ", count := [ 6, 1, 7, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sEmptyDigraph", count := [ 6, 1, 7, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 7, 6 ], mathmode := "Text", name := "C", next := 239476, root := ~, start := 239455, stop := 239475 ), rec( content := ".\n " , count := [ 6, 1, 7, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 7, 7 ], mathmode := "Text", name := "P", next := 239486, root := ~, start := 239482, stop := 239485 ), rec( content := "\n \ \n If the argument ", count := [ 6, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 7, 7 ], mathmode := "Text", name := "A", next := 239528, root := ~, start := 239514, stop := 239527 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n ", count := [ 6, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[], []]);\n\ngap>\ IsEmptyDigraph(D);\ntrue\ngap> IsNullDigraph(D);\ntrue\ngap> D := Digraph([[]\ , [1]]);\n\ngap> IsEmptyDigraph(D);\ \nfalse\ngap> IsNullDigraph(D);\nfalse", count := [ 6, 1, 7, 8 ], name := "PCD\ ATA", root := ~ ) ], count := [ 6, 1, 7, 8 ], mathmode := "Text", name := "Example", next := 239921, root := ~, start := 239629, stop := 239920 ), rec( content := "\n ", count := [ 6, 1, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "Description", next := 239938, root := ~, start := 239245, stop := 239937 ) ], count := [ 6, 1, 7, 1 ], mathmode := "Text", name := "ManSection", next := 239952, root := ~, start := 239089, stop := 239951 ), rec( content := "\n\n ", count := [ 6, 1, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsEquivalenceDi\ graph" ), content := 0, count := [ 6, 1, 8, 2 ], mathmode := "Text", name := "Prop", next := 240022, root := ~, start := 239973, stop := 240021 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "K", next := 240045, root := ~, start := 240034, stop := 240044 ), rec( content := " or ", count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "K", next := 240061, root := ~, start := 240049, stop := 240060 ), rec( content := ".", count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "Returns", next := 240072, root := ~, start := 240025, stop := 240071 ), rec( attributes := rec( ), content := [ rec( content := "\n A d\ igraph is an equivalence digraph if and only if the digraph satisifies\n al\ l of ", count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsRefle\ xiveDigraph" ), content := 0, count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "Ref", next := 240210, root := ~, start := 240178, stop := 240209 ), rec( content := ",\n " , count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsSymme\ tricDigraph" ), content := 0, count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "Ref", next := 240248, root := ~, start := 240216, stop := 240247 ), rec( content := " and ", count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsTrans\ itiveDigraph" ), content := 0, count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "Ref", next := 240286, root := ~, start := 240253, stop := 240285 ), rec( content := ".\n A\ partial order ", count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "A", next := 240322, root := ~, start := 240308, stop := 240321 ), rec( content := " corresp\ onds to an equivalence relation.\n ", count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 8, 4 ], mathmode := "Text", name := "P", next := 240371, root := ~, start := 240367, stop := 240370 ), rec( content := "\n \ \n If the argument ", count := [ 6, 1, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 8, 4 ], mathmode := "Text", name := "A", next := 240413, root := ~, start := 240399, stop := 240412 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n", count := [ 6, 1, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 3], [2], [1, 3]]);\n\ngap> IsEquivalenceDigraph(D);\ntrue\n", count := [ 6, 1, 8, 5 ], name := "PCD\ ATA", root := ~ ) ], count := [ 6, 1, 8, 5 ], mathmode := "Text", name := "Example", next := 240664, root := ~, start := 240510, stop := 240663 ), rec( content := "\n ", count := [ 6, 1, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "Description", next := 240681, root := ~, start := 240075, stop := 240680 ) ], count := [ 6, 1, 8, 1 ], mathmode := "Text", name := "ManSection", next := 240695, root := ~, start := 239958, stop := 240694 ), rec( content := "\n\n ", count := [ 6, 1, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsFunctionalDig\ raph" ), content := 0, count := [ 6, 1, 9, 2 ], mathmode := "Text", name := "Prop", next := 240764, root := ~, start := 240716, stop := 240763 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "K", next := 240787, root := ~, start := 240776, stop := 240786 ), rec( content := " or ", count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "K", next := 240803, root := ~, start := 240791, stop := 240802 ), rec( content := ".", count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "Returns", next := 240814, root := ~, start := 240767, stop := 240813 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s property is ", count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "K", next := 240863, root := ~, start := 240852, stop := 240862 ), rec( content := " if the \ digraph ", count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "A", next := 240893, root := ~, start := 240879, stop := 240892 ), rec( content := " is\n \ functional. ", count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 9, 4 ], mathmode := "Text", name := "P", next := 240917, root := ~, start := 240913, stop := 240916 ), rec( content := "\n\n \ A digraph is ", count := [ 6, 1, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ unctional", count := [ 6, 1, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 9, 4 ], mathmode := "Text", name := "E", next := 240953, root := ~, start := 240936, stop := 240952 ), rec( content := " if ever\ y vertex is the source of a\n unique edge.\n ", count := [ 6, 1, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 9, 5 ], mathmode := "Text", name := "P", next := 241014, root := ~, start := 241010, stop := 241013 ), rec( content := "\n \ \n If the argument ", count := [ 6, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 9, 5 ], mathmode := "Text", name := "A", next := 241056, root := ~, start := 241042, stop := 241055 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n ", count := [ 6, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr1 := Digraph([[3], [2], [2], [1], [6], [5]]);\n\ngap> IsFunctionalDigraph(gr1);\ntrue\ngap> gr2 := Digra\ ph([[1, 2], [1]]);\n\ngap> IsFunct\ ionalDigraph(gr2);\nfalse\ngap> gr3 := Digraph(3, [1, 2, 3], [2, 3, 1]);\n\ngap> IsFunctionalDigraph(gr3);\ntrue\ \n", count := [ 6, 1, 9, 6 ], name := "PCDATA", root := ~ ) ], count := [ 6, 1, 9, 6 ], mathmode := "Text", name := "Example", next := 241567, root := ~, start := 241156, stop := 241566 ), rec( content := "\n ", count := [ 6, 1, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "Description", next := 241584, root := ~, start := 240817, stop := 241583 ) ], count := [ 6, 1, 9, 1 ], mathmode := "Text", name := "ManSection", next := 241598, root := ~, start := 240701, stop := 241597 ), rec( content := "\n\n ", count := [ 6, 1, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsMultiDigraph"\ ), content := 0, count := [ 6, 1, 10, 2 ], mathmode := "Text", name := "Prop", next := 241662, root := ~, start := 241619, stop := 241661 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 10, 3 ], mathmode := "Text", name := "K", next := 241685, root := ~, start := 241674, stop := 241684 ), rec( content := " or ", count := [ 6, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 10, 3 ], mathmode := "Text", name := "K", next := 241701, root := ~, start := 241689, stop := 241700 ), rec( content := ".", count := [ 6, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 10, 3 ], mathmode := "Text", name := "Returns", next := 241712, root := ~, start := 241665, stop := 241711 ), rec( attributes := rec( ), content := [ rec( content := "\n A " , count := [ 6, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ultidigraph", count := [ 6, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 10, 3 ], mathmode := "Text", name := "E", next := 241754, root := ~, start := 241735, stop := 241753 ), rec( content := " is one \ that has at least two\n edges with equal source and range.", count := [ 6, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 10, 4 ], mathmode := "Text", name := "P", next := 241826, root := ~, start := 241822, stop := 241825 ), rec( content := "\n\n \ If the argument ", count := [ 6, 1, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 10, 4 ], mathmode := "Text", name := "A", next := 241862, root := ~, start := 241848, stop := 241861 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n ", count := [ 6, 1, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([\"a\", \"b\", \"c\"], [\"a\", \"b\", \"b\"], [\"b\", \"c\"\ , \"a\"]);\n\ngap> IsMultiDigraph(\ D);\nfalse\ngap> D := DigraphFromDigraph6String(\"&Bug\");\n\ngap> IsDuplicateFree(DigraphEdges(D));\ntrue\ngap>\ IsMultiDigraph(D);\nfalse\ngap> D := Digraph([[1, 2, 3, 2], [2, 1], [3]]);\n<\ immutable multidigraph with 3 vertices, 7 edges>\ngap> IsDuplicateFree(Digraph\ Edges(D));\nfalse\ngap> IsMultiDigraph(D);\ntrue\ngap> D := DigraphMutableCopy\ (D); \n\ngap> IsMultiDigraph(D)\ ;\ntrue", count := [ 6, 1, 10, 5 ], name := "PCDATA", root := ~ ) ], count := [ 6, 1, 10, 5 ], mathmode := "Text", name := "Example", next := 242586, root := ~, start := 241963, stop := 242585 ), rec( content := "\n ", count := [ 6, 1, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 10, 3 ], mathmode := "Text", name := "Description", next := 242603, root := ~, start := 241715, stop := 242602 ) ], count := [ 6, 1, 10, 1 ], mathmode := "Text", name := "ManSection", next := 242617, root := ~, start := 241604, stop := 242616 ), rec( content := "\n\n ", count := [ 6, 1, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsReflexiveDigr\ aph" ), content := 0, count := [ 6, 1, 11, 2 ], mathmode := "Text", name := "Prop", next := 242685, root := ~, start := 242638, stop := 242684 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "K", next := 242708, root := ~, start := 242697, stop := 242707 ), rec( content := " or ", count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "K", next := 242724, root := ~, start := 242712, stop := 242723 ), rec( content := ".", count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "Returns", next := 242735, root := ~, start := 242688, stop := 242734 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s property is ", count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "K", next := 242784, root := ~, start := 242773, stop := 242783 ), rec( content := " if the \ digraph ", count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "A", next := 242814, root := ~, start := 242800, stop := 242813 ), rec( content := " is\n \ reflexive, and ", count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "K", next := 242849, root := ~, start := 242837, stop := 242848 ), rec( content := " if it i\ s not.\n A digraph is ", count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "r\ eflexive", count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "E", next := 242897, root := ~, start := 242881, stop := 242896 ), rec( content := " if it h\ as a loop at every vertex. ", count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 11, 4 ], mathmode := "Text", name := "P", next := 242936, root := ~, start := 242932, stop := 242935 ), rec( content := "\n ", count := [ 6, 1, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 11, 5 ], mathmode := "Text", name := "P", next := 242945, root := ~, start := 242941, stop := 242944 ), rec( content := "\n \ \n If the argument ", count := [ 6, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 11, 5 ], mathmode := "Text", name := "A", next := 242987, root := ~, start := 242973, stop := 242986 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n ", count := [ 6, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 2], [2]]);\n\ngap> IsReflexiveDigraph(D);\ntrue\ngap> D := Digraph([[3, 1], [4, 2], [3],\ [2, 1]]);\n\ngap> IsReflexiveDigr\ aph(D);\nfalse\n", count := [ 6, 1, 11, 6 ], name := "PCDATA", root := ~ ) ], count := [ 6, 1, 11, 6 ], mathmode := "Text", name := "Example", next := 243360, root := ~, start := 243087, stop := 243359 ), rec( content := "\n ", count := [ 6, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "Description", next := 243377, root := ~, start := 242738, stop := 243376 ) ], count := [ 6, 1, 11, 1 ], mathmode := "Text", name := "ManSection", next := 243391, root := ~, start := 242623, stop := 243390 ), rec( content := "\n\n ", count := [ 6, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsSymmetricDigr\ aph" ), content := 0, count := [ 6, 1, 12, 2 ], mathmode := "Text", name := "Prop", next := 243459, root := ~, start := 243412, stop := 243458 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "K", next := 243482, root := ~, start := 243471, stop := 243481 ), rec( content := " or ", count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "K", next := 243498, root := ~, start := 243486, stop := 243497 ), rec( content := ".", count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "Returns", next := 243509, root := ~, start := 243462, stop := 243508 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s property is ", count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "K", next := 243558, root := ~, start := 243547, stop := 243557 ), rec( content := " if the \ digraph ", count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "A", next := 243588, root := ~, start := 243574, stop := 243587 ), rec( content := "\n is\ symmetric, and ", count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "K", next := 243623, root := ~, start := 243611, stop := 243622 ), rec( content := " if it i\ s not.", count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "P", next := 243641, root := ~, start := 243637, stop := 243640 ), rec( content := "\n\n \ A ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ymmetric digraph", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "E", next := 243673, root := ~, start := 243649, stop := 243672 ), rec( content := " is one \ where for each non-loop edge, having\n source ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "C", next := 243737, root := ~, start := 243729, stop := 243736 ), rec( content := " and ran\ ge ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "C", next := 243756, root := ~, start := 243748, stop := 243755 ), rec( content := ", there \ is a corresponding edge with\n source ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "C", next := 243812, root := ~, start := 243804, stop := 243811 ), rec( content := " and ran\ ge ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "C", next := 243831, root := ~, start := 243823, stop := 243830 ), rec( content := ". If th\ ere are ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "C", next := 243855, root := ~, start := 243847, stop := 243854 ), rec( content := " edges w\ ith\n source ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "C", next := 243886, root := ~, start := 243878, stop := 243885 ), rec( content := " and ran\ ge ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "C", next := 243905, root := ~, start := 243897, stop := 243904 ), rec( content := ", then t\ here must be precisely ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "C", next := 243944, root := ~, start := 243936, stop := 243943 ), rec( content := "\n ed\ ges with source ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "C", next := 243975, root := ~, start := 243967, stop := 243974 ), rec( content := " and ran\ ge ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "C", next := 243994, root := ~, start := 243986, stop := 243993 ), rec( content := ". In ot\ her words, a symmetric\n digraph has a symmetric adjacency matrix ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Adjacen\ cyMatrix" ), content := 0, count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "Ref", next := 244099, root := ~, start := 244070, stop := 244098 ), rec( content := ".\n " , count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 12, 5 ], mathmode := "Text", name := "P", next := 244109, root := ~, start := 244105, stop := 244108 ), rec( content := "\n \ \n If the argument ", count := [ 6, 1, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 12, 5 ], mathmode := "Text", name := "A", next := 244151, root := ~, start := 244137, stop := 244150 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n ", count := [ 6, 1, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr1 := Digraph([[2], [1, 3], [2, 3]]);\n\ngap> IsSymmetricDigraph(gr1);\ntrue\ngap> adj1 := AdjacencyMatri\ x(gr1);;\ngap> Display(adj1);\n[ [ 0, 1, 0 ],\n [ 1, 0, 1 ],\n [ 0, \ 1, 1 ] ]\ngap> adj1 = TransposedMat(adj1);\ntrue\ngap> gr1 = DigraphReverse(g\ r1);\ntrue\ngap> gr2 := Digraph([[2, 3], [1, 3], [2, 3]]);\n\ngap> IsSymmetricDigraph(gr2);\nfalse\ngap> adj2 :=\ AdjacencyMatrix(gr2);;\ngap> Display(adj2);\n[ [ 0, 1, 1 ],\n [ 1, 0, \ 1 ],\n [ 0, 1, 1 ] ]\ngap> adj2 = TransposedMat(adj2);\nfalse\n", count := [ 6, 1, 12, 6 ], name := "PCD\ ATA", root := ~ ) ], count := [ 6, 1, 12, 6 ], mathmode := "Text", name := "Example", next := 244871, root := ~, start := 244251, stop := 244870 ), rec( content := "\n ", count := [ 6, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "Description", next := 244888, root := ~, start := 243512, stop := 244887 ) ], count := [ 6, 1, 12, 1 ], mathmode := "Text", name := "ManSection", next := 244902, root := ~, start := 243397, stop := 244901 ), rec( content := "\n\n ", count := [ 6, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsTournament" ) , content := 0, count := [ 6, 1, 13, 2 ], mathmode := "Text", name := "Prop", next := 244964, root := ~, start := 244923, stop := 244963 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "K", next := 244987, root := ~, start := 244976, stop := 244986 ), rec( content := " or ", count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "K", next := 245003, root := ~, start := 244991, stop := 245002 ), rec( content := ".", count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "Returns", next := 245014, root := ~, start := 244967, stop := 245013 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s property is ", count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "K", next := 245063, root := ~, start := 245052, stop := 245062 ), rec( content := " if the \ digraph ", count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "A", next := 245093, root := ~, start := 245079, stop := 245092 ), rec( content := " is a to\ urnament,\n and ", count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "K", next := 245131, root := ~, start := 245119, stop := 245130 ), rec( content := " if it i\ s not. ", count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 13, 4 ], mathmode := "Text", name := "P", next := 245150, root := ~, start := 245146, stop := 245149 ), rec( content := "\n\n \ A tournament is an orientation of a complete (undirected) graph.\n Specific\ ally, a tournament is a digraph which has a unique directed edge\n (of some\ orientation) between any pair of distinct vertices, and no loops.\n ", count := [ 6, 1, 13, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 13, 5 ], mathmode := "Text", name := "P", next := 245385, root := ~, start := 245381, stop := 245384 ), rec( content := "\n \ \n If the argument ", count := [ 6, 1, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 13, 5 ], mathmode := "Text", name := "A", next := 245427, root := ~, start := 245413, stop := 245426 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n ", count := [ 6, 1, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[2, 3, 4], [3, 4], [4], []]);\n\ngap> IsTournament(D);\ntrue\ngap> D := Digraph([[2], [1], [\ 3]]);\n\ngap> IsTournament(D);\nfa\ lse\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n\ngap> IsTournament(D);\ntrue\ngap> DigraphRemoveEdge(D, 1, 2);\ \n\ngap> IsTournament(D);\nfalse\n", count := [ 6, 1, 13, 6 ], name := "PCD\ ATA", root := ~ ) ], count := [ 6, 1, 13, 6 ], mathmode := "Text", name := "Example", next := 246008, root := ~, start := 245527, stop := 246007 ), rec( content := "\n ", count := [ 6, 1, 13, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "Description", next := 246025, root := ~, start := 245017, stop := 246024 ) ], count := [ 6, 1, 13, 1 ], mathmode := "Text", name := "ManSection", next := 246039, root := ~, start := 244908, stop := 246038 ), rec( content := "\n\n ", count := [ 6, 1, 13, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsTransitiveDig\ raph" ), content := 0, count := [ 6, 1, 14, 2 ], mathmode := "Text", name := "Prop", next := 246108, root := ~, start := 246060, stop := 246107 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "K", next := 246131, root := ~, start := 246120, stop := 246130 ), rec( content := " or ", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "K", next := 246147, root := ~, start := 246135, stop := 246146 ), rec( content := ".", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "Returns", next := 246158, root := ~, start := 246111, stop := 246157 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s property is ", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "K", next := 246207, root := ~, start := 246196, stop := 246206 ), rec( content := " if the \ digraph ", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "A", next := 246237, root := ~, start := 246223, stop := 246236 ), rec( content := "\n is\ transitive, and ", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "K", next := 246273, root := ~, start := 246261, stop := 246272 ), rec( content := " if it i\ s not.\n\n A digraph is ", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ ransitive", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "E", next := 246323, root := ~, start := 246306, stop := 246322 ), rec( content := " if when\ ever ", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ i, j ]", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "C", next := 246351, root := ~, start := 246336, stop := 246350 ), rec( content := " and\n \ ", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ j, k ]", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "C", next := 246375, root := ~, start := 246360, stop := 246374 ), rec( content := " are edg\ es of the digraph, then ", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ i, k ]", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "C", next := 246422, root := ~, start := 246407, stop := 246421 ), rec( content := " is also\ an\n edge of the digraph. ", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 14, 4 ], mathmode := "Text", name := "P", next := 246463, root := ~, start := 246459, stop := 246462 ), rec( content := "\n\n \ Let ", count := [ 6, 1, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 6, 1, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 14, 4 ], mathmode := "Text", name := "M", next := 246481, root := ~, start := 246473, stop := 246480 ), rec( content := " be the \ number of vertices of an arbitrary digraph, and let\n ", count := [ 6, 1, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 6, 1, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 14, 4 ], mathmode := "Text", name := "M", next := 246557, root := ~, start := 246549, stop := 246556 ), rec( content := " be the \ number of edges.\n For general digraphs, the methods used for this property\ use a version\n of the Floyd-Warshall algorithm, and have complexity ", count := [ 6, 1, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (n^3)", count := [ 6, 1, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 14, 4 ], mathmode := "Text", name := "M", next := 246727, root := ~, start := 246714, stop := 246726 ), rec( content := ".\n\n \ However for digraphs which are topologically sortable\n [", count := [ 6, 1, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ TopologicalSort" ), content := 0, count := [ 6, 1, 14, 4 ], mathmode := "Text", name := "Ref", next := 246829, root := ~, start := 246793, stop := 246828 ), rec( content := "], then \ methods with\n complexity ", count := [ 6, 1, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (m + n + m \\cdot n)", count := [ 6, 1, 14, 4 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 6, 1, 14, 4 ], mathmode := "Text", name := "M", next := 246892, root := ~, start := 246865, stop := 246891 ), rec( content := " will be\ used when appropriate.\n ", count := [ 6, 1, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 14, 5 ], mathmode := "Text", name := "P", next := 246932, root := ~, start := 246928, stop := 246931 ), rec( content := "\n \ \n If the argument ", count := [ 6, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 14, 5 ], mathmode := "Text", name := "A", next := 246974, root := ~, start := 246960, stop := 246973 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n ", count := [ 6, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 14, 6 ], mathmode := "Text", name := "P", next := 247078, root := ~, start := 247074, stop := 247077 ), rec( content := "\n ", count := [ 6, 1, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 2], [3], [3]]);\n\ngap> IsTransitiveDigraph(D);\nfalse\ngap> gr2 := Digraph([[1, 2, 3], \ [3], [3]]);\n\ngap> IsTransitiveDi\ graph(gr2);\ntrue\ngap> gr2 = DigraphTransitiveClosure(D);\ntrue\ngap> gr3 := \ Digraph([[1, 2, 2, 3], [3, 3], [3]]);\n\ngap> IsTransitiveDigraph(gr3);\ntrue\n", count := [ 6, 1, 14, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 6, 1, 14, 7 ], mathmode := "Text", name := "Example", next := 247540, root := ~, start := 247083, stop := 247539 ), rec( content := "\n ", count := [ 6, 1, 14, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "Description", next := 247557, root := ~, start := 246161, stop := 247556 ) ], count := [ 6, 1, 14, 1 ], mathmode := "Text", name := "ManSection", next := 247571, root := ~, start := 246045, stop := 247570 ), rec( content := "\n\n ", count := [ 6, 1, 14, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsPreorderDigra\ ph" ), content := 0, count := [ 6, 1, 15, 2 ], mathmode := "Text", name := "Prop", next := 247638, root := ~, start := 247592, stop := 247637 ), rec( attributes := rec( Arg := "digraph", Name := "IsQuasiorderDig\ raph" ), content := 0, count := [ 6, 1, 15, 4 ], mathmode := "Text", name := "Prop", next := 247689, root := ~, start := 247641, stop := 247688 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "K", next := 247712, root := ~, start := 247701, stop := 247711 ), rec( content := " or ", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "K", next := 247728, root := ~, start := 247716, stop := 247727 ), rec( content := ".", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "Returns", next := 247739, root := ~, start := 247692, stop := 247738 ), rec( attributes := rec( ), content := [ rec( content := "\n A d\ igraph is a preorder digraph if and only if the digraph satisifies both\n " , count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsRefle\ xiveDigraph" ), content := 0, count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "Ref", next := 247871, root := ~, start := 247839, stop := 247870 ), rec( content := " and ", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsTrans\ itiveDigraph" ), content := 0, count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "Ref", next := 247909, root := ~, start := 247876, stop := 247908 ), rec( content := ".\n A\ preorder digraph (or quasiorder digraph) ", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "A", next := 247972, root := ~, start := 247958, stop := 247971 ), rec( content := " corresp\ onds to\n the preorder relation ", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ \leq", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "M", next := 248025, root := ~, start := 248014, stop := 248024 ), rec( content := " defined\ by ", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ \\leq y", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "M", next := 248052, root := ~, start := 248037, stop := 248051 ), rec( content := " if and \ only\n if ", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ x, y]", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "C", next := 248085, root := ~, start := 248072, stop := 248084 ), rec( content := " is an e\ dge of ", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "A", next := 248114, root := ~, start := 248100, stop := 248113 ), rec( content := ".\n " , count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 15, 6 ], mathmode := "Text", name := "P", next := 248124, root := ~, start := 248120, stop := 248123 ), rec( content := "\n \ \n If the argument ", count := [ 6, 1, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 15, 6 ], mathmode := "Text", name := "A", next := 248166, root := ~, start := 248152, stop := 248165 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n", count := [ 6, 1, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1], [2, 3], [2, 3]]);\n\ngap> IsPreorderDigraph(D);\ntrue\ngap> D := Digraph([[1 .. 4], [1 \ .. 4], [1 .. 4], [1 .. 4]]);\n\ng\ ap> IsPreorderDigraph(D);\ntrue\ngap> D := Digraph([[2], [3], [4], [5], [1]]);\ \n\ngap> IsPreorderDigraph(D);\nfa\ lse\ngap> D := Digraph([[1], [1, 2], [2, 3]]);\n\ngap> IsQuasiorderDigraph(D);\nfalse\n", count := [ 6, 1, 15, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 6, 1, 15, 7 ], mathmode := "Text", name := "Example", next := 248799, root := ~, start := 248263, stop := 248798 ), rec( content := "\n ", count := [ 6, 1, 15, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "Description", next := 248816, root := ~, start := 247742, stop := 248815 ) ], count := [ 6, 1, 15, 1 ], mathmode := "Text", name := "ManSection", next := 248830, root := ~, start := 247577, stop := 248829 ), rec( content := "\n\n ", count := [ 6, 1, 15, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsPartialOrderD\ igraph" ), content := 0, count := [ 6, 1, 16, 2 ], mathmode := "Text", name := "Prop", next := 248901, root := ~, start := 248851, stop := 248900 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "K", next := 248924, root := ~, start := 248913, stop := 248923 ), rec( content := " or ", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "K", next := 248940, root := ~, start := 248928, stop := 248939 ), rec( content := ".", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "Returns", next := 248951, root := ~, start := 248904, stop := 248950 ), rec( attributes := rec( ), content := [ rec( content := "\n A d\ igraph is a partial order digraph if and only if the digraph satisifies\n a\ ll of ", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsRefle\ xiveDigraph" ), content := 0, count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "Ref", next := 249090, root := ~, start := 249058, stop := 249089 ), rec( content := ",\n " , count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsAntis\ ymmetricDigraph" ), content := 0, count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "Ref", next := 249132, root := ~, start := 249096, stop := 249131 ), rec( content := " and ", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsTrans\ itiveDigraph" ), content := 0, count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "Ref", next := 249170, root := ~, start := 249137, stop := 249169 ), rec( content := ".\n A\ partial order ", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "A", next := 249206, root := ~, start := 249192, stop := 249205 ), rec( content := " corresp\ onds\n to the partial order relation ", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ \leq", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "M", next := 249264, root := ~, start := 249253, stop := 249263 ), rec( content := " defined\ by ", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ \\leq y", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "M", next := 249291, root := ~, start := 249276, stop := 249290 ), rec( content := " if and\\ n only if ", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ x, y]", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "C", next := 249324, root := ~, start := 249311, stop := 249323 ), rec( content := " is an e\ dge of ", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "A", next := 249353, root := ~, start := 249339, stop := 249352 ), rec( content := ".\n " , count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 16, 4 ], mathmode := "Text", name := "P", next := 249363, root := ~, start := 249359, stop := 249362 ), rec( content := "\n \ \n If the argument ", count := [ 6, 1, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 16, 4 ], mathmode := "Text", name := "A", next := 249405, root := ~, start := 249391, stop := 249404 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n", count := [ 6, 1, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 3], [2, 3], [3]]);\n\ngap> IsPartialOrderDigraph(D);\ntrue\ngap> D := CycleDigraph(5);\n\ \ngap> IsPartialOrderDigraph(D);\nfal\ se\ngap> D := Digraph([[1, 1], [1, 1, 2], [3], [3, 3, 4, 4]]);\n\ngap> IsPartialOrderDigraph(D);\ntrue\n", count := [ 6, 1, 16, 5 ], name := "PCD\ ATA", root := ~ ) ], count := [ 6, 1, 16, 5 ], mathmode := "Text", name := "Example", next := 249909, root := ~, start := 249502, stop := 249908 ), rec( content := "\n ", count := [ 6, 1, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "Description", next := 249926, root := ~, start := 248954, stop := 249925 ) ], count := [ 6, 1, 16, 1 ], mathmode := "Text", name := "ManSection", next := 249940, root := ~, start := 248836, stop := 249939 ), rec( content := "\n\n ", count := [ 6, 1, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsMeetSemilatti\ ceDigraph" ), content := 0, count := [ 6, 1, 17, 2 ], mathmode := "Text", name := "Prop", next := 250014, root := ~, start := 249961, stop := 250013 ), rec( attributes := rec( Arg := "digraph", Name := "IsJoinSemilatti\ ceDigraph" ), content := 0, count := [ 6, 1, 17, 4 ], mathmode := "Text", name := "Prop", next := 250070, root := ~, start := 250017, stop := 250069 ), rec( attributes := rec( Arg := "digraph", Name := "IsLatticeDigrap\ h" ), content := 0, count := [ 6, 1, 17, 6 ], mathmode := "Text", name := "Prop", next := 250118, root := ~, start := 250073, stop := 250117 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "K", next := 250141, root := ~, start := 250130, stop := 250140 ), rec( content := " or ", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "K", next := 250157, root := ~, start := 250145, stop := 250156 ), rec( content := ".", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "Returns", next := 250168, root := ~, start := 250121, stop := 250167 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sMeetSemilatticeDigraph", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "C", next := 250220, root := ~, start := 250189, stop := 250219 ), rec( content := " returns\ ", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "K", next := 250240, root := ~, start := 250229, stop := 250239 ), rec( content := " if the \ digraph\n ", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "A", next := 250274, root := ~, start := 250260, stop := 250273 ), rec( content := " is a me\ et semilattice; ", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sJoinSemilatticeDigraph", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "C", next := 250329, root := ~, start := 250298, stop := 250328 ), rec( content := "\n re\ turns ", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "K", next := 250353, root := ~, start := 250342, stop := 250352 ), rec( content := " if the \ digraph ", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "A", next := 250383, root := ~, start := 250369, stop := 250382 ), rec( content := " is a jo\ in semilattice;\n and ", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sLatticeDigraph", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "C", next := 250439, root := ~, start := 250416, stop := 250438 ), rec( content := " returns\ ", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "K", next := 250459, root := ~, start := 250448, stop := 250458 ), rec( content := " if the \ digraph\n ", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "A", next := 250493, root := ~, start := 250479, stop := 250492 ), rec( content := " is both\ a meet and a join semilattice.\n ", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "P", next := 250541, root := ~, start := 250537, stop := 250540 ), rec( content := "\n\n \ For a partial order digraph ", count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsParti\ alOrderDigraph" ), content := 0, count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "Ref", next := 250610, root := ~, start := 250575, stop := 250609 ), rec( content := " the\n \ corresponding partial order is the relation ", count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ \leq", count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "M", next := 250674, root := ~, start := 250663, stop := 250673 ), rec( content := ", define\ d by\n ", count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ \\leq y", count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "M", next := 250706, root := ~, start := 250691, stop := 250705 ), rec( content := " if and \ only if ", count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ x, y]", count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "C", next := 250735, root := ~, start := 250722, stop := 250734 ), rec( content := " is an e\ dge.\n A digraph is a ", count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ eet semilattice", count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "E", next := 250790, root := ~, start := 250767, stop := 250789 ), rec( content := " if it i\ s a partial order and every\n pair of vertices has a greatest lower bound (\ meet) with respect to the\n aforementioned relation. A ", count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ oin semilattice", count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "E", next := 250955, root := ~, start := 250932, stop := 250954 ), rec( content := " is a pa\ rtial order where\n every pair of vertices has a least upper bound (join) w\ ith respect to\n the relation.\n ", count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 1, 17, 9 ], mathmode := "Text", name := "P", next := 251081, root := ~, start := 251077, stop := 251080 ), rec( content := "\n \ \n If the argument ", count := [ 6, 1, 17, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 1, 17, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 17, 9 ], mathmode := "Text", name := "A", next := 251123, root := ~, start := 251109, stop := 251122 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n ", count := [ 6, 1, 17, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 3], [2, 3], [3]]);\n\ngap> IsMeetSemilatticeDigraph(D);\nfalse\ngap> IsJoinSemilatticeDi\ graph(D);\ntrue\ngap> IsLatticeDigraph(D);\nfalse\ngap> D := Digraph([[1], [2]\ , [1 .. 3]]);\n\ngap> IsJoinSemila\ tticeDigraph(D);\nfalse\ngap> IsMeetSemilatticeDigraph(D);\ntrue\ngap> IsLatti\ ceDigraph(D);\nfalse\ngap> D := Digraph([[1 .. 4], [2, 4], [3, 4], [4]]);\n\ngap> IsMeetSemilatticeDigraph(D);\n\ true\ngap> IsJoinSemilatticeDigraph(D);\ntrue\ngap> IsLatticeDigraph(D);\ntrue\ \ngap> D := Digraph([[1, 1, 1], [1, 1, 2, 2],\n> [1, 3, 3], \ [1, 2, 3, 3, 4]]);\n\ngap> I\ sMeetSemilatticeDigraph(D);\ntrue\ngap> IsJoinSemilatticeDigraph(D);\ntrue\nga\ p> IsLatticeDigraph(D);\ntrue\n", count := [ 6, 1, 17, 10 ], name := "PCDATA", root := ~ ) ], count := [ 6, 1, 17, 10 ], mathmode := "Text", name := "Example", next := 252111, root := ~, start := 251224, stop := 252110 ), rec( content := "\n ", count := [ 6, 1, 17, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "Description", next := 252128, root := ~, start := 250171, stop := 252127 ) ], count := [ 6, 1, 17, 1 ], mathmode := "Text", name := "ManSection", next := 252142, root := ~, start := 249946, stop := 252141 ), rec( content := "\n\n ", count := [ 6, 1, 17, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 1, 0, 1 ], mathmode := "Text", name := "Section", next := 252156, root := ~, start := 232082, stop := 252155 ) , rec( content := "\n\n ", count := [ 6, 1, 17, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Regularity", count := [ 6, 2, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 0, 2 ], mathmode := "Text", name := "Heading", next := 252198, root := ~, start := 252169, stop := 252197 ), rec( content := "\n ", count := [ 6, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsInRegularDigr\ aph" ), content := 0, count := [ 6, 2, 1, 2 ], mathmode := "Text", name := "Prop", next := 252265, root := ~, start := 252218, stop := 252264 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "K", next := 252288, root := ~, start := 252277, stop := 252287 ), rec( content := " or ", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "K", next := 252304, root := ~, start := 252292, stop := 252303 ), rec( content := ".", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "Returns", next := 252315, root := ~, start := 252268, stop := 252314 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s property is ", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "K", next := 252364, root := ~, start := 252353, stop := 252363 ), rec( content := " if ther\ e is an integer ", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "C", next := 252396, root := ~, start := 252388, stop := 252395 ), rec( content := " such th\ at\n for every vertex ", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "C", next := 252436, root := ~, start := 252428, stop := 252435 ), rec( content := " of digr\ aph ", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "A", next := 252462, root := ~, start := 252448, stop := 252461 ), rec( content := " there a\ re exactly\n ", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "C", next := 252493, root := ~, start := 252485, stop := 252492 ), rec( content := " edges t\ erminating in ", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "C", next := 252523, root := ~, start := 252515, stop := 252522 ), rec( content := ".\n\n \ See also ", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsOutRe\ gularDigraph" ), content := 0, count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "Ref", next := 252572, root := ~, start := 252539, stop := 252571 ), rec( content := " and\n \ ", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsRegul\ arDigraph" ), content := 0, count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "Ref", next := 252611, root := ~, start := 252581, stop := 252610 ), rec( content := ".\n " , count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 2, 1, 4 ], mathmode := "Text", name := "P", next := 252621, root := ~, start := 252617, stop := 252620 ), rec( content := "\n \ \n If the argument ", count := [ 6, 2, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 2, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 1, 4 ], mathmode := "Text", name := "A", next := 252663, root := ~, start := 252649, stop := 252662 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n ", count := [ 6, 2, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> IsInRegularDigraph(CompleteDigraph(4));\ntrue\ngap> IsInRegularDigraph(C\ hainDigraph(4));\nfalse\n", count := [ 6, 2, 1, 5 ], name := "PCDATA", root := ~ ) ], count := [ 6, 2, 1, 5 ], mathmode := "Text", name := "Example", next := 252893, root := ~, start := 252763, stop := 252892 ), rec( content := "\n ", count := [ 6, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "Description", next := 252910, root := ~, start := 252318, stop := 252909 ) ], count := [ 6, 2, 1, 1 ], mathmode := "Text", name := "ManSection", next := 252924, root := ~, start := 252203, stop := 252923 ), rec( content := "\n\n ", count := [ 6, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsOutRegularDig\ raph" ), content := 0, count := [ 6, 2, 2, 2 ], mathmode := "Text", name := "Prop", next := 252993, root := ~, start := 252945, stop := 252992 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "K", next := 253016, root := ~, start := 253005, stop := 253015 ), rec( content := " or ", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "K", next := 253032, root := ~, start := 253020, stop := 253031 ), rec( content := ".", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "Returns", next := 253043, root := ~, start := 252996, stop := 253042 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s property is ", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "K", next := 253092, root := ~, start := 253081, stop := 253091 ), rec( content := " if ther\ e is an integer ", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "C", next := 253124, root := ~, start := 253116, stop := 253123 ), rec( content := " such th\ at\n for every vertex ", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "C", next := 253164, root := ~, start := 253156, stop := 253163 ), rec( content := " of digr\ aph ", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "A", next := 253190, root := ~, start := 253176, stop := 253189 ), rec( content := " there a\ re exactly\n ", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "C", next := 253221, root := ~, start := 253213, stop := 253220 ), rec( content := " edges s\ tarting at ", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "C", next := 253248, root := ~, start := 253240, stop := 253247 ), rec( content := ".\n " , count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 2, 2, 4 ], mathmode := "Text", name := "P", next := 253258, root := ~, start := 253254, stop := 253257 ), rec( content := "\n\n \ See also ", count := [ 6, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsInReg\ ularDigraph" ), content := 0, count := [ 6, 2, 2, 4 ], mathmode := "Text", name := "Ref", next := 253305, root := ~, start := 253273, stop := 253304 ), rec( content := " and\n \ ", count := [ 6, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsRegul\ arDigraph" ), content := 0, count := [ 6, 2, 2, 4 ], mathmode := "Text", name := "Ref", next := 253344, root := ~, start := 253314, stop := 253343 ), rec( content := ".\n " , count := [ 6, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 2, 2, 5 ], mathmode := "Text", name := "P", next := 253354, root := ~, start := 253350, stop := 253353 ), rec( content := "\n \ \n If the argument ", count := [ 6, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 2, 5 ], mathmode := "Text", name := "A", next := 253396, root := ~, start := 253382, stop := 253395 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n ", count := [ 6, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> IsOutRegularDigraph(CompleteDigraph(4));\ntrue\ngap> IsOutRegularDigraph\ (ChainDigraph(4));\nfalse\n", count := [ 6, 2, 2, 6 ], name := "PCDATA", root := ~ ) ], count := [ 6, 2, 2, 6 ], mathmode := "Text", name := "Example", next := 253628, root := ~, start := 253496, stop := 253627 ), rec( content := "\n ", count := [ 6, 2, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "Description", next := 253645, root := ~, start := 253046, stop := 253644 ) ], count := [ 6, 2, 2, 1 ], mathmode := "Text", name := "ManSection", next := 253659, root := ~, start := 252930, stop := 253658 ), rec( content := "\n\n ", count := [ 6, 2, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsRegularDigrap\ h" ), content := 0, count := [ 6, 2, 3, 2 ], mathmode := "Text", name := "Prop", next := 253725, root := ~, start := 253680, stop := 253724 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "K", next := 253748, root := ~, start := 253737, stop := 253747 ), rec( content := " or ", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "K", next := 253764, root := ~, start := 253752, stop := 253763 ), rec( content := ".", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "Returns", next := 253775, root := ~, start := 253728, stop := 253774 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s property is ", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "K", next := 253824, root := ~, start := 253813, stop := 253823 ), rec( content := " if ther\ e is an integer ", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "C", next := 253856, root := ~, start := 253848, stop := 253855 ), rec( content := " such th\ at\n for every vertex ", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "C", next := 253896, root := ~, start := 253888, stop := 253895 ), rec( content := " of digr\ aph ", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "A", next := 253922, root := ~, start := 253908, stop := 253921 ), rec( content := " there a\ re exactly\n ", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "C", next := 253953, root := ~, start := 253945, stop := 253952 ), rec( content := " edges s\ tarting and terminating at ", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "C", next := 253996, root := ~, start := 253988, stop := 253995 ), rec( content := ". In oth\ er words,\n the property is ", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "K", next := 254045, root := ~, start := 254034, stop := 254044 ), rec( content := " if ", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "A", next := 254063, root := ~, start := 254049, stop := 254062 ), rec( content := " is both\ in-regular and\n and out-regular.\n\n See also ", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsInReg\ ularDigraph" ), content := 0, count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "Ref", next := 254154, root := ~, start := 254122, stop := 254153 ), rec( content := " and\n \ ", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsOutRe\ gularDigraph" ), content := 0, count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "Ref", next := 254196, root := ~, start := 254163, stop := 254195 ), rec( content := ".\n " , count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 2, 3, 4 ], mathmode := "Text", name := "P", next := 254206, root := ~, start := 254202, stop := 254205 ), rec( content := "\n \ \n If the argument ", count := [ 6, 2, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 2, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 3, 4 ], mathmode := "Text", name := "A", next := 254248, root := ~, start := 254234, stop := 254247 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n ", count := [ 6, 2, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> IsRegularDigraph(CompleteDigraph(4));\ntrue\ngap> IsRegularDigraph(Chain\ Digraph(4));\nfalse\n", count := [ 6, 2, 3, 5 ], name := "PCDATA", root := ~ ) ], count := [ 6, 2, 3, 5 ], mathmode := "Text", name := "Example", next := 254474, root := ~, start := 254348, stop := 254473 ), rec( content := "\n ", count := [ 6, 2, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "Description", next := 254491, root := ~, start := 253778, stop := 254490 ) ], count := [ 6, 2, 3, 1 ], mathmode := "Text", name := "ManSection", next := 254505, root := ~, start := 253665, stop := 254504 ), rec( content := "\n\n ", count := [ 6, 2, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsDistanceRegul\ arDigraph" ), content := 0, count := [ 6, 2, 4, 2 ], mathmode := "Text", name := "Prop", next := 254579, root := ~, start := 254526, stop := 254578 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "K", next := 254602, root := ~, start := 254591, stop := 254601 ), rec( content := " or ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "K", next := 254618, root := ~, start := 254606, stop := 254617 ), rec( content := ".", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "Returns", next := 254629, root := ~, start := 254582, stop := 254628 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "A", next := 254667, root := ~, start := 254653, stop := 254666 ), rec( content := " is a co\ nnected symmetric graph, this property returns\n ", count := [ 6, 2, 4, 3 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "K", next := 254737, root := ~, start := 254726, stop := 254736 ), rec( content := " if for \ any two vertices ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "C", next := 254770, root := ~, start := 254762, stop := 254769 ), rec( content := " and ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "C", next := 254783, root := ~, start := 254775, stop := 254782 ), rec( content := " of ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "A", next := 254801, root := ~, start := 254787, stop := 254800 ), rec( content := "\n an\ d any two integers ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "C", next := 254835, root := ~, start := 254827, stop := 254834 ), rec( content := " and ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "C", next := 254848, root := ~, start := 254840, stop := 254847 ), rec( content := " between\ ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "0\ ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "C", next := 254865, root := ~, start := 254857, stop := 254864 ), rec( content := " and the\ \n diameter of ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "A", next := 254904, root := ~, start := 254890, stop := 254903 ), rec( content := ", the nu\ mber of vertices at distance ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "C", next := 254949, root := ~, start := 254941, stop := 254948 ), rec( content := "\n fr\ om ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "C", next := 254967, root := ~, start := 254959, stop := 254966 ), rec( content := " and dis\ tance ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "C", next := 254989, root := ~, start := 254981, stop := 254988 ), rec( content := " from ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "C", next := 255003, root := ~, start := 254995, stop := 255002 ), rec( content := " depends\ only on\n ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "C", next := 255032, root := ~, start := 255024, stop := 255031 ), rec( content := ", ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "C", next := 255042, root := ~, start := 255034, stop := 255041 ), rec( content := ", and th\ e distance between vertices ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "C", next := 255086, root := ~, start := 255078, stop := 255085 ), rec( content := " and\n \ ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "C", next := 255103, root := ~, start := 255095, stop := 255102 ), rec( content := ".", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "P", next := 255108, root := ~, start := 255104, stop := 255107 ), rec( content := "\n\n \ Alternatively, a distance regular graph is a graph for which there exist\n \ integers ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "b\ _i", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "C", next := 255210, root := ~, start := 255200, stop := 255209 ), rec( content := ", ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ _i", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "C", next := 255222, root := ~, start := 255212, stop := 255221 ), rec( content := ", and ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "C", next := 255236, root := ~, start := 255228, stop := 255235 ), rec( content := " such th\ at for any two\n vertices ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "C", next := 255280, root := ~, start := 255272, stop := 255279 ), rec( content := ", ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "C", next := 255290, root := ~, start := 255282, stop := 255289 ), rec( content := " in ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "A", next := 255308, root := ~, start := 255294, stop := 255307 ), rec( content := " which a\ re distance ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "C", next := 255336, root := ~, start := 255328, stop := 255335 ), rec( content := "\n ap\ art, there are exactly ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "b\ _i", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "C", next := 255376, root := ~, start := 255366, stop := 255375 ), rec( content := " neighbo\ rs of ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "C", next := 255398, root := ~, start := 255390, stop := 255397 ), rec( content := " which a\ re at\n distance ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ - 1", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "C", next := 255437, root := ~, start := 255425, stop := 255436 ), rec( content := " away fr\ om ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "C", next := 255456, root := ~, start := 255448, stop := 255455 ), rec( content := ", and ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ _i", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "C", next := 255472, root := ~, start := 255462, stop := 255471 ), rec( content := " neighbo\ rs of\n ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "C", next := 255498, root := ~, start := 255490, stop := 255497 ), rec( content := " which a\ re at distance ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ + 1", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "C", next := 255533, root := ~, start := 255521, stop := 255532 ), rec( content := " away fr\ om ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "C", next := 255552, root := ~, start := 255544, stop := 255551 ), rec( content := ". This\n\ definition is used to check whether ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "A", next := 255613, root := ~, start := 255599, stop := 255612 ), rec( content := " is dist\ ance regular.", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 2, 4, 5 ], mathmode := "Text", name := "P", next := 255638, root := ~, start := 255634, stop := 255637 ), rec( content := "\n\n \ In the case where ", count := [ 6, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 5 ], mathmode := "Text", name := "A", next := 255676, root := ~, start := 255662, stop := 255675 ), rec( content := " is not \ symmetric or not connected, the\n property is ", count := [ 6, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 5 ], mathmode := "Text", name := "K", next := 255744, root := ~, start := 255732, stop := 255743 ), rec( content := ".\n " , count := [ 6, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 2, 4, 6 ], mathmode := "Text", name := "P", next := 255754, root := ~, start := 255750, stop := 255753 ), rec( content := "\n \ \n If the argument ", count := [ 6, 2, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 2, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 6 ], mathmode := "Text", name := "A", next := 255796, root := ~, start := 255782, stop := 255795 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n ", count := [ 6, 2, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := DigraphSymmetricClosure(ChainDigraph(5));;\ngap> IsDistanceRegularD\ igraph(D);\nfalse\ngap> D := Digraph([[2, 3, 4], [1, 3, 4], [1, 2, 4], [1, 2, \ 3]]);\n\ngap> IsDistanceRegularDi\ graph(D);\ntrue\n", count := [ 6, 2, 4, 7 ], name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 7 ], mathmode := "Text", name := "Example", next := 256172, root := ~, start := 255897, stop := 256171 ), rec( content := "\n ", count := [ 6, 2, 4, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "Description", next := 256189, root := ~, start := 254632, stop := 256188 ) ], count := [ 6, 2, 4, 1 ], mathmode := "Text", name := "ManSection", next := 256203, root := ~, start := 254511, stop := 256202 ), rec( content := "\n\n ", count := [ 6, 2, 4, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 2, 0, 1 ], mathmode := "Text", name := "Section", next := 256217, root := ~, start := 252160, stop := 256216 ) , rec( content := "\n\n ", count := [ 6, 2, 4, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Connectivity and \ cycles", count := [ 6, 3, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 0, 2 ], mathmode := "Text", name := "Heading", next := 256272, root := ~, start := 256230, stop := 256271 ), rec( content := "\n ", count := [ 6, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsAcyclicDigrap\ h" ), content := 0, count := [ 6, 3, 1, 2 ], mathmode := "Text", name := "Prop", next := 256337, root := ~, start := 256292, stop := 256336 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "K", next := 256360, root := ~, start := 256349, stop := 256359 ), rec( content := " or ", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "K", next := 256376, root := ~, start := 256364, stop := 256375 ), rec( content := ".", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "Returns", next := 256387, root := ~, start := 256340, stop := 256386 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s property is ", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "K", next := 256436, root := ~, start := 256425, stop := 256435 ), rec( content := " if the \ digraph ", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "A", next := 256466, root := ~, start := 256452, stop := 256465 ), rec( content := " is acyc\ lic, and\n ", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "K", next := 256499, root := ~, start := 256487, stop := 256498 ), rec( content := " if it i\ s not. A digraph is ", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "a\ cyclic", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "E", next := 256541, root := ~, start := 256527, stop := 256540 ), rec( content := " if ever\ y directed\n cycle on the digraph is trivial. See section ", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Style := "Number\ ", Subsect := "Definitions" ), content := 0, count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "Ref", next := 256659, root := ~, start := 256609, stop := 256658 ), rec( content := " for the\ definition of a directed cycle, and of a trivial\n directed cycle.", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 1, 4 ], mathmode := "Text", name := "P", next := 256740, root := ~, start := 256736, stop := 256739 ), rec( content := "\n\n \ The method used in this operation has complexity ", count := [ 6, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (m+n)", count := [ 6, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 1, 4 ], mathmode := "Text", name := "M", next := 256808, root := ~, start := 256795, stop := 256807 ), rec( content := " where\n\ ", count := [ 6, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 6, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 1, 4 ], mathmode := "Text", name := "M", next := 256827, root := ~, start := 256819, stop := 256826 ), rec( content := " is the \ number of edges (counting multiple edges as one) and\n ", count := [ 6, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 6, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 1, 4 ], mathmode := "Text", name := "M", next := 256900, root := ~, start := 256892, stop := 256899 ), rec( content := " is the \ number of vertices in the digraph. ", count := [ 6, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 1, 5 ], mathmode := "Text", name := "P", next := 256947, root := ~, start := 256943, stop := 256946 ), rec( content := "\n\n \ If the argument ", count := [ 6, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 1, 5 ], mathmode := "Text", name := "A", next := 256983, root := ~, start := 256969, stop := 256982 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n ", count := [ 6, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> Petersen := Graph(SymmetricGroup(5), [[1, 2]], OnSets,\n> function(x, y)\ \n> return IsEmpty(Intersection(x, y));\n> end);;\ngap> D := Digraph(Peterse\ n);\n\ngap> IsAcyclicDigraph(D);\ \nfalse\ngap> D := DigraphFromDiSparse6String(\n> \".b_OGCIDBaPGkULEbQHCeRIdrH\ cuZMfRyDAbPhTi|zF\");\n\ngap> Is\ AcyclicDigraph(D);\ntrue\ngap> IsAcyclicDigraph(ChainDigraph(10));\ntrue\ngap>\ D := CompleteDigraph(IsMutableDigraph, 4);\n\ngap> IsAcyclicDigraph(D);\nfalse\ngap> IsAcyclicDigraph(CycleDigra\ ph(10));\nfalse", count := [ 6, 3, 1, 6 ], name := "PCDATA", root := ~ ) ], count := [ 6, 3, 1, 6 ], mathmode := "Text", name := "Example", next := 257732, root := ~, start := 257084, stop := 257731 ), rec( content := "\n ", count := [ 6, 3, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "Description", next := 257749, root := ~, start := 256390, stop := 257748 ) ], count := [ 6, 3, 1, 1 ], mathmode := "Text", name := "ManSection", next := 257763, root := ~, start := 256277, stop := 257762 ), rec( content := "\n\n ", count := [ 6, 3, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsChainDigraph"\ ), content := 0, count := [ 6, 3, 2, 2 ], mathmode := "Text", name := "Prop", next := 257827, root := ~, start := 257784, stop := 257826 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "K", next := 257850, root := ~, start := 257839, stop := 257849 ), rec( content := " or ", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "K", next := 257866, root := ~, start := 257854, stop := 257865 ), rec( content := ".", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "Returns", next := 257877, root := ~, start := 257830, stop := 257876 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sChainDigraph", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "C", next := 257919, root := ~, start := 257898, stop := 257918 ), rec( content := " returns\ ", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "K", next := 257939, root := ~, start := 257928, stop := 257938 ), rec( content := " if the \ digraph ", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "A", next := 257969, root := ~, start := 257955, stop := 257968 ), rec( content := " is\n \ isomorphic to the chain digraph with the same number of vertices as\n ", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "A", next := 258063, root := ~, start := 258049, stop := 258062 ), rec( content := ", and ", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "K", next := 258081, root := ~, start := 258069, stop := 258080 ), rec( content := " if it i\ s not; see ", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "ChainDi\ graph" ), content := 0, count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "Ref", next := 258132, root := ~, start := 258100, stop := 258131 ), rec( content := ".", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 2, 4 ], mathmode := "Text", name := "P", next := 258137, root := ~, start := 258133, stop := 258136 ), rec( content := "\n\n \ A digraph is a ", count := [ 6, 3, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ hain", count := [ 6, 3, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 2, 4 ], mathmode := "Text", name := "E", next := 258170, root := ~, start := 258158, stop := 258169 ), rec( content := " if and \ only if it is a directed tree, in which\n every vertex has out degree at mo\ st one; see ", count := [ 6, 3, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsDirec\ tedTree" ), content := 0, count := [ 6, 3, 2, 4 ], mathmode := "Text", name := "Ref", next := 258295, root := ~, start := 258267, stop := 258294 ), rec( content := "\n an\ d ", count := [ 6, 3, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "OutDegr\ ees" ), content := 0, count := [ 6, 3, 2, 4 ], mathmode := "Text", name := "Ref", next := 258328, root := ~, start := 258304, stop := 258327 ), rec( content := ".\n " , count := [ 6, 3, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 2, 5 ], mathmode := "Text", name := "P", next := 258338, root := ~, start := 258334, stop := 258337 ), rec( content := "\n \ \n If the argument ", count := [ 6, 3, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 2, 5 ], mathmode := "Text", name := "A", next := 258380, root := ~, start := 258366, stop := 258379 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n", count := [ 6, 3, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 3], [2, 3], [3]]);\n\ngap> IsChainDigraph(D);\nfalse\ngap> D := ChainDigraph(5);\n\ngap> IsChainDigraph(D);\ntrue\ngap> D := \ DigraphReverse(D);\n\ngap> IsChain\ Digraph(D);\ntrue\ngap> D := ChainDigraph(IsMutableDigraph, 5);\n\ngap> IsChainDigraph(D);\ntrue\ngap> DigraphReve\ rse(D);\n\ngap> IsChainDigraph(D);\n\ true", count := [ 6, 3, 2, 6 ], name := "PCDATA", root := ~ ) ], count := [ 6, 3, 2, 6 ], mathmode := "Text", name := "Example", next := 259039, root := ~, start := 258477, stop := 259038 ), rec( content := "\n ", count := [ 6, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "Description", next := 259056, root := ~, start := 257880, stop := 259055 ) ], count := [ 6, 3, 2, 1 ], mathmode := "Text", name := "ManSection", next := 259070, root := ~, start := 257769, stop := 259069 ), rec( content := "\n\n ", count := [ 6, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsConnectedDigr\ aph" ), content := 0, count := [ 6, 3, 3, 2 ], mathmode := "Text", name := "Prop", next := 259138, root := ~, start := 259091, stop := 259137 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "K", next := 259161, root := ~, start := 259150, stop := 259160 ), rec( content := " or ", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "K", next := 259177, root := ~, start := 259165, stop := 259176 ), rec( content := ".", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "Returns", next := 259188, root := ~, start := 259141, stop := 259187 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s property is ", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "K", next := 259237, root := ~, start := 259226, stop := 259236 ), rec( content := " if the \ digraph ", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "A", next := 259267, root := ~, start := 259253, stop := 259266 ), rec( content := "\n is\ weakly connected and ", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "K", next := 259308, root := ~, start := 259296, stop := 259307 ), rec( content := " if it i\ s not. A digraph\n ", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "A", next := 259352, root := ~, start := 259338, stop := 259351 ), rec( content := " is ", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "w\ eakly connected", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "E", next := 259379, root := ~, start := 259356, stop := 259378 ), rec( content := " if it i\ s possible to travel\n from any vertex to any other vertex by traversing ed\ ges in either\n direction (possibly against the orientation of some of them\ ). ", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "P", next := 259548, root := ~, start := 259544, stop := 259547 ), rec( content := "\n\n \ The method used in this function has complexity ", count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (m)", count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "M", next := 259613, root := ~, start := 259602, stop := 259612 ), rec( content := " if the\\ n digraph's ", count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Source" ), content := 0, count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "Ref", next := 259662, root := ~, start := 259635, stop := 259661 ), rec( content := " attribu\ te is set, otherwise it has\n complexity ", count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (m+n)", count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "M", next := 259726, root := ~, start := 259713, stop := 259725 ), rec( content := " (where\\ n ", count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "M", next := 259746, root := ~, start := 259738, stop := 259745 ), rec( content := " is the \ number of edges and\n ", count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "M", next := 259786, root := ~, start := 259778, stop := 259785 ), rec( content := " is the \ number of vertices of the digraph).\n ", count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 3, 5 ], mathmode := "Text", name := "P", next := 259838, root := ~, start := 259834, stop := 259837 ), rec( content := "\n \ \n If the argument ", count := [ 6, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 3, 5 ], mathmode := "Text", name := "A", next := 259880, root := ~, start := 259866, stop := 259879 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n ", count := [ 6, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[2], [3], []]);;\ngap> IsConnectedDigraph(D);\ntrue\ngap> \ D := Digraph([[1, 3], [4], [3], []]);;\ngap> IsConnectedDigraph(D);\nfalse\nga\ p> D := Digraph(IsMutableDigraph, [[2], [3], []]);;\ngap> IsConnectedDigraph(D\ );\ntrue\ngap> D := Digraph(IsMutableDigraph, [[1, 3], [4], [3], []]);;\ngap> \ IsConnectedDigraph(D);\nfalse", count := [ 6, 3, 3, 6 ], name := "PCDATA", root := ~ ) ], count := [ 6, 3, 3, 6 ], mathmode := "Text", name := "Example", next := 260342, root := ~, start := 259981, stop := 260341 ), rec( content := "\n ", count := [ 6, 3, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "Description", next := 260359, root := ~, start := 259191, stop := 260358 ) ], count := [ 6, 3, 3, 1 ], mathmode := "Text", name := "ManSection", next := 260373, root := ~, start := 259076, stop := 260372 ), rec( content := "\n\n ", count := [ 6, 3, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsBiconnectedDi\ graph" ), content := 0, count := [ 6, 3, 4, 2 ], mathmode := "Text", name := "Prop", next := 260443, root := ~, start := 260394, stop := 260442 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "K", next := 260466, root := ~, start := 260455, stop := 260465 ), rec( content := " or ", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "K", next := 260482, root := ~, start := 260470, stop := 260481 ), rec( content := ".", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "Returns", next := 260493, root := ~, start := 260446, stop := 260492 ), rec( attributes := rec( ), content := [ rec( content := "\n A c\ onnected digraph is ", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "b\ iconnected", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "E", next := 260555, root := ~, start := 260537, stop := 260554 ), rec( content := " if it i\ s still connected (in the\n sense of ", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsConne\ ctedDigraph" ), content := 0, count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "Ref", next := 260634, root := ~, start := 260602, stop := 260633 ), rec( content := ") when a\ ny vertex is removed. \n ", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sBiconnectedDigraph", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "C", next := 260696, root := ~, start := 260669, stop := 260695 ), rec( content := " returns\ ", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "K", next := 260716, root := ~, start := 260705, stop := 260715 ), rec( content := " if the \ digraph\n ", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "A", next := 260750, root := ~, start := 260736, stop := 260749 ), rec( content := " is bico\ nnected, and ", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "K", next := 260783, root := ~, start := 260771, stop := 260782 ), rec( content := " if it i\ s not. In\n particular, ", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sBiconnectedDigraph", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "C", next := 260844, root := ~, start := 260817, stop := 260843 ), rec( content := " returns\ ", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "K", next := 260865, root := ~, start := 260853, stop := 260864 ), rec( content := " if\n \ ", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "A", next := 260887, root := ~, start := 260873, stop := 260886 ), rec( content := " is not \ connected. ", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 4, 4 ], mathmode := "Text", name := "P", next := 260910, root := ~, start := 260906, stop := 260909 ), rec( content := "\n\n \ Multiple edges and loops are ignored by this method. ", count := [ 6, 3, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 4, 5 ], mathmode := "Text", name := "P", next := 260973, root := ~, start := 260969, stop := 260972 ), rec( content := "\n\n \ The method used in this operation has complexity ", count := [ 6, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (m+n)", count := [ 6, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 4, 5 ], mathmode := "Text", name := "M", next := 261041, root := ~, start := 261028, stop := 261040 ), rec( content := " where\n\ ", count := [ 6, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 6, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 4, 5 ], mathmode := "Text", name := "M", next := 261060, root := ~, start := 261052, stop := 261059 ), rec( content := " is the \ number of edges (counting multiple edges as one, and not\n counting loops) \ and ", count := [ 6, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 6, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 4, 5 ], mathmode := "Text", name := "M", next := 261157, root := ~, start := 261149, stop := 261156 ), rec( content := " is the \ number of vertices in the digraph.\n ", count := [ 6, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 4, 6 ], mathmode := "Text", name := "P", next := 261208, root := ~, start := 261204, stop := 261207 ), rec( content := "\n\n \ See also ", count := [ 6, 3, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Articul\ ationPoints" ), content := 0, count := [ 6, 3, 4, 6 ], mathmode := "Text", name := "Ref", next := 261255, root := ~, start := 261223, stop := 261254 ), rec( content := ".\n " , count := [ 6, 3, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 4, 7 ], mathmode := "Text", name := "P", next := 261265, root := ~, start := 261261, stop := 261264 ), rec( content := "\n \ \n If the argument ", count := [ 6, 3, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 4, 7 ], mathmode := "Text", name := "A", next := 261307, root := ~, start := 261293, stop := 261306 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n", count := [ 6, 3, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> IsBiconnectedDigraph(Digraph([[1, 3], [2, 3], [3]]));\nfalse\ngap> IsBic\ onnectedDigraph(CycleDigraph(5));\ntrue\ngap> D := Digraph([[1, 1], [1, 1, 2],\ [3], [3, 3, 4, 4]]);;\ngap> IsBiconnectedDigraph(D);\nfalse\ngap> D := Comple\ teBipartiteDigraph(IsMutableDigraph, 5, 4);\n\ngap> IsBiconnectedDigraph(D);\ntrue", count := [ 6, 3, 4, 8 ], name := "PCD\ ATA", root := ~ ) ], count := [ 6, 3, 4, 8 ], mathmode := "Text", name := "Example", next := 261783, root := ~, start := 261403, stop := 261782 ), rec( content := "\n ", count := [ 6, 3, 4, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "Description", next := 261800, root := ~, start := 260496, stop := 261799 ) ], count := [ 6, 3, 4, 1 ], mathmode := "Text", name := "ManSection", next := 261814, root := ~, start := 260379, stop := 261813 ), rec( content := "\n\n ", count := [ 6, 3, 4, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsStronglyConne\ ctedDigraph" ), content := 0, count := [ 6, 3, 5, 2 ], mathmode := "Text", name := "Prop", next := 261890, root := ~, start := 261835, stop := 261889 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "K", next := 261913, root := ~, start := 261902, stop := 261912 ), rec( content := " or ", count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "K", next := 261929, root := ~, start := 261917, stop := 261928 ), rec( content := ".", count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "Returns", next := 261940, root := ~, start := 261893, stop := 261939 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s property is ", count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "K", next := 261989, root := ~, start := 261978, stop := 261988 ), rec( content := " if the \ digraph ", count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "A", next := 262019, root := ~, start := 262005, stop := 262018 ), rec( content := " is stro\ ngly\n connected and ", count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "K", next := 262062, root := ~, start := 262050, stop := 262061 ), rec( content := " if it i\ s not. ", count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "P", next := 262081, root := ~, start := 262077, stop := 262080 ), rec( content := "\n\n \ A digraph ", count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "A", next := 262111, root := ~, start := 262097, stop := 262110 ), rec( content := " is ", count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ trongly connected", count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "E", next := 262140, root := ~, start := 262115, stop := 262139 ), rec( content := " if ther\ e is a directed\n path from every vertex to every other vertex. See sectio\ n ", count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Style := "Number\ ", Subsect := "Definitions" ), content := 0, count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "Ref", next := 262277, root := ~, start := 262227, stop := 262276 ), rec( content := " for the\ definition of a directed\n path. ", count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 5, 5 ], mathmode := "Text", name := "P", next := 262328, root := ~, start := 262324, stop := 262327 ), rec( content := "\n\n \ The method used in this operation is based on Gabow's Algorithm ", count := [ 6, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "Gab00" ) , content := 0, count := [ 6, 3, 5, 5 ], mathmode := "Text", name := "Cite", next := 262423, root := ~, start := 262398, stop := 262422 ), rec( content := " and has\ complexity ", count := [ 6, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ (m+n)", count := [ 6, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 5, 5 ], mathmode := "Text", name := "M", next := 262456, root := ~, start := 262443, stop := 262455 ), rec( content := ", where \ ", count := [ 6, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 6, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 5, 5 ], mathmode := "Text", name := "M", next := 262472, root := ~, start := 262464, stop := 262471 ), rec( content := " is\n \ the number of edges (counting multiple edges as one) and ", count := [ 6, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 6, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 5, 5 ], mathmode := "Text", name := "M", next := 262545, root := ~, start := 262537, stop := 262544 ), rec( content := " is the\\ n number of vertices in the digraph.\n ", count := [ 6, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 5, 6 ], mathmode := "Text", name := "P", next := 262600, root := ~, start := 262596, stop := 262599 ), rec( content := "\n \ \n If the argument ", count := [ 6, 3, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 5, 6 ], mathmode := "Text", name := "A", next := 262642, root := ~, start := 262628, stop := 262641 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n ", count := [ 6, 3, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CycleDigraph(250000);\n\ngap> IsStronglyConnectedDigraph(D);\ntrue\ngap> D := DigraphRemoveEdges(D,\ [[250000, 1]]);\n\ngap>\ IsStronglyConnectedDigraph(D);\nfalse\ngap> D := CycleDigraph(IsMutableDigrap\ h, 250000);\n\ngap> IsStro\ nglyConnectedDigraph(D);\ntrue\ngap> DigraphRemoveEdge(D, [250000, 1]);\n\ngap> IsStronglyConnectedDigra\ ph(D);\nfalse\n", count := [ 6, 3, 5, 7 ], name := "PCDATA", root := ~ ) ], count := [ 6, 3, 5, 7 ], mathmode := "Text", name := "Example", next := 263319, root := ~, start := 262743, stop := 263318 ), rec( content := "\n ", count := [ 6, 3, 5, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "Description", next := 263336, root := ~, start := 261943, stop := 263335 ) ], count := [ 6, 3, 5, 1 ], mathmode := "Text", name := "ManSection", next := 263350, root := ~, start := 261820, stop := 263349 ), rec( content := "\n\n ", count := [ 6, 3, 5, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsAperiodicDigr\ aph" ), content := 0, count := [ 6, 3, 6, 2 ], mathmode := "Text", name := "Prop", next := 263418, root := ~, start := 263371, stop := 263417 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "K", next := 263441, root := ~, start := 263430, stop := 263440 ), rec( content := " or ", count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "K", next := 263457, root := ~, start := 263445, stop := 263456 ), rec( content := ".", count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "Returns", next := 263468, root := ~, start := 263421, stop := 263467 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s property is ", count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "K", next := 263517, root := ~, start := 263506, stop := 263516 ), rec( content := " if the \ digraph ", count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "A", next := 263547, root := ~, start := 263533, stop := 263546 ), rec( content := "\n is\ aperiodic, i.e. if its ", count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Period" ), content := 0, count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "Ref", next := 263607, root := ~, start := 263578, stop := 263606 ), rec( content := " is equa\ l to 1.\n Otherwise, the property is ", count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "K", next := 263666, root := ~, start := 263654, stop := 263665 ), rec( content := ".\n " , count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 6, 4 ], mathmode := "Text", name := "P", next := 263676, root := ~, start := 263672, stop := 263675 ), rec( content := "\n \ \n If the argument ", count := [ 6, 3, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 6, 4 ], mathmode := "Text", name := "A", next := 263718, root := ~, start := 263704, stop := 263717 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n ", count := [ 6, 3, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[6], [1], [2], [3], [4, 4], [5]]);\n\ngap> IsAperiodicDigraph(D);\nfalse\ngap> D := Dig\ raph([[2], [3, 5], [4], [5], [1, 2]]);\n\ngap> IsAperiodicDigraph(D);\ntrue\ngap> D := Digraph(IsMutableDigraph,\ [[2], [3, 5], [4], [5], [1, 2]]);\n\ \ngap> IsAperiodicDigraph(D);\ntrue", count := [ 6, 3, 6, 5 ], name := "PCDATA\ ", root := ~ ) ], count := [ 6, 3, 6, 5 ], mathmode := "Text", name := "Example", next := 264263, root := ~, start := 263818, stop := 264262 ), rec( content := "\n ", count := [ 6, 3, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "Description", next := 264280, root := ~, start := 263471, stop := 264279 ) ], count := [ 6, 3, 6, 1 ], mathmode := "Text", name := "ManSection", next := 264294, root := ~, start := 263356, stop := 264293 ), rec( content := "\n\n ", count := [ 6, 3, 6, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsDirectedTree"\ ), content := 0, count := [ 6, 3, 7, 2 ], mathmode := "Text", name := "Prop", next := 264358, root := ~, start := 264315, stop := 264357 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "K", next := 264381, root := ~, start := 264370, stop := 264380 ), rec( content := " or ", count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "K", next := 264397, root := ~, start := 264385, stop := 264396 ), rec( content := ".", count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "Returns", next := 264408, root := ~, start := 264361, stop := 264407 ), rec( attributes := rec( ), content := [ rec( content := "\n Ret\ urns ", count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "K", next := 264448, root := ~, start := 264437, stop := 264447 ), rec( content := " if the \ digraph ", count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "A", next := 264478, root := ~, start := 264464, stop := 264477 ), rec( content := " is a di\ rected tree, and\n ", count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "K", next := 264519, root := ~, start := 264507, stop := 264518 ), rec( content := " if it i\ s not. ", count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 7, 4 ], mathmode := "Text", name := "P", next := 264538, root := ~, start := 264534, stop := 264537 ), rec( content := "\n\n \ A ", count := [ 6, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ irected tree", count := [ 6, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 7, 4 ], mathmode := "Text", name := "E", next := 264566, root := ~, start := 264546, stop := 264565 ), rec( content := " is an a\ cyclic digraph with precisely 1 source,\n such that no two vertices share a\ n out-neighbour.\n Note the empty digraph is not considered a directed\n \ tree as it has no source. ", count := [ 6, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 7, 5 ], mathmode := "Text", name := "P", next := 264758, root := ~, start := 264754, stop := 264757 ), rec( content := "\n\n \ See also ", count := [ 6, 3, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Sources" ), content := 0, count := [ 6, 3, 7, 5 ], mathmode := "Text", name := "Ref", next := 264801, root := ~, start := 264773, stop := 264800 ), rec( content := ".\n " , count := [ 6, 3, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 7, 6 ], mathmode := "Text", name := "P", next := 264811, root := ~, start := 264807, stop := 264810 ), rec( content := "\n \ \n If the argument ", count := [ 6, 3, 7, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 7, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 7, 6 ], mathmode := "Text", name := "A", next := 264853, root := ~, start := 264839, stop := 264852 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n ", count := [ 6, 3, 7, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[], [2]]);\n\ng\ ap> IsDirectedTree(D);\nfalse\ngap> D := Digraph([[3], [3], []]);\n\ngap> IsDirectedTree(D);\nfalse\ngap> D := D\ igraph([[2], [3], []]);\n\ngap> Is\ DirectedTree(D);\ntrue\ngap> D := Digraph([[2, 3], [6], [4, 5], [], [], []]);\ \n\ngap> IsDirectedTree(D);\ntrue\ \n", count := [ 6, 3, 7, 7 ], name := "PCDATA", root := ~ ) ], count := [ 6, 3, 7, 7 ], mathmode := "Text", name := "Example", next := 265437, root := ~, start := 264954, stop := 265436 ), rec( content := "\n ", count := [ 6, 3, 7, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "Description", next := 265454, root := ~, start := 264411, stop := 265453 ) ], count := [ 6, 3, 7, 1 ], mathmode := "Text", name := "ManSection", next := 265468, root := ~, start := 264300, stop := 265467 ), rec( content := "\n\n ", count := [ 6, 3, 7, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsUndirectedTre\ e" ), content := 0, count := [ 6, 3, 8, 2 ], mathmode := "Text", name := "Prop", next := 265534, root := ~, start := 265489, stop := 265533 ), rec( attributes := rec( Arg := "digraph", Name := "IsUndirectedFor\ est" ), content := 0, count := [ 6, 3, 8, 4 ], mathmode := "Text", name := "Prop", next := 265584, root := ~, start := 265537, stop := 265583 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "K", next := 265607, root := ~, start := 265596, stop := 265606 ), rec( content := " or ", count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "K", next := 265623, root := ~, start := 265611, stop := 265622 ), rec( content := ".", count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "Returns", next := 265634, root := ~, start := 265587, stop := 265633 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ property ", count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sUndirectedTree", count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "C", next := 265691, root := ~, start := 265668, stop := 265690 ), rec( content := " returns\ ", count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "K", next := 265711, root := ~, start := 265700, stop := 265710 ), rec( content := " if the \ digraph\n ", count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "A", next := 265745, root := ~, start := 265731, stop := 265744 ), rec( content := " is an u\ ndirected tree, and the property\n ", count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sUndirectedForest", count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "C", next := 265815, root := ~, start := 265790, stop := 265814 ), rec( content := " returns\ ", count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "K", next := 265835, root := ~, start := 265824, stop := 265834 ), rec( content := " if ", count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "A", next := 265853, root := ~, start := 265839, stop := 265852 ), rec( content := " is an\n\ undirected forest; otherwise, these properties return ", count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "K", next := 265930, root := ~, start := 265918, stop := 265929 ), rec( content := ". ", count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "P", next := 265936, root := ~, start := 265932, stop := 265935 ), rec( content := "\n\n \ An ", count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ndirected tree", count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "E", next := 265967, root := ~, start := 265945, stop := 265966 ), rec( content := " is a sy\ mmetric digraph without loops, in which for\n any pair of distinct vertices\ ", count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "C", next := 266061, root := ~, start := 266053, stop := 266060 ), rec( content := " and ", count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "C", next := 266074, root := ~, start := 266066, stop := 266073 ), rec( content := ", there \ is exactly one\n directed path from ", count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "C", next := 266128, root := ~, start := 266120, stop := 266127 ), rec( content := " to ", count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "C", next := 266140, root := ~, start := 266132, stop := 266139 ), rec( content := ". See ", count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsSymme\ tricDigraph" ), content := 0, count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "Ref", next := 266184, root := ~, start := 266146, stop := 266183 ), rec( content := " and ", count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "Digraph\ HasLoops" ), content := 0, count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "Ref", next := 266218, root := ~, start := 266189, stop := 266217 ), rec( content := ", and se\ e\n section ", count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Style := "Number\ ", Subsect := "Definitions" ), content := 0, count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "Ref", next := 266284, root := ~, start := 266240, stop := 266283 ), rec( content := " for the\ definition of\n directed path. This definition implies that an undirected \ tree has\n no multiple edges. ", count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 8, 7 ], mathmode := "Text", name := "P", next := 266405, root := ~, start := 266401, stop := 266404 ), rec( content := "\n\n \ An ", count := [ 6, 3, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ndirected forest", count := [ 6, 3, 8, 7 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 6, 3, 8, 7 ], mathmode := "Text", name := "E", next := 266438, root := ~, start := 266414, stop := 266437 ), rec( content := " is a di\ graph, each of whose connected components\n is an undirected tree. In other\ words, an undirected forest is isomorphic to\n a disjoint union of undirec\ ted trees. See ", count := [ 6, 3, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ ConnectedComponents" ), content := 0, count := [ 6, 3, 8, 7 ], mathmode := "Text", name := "Ref", next := 266662, root := ~, start := 266615, stop := 266661 ), rec( content := " and ", count := [ 6, 3, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ DisjointUnion", Label := "for a list of digraphs" ), content := 0, count := [ 6, 3, 8, 7 ], mathmode := "Text", name := "Ref", next := 266739, root := ~, start := 266667, stop := 266738 ), rec( content := ". In par\ ticular, every\n undirected tree is an undirected forest. ", count := [ 6, 3, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 8, 8 ], mathmode := "Text", name := "P", next := 266811, root := ~, start := 266807, stop := 266810 ), rec( content := "\n\n \ Please note that the digraph with zero vertices is considered to be neither\n \ an undirected tree nor an undirected forest.\n ", count := [ 6, 3, 8, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 8, 9 ], mathmode := "Text", name := "P", next := 266950, root := ~, start := 266946, stop := 266949 ), rec( content := "\n \ \n If the argument ", count := [ 6, 3, 8, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 8, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 8, 9 ], mathmode := "Text", name := "A", next := 266992, root := ~, start := 266978, stop := 266991 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n ", count := [ 6, 3, 8, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[3], [3], [1, 2]]);\n\ngap> IsUndirectedTree(D);\ntrue\ngap> IsSymmetricDigraph(D) and not D\ igraphHasLoops(D);\ntrue\ngap> D := Digraph([[3], [5], [1, 4], [3], [2]]);\n\ngap> IsConnectedDigraph(D);\nfalse\ \ngap> IsUndirectedTree(D);\nfalse\ngap> IsUndirectedForest(D);\ntrue\ngap> D \ := Digraph([[1, 2], [1], [2]]);\n\ \ngap> IsUndirectedTree(D) or IsUndirectedForest(D);\nfalse\ngap> IsSymmetricD\ igraph(D) or not DigraphHasLoops(D);\nfalse", count := [ 6, 3, 8, 10 ], name := "PCD\ ATA", root := ~ ) ], count := [ 6, 3, 8, 10 ], mathmode := "Text", name := "Example", next := 267693, root := ~, start := 267093, stop := 267692 ), rec( content := "\n ", count := [ 6, 3, 8, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "Description", next := 267710, root := ~, start := 265637, stop := 267709 ) ], count := [ 6, 3, 8, 1 ], mathmode := "Text", name := "ManSection", next := 267724, root := ~, start := 265474, stop := 267723 ), rec( content := "\n\n ", count := [ 6, 3, 8, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsEulerianDigra\ ph" ), content := 0, count := [ 6, 3, 9, 2 ], mathmode := "Text", name := "Prop", next := 267791, root := ~, start := 267745, stop := 267790 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 3, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 9, 3 ], mathmode := "Text", name := "K", next := 267814, root := ~, start := 267803, stop := 267813 ), rec( content := " or ", count := [ 6, 3, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 9, 3 ], mathmode := "Text", name := "K", next := 267830, root := ~, start := 267818, stop := 267829 ), rec( content := ".", count := [ 6, 3, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 9, 3 ], mathmode := "Text", name := "Returns", next := 267841, root := ~, start := 267794, stop := 267840 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s property returns true if the digraph ", count := [ 6, 3, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 9, 3 ], mathmode := "Text", name := "A", next := 267918, root := ~, start := 267904, stop := 267917 ), rec( content := " is Eule\ rian.\n ", count := [ 6, 3, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 9, 4 ], mathmode := "Text", name := "P", next := 267940, root := ~, start := 267936, stop := 267939 ), rec( content := "\n\n \ A connected digraph is called ", count := [ 6, 3, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "E\ ulerian", count := [ 6, 3, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 9, 4 ], mathmode := "Text", name := "E", next := 267991, root := ~, start := 267976, stop := 267990 ), rec( content := " if ther\ e exists a directed\n circuit on the digraph which includes every edge exac\ tly once. See\n section ", count := [ 6, 3, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Style := "Number\ ", Subsect := "Definitions" ), content := 0, count := [ 6, 3, 9, 4 ], mathmode := "Text", name := "Ref", next := 268147, root := ~, start := 268103, stop := 268146 ), rec( content := " for the\ definition of\n a directed circuit. Note that the empty digraph with at mo\ st one vertex is\n considered to be Eulerian.\n ", count := [ 6, 3, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 9, 5 ], mathmode := "Text", name := "P", next := 268288, root := ~, start := 268284, stop := 268287 ), rec( content := "\n \ \n If the argument ", count := [ 6, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 9, 5 ], mathmode := "Text", name := "A", next := 268330, root := ~, start := 268316, stop := 268329 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n ", count := [ 6, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[]]);\n\ngap> IsEul\ erianDigraph(D);\ntrue\ngap> D := Digraph([[2], []]);\n\ngap> IsEulerianDigraph(D);\nfalse\ngap> D := Digraph([[3\ ], [], [2]]);\n\ngap> IsEulerianDi\ graph(D);\nfalse\ngap> D := Digraph([[2], [3], [1]]);\n\ngap> IsEulerianDigraph(D);\ntrue\n", count := [ 6, 3, 9, 6 ], name := "PCD\ ATA", root := ~ ) ], count := [ 6, 3, 9, 6 ], mathmode := "Text", name := "Example", next := 268893, root := ~, start := 268431, stop := 268892 ), rec( content := "\n ", count := [ 6, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 9, 3 ], mathmode := "Text", name := "Description", next := 268910, root := ~, start := 267844, stop := 268909 ) ], count := [ 6, 3, 9, 1 ], mathmode := "Text", name := "ManSection", next := 268924, root := ~, start := 267730, stop := 268923 ), rec( content := "\n\n ", count := [ 6, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsHamiltonianDi\ graph" ), content := 0, count := [ 6, 3, 10, 2 ], mathmode := "Text", name := "Prop", next := 268994, root := ~, start := 268945, stop := 268993 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "K", next := 269017, root := ~, start := 269006, stop := 269016 ), rec( content := " or ", count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "K", next := 269033, root := ~, start := 269021, stop := 269032 ), rec( content := ".", count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "Returns", next := 269044, root := ~, start := 268997, stop := 269043 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "A", next := 269082, root := ~, start := 269068, stop := 269081 ), rec( content := " is Hami\ ltonian, then this property returns\n ", count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "K", next := 269141, root := ~, start := 269130, stop := 269140 ), rec( content := ", and ", count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "K", next := 269159, root := ~, start := 269147, stop := 269158 ), rec( content := " if it i\ s not. ", count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 10, 4 ], mathmode := "Text", name := "P", next := 269178, root := ~, start := 269174, stop := 269177 ), rec( content := "\n\n \ A digraph with ", count := [ 6, 3, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 6, 3, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 10, 4 ], mathmode := "Text", name := "C", next := 269207, root := ~, start := 269199, stop := 269206 ), rec( content := " vertice\ s is ", count := [ 6, 3, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "H\ amiltonian", count := [ 6, 3, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 10, 4 ], mathmode := "Text", name := "E", next := 269238, root := ~, start := 269220, stop := 269237 ), rec( content := " if it h\ as a\n directed cycle of length ", count := [ 6, 3, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 6, 3, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 10, 4 ], mathmode := "Text", name := "C", next := 269288, root := ~, start := 269280, stop := 269287 ), rec( content := ". See Se\ ction ", count := [ 6, 3, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Style := "Number\ ", Subsect := "Definitions" ), content := 0, count := [ 6, 3, 10, 4 ], mathmode := "Text", name := "Ref", next := 269351, root := ~, start := 269302, stop := 269350 ), rec( content := " for the\ definition of a directed cycle.\n Note the empty digraphs on 0 and 1 verti\ ces are considered to be\n Hamiltonian.", count := [ 6, 3, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 10, 5 ], mathmode := "Text", name := "P", next := 269481, root := ~, start := 269477, stop := 269480 ), rec( content := "\n\n \ The method used in this operation has the worst case complexity as\n ", count := [ 6, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ Monomorphism" ), content := 0, count := [ 6, 3, 10, 5 ], mathmode := "Text", name := "Ref", next := 269591, root := ~, start := 269558, stop := 269590 ), rec( content := ".\n " , count := [ 6, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 10, 6 ], mathmode := "Text", name := "P", next := 269601, root := ~, start := 269597, stop := 269600 ), rec( content := "\n \ \n If the argument ", count := [ 6, 3, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 10, 6 ], mathmode := "Text", name := "A", next := 269643, root := ~, start := 269629, stop := 269642 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n ", count := [ 6, 3, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> g := Digraph([[]]);\n\ngap> IsHam\ iltonianDigraph(g);\ntrue\ngap> g := Digraph([[2], [1]]);\n\ngap> IsHamiltonianDigraph(g);\ntrue\ngap> g := Digr\ aph([[3], [], [2]]);\n\ngap> IsHam\ iltonianDigraph(g);\nfalse\ngap> g := Digraph([[2], [3], [1]]);\n\ngap> IsHamiltonianDigraph(g);\ntrue\n", count := [ 6, 3, 10, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 6, 3, 10, 7 ], mathmode := "Text", name := "Example", next := 270219, root := ~, start := 269744, stop := 270218 ), rec( content := "\n ", count := [ 6, 3, 10, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "Description", next := 270236, root := ~, start := 269047, stop := 270235 ) ], count := [ 6, 3, 10, 1 ], mathmode := "Text", name := "ManSection", next := 270250, root := ~, start := 268930, stop := 270249 ), rec( content := "\n\n ", count := [ 6, 3, 10, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsCycleDigraph"\ ), content := 0, count := [ 6, 3, 11, 2 ], mathmode := "Text", name := "Prop", next := 270314, root := ~, start := 270271, stop := 270313 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "K", next := 270337, root := ~, start := 270326, stop := 270336 ), rec( content := " or ", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "K", next := 270353, root := ~, start := 270341, stop := 270352 ), rec( content := ".", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "Returns", next := 270364, root := ~, start := 270317, stop := 270363 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sCycleDigraph", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "C", next := 270406, root := ~, start := 270385, stop := 270405 ), rec( content := " returns\ ", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "K", next := 270426, root := ~, start := 270415, stop := 270425 ), rec( content := " if the \ digraph ", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "A", next := 270456, root := ~, start := 270442, stop := 270455 ), rec( content := " is\n \ isomorphic to the cycle digraph with the same number of vertices as\n ", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "A", next := 270550, root := ~, start := 270536, stop := 270549 ), rec( content := ", and ", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "K", next := 270568, root := ~, start := 270556, stop := 270567 ), rec( content := " if it i\ s not; see ", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "CycleDi\ graph" ), content := 0, count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "Ref", next := 270619, root := ~, start := 270587, stop := 270618 ), rec( content := ".", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 11, 4 ], mathmode := "Text", name := "P", next := 270624, root := ~, start := 270620, stop := 270623 ), rec( content := "\n\n \ A digraph is a ", count := [ 6, 3, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ ycle", count := [ 6, 3, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 11, 4 ], mathmode := "Text", name := "E", next := 270657, root := ~, start := 270645, stop := 270656 ), rec( content := " if and \ only if it is strongly connected and has\n the same number of edges as vert\ ices. \n ", count := [ 6, 3, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 3, 11, 5 ], mathmode := "Text", name := "P", next := 270757, root := ~, start := 270753, stop := 270756 ), rec( content := "\n \ \n If the argument ", count := [ 6, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 11, 5 ], mathmode := "Text", name := "A", next := 270799, root := ~, start := 270785, stop := 270798 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n", count := [ 6, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[1, 3], [2, 3], [3]]);\n\ngap> IsCycleDigraph(D);\nfalse\ngap> D := CycleDigraph(5);\n\ngap> IsCycleDigraph(D);\ntrue\ngap> D := \ OnDigraphs(D, (1, 2, 3));\n\ngap> \ D = CycleDigraph(5);\nfalse\ngap> IsCycleDigraph(D);\ntrue", count := [ 6, 3, 11, 6 ], name := "PCD\ ATA", root := ~ ) ], count := [ 6, 3, 11, 6 ], mathmode := "Text", name := "Example", next := 271284, root := ~, start := 270896, stop := 271283 ), rec( content := "\n ", count := [ 6, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "Description", next := 271301, root := ~, start := 270367, stop := 271300 ) ], count := [ 6, 3, 11, 1 ], mathmode := "Text", name := "ManSection", next := 271315, root := ~, start := 270256, stop := 271314 ), rec( content := "\n\n ", count := [ 6, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 3, 0, 1 ], mathmode := "Text", name := "Section", next := 271329, root := ~, start := 256221, stop := 271328 ) , rec( content := "\n \n ", count := [ 6, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Planarity", count := [ 6, 4, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 0, 2 ], mathmode := "Text", name := "Heading", next := 271372, root := ~, start := 271344, stop := 271371 ), rec( content := "\n ", count := [ 6, 4, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsPlanarDigraph\ " ), content := 0, count := [ 6, 4, 1, 2 ], mathmode := "Text", name := "Prop", next := 271436, root := ~, start := 271392, stop := 271435 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "K", next := 271459, root := ~, start := 271448, stop := 271458 ), rec( content := " or ", count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "K", next := 271475, root := ~, start := 271463, stop := 271474 ), rec( content := ".", count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "Returns", next := 271486, root := ~, start := 271439, stop := 271485 ), rec( attributes := rec( ), content := [ rec( content := "\n A " , count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ lanar", count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "E", next := 271522, root := ~, start := 271509, stop := 271521 ), rec( content := " digraph\ is a digraph that can be embedded in the plane in\n such a way that its ed\ ges do not intersect. A digraph is planar if and only\n if it does not have\ a subdigraph that is homeomorphic to either the\n complete graph on ", count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "5\ ", count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "C", next := 271763, root := ~, start := 271755, stop := 271762 ), rec( content := " vertice\ s or the complete bipartite graph with\n vertex sets of sizes ", count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "3\ ", count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "C", next := 271843, root := ~, start := 271835, stop := 271842 ), rec( content := " and ", count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "3\ ", count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "C", next := 271856, root := ~, start := 271848, stop := 271855 ), rec( content := ".\n " , count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "P", next := 271866, root := ~, start := 271862, stop := 271865 ), rec( content := "\n \n\ ", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sPlanarDigraph", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "C", next := 271898, root := ~, start := 271876, stop := 271897 ), rec( content := " returns\ ", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "K", next := 271918, root := ~, start := 271907, stop := 271917 ), rec( content := " if the \ digraph ", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "A", next := 271948, root := ~, start := 271934, stop := 271947 ), rec( content := " is\n \ planar and ", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "K", next := 271979, root := ~, start := 271967, stop := 271978 ), rec( content := " if it i\ s not. The directions and multiplicities of\n any edges in ", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "A", next := 272062, root := ~, start := 272048, stop := 272061 ), rec( content := " are ign\ ored by ", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sPlanarDigraph", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "C", next := 272100, root := ~, start := 272078, stop := 272099 ), rec( content := ".\n " , count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 4, 1, 5 ], mathmode := "Text", name := "P", next := 272110, root := ~, start := 272106, stop := 272109 ), rec( content := " \n\n \ See also ", count := [ 6, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsOuter\ PlanarDigraph" ), content := 0, count := [ 6, 4, 1, 5 ], mathmode := "Text", name := "Ref", next := 272160, root := ~, start := 272126, stop := 272159 ), rec( content := ".\n " , count := [ 6, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 4, 1, 6 ], mathmode := "Text", name := "P", next := 272170, root := ~, start := 272166, stop := 272169 ), rec( content := "\n\n \ This method uses the reference implementation in\n ", count := [ 6, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "edge-addition-planarity-suite" ), content := [ rec( content := \ "https://github.com/graph-algorithms/edge-addition-planarity-suite", count := [ \ 6, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 1, 6 ], mathmode := \ "Text", name := "URL", next := 140, root := ~, start := 17, stop := 139 ) ], count := [ 6, 4, 1, 6 ], name := "Alt", next := 146, root := ~, start := 1, stop := 145 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "edge-addition-planarity-suite", count \ := [ 6, 4, 1, 6 ], name := "PCDATA", root := ~ ) ], count := [ 6, 4, 1, 6 ], name := "Pac\ kage", next := 218, root := ~, start := 170, stop := 217 ) ], count := [ 6, 4, 1, 6 ], mathmode := "Text", name := "Alt", next := 224, root := ~, start := 146, stop := 223 ), rec( content := " by John\ Boyer of the algorithms described\n in ", count := [ 6, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "BM06" ), content := 0, count := [ 6, 4, 1, 6 ], mathmode := "Text", name := "Cite", next := 272328, root := ~, start := 272310, stop := 272327 ), rec( content := ".\n\n \ ", count := [ 6, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> IsPlanarDigraph(CompleteDigraph(4));\ntrue\ngap> IsPlanarDigraph(Complet\ eDigraph(5));\nfalse\ngap> IsPlanarDigraph(CompleteBipartiteDigraph(2, 3));\nt\ rue\ngap> IsPlanarDigraph(CompleteBipartiteDigraph(3, 3));\nfalse\ngap> IsPlan\ arDigraph(CompleteDigraph(IsMutableDigraph, 4));\ntrue\ngap> IsPlanarDigraph(C\ ompleteDigraph(IsMutableDigraph, 5));\nfalse\ngap> IsPlanarDigraph(CompleteBip\ artiteDigraph(IsMutableDigraph, 2, 3));\ntrue\ngap> IsPlanarDigraph(CompleteBi\ partiteDigraph(IsMutableDigraph, 3, 3));\nfalse\n", count := [ 6, 4, 1, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 6, 4, 1, 7 ], mathmode := "Text", name := "Example", next := 272867, root := ~, start := 272335, stop := 272866 ), rec( content := "\n ", count := [ 6, 4, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "Description", next := 272884, root := ~, start := 271489, stop := 272883 ) ], count := [ 6, 4, 1, 1 ], mathmode := "Text", name := "ManSection", next := 272898, root := ~, start := 271377, stop := 272897 ), rec( content := "\n\n ", count := [ 6, 4, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsOuterPlanarDi\ graph" ), content := 0, count := [ 6, 4, 2, 2 ], mathmode := "Text", name := "Prop", next := 272968, root := ~, start := 272919, stop := 272967 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "K", next := 272991, root := ~, start := 272980, stop := 272990 ), rec( content := " or ", count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "K", next := 273007, root := ~, start := 272995, stop := 273006 ), rec( content := ".", count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "Returns", next := 273018, root := ~, start := 272971, stop := 273017 ), rec( attributes := rec( ), content := [ rec( content := "\n An \ ", count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ uter planar", count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "E", next := 273061, root := ~, start := 273042, stop := 273060 ), rec( content := " digraph\ is a digraph that can be embedded in the\n plane in such a way that its ed\ ges do not intersect, and all vertices\n belong to the unbounded face of th\ e embedding. A digraph is outer planar\n if and only if it does not have a\ subdigraph that is homeomorphic to either\n the complete graph on ", count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "4\ ", count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "C", next := 273377, root := ~, start := 273369, stop := 273376 ), rec( content := " vertice\ s or the complete bipartite graph\n with vertex sets of sizes ", count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "2\ ", count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "C", next := 273457, root := ~, start := 273449, stop := 273456 ), rec( content := " and ", count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "3\ ", count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "C", next := 273470, root := ~, start := 273462, stop := 273469 ), rec( content := ".\n " , count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "P", next := 273480, root := ~, start := 273476, stop := 273479 ), rec( content := "\n \n\ ", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sOuterPlanarDigraph", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "C", next := 273517, root := ~, start := 273490, stop := 273516 ), rec( content := " returns\ ", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "K", next := 273537, root := ~, start := 273526, stop := 273536 ), rec( content := " if the \ digraph\n ", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "A", next := 273571, root := ~, start := 273557, stop := 273570 ), rec( content := " is oute\ r planar and ", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "K", next := 273604, root := ~, start := 273592, stop := 273603 ), rec( content := " if it i\ s not. The\n directions and multiplicities of any edges in ", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "A", next := 273687, root := ~, start := 273673, stop := 273686 ), rec( content := " are ign\ ored by\n ", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sPlanarDigraph", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "C", next := 273729, root := ~, start := 273707, stop := 273728 ), rec( content := ". ", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 4, 2, 5 ], mathmode := "Text", name := "P", next := 273736, root := ~, start := 273732, stop := 273735 ), rec( content := "\n\n \ See also ", count := [ 6, 4, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsPlana\ rDigraph" ), content := 0, count := [ 6, 4, 2, 5 ], mathmode := "Text", name := "Ref", next := 273780, root := ~, start := 273751, stop := 273779 ), rec( content := ".\n\n \ This method uses the reference implementation in\n ", count := [ 6, 4, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "edge-addition-planarity-suite" ), content := [ rec( content := \ "https://github.com/graph-algorithms/edge-addition-planarity-suite", count := [ \ 6, 4, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 2, 5 ], mathmode := \ "Text", name := "URL", next := 140, root := ~, start := 17, stop := 139 ) ], count := [ 6, 4, 2, 5 ], name := "Alt", next := 146, root := ~, start := 1, stop := 145 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "edge-addition-planarity-suite", count \ := [ 6, 4, 2, 5 ], name := "PCDATA", root := ~ ) ], count := [ 6, 4, 2, 5 ], name := "Pac\ kage", next := 218, root := ~, start := 170, stop := 217 ) ], count := [ 6, 4, 2, 5 ], mathmode := "Text", name := "Alt", next := 224, root := ~, start := 146, stop := 223 ), rec( content := " by John\ Boyer of the algorithms described\n in ", count := [ 6, 4, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "BM06" ), content := 0, count := [ 6, 4, 2, 5 ], mathmode := "Text", name := "Cite", next := 273939, root := ~, start := 273921, stop := 273938 ), rec( content := ".\n\n", count := [ 6, 4, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> IsOuterPlanarDigraph(CompleteDigraph(4));\nfalse\ngap> IsOuterPlanarDigr\ aph(CompleteDigraph(5));\nfalse\ngap> IsOuterPlanarDigraph(CompleteBipartiteDi\ graph(2, 3));\nfalse\ngap> IsOuterPlanarDigraph(CompleteBipartiteDigraph(3, 3)\ );\nfalse\ngap> IsOuterPlanarDigraph(CycleDigraph(10));\ntrue\ngap> IsOuterPla\ narDigraph(CompleteDigraph(IsMutableDigraph, 4));\nfalse\ngap> IsOuterPlanarDi\ graph(CompleteDigraph(IsMutableDigraph, 5));\nfalse\ngap> IsOuterPlanarDigraph\ (CompleteBipartiteDigraph(IsMutableDigraph,\n> \ 2, 3));\nfalse\ngap> IsOuterPlanarDigraph(CompleteBipartiteD\ igraph(IsMutableDigraph,\n> 3\ , 3));\nfalse\ngap> IsOuterPlanarDigraph(CycleDigraph(IsMutableDigraph, 10));\ \ntrue\n\n", count := [ 6, 4, 2, 6 ], name := "PCDATA", root := ~ ) ], count := [ 6, 4, 2, 6 ], mathmode := "Text", name := "Example", next := 274739, root := ~, start := 273942, stop := 274738 ), rec( content := "\n ", count := [ 6, 4, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "Description", next := 274756, root := ~, start := 273021, stop := 274755 ) ], count := [ 6, 4, 2, 1 ], mathmode := "Text", name := "ManSection", next := 274770, root := ~, start := 272904, stop := 274769 ), rec( content := "\n\n ", count := [ 6, 4, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 4, 0, 1 ], mathmode := "Text", name := "Section", next := 274784, root := ~, start := 271335, stop := 274783 ) , rec( content := "\n\n ", count := [ 6, 4, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Homomorphisms and\ transformations", count := [ 6, 5, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 0, 2 ], mathmode := "Text", name := "Heading", next := 274849, root := ~, start := 274797, stop := 274848 ), rec( content := "\n ", count := [ 6, 5, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsDigraphCore" ), content := 0, count := [ 6, 5, 1, 2 ], mathmode := "Text", name := "Prop", next := 274911, root := ~, start := 274869, stop := 274910 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "K", next := 274934, root := ~, start := 274923, stop := 274933 ), rec( content := " or ", count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "K", next := 274950, root := ~, start := 274938, stop := 274949 ), rec( content := ".", count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "Returns", next := 274961, root := ~, start := 274914, stop := 274960 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s property returns ", count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "K", next := 275015, root := ~, start := 275004, stop := 275014 ), rec( content := " if ", count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "A", next := 275033, root := ~, start := 275019, stop := 275032 ), rec( content := " is a co\ re,\n and ", count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "K", next := 275065, root := ~, start := 275053, stop := 275064 ), rec( content := " if it i\ s not.", count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "P", next := 275083, root := ~, start := 275079, stop := 275082 ), rec( content := "\n\n \ A digraph ", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ ", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "C", next := 275107, root := ~, start := 275099, stop := 275106 ), rec( content := " is a ", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ ore", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "E", next := 275124, root := ~, start := 275113, stop := 275123 ), rec( content := " if and \ only if it has no proper\n subdigraphs ", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A\ ", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "C", next := 275181, root := ~, start := 275173, stop := 275180 ), rec( content := " such th\ at there exists a homomorphism from ", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ ", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "C", next := 275233, root := ~, start := 275225, stop := 275232 ), rec( content := "\n to\ ", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "A\ ", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "C", next := 275249, root := ~, start := 275241, stop := 275248 ), rec( content := ". In oth\ er words, a digraph ", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ ", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "C", next := 275285, root := ~, start := 275277, stop := 275284 ), rec( content := " is a co\ re if and only if\n every endomorphism on ", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ ", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "C", next := 275345, root := ~, start := 275337, stop := 275344 ), rec( content := " is an a\ utomorphism on ", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ ", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "C", next := 275376, root := ~, start := 275368, stop := 275375 ), rec( content := ".\n " , count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 5, 1, 5 ], mathmode := "Text", name := "P", next := 275386, root := ~, start := 275382, stop := 275385 ), rec( content := "\n \ \n If the argument ", count := [ 6, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 1, 5 ], mathmode := "Text", name := "A", next := 275428, root := ~, start := 275414, stop := 275427 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n ", count := [ 6, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CompleteDigraph(6);\n\n\ gap> IsDigraphCore(D);\ntrue\ngap> D := DigraphSymmetricClosure(CycleDigraph(6\ ));\n\ngap> DigraphHomo\ morphism(D, CompleteDigraph(2));\nTransformation( [ 1, 2, 1, 2, 1, 2 ] )\ngap>\ IsDigraphCore(D);\nfalse\n", count := [ 6, 5, 1, 6 ], name := "PCDATA", root := ~ ) ], count := [ 6, 5, 1, 6 ], mathmode := "Text", name := "Example", next := 275889, root := ~, start := 275529, stop := 275888 ), rec( content := "\n ", count := [ 6, 5, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "Description", next := 275906, root := ~, start := 274964, stop := 275905 ) ], count := [ 6, 5, 1, 1 ], mathmode := "Text", name := "ManSection", next := 275920, root := ~, start := 274854, stop := 275919 ), rec( content := "\n\n ", count := [ 6, 5, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsEdgeTransitiv\ e" ), content := 0, count := [ 6, 5, 2, 2 ], mathmode := "Text", name := "Prop", next := 275986, root := ~, start := 275941, stop := 275985 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "K", next := 276009, root := ~, start := 275998, stop := 276008 ), rec( content := " or ", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "K", next := 276025, root := ~, start := 276013, stop := 276024 ), rec( content := ".", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "Returns", next := 276036, root := ~, start := 275989, stop := 276035 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "A", next := 276074, root := ~, start := 276060, stop := 276073 ), rec( content := " is a di\ graph without multiple edges, then\n ", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sEdgeTransitive", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "C", next := 276144, root := ~, start := 276121, stop := 276143 ), rec( content := " returns\ ", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "K", next := 276164, root := ~, start := 276153, stop := 276163 ), rec( content := " if ", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "A", next := 276182, root := ~, start := 276168, stop := 276181 ), rec( content := "\n is\ edge transitive, and ", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "K", next := 276223, root := ~, start := 276211, stop := 276222 ), rec( content := " otherwi\ se. A digraph is\n ", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dge transitive", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "E", next := 276274, root := ~, start := 276252, stop := 276273 ), rec( content := " if its \ automorphism group acts\n transitively on its edges (via the action\n ", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "ref\ ", Func := "OnPairs" ), content := 0, count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "Ref", next := 276392, root := ~, start := 276356, stop := 276391 ), rec( content := ").\n \ ", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 5, 2, 4 ], mathmode := "Text", name := "P", next := 276403, root := ~, start := 276399, stop := 276402 ), rec( content := "\n \ \n If the argument ", count := [ 6, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 2, 4 ], mathmode := "Text", name := "A", next := 276445, root := ~, start := 276431, stop := 276444 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n ", count := [ 6, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> IsEdgeTransitive(CompleteDigraph(2));\ntrue\ngap> IsEdgeTransitive(Chain\ Digraph(3));\nfalse\ngap> IsEdgeTransitive(Digraph([[2], [3, 3, 3], []]));\nEr\ ror, the argument must be a digraph with no multiple edges,\n", count := [ 6, 5, 2, 5 ], name := "PCD\ ATA", root := ~ ) ], count := [ 6, 5, 2, 5 ], mathmode := "Text", name := "Example", next := 276792, root := ~, start := 276546, stop := 276791 ), rec( content := "\n ", count := [ 6, 5, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "Description", next := 276809, root := ~, start := 276039, stop := 276808 ) ], count := [ 6, 5, 2, 1 ], mathmode := "Text", name := "ManSection", next := 276823, root := ~, start := 275926, stop := 276822 ), rec( content := "\n\n ", count := [ 6, 5, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "IsVertexTransit\ ive" ), content := 0, count := [ 6, 5, 3, 2 ], mathmode := "Text", name := "Prop", next := 276891, root := ~, start := 276844, stop := 276890 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "K", next := 276914, root := ~, start := 276903, stop := 276913 ), rec( content := " or ", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "K", next := 276930, root := ~, start := 276918, stop := 276929 ), rec( content := ".", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "Returns", next := 276941, root := ~, start := 276894, stop := 276940 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "A", next := 276979, root := ~, start := 276965, stop := 276978 ), rec( content := " is a di\ graph, then ", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sVertexTransitive", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "C", next := 277024, root := ~, start := 276999, stop := 277023 ), rec( content := " returns\ \n ", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "K", next := 277048, root := ~, start := 277037, stop := 277047 ), rec( content := " if ", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "A", next := 277066, root := ~, start := 277052, stop := 277065 ), rec( content := " is vert\ ex transitive, and ", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "K", next := 277105, root := ~, start := 277093, stop := 277104 ), rec( content := "\n ot\ herwise. A digraph is ", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ertex transitive", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "E", next := 277158, root := ~, start := 277134, stop := 277157 ), rec( content := " if its \ automorphism group\n acts transitively on its vertices.\n ", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 6, 5, 3, 4 ], mathmode := "Text", name := "P", next := 277232, root := ~, start := 277228, stop := 277231 ), rec( content := "\n \ \n If the argument ", count := [ 6, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 6, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 3, 4 ], mathmode := "Text", name := "A", next := 277274, root := ~, start := 277260, stop := 277273 ), rec( content := " is muta\ ble, then the return value of\n this property is recomputed every time it i\ s called. \n\n ", count := [ 6, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> IsVertexTransitive(CompleteDigraph(2));\ntrue\ngap> IsVertexTransitive(C\ hainDigraph(3));\nfalse\n", count := [ 6, 5, 3, 5 ], name := "PCDATA", root := ~ ) ], count := [ 6, 5, 3, 5 ], mathmode := "Text", name := "Example", next := 277505, root := ~, start := 277375, stop := 277504 ), rec( content := "\n ", count := [ 6, 5, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "Description", next := 277522, root := ~, start := 276944, stop := 277521 ) ], count := [ 6, 5, 3, 1 ], mathmode := "Text", name := "ManSection", next := 277536, root := ~, start := 276829, stop := 277535 ), rec( content := "\n\n ", count := [ 6, 5, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 5, 0, 1 ], mathmode := "Text", name := "Section", next := 277550, root := ~, start := 274788, stop := 277549 ) , rec( content := "\n\n \n", count := [ 6, 5, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 6, 0, 0, 1 ], mathmode := "Text", name := "Chapter", next := 277565, root := ~, start := 231997, stop := 277564 ), rec( content := "\n ", count := [ 6, 5, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := " properties ", count := [ 6, 5, 3, 6 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n ", count := [ 6, 5, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "Homomorphisms" ), content := [ rec( attributes := rec( ), content := [ rec( content := "Homomorphisms", count := [ 7, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 0, 0, 2 ], mathmode := "Text", name := "Heading", next := 277652, root := ~, start := 277620, stop := 277651 ) , rec( content := "\n ", count := [ 7, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := "Let $E_a=(E_a^0,E_a^1,\\ra_a,\\s\ o_a)$ and $E_b=(E_b^0,E_b^1,\\ra_b,\\so_b)$ be two\ngraphs, and let $\\phi_0 :\ E_a^0 \\to E_b^0$ and $\\phi_1 : E_a^1 \\to E_b^1$ be\nfunctions. Then the pa\ ir $\\phi = (\\phi_0, \\phi_1)$ is a \\emph{graph homomorphism\nfrom} $E_a$ \\\ emph{to} $E_b$ if $\\phi_0(\\so_a(e)) = \\so_b(\\phi_1(e))$ and\n$\\phi_0(\\ra\ _a(e)) = \\ra_b(\\phi_1(e))$ for every $e \\in E_a^1$. If $\\phi_0$ and\n$\\ph\ i_1$ are in addition bijective, then $\\phi$ is a \\emph{graph isomorphism\nfr\ om} $E_a$ \\emph{to} $E_b$. In this case we say that $E_a$ and $E_b$ are\n\\em\ ph{isomorphic} and write $E_a \\cong E_b$.", count := [ 7, 0, 0, 3 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n\n ", count := [ 7, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Acting on digraph\ s", count := [ 7, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 0, 2 ], mathmode := "Text", name := "Heading", next := 278296, root := ~, start := 278259, stop := 278295 ), rec( content := "\n ", count := [ 7, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, perm", Label := "for a digraph \ and a perm", Name := "OnDigraphs" ), content := 0, count := [ 7, 1, 1, 2 ], mathmode := "Text", name := "Oper", next := 278398, root := ~, start := 278316, stop := 278397 ), rec( attributes := rec( Arg := "digraph, trans", Label := "for a digraph \ and a transformation", Name := "OnDigraphs" ), content := 0, count := [ 7, 1, 1, 4 ], mathmode := "Text", name := "Oper", next := 278494, root := ~, start := 278401, stop := 278493 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "Returns", next := 278526, root := ~, start := 278497, stop := 278525 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "A", next := 278564, root := ~, start := 278550, stop := 278563 ), rec( content := " is a di\ graph, and the second argument ", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ erm", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "A", next := 278614, root := ~, start := 278603, stop := 278613 ), rec( content := " is a\n \ ", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ ermutation", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "E", next := 278642, root := ~, start := 278624, stop := 278641 ), rec( content := " of the \ vertices of ", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "A", next := 278676, root := ~, start := 278662, stop := 278675 ), rec( content := ", then t\ his operation\n returns a digraph constructed by relabelling the vertices o\ f\n ", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "A", next := 278781, root := ~, start := 278767, stop := 278780 ), rec( content := " accordi\ ng to ", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ erm", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "A", next := 278806, root := ~, start := 278795, stop := 278805 ), rec( content := ". Note \ that for an automorphism\n ", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "C", next := 278851, root := ~, start := 278843, stop := 278850 ), rec( content := " of a di\ graph, we have ", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ nDigraphs(", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "digraph", count := [ 7, 1, 1, 5 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 5 ], mathmode := \ "Text", name := "A", next := 278902, root := ~, start := 278888, stop := 27890\ 1 ), rec( content := ", f) =\n ", count := [ 7, 1, 1, 5 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "C", next := 278917, root := ~, start := 278874, stop := 278916 ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "A", next := 278931, root := ~, start := 278917, stop := 278930 ), rec( content := ".\n " , count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "P", next := 278941, root := ~, start := 278937, stop := 278940 ), rec( content := "\n\n \ If the second argument is a ", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ ransformation", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "E", next := 278996, root := ~, start := 278975, stop := 278995 ), rec( content := " ", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rans", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "A", next := 279009, root := ~, start := 278997, stop := 279008 ), rec( content := " of the\\ n vertices of ", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "A", next := 279047, root := ~, start := 279033, stop := 279046 ), rec( content := ", then t\ his operation returns a digraph\n constructed by transforming the source an\ d range of each edge according to\n ", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rans", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "A", next := 279182, root := ~, start := 279170, stop := 279181 ), rec( content := ". Thus a\ vertex which does not appear in the image of\n ", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rans", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "A", next := 279252, root := ~, start := 279240, stop := 279251 ), rec( content := " will be\ isolated in the returned digraph, and the returned\n digraph may contain m\ ultiple edges, even if ", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "A", next := 279374, root := ~, start := 279360, stop := 279373 ), rec( content := " does no\ t.\n If ", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rans", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "A", next := 279404, root := ~, start := 279392, stop := 279403 ), rec( content := " is math\ ematically a permutation, then the result coincides\n with ", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ nDigraphs(", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "digraph", count := [ 7, 1, 1, 6 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 6 ], mathmode := \ "Text", name := "A", next := 279501, root := ~, start := 279487, stop := 27950\ 0 ), rec( content := ", AsPermutation(", count := [ 7, 1, 1, 6 ], mathmode := \ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( cont\ ent := "trans", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "A", next := 2795\ 29, root := ~, start := 279517, stop := 279528 ), rec( content := "))", count := [ 7, 1, 1, 6 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "C", next := 279535, root := ~, start := 279473, stop := 279534 ), rec( content := ".\n " , count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 1, 1, 7 ], mathmode := "Text", name := "P", next := 279545, root := ~, start := 279541, stop := 279544 ), rec( content := "\n\n \ The ", count := [ 7, 1, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ VertexLabels" ), content := 0, count := [ 7, 1, 1, 7 ], mathmode := "Text", name := "Ref", next := 279588, root := ~, start := 279555, stop := 279587 ), rec( content := " of ", count := [ 7, 1, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 1, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 7 ], mathmode := "Text", name := "A", next := 279606, root := ~, start := 279592, stop := 279605 ), rec( content := " will no\ t be retained\n in the returned digraph. ", count := [ 7, 1, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "P", next := 279661, root := ~, start := 279657, stop := 279660 ), rec( content := "\n\n \ If ", count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "A", next := 279684, root := ~, start := 279670, stop := 279683 ), rec( content := " belongs\ to ", count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "Ref", next := 279726, root := ~, start := 279696, stop := 279725 ), rec( content := ", then\n\ relabelling of the vertices is performed directly on ", count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "A", next := 279804, root := ~, start := 279790, stop := 279803 ), rec( content := ".\n I\ f ", count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "A", next := 279827, root := ~, start := 279813, stop := 279826 ), rec( content := " belongs\ to ", count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "Ref", next := 279871, root := ~, start := 279839, stop := 279870 ), rec( content := ", an imm\ utable\n copy of ", count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "A", next := 279912, root := ~, start := 279898, stop := 279911 ), rec( content := " with th\ e vertices relabelled is returned.", count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 1, 1, 9 ], mathmode := "Text", name := "P", next := 279958, root := ~, start := 279954, stop := 279957 ), rec( content := "\n\n \ ", count := [ 7, 1, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[3], [1, 3, 5], [1], [1, 2, 4], [2, 3, 5]]);\n\ngap> new := OnDigraphs(D, (1, 2));\n\ngap> OutNeighbours(new);\n[ [ 2, 3, 5 \ ], [ 3 ], [ 2 ], [ 2, 1, 4 ], [ 1, 3, 5 ] ]\ngap> D := Digraph([[2], [], [2]])\ ;\n\ngap> t := Transformation([1, \ 2, 1]);;\ngap> new := OnDigraphs(D, t);\n\ngap> OutNeighbours(new);\n[ [ 2, 2 ], [ ], [ ] ]\ngap> ForAll(\ DigraphEdges(D),\n> e -> IsDigraphEdge(new, [e[1] ^ t, e[2] ^ t]));\ntrue\n", count := [ 7, 1, 1, 10 ], name := "PCD\ ATA", root := ~ ) ], count := [ 7, 1, 1, 10 ], mathmode := "Text", name := "Example", next := 280601, root := ~, start := 279964, stop := 280600 ), rec( content := "\n ", count := [ 7, 1, 1, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "Description", next := 280618, root := ~, start := 278529, stop := 280617 ) ], count := [ 7, 1, 1, 1 ], mathmode := "Text", name := "ManSection", next := 280632, root := ~, start := 278301, stop := 280631 ), rec( content := "\n\n ", count := [ 7, 1, 1, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, pair", Name := "OnMultiDigraphs\ " ), content := 0, count := [ 7, 1, 2, 2 ], mathmode := "Text", name := "Oper", next := 280703, root := ~, start := 280653, stop := 280702 ), rec( attributes := rec( Arg := "digraph, perm1, \ perm2", Label := "for a digraph, perm, and perm", Name := "OnMultiDigraphs" ), content := 0, count := [ 7, 1, 2, 4 ], mathmode := "Text", name := "Oper", next := 280806, root := ~, start := 280706, stop := 280805 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "Returns", next := 280838, root := ~, start := 280809, stop := 280837 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "A", next := 280876, root := ~, start := 280862, stop := 280875 ), rec( content := " is a di\ graph, and ", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ air", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "A", next := 280906, root := ~, start := 280895, stop := 280905 ), rec( content := " is a pa\ ir consisting of a\n permutation of the vertices and a permutation of the e\ dges of\n ", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "A", next := 281017, root := ~, start := 281003, stop := 281016 ), rec( content := ", then t\ his operation returns a digraph\n constructed by relabelling the vertices a\ nd edges of ", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "A", next := 281128, root := ~, start := 281114, stop := 281127 ), rec( content := "\n ac\ cording to ", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ erm[1]", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "A", next := 281160, root := ~, start := 281146, stop := 281159 ), rec( content := " and ", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ erm[2]", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "A", next := 281179, root := ~, start := 281165, stop := 281178 ), rec( content := ", respec\ tively. ", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 1, 2, 6 ], mathmode := "Text", name := "P", next := 281199, root := ~, start := 281195, stop := 281198 ), rec( content := "\n\n \ In its second form, ", count := [ 7, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ nMultiDigraphs", count := [ 7, 1, 2, 6 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 7, 1, 2, 6 ], mathmode := "Text", name := "C", next := 281247, root := ~, start := 281225, stop := 281246 ), rec( content := " returns\ a digraph with vertices\n and edges permuted by ", count := [ 7, 1, 2, 6 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ erm1", count := [ 7, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 6 ], mathmode := "Text", name := "A", next := 281318, root := ~, start := 281306, stop := 281317 ), rec( content := " and ", count := [ 7, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ erm2", count := [ 7, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 6 ], mathmode := "Text", name := "A", next := 281335, root := ~, start := 281323, stop := 281334 ), rec( content := ", respec\ tively. ", count := [ 7, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "P", next := 281355, root := ~, start := 281351, stop := 281354 ), rec( content := "\n\n \ Note that ", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ nDigraphs(", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "digraph", count := [ 7, 1, 2, 7 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 7 ], mathmode := \ "Text", name := "A", next := 281399, root := ~, start := 281385, stop := 28139\ 8 ), rec( content := ",\n perm)=OnMultiDigraphs(", count := [ 7, 1, 2, 7 ], mathmode := \ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( cont\ ent := "digraph", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "A", next := 2814\ 43, root := ~, start := 281429, stop := 281442 ), rec( content := ", [perm, ()\ ])", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "C", next := 281460, root := ~, start := 281371, stop := 281459 ), rec( content := " where " , count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ erm", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "C", next := 281478, root := ~, start := 281467, stop := 281477 ), rec( content := " is\n \ a permutation of the vertices of ", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "A", next := 281533, root := ~, start := 281519, stop := 281532 ), rec( content := ". If you\ are only interested\n in the action of a permutation on the vertices of a \ digraph, then you can\n use ", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ nDigraphs", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "C", next := 281665, root := ~, start := 281648, stop := 281664 ), rec( content := " instead\ of ", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "O\ nMultiDigraphs", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "C", next := 281699, root := ~, start := 281677, stop := 281698 ), rec( content := ".\n\n \ If ", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "A", next := 281723, root := ~, start := 281709, stop := 281722 ), rec( content := " belongs\ to ", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "Ref", next := 281765, root := ~, start := 281735, stop := 281764 ), rec( content := ", then\n\ relabelling of the vertices is performed directly on ", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "A", next := 281843, root := ~, start := 281829, stop := 281842 ), rec( content := ".\n I\ f ", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "A", next := 281866, root := ~, start := 281852, stop := 281865 ), rec( content := " belongs\ to ", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "Ref", next := 281910, root := ~, start := 281878, stop := 281909 ), rec( content := ", an imm\ utable\n copy of ", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "A", next := 281951, root := ~, start := 281937, stop := 281950 ), rec( content := " with th\ e vertices relabelled is returned.", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 1, 2, 8 ], mathmode := "Text", name := "P", next := 281997, root := ~, start := 281993, stop := 281996 ), rec( content := "\n\n \ ", count := [ 7, 1, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D1 := Digraph([\n> [3, 6, 3], [], [3], [9, 10], [9], [], [], [10, 4, 10\ ], [], []]);\n\ngap> p := B\ lissCanonicalLabelling(D1);\n[ (1,7)(3,6)(4,10)(5,9), () ]\ngap> D2 := OnMulti\ Digraphs(D1, p);\n\ngap> Ou\ tNeighbours(D2);\n[ [ ], [ ], [ ], [ ], [ ], [ 6 ], [ 6, 3, 6 ], [ 4, 10,\ 4 ], \n [ 5 ], [ 5, 4 ] ]", count := [ 7, 1, 2, 9 ], name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 9 ], mathmode := "Text", name := "Example", next := 282442, root := ~, start := 282003, stop := 282441 ), rec( content := "\n ", count := [ 7, 1, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "Description", next := 282459, root := ~, start := 280841, stop := 282458 ) ], count := [ 7, 1, 2, 1 ], mathmode := "Text", name := "ManSection", next := 282473, root := ~, start := 280638, stop := 282472 ), rec( content := "\n\n ", count := [ 7, 1, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 0, 1 ], mathmode := "Text", name := "Section", next := 282487, root := ~, start := 278250, stop := 282486 ) , rec( content := "\n\n ", count := [ 7, 1, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "Isomorphisms and canonical lab\ ellings" ), content := [ rec( content := "\n ", count := [ 7, 2, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Isomorphisms and \ canonical labellings", count := [ 7, 2, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 0, 2 ], mathmode := "Text", name := "Heading", next := 282607, root := ~, start := 282551, stop := 282606 ), rec( content := "\n From version 0.11.\ 0 of ", count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " it is possible to use e\ ither ", count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "bliss" ), content := [ rec( content := "http://ww\ w.tcs.tkk.fi/Software/bliss/", count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "URL", next := 81, root := ~, start := 17, stop := 80 ) ], count := [ 7, 2, 0, 3 ], name := "Alt", next := 87, root := ~, start := 1, stop := 86 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes := rec( ), content := [ rec( content := "bliss", count := [ 7, 2, 0, 3 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 0, 3 ], name := "Package", next := 131, root := ~, start := 107, stop := 130 ) ], count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "Alt", next := 137, root := ~, start := 87, stop := 136 ), rec( content := " or\n ", count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "nauty" ), content := [ rec( content := "http://pa\ llini.di.uniroma1.it/", count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "URL", next := 74, root := ~, start := 17, stop := 73 ) ], count := [ 7, 2, 0, 3 ], name := "Alt", next := 80, root := ~, start := 1, stop := 79 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes := rec( ), content := [ rec( content := "nauty", count := [ 7, 2, 0, 3 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 0, 3 ], name := "Package", next := 124, root := ~, start := 100, stop := 123 ) ], count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "Alt", next := 130, root := ~, start := 80, stop := 129 ), rec( content := " (via ", count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "NautyTracesInte\ rface" ), content := [ rec( content := "https://github.com/gap-packages/NautyT\ racesInterface", count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], count := [ 7, 2, 0, 3 ], name := "Alt", next := 117, root := ~, start := 1, stop := 116 ) , rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes := rec( ), content := [ rec( content := "NautyTrac\ esInterface", count := [ 7, 2, 0, 3 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 0, 3 ], name := "Package", next := 176, root := ~, start := 137, stop := 175 ) ], count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "Alt", next := 182, root := ~, start := 117, stop := 181 ), rec( content := ") to calculate canonical\ labellings and\n automorphism groups of digraphs; see ", count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "JK07" ), content := 0, count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "Cite", next := 282824, root := ~, start := 282806, stop := 282823 ), rec( content := " and ", count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "MP14" ), content := 0, count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "Cite", next := 282853, root := ~, start := 282829, stop := 282852 ), rec( content := " for more details about \ ", count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "bliss" ), content := [ rec( content := "http://ww\ w.tcs.tkk.fi/Software/bliss/", count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "URL", next := 81, root := ~, start := 17, stop := 80 ) ], count := [ 7, 2, 0, 3 ], name := "Alt", next := 87, root := ~, start := 1, stop := 86 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes := rec( ), content := [ rec( content := "bliss", count := [ 7, 2, 0, 3 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 0, 3 ], name := "Package", next := 131, root := ~, start := 107, stop := 130 ) ], count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "Alt", next := 137, root := ~, start := 87, stop := 136 ), rec( content := " and ", count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "nauty" ), content := [ rec( content := "http://pa\ llini.di.uniroma1.it/", count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "URL", next := 74, root := ~, start := 17, stop := 73 ) ], count := [ 7, 2, 0, 3 ], name := "Alt", next := 80, root := ~, start := 1, stop := 79 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes := rec( ), content := [ rec( content := "nauty", count := [ 7, 2, 0, 3 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 0, 3 ], name := "Package", next := 124, root := ~, start := 100, stop := 123 ) ], count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "Alt", next := 130, root := ~, start := 80, stop := 129 ), rec( content := ",\n respectively. \n\\ n ", count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "", Name := "DigraphsUseNaut\ y" ), content := 0, count := [ 7, 2, 1, 2 ], mathmode := "Text", name := "Func", next := 282975, root := ~, start := 282937, stop := 282974 ), rec( attributes := rec( Arg := "", Name := "DigraphsUseBlis\ s" ), content := 0, count := [ 7, 2, 1, 4 ], mathmode := "Text", name := "Func", next := 283016, root := ~, start := 282978, stop := 283015 ), rec( attributes := rec( ), content := [ rec( content := "Nothing." , count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "Returns", next := 283046, root := ~, start := 283019, stop := 283045 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ se functions can be used to specify whether ", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\ ma1.it/", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root \ := ~ ) ], count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "URL", next := 74, root := ~, start := 17, stop := 73 ) ], count := [ 7, 2, 1, 5 ], name := "Alt", next := 80, root := ~, start := 1, stop := 79 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "nauty", count := [ 7, 2, 1, 5 ], name \ := "PCDATA", root := ~ ) ], count := [ 7, 2, 1, 5 ], name := "Package", next := 124, root := ~, start := 100 , stop := 123 ) ], count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "Alt", next := 130, root := ~, start := 80, stop := 129 ), rec( content := " or ", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\ oftware/bliss/", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA" , root\ := ~ ) ], count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "URL", next := 81, root := ~, start := 17, stop := 80 ) ], count := [ 7, 2, 1, 5 ], name := "Alt", next := 87, root := ~, start := 1, stop := 86 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "bliss", count := [ 7, 2, 1, 5 ], name \ := "PCDATA", root := ~ ) ], count := [ 7, 2, 1, 5 ], name := "Package", next := 131, root := ~, start := 107 , stop := 130 ) ], count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "Alt", next := 137, root := ~, start := 87, stop := 136 ), rec( content := " should \ be\n used by default by ", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphs", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := ". If ", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\ github.com/gap-packages/NautyTracesInterface", count := [ 7, 2, 1, 5 ], mathmo\ de := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 1, 5 ], mathmode := \ "Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], count := [ 7, 2, 1, 5 ], name := "Alt", next := 117, root := ~, start := 1, stop := 116 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "NautyTracesInterface", count := [ 7, 2\ , 1, 5 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 1, 5 ], name := "Pac\ kage", next := 176, root := ~, start := 137, stop := 175 ) ], count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "Alt", next := 182, root := ~, start := 117, stop := 181 ), rec( content := " is not \ available,\n then these functions do nothing. Otherwise, by calling\n ", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphsUseNauty", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "C", next := 283308, root := ~, start := 283285, stop := 283307 ), rec( content := " subsequ\ ent computations will default to using\n ", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\ ma1.it/", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root \ := ~ ) ], count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "URL", next := 74, root := ~, start := 17, stop := 73 ) ], count := [ 7, 2, 1, 5 ], name := "Alt", next := 80, root := ~, start := 1, stop := 79 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "nauty", count := [ 7, 2, 1, 5 ], name \ := "PCDATA", root := ~ ) ], count := [ 7, 2, 1, 5 ], name := "Package", next := 124, root := ~, start := 100 , stop := 123 ) ], count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "Alt", next := 130, root := ~, start := 80, stop := 129 ), rec( content := " rather \ than ", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\ oftware/bliss/", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA" , root\ := ~ ) ], count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "URL", next := 81, root := ~, start := 17, stop := 80 ) ], count := [ 7, 2, 1, 5 ], name := "Alt", next := 87, root := ~, start := 1, stop := 86 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "bliss", count := [ 7, 2, 1, 5 ], name \ := "PCDATA", root := ~ ) ], count := [ 7, 2, 1, 5 ], name := "Package", next := 131, root := ~, start := 107 , stop := 130 ) ], count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "Alt", next := 137, root := ~, start := 87, stop := 136 ), rec( content := ", where \ possible.\n ", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 1, 6 ], mathmode := "Text", name := "P", next := 283412, root := ~, start := 283408, stop := 283411 ), rec( content := "\n\n \ You can call these functions at any point in a ", count := [ 7, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ AP", count := [ 7, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 1, 6 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " session\ , as many\n times as you like, it is guaranteed that existing digraphs rema\ in\n valid, and that comparison of existing digraphs and newly created digr\ aphs\n via\n ", count := [ 7, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for di\ graphs", Oper := "IsIsomorphicDigraph" ), content := 0, count := [ 7, 2, 1, 6 ], mathmode := "Text", name := "Ref", next := 283703, root := ~, start := 283649, stop := 283702 ), rec( content := ",\n " , count := [ 7, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for di\ graphs and homogeneous lists", Oper := "IsIsomorphicDigraph" ), content := 0, count := [ 7, 2, 1, 6 ], mathmode := "Text", name := "Ref", next := 283791, root := ~, start := 283709, stop := 283790 ), rec( content := ",\n " , count := [ 7, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for di\ graphs", Oper := "IsomorphismDigraphs" ), content := 0, count := [ 7, 2, 1, 6 ], mathmode := "Text", name := "Ref", next := 283851, root := ~, start := 283797, stop := 283850 ), rec( content := ", and\n \ ", count := [ 7, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for di\ graphs and homogeneous lists", Oper := "IsomorphismDigraphs" ), content := 0, count := [ 7, 2, 1, 6 ], mathmode := "Text", name := "Ref", next := 283943, root := ~, start := 283861, stop := 283942 ), rec( content := " are als\ o valid.", count := [ 7, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "P", next := 283963, root := ~, start := 283959, stop := 283962 ), rec( content := "\n\n \ It is also possible to compute the automorphism group of a specific digraph\n \ using both ", count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\ ma1.it/", count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root \ := ~ ) ], count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "URL", next := 74, root := ~, start := 17, stop := 73 ) ], count := [ 7, 2, 1, 7 ], name := "Alt", next := 80, root := ~, start := 1, stop := 79 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "nauty", count := [ 7, 2, 1, 7 ], name \ := "PCDATA", root := ~ ) ], count := [ 7, 2, 1, 7 ], name := "Package", next := 124, root := ~, start := 100 , stop := 123 ) ], count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "Alt", next := 130, root := ~, start := 80, stop := 129 ), rec( content := " and ", count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\ oftware/bliss/", count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "PCDATA" , root\ := ~ ) ], count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "URL", next := 81, root := ~, start := 17, stop := 80 ) ], count := [ 7, 2, 1, 7 ], name := "Alt", next := 87, root := ~, start := 1, stop := 86 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "bliss", count := [ 7, 2, 1, 7 ], name \ := "PCDATA", root := ~ ) ], count := [ 7, 2, 1, 7 ], name := "Package", next := 131, root := ~, start := 107 , stop := 130 ) ], count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "Alt", next := 137, root := ~, start := 87, stop := 136 ), rec( content := " using " , count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "NautyAu\ tomorphismGroup" ), content := 0, count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "Ref", next := 284122, root := ~, start := 284086, stop := 284121 ), rec( content := "\n an\ d ", count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "BlissAu\ tomorphismGroup", Label := "for a digraph" ), content := 0, count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "Ref", next := 284189, root := ~, start := 284131, stop := 284188 ), rec( content := ", respec\ tively.\n ", count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "Description", next := 284221, root := ~, start := 283049, stop := 284220 ) ], count := [ 7, 2, 1, 1 ], mathmode := "Text", name := "ManSection", next := 284235, root := ~, start := 282922, stop := 284234 ), rec( content := "\n\n ", count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Label := "for a digraph" , Name := "AutomorphismGro\ up" ), content := 0, count := [ 7, 2, 2, 2 ], mathmode := "Text", name := "Attr", next := 284324, root := ~, start := 284256, stop := 284323 ), rec( attributes := rec( ), content := [ rec( content := "A permuta\ tion group.", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "Returns", next := 284366, root := ~, start := 284327, stop := 284365 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "A", next := 284404, root := ~, start := 284390, stop := 284403 ), rec( content := " is a di\ graph, then this attribute contains the group of\n automorphisms of ", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "A", next := 284496, root := ~, start := 284482, stop := 284495 ), rec( content := ". An ", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "a\ utomorphism", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "E", next := 284521, root := ~, start := 284502, stop := 284520 ), rec( content := " of ", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "A", next := 284539, root := ~, start := 284525, stop := 284538 ), rec( content := "\n is\ an isomorphism from ", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "A", next := 284581, root := ~, start := 284567, stop := 284580 ), rec( content := " to itse\ lf. See ", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for di\ graphs", Oper := "IsomorphismDigraphs" ), content := 0, count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "Ref", next := 284658, root := ~, start := 284597, stop := 284657 ), rec( content := " for mor\ e information\n about isomorphisms of digraphs. ", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 2, 4 ], mathmode := "Text", name := "P", next := 284720, root := ~, start := 284716, stop := 284719 ), rec( content := "\n\n \ If ", count := [ 7, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 4 ], mathmode := "Text", name := "A", next := 284743, root := ~, start := 284729, stop := 284742 ), rec( content := " is not \ a multidigraph then the automorphism group is\n returned as a group of perm\ utations on the set of vertices of\n ", count := [ 7, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 4 ], mathmode := "Text", name := "A", next := 284881, root := ~, start := 284867, stop := 284880 ), rec( content := ". ", count := [ 7, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 2, 5 ], mathmode := "Text", name := "P", next := 284887, root := ~, start := 284883, stop := 284886 ), rec( content := "\n\n \ If ", count := [ 7, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 5 ], mathmode := "Text", name := "A", next := 284910, root := ~, start := 284896, stop := 284909 ), rec( content := " is a mu\ ltidigraph then the automorphism group is returned\n as the direct product \ of a group of permutations on the set of vertices of\n ", count := [ 7, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 5 ], mathmode := "Text", name := "A", next := 285066, root := ~, start := 285052, stop := 285065 ), rec( content := " with a \ group of permutations on the set of edges of\n ", count := [ 7, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 5 ], mathmode := "Text", name := "A", next := 285137, root := ~, start := 285123, stop := 285136 ), rec( content := ". These \ groups can be accessed using ", count := [ 7, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "ref\ ", Label := "for a domain and a positive integer", Oper := "Projection" ), content := 0, count := [ 7, 2, 2, 5 ], mathmode := "Text", name := "Ref", next := 285263, root := ~, start := 285174, stop := 285262 ), rec( content := " on the\\ n returned group.", count := [ 7, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "P", next := 285294, root := ~, start := 285290, stop := 285293 ), rec( content := "\n\n \ By default, the automorphism group is found using ", count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\ oftware/bliss/", count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "PCDATA" , root\ := ~ ) ], count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "URL", next := 81, root := ~, start := 17, stop := 80 ) ], count := [ 7, 2, 2, 6 ], name := "Alt", next := 87, root := ~, start := 1, stop := 86 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "bliss", count := [ 7, 2, 2, 6 ], name \ := "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 6 ], name := "Package", next := 131, root := ~, start := 107 , stop := 130 ) ], count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "Alt", next := 137, root := ~, start := 87, stop := 136 ), rec( content := " by Tomm\ i Junttila\n and Petteri Kaski. If ", count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\ github.com/gap-packages/NautyTracesInterface", count := [ 7, 2, 2, 6 ], mathmo\ de := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 6 ], mathmode := \ "Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], count := [ 7, 2, 2, 6 ], name := "Alt", next := 117, root := ~, start := 1, stop := 116 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "NautyTracesInterface", count := [ 7, 2\ , 2, 6 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 6 ], name := "Pac\ kage", next := 176, root := ~, start := 137, stop := 175 ) ], count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "Alt", next := 182, root := ~, start := 117, stop := 181 ), rec( content := " is avai\ lable, then ", count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\ ma1.it/", count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root \ := ~ ) ], count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "URL", next := 74, root := ~, start := 17, stop := 73 ) ], count := [ 7, 2, 2, 6 ], name := "Alt", next := 80, root := ~, start := 1, stop := 79 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "nauty", count := [ 7, 2, 2, 6 ], name \ := "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 6 ], name := "Package", next := 124, root := ~, start := 100 , stop := 123 ) ], count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "Alt", next := 130, root := ~, start := 80, stop := 129 ), rec( content := " by\n \ Brendan Mckay and Adolfo Piperno can be used instead; see\n ", count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "BlissAu\ tomorphismGroup", Label := "for a digraph" ), content := 0, count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "Ref", next := 285579, root := ~, start := 285521, stop := 285578 ), rec( content := ", \n \ ", count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "NautyAu\ tomorphismGroup" ), content := 0, count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "Ref", next := 285622, root := ~, start := 285586, stop := 285621 ), rec( content := ", ", count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sUseBliss" ), content := 0, count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "Ref", next := 285654, root := ~, start := 285624, stop := 285653 ), rec( content := ",\n a\ nd ", count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sUseNauty" ), content := 0, count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "Ref", next := 285694, root := ~, start := 285664, stop := 285693 ), rec( content := ".\n " , count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 2, 7 ], mathmode := "Text", name := "P", next := 285704, root := ~, start := 285700, stop := 285703 ), rec( content := "\n\n \ If the argument ", count := [ 7, 2, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 7 ], mathmode := "Text", name := "A", next := 285740, root := ~, start := 285726, stop := 285739 ), rec( content := " is muta\ ble, then the return value of\n this attribute is recomputed every time it \ is called. \n\n ", count := [ 7, 2, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> johnson := DigraphFromGraph6String(\"E}lw\");\n\ngap> G := AutomorphismGroup(johnson);\nGroup([ (3,4), (2\ ,3)(4,5), (1,2)(5,6) ])\ngap> cycle := CycleDigraph(9);\n\ngap> G := AutomorphismGroup(cycle);\nGroup([ (1,2,3,4,5,\ 6,7,8,9) ])\ngap> IsCyclic(G) and Size(G) = 9;\ntrue", count := [ 7, 2, 2, 8 ] , name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 2, 8 ], mathmode := "Text", name := "Example", next := 286226, root := ~, start := 285842, stop := 286225 ), rec( content := "\n ", count := [ 7, 2, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "Description", next := 286245, root := ~, start := 284369, stop := 286244 ) ], count := [ 7, 2, 2, 1 ], mathmode := "Text", name := "ManSection", next := 286261, root := ~, start := 284241, stop := 286260 ), rec( content := "\n\n ", count := [ 7, 2, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Label := "for a digraph" , Name := "BlissAutomorphi\ smGroup" ), content := 0, count := [ 7, 2, 3, 2 ], mathmode := "Text", name := "Attr", next := 286355, root := ~, start := 286282, stop := 286354 ), rec( attributes := rec( Arg := "digraph, vertex_\ colours", Label := "for a digraph and homogenous list", Name := "BlissAutomorphi\ smGroup" ), content := 0, count := [ 7, 2, 3, 4 ], mathmode := "Text", name := "Oper", next := 286472, root := ~, start := 286358, stop := 286471 ), rec( attributes := rec( Arg := "digraph, vertex_\ colours, edge_colours", Label := "for a digraph, homogenous list, and list", Name := "BlissAutomorphi\ smGroup" ), content := 0, count := [ 7, 2, 3, 6 ], mathmode := "Text", name := "Oper", next := 286610, root := ~, start := 286475, stop := 286609 ), rec( attributes := rec( ), content := [ rec( content := "A permuta\ tion group.", count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "Returns", next := 286652, root := ~, start := 286613, stop := 286651 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "A", next := 286690, root := ~, start := 286676, stop := 286689 ), rec( content := " is a di\ graph, then this attribute contains the group of\n automorphisms of ", count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "A", next := 286782, root := ~, start := 286768, stop := 286781 ), rec( content := " as calc\ ulated using ", count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\ oftware/bliss/", count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "PCDATA" , root\ := ~ ) ], count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "URL", next := 81, root := ~, start := 17, stop := 80 ) ], count := [ 7, 2, 3, 7 ], name := "Alt", next := 87, root := ~, start := 1, stop := 86 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "bliss", count := [ 7, 2, 3, 7 ], name \ := "PCDATA", root := ~ ) ], count := [ 7, 2, 3, 7 ], name := "Package", next := 131, root := ~, start := 107 , stop := 130 ) ], count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "Alt", next := 137, root := ~, start := 87, stop := 136 ), rec( content := " by Tomm\ i Junttila\n and Petteri Kaski. ", count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 3, 8 ], mathmode := "Text", name := "P", next := 286856, root := ~, start := 286852, stop := 286855 ), rec( content := "\n\n \ The attribute ", count := [ 7, 2, 3, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Automor\ phismGroup", Label := "for a digraph" ), content := 0, count := [ 7, 2, 3, 8 ] , mathmode := "Text", name := "Ref", next := 286929, root := ~, start := 286876, stop := 286928 ), rec( content := " and\n \ operation ", count := [ 7, 2, 3, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for a \ digraph and a homogeneous list", Oper := "AutomorphismGroup" ), content := 0, count := [ 7, 2, 3, 8 ], mathmode := "Text", name := "Ref", next := 287031, root := ~, start := 286948, stop := 287030 ), rec( content := " returns\ \n the value of either ", count := [ 7, 2, 3, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "B\ lissAutomorphismGroup", count := [ 7, 2, 3, 8 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 3, 8 ], mathmode := "Text", name := "C", next := 287093, root := ~, start := 287064, stop := 287092 ), rec( content := " or ", count := [ 7, 2, 3, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "NautyAu\ tomorphismGroup" ), content := 0, count := [ 7, 2, 3, 8 ], mathmode := "Text", name := "Ref", next := 287139, root := ~, start := 287097, stop := 287138 ), rec( content := ". These \ groups are, of course, equal but\n their generating sets may differ. ", count := [ 7, 2, 3, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "P", next := 287222, root := ~, start := 287218, stop := 287221 ), rec( content := "\n Th\ e attribute ", count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Automor\ phismGroup", Label := "for a digraph, homogeneous list, and list" ), content := 0, count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "Ref", next := 287329, root := ~, start := 287241, stop := 287328 ), rec( content := " returns\ the value of\n ", count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "B\ lissAutomorphismGroup", count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "C", next := 287384, root := ~, start := 287355, stop := 287383 ), rec( content := " as it i\ s not implemented for ", count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\ ma1.it/", count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", root \ := ~ ) ], count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "URL", next := 74, root := ~, start := 17, stop := 73 ) ], count := [ 7, 2, 3, 9 ], name := "Alt", next := 80, root := ~, start := 1, stop := 79 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "nauty", count := [ 7, 2, 3, 9 ], name \ := "PCDATA", root := ~ ) ], count := [ 7, 2, 3, 9 ], name := "Package", next := 124, root := ~, start := 100 , stop := 123 ) ], count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "Alt", next := 130, root := ~, start := 80, stop := 129 ), rec( content := " The \n \ requirements for the optional arguments ", count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ertex_colours", count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "A", next := 287492, root := ~, start := 287471, stop := 287491 ), rec( content := " and \n \ ", count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dge_colours", count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "A", next := 287521, root := ~, start := 287502, stop := 287520 ), rec( content := " are doc\ umented in ", count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Automor\ phismGroup", Label := "for a digraph, homogeneous list, and list" ), content := 0, count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "Ref", next := 287628, root := ~, start := 287540, stop := 287627 ), rec( content := ".\n\n \ See also ", count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sUseBliss" ), content := 0, count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "Ref", next := 287674, root := ~, start := 287644, stop := 287673 ), rec( content := ", and ", count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sUseNauty" ), content := 0, count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "Ref", next := 287710, root := ~, start := 287680, stop := 287709 ), rec( content := ".\n " , count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 3, 10 ], mathmode := "Text", name := "P", next := 287720, root := ~, start := 287716, stop := 287719 ), rec( content := "\n\n \ If the argument ", count := [ 7, 2, 3, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 3, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 3, 10 ], mathmode := "Text", name := "A", next := 287756, root := ~, start := 287742, stop := 287755 ), rec( content := " is muta\ ble, then the return value of\n this attribute is recomputed every time it \ is called. \n\n ", count := [ 7, 2, 3, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> G := BlissAutomorphismGroup(JohnsonDigraph(5, 2));;\ngap> IsSymmetricGro\ up(G);\ntrue\ngap> Size(G);\n120", count := [ 7, 2, 3, 11 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 3, 11 ], mathmode := "Text", name := "Example", next := 287995, root := ~, start := 287858, stop := 287994 ), rec( content := "\n ", count := [ 7, 2, 3, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "Description", next := 288014, root := ~, start := 286655, stop := 288013 ) ], count := [ 7, 2, 3, 1 ], mathmode := "Text", name := "ManSection", next := 288030, root := ~, start := 286267, stop := 288029 ), rec( content := "\n\n ", count := [ 7, 2, 3, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph[, vert_c\ olours]", Name := "NautyAutomorphismGroup" ), content := 0, count := [ 7, 2, 4, 2 ], mathmode := "Text", name := "Attr", next := 288118, root := ~, start := 288051, stop := 288117 ), rec( attributes := rec( ), content := [ rec( content := "A permuta\ tion group.", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "Returns", next := 288160, root := ~, start := 288121, stop := 288159 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "A", next := 288198, root := ~, start := 288184, stop := 288197 ), rec( content := " is a di\ graph, then this attribute contains the group of\n automorphisms of ", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "A", next := 288290, root := ~, start := 288276, stop := 288289 ), rec( content := " as calc\ ulated using ", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\ ma1.it/", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root \ := ~ ) ], count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "URL", next := 74, root := ~, start := 17, stop := 73 ) ], count := [ 7, 2, 4, 3 ], name := "Alt", next := 80, root := ~, start := 1, stop := 79 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "nauty", count := [ 7, 2, 4, 3 ], name \ := "PCDATA", root := ~ ) ], count := [ 7, 2, 4, 3 ], name := "Package", next := 124, root := ~, start := 100 , stop := 123 ) ], count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "Alt", next := 130, root := ~, start := 80, stop := 129 ), rec( content := " by\n \ Brendan Mckay and Adolfo Piperno via ", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\ github.com/gap-packages/NautyTracesInterface", count := [ 7, 2, 4, 3 ], mathmo\ de := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 4, 3 ], mathmode := \ "Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], count := [ 7, 2, 4, 3 ], name := "Alt", next := 117, root := ~, start := 1, stop := 116 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "NautyTracesInterface", count := [ 7, 2\ , 4, 3 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 4, 3 ], name := "Pac\ kage", next := 176, root := ~, start := 137, stop := 175 ) ], count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "Alt", next := 182, root := ~, start := 117, stop := 181 ), rec( content := ".\n\n \ ", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( content := " FIXME b\ e more explicit about what the second arg is ", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "XMLCOMMENT" , root := ~ ), rec( content := "\n\n \ The attribute ", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Automor\ phismGroup", Label := "for a digraph" ), content := 0, count := [ 7, 2, 4, 3 ] , mathmode := "Text", name := "Ref", next := 288525, root := ~, start := 288472, stop := 288524 ), rec( content := " and\n \ operation ", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for a \ digraph and a homogeneous list", Oper := "AutomorphismGroup" ), content := 0, count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "Ref", next := 288627, root := ~, start := 288544, stop := 288626 ), rec( content := " returns\ \n the value of either ", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "N\ autyAutomorphismGroup", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "C", next := 288689, root := ~, start := 288660, stop := 288688 ), rec( content := " or ", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "BlissAu\ tomorphismGroup", Label := "for a digraph" ), content := 0, count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "Ref", next := 288758, root := ~, start := 288694, stop := 288757 ), rec( content := ".\n T\ hese groups are, of course, equal but their generating sets may differ.", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 4, 4 ], mathmode := "Text", name := "P", next := 288840, root := ~, start := 288836, stop := 288839 ), rec( content := "\n\n \ See also ", count := [ 7, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sUseBliss" ), content := 0, count := [ 7, 2, 4, 4 ], mathmode := "Text", name := "Ref", next := 288885, root := ~, start := 288855, stop := 288884 ), rec( content := ", and ", count := [ 7, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sUseNauty" ), content := 0, count := [ 7, 2, 4, 4 ], mathmode := "Text", name := "Ref", next := 288921, root := ~, start := 288891, stop := 288920 ), rec( content := ".\n " , count := [ 7, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 4, 5 ], mathmode := "Text", name := "P", next := 288931, root := ~, start := 288927, stop := 288930 ), rec( content := "\n\n \ If the argument ", count := [ 7, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 4, 5 ], mathmode := "Text", name := "A", next := 288967, root := ~, start := 288953, stop := 288966 ), rec( content := " is muta\ ble, then the return value of\n this attribute is recomputed every time it \ is called. \n\n ", count := [ 7, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> NautyAutomorphismGroup(JohnsonDigraph(5, 2));\nGroup([ (3,4)(6,7)(8,9), \ (2,3)(5,6)(9,10), (2,5)(3,6)(4,7),\n (1,2)(6,8)(7,9) ])", count := [ 7, 2, 4, 6 ], name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 4, 6 ], mathmode := "Text", name := "Log", next := 289223, root := ~, start := 289069, stop := 289222 ), rec( content := "\n ", count := [ 7, 2, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "Description", next := 289242, root := ~, start := 288163, stop := 289241 ) ], count := [ 7, 2, 4, 1 ], mathmode := "Text", name := "ManSection", next := 289258, root := ~, start := 288036, stop := 289257 ), rec( content := "\n\n ", count := [ 7, 2, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, vert_co\ lours", Label := "for a digraph and a homogeneous list", Name := "AutomorphismGro\ up" ), content := 0, count := [ 7, 2, 5, 2 ], mathmode := "Text", name := "Oper", next := 289388, root := ~, start := 289279, stop := 289387 ), rec( attributes := rec( ), content := [ rec( content := "A permuta\ tion group.", count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "Returns", next := 289430, root := ~, start := 289391, stop := 289429 ), rec( attributes := rec( ), content := [ rec( content := "\n\n T\ his operation computes the automorphism group of a vertex-coloured digraph.\n \ A vertex-coloured digraph can be specified by its underlying digraph\n " , count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "A", next := 289620, root := ~, start := 289606, stop := 289619 ), rec( content := " and its\ colouring ", count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ert_colours", count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "A", next := 289658, root := ~, start := 289639, stop := 289657 ), rec( content := ". Let ", count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "C", next := 289672, root := ~, start := 289664, stop := 289671 ), rec( content := " be the\\ n number of vertices of ", count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "A", next := 289720, root := ~, start := 289706, stop := 289719 ), rec( content := ". The co\ louring ", count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ert_colours", count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "A", next := 289755, root := ~, start := 289736, stop := 289754 ), rec( content := " may\n \ have one of the following two forms:\n\n ", count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "\n a list of ", count := [ 7, 2\ , 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "n", count := [ 7, 2, 5, 5 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 5 ], mathmode\ := "Text", name := "C", next := 289852, root := ~, start := 289844, stop := 2\ 89851 ), rec( content := " integers, where ", count := [ 7, 2, 5, 5 ], mathmod\ e := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), conten\ t := [ rec( content := "vert_colours", count := [ 7, 2, 5, 5 ], mathmode := "T\ ext", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 5 ], mathmode := "T\ ext", name := "A", next := 289888, root := ~, start := 289869, stop := 289887 ), rec( attr\ ibutes := rec( ), content := [ rec( content := "[i]", count := [ 7, 2, 5, 5 ]\ , mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 5 ] , math\ mode := "Text", name := "C", next := 289898, root := ~, start := 289888, stop \ := 289897 ), rec( content := " is the\n colour of vertex ", count := [ \ 7, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribut\ es := rec( ), content := [ rec( content := "i", count := [ 7, 2, 5, 5 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 5 ], math\ mode := "Text", name := "C", next := 289939, root := ~, start := 289931, stop \ := 289938 ), rec( content := ", using the colours ", count := [ 7, 2, 5, 5 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "[1 .. m]", count := [ 7, 2, 5, 5 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 5 ], mathmode := "Tex\ t", name := "C", next := 289974, root := ~, start := 289959, stop := 289973 ), rec( cont\ ent := " for some\n ", count := [ 7, 2, 5, 5 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "m <= n", count := [ 7, 2, 5, 5 ], mathmode := "Text", name := "PCDATA",\ root := ~ ) ], count := [ 7, 2, 5, 5 ], mathmode := "Text", name := "C", next\ := 290008, root := ~, start := 289992, stop := 290007 ), rec( content := "; o\ r\n ", count := [ 7, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 2, 5, 5 ], name := "Item", next := 290026, root := ~, start := 289\ 819, stop := 290025 ), rec( attributes := rec( ), content := [ rec( content :\ = "\n a list of non-empty disjoint lists whose union is\n ", coun\ t := [ 7, 2, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "DigraphVertices(", count := [\ 7, 2, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\ tes := rec( ), content := [ rec( content := "digraph", count := [ 7, 2, 5, 7 \ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 7 \ ], mathmode := "Text", name := "A", next := 290139, root := ~, start := 290125\ , stop := 290138 ), rec( content := ")", count := [ 7, 2, 5, 7 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 7 ], mathmode := \ "Text", name := "C", next := 290144, root := ~, start := 290106, stop := 29014\ 3 ), rec( content := ", such that\n ", count := [ 7, 2, 5, 7 ], mathmod\ e := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), conten\ t := [ rec( content := "vert_colours", count := [ 7, 2, 5, 7 ], mathmode := "T\ ext", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 7 ], mathmode := "T\ ext", name := "A", next := 290183, root := ~, start := 290164, stop := 290182 ), rec( attr\ ibutes := rec( ), content := [ rec( content := "[i]", count := [ 7, 2, 5, 7 ]\ , mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 7 ] , math\ mode := "Text", name := "C", next := 290193, root := ~, start := 290183, stop \ := 290192 ), rec( content := " is the list of all vertices with colour\n \ ", count := [ 7, 2, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "i", count := [ 7, 2, 5, 7 ], \ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 7 ], math\ mode := "Text", name := "C", next := 290250, root := ~, start := 290242, stop \ := 290249 ), rec( content := ".\n ", count := [ 7, 2, 5, 7 ], mathmode :=\ "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 7 ], name := "Ite\ m", next := 290265, root := ~, start := 290033, stop := 290264 ) ], count := [ 7, 2, 5, 4 ], mathmode := "Text", name := "List", next := 290277, root := ~, start := 289806, stop := 290276 ), rec( content := "\n\n \ The ", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "a\ utomorphism group", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "E", next := 290312, root := ~, start := 290287, stop := 290311 ), rec( content := " of a co\ loured digraph ", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "A", next := 290349, root := ~, start := 290335, stop := 290348 ), rec( content := " with\n \ colouring ", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ert_colours", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "A", next := 290388, root := ~, start := 290369, stop := 290387 ), rec( content := " is the \ group consisting of its automorphisms; an\n ", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "a\ utomorphism", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "E", next := 290461, root := ~, start := 290442, stop := 290460 ), rec( content := " of ", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "A", next := 290479, root := ~, start := 290465, stop := 290478 ), rec( content := " is an i\ somorphism of coloured\n digraphs from ", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "A", next := 290542, root := ~, start := 290528, stop := 290541 ), rec( content := " to itse\ lf. This group is equal to the\n subgroup of ", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A\ utomorphismGroup(", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "di\ graph", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", root :=\ ~ ) ], count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "A", next := 2906\ 33, root := ~, start := 290619, stop := 290632 ), rec( content := ")", count := [ 7, 2, 5, 9 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "C", next := 290638, root := ~, start := 290598, stop := 290637 ), rec( content := " consist\ ing of those\n automorphisms that preserve the colouring specified by ", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ert_colours", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "A", next := 290737, root := ~, start := 290718, stop := 290736 ), rec( content := ". See\n \ ", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Automor\ phismGroup", Label := "for a digraph" ), content := 0, count := [ 7, 2, 5, 9 ] , mathmode := "Text", name := "Ref", next := 290801, root := ~, start := 290747, stop := 290800 ), rec( content := ", and se\ e ", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for di\ graphs and homogeneous lists", Oper := "IsomorphismDigraphs" ), content := 0, count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "Ref", next := 290894, root := ~, start := 290811, stop := 290893 ), rec( content := "\n fo\ r more information about isomorphisms of coloured digraphs. ", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 5, 10 ], mathmode := "Text", name := "P", next := 290965, root := ~, start := 290961, stop := 290964 ), rec( content := "\n\n \ If ", count := [ 7, 2, 5, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 5, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 10 ], mathmode := "Text", name := "A", next := 290988, root := ~, start := 290974, stop := 290987 ), rec( content := " is not \ a multidigraph then the automorphism group is\n returned as a group of perm\ utations on the set of vertices of\n ", count := [ 7, 2, 5, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 5, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 10 ], mathmode := "Text", name := "A", next := 291126, root := ~, start := 291112, stop := 291125 ), rec( content := ". ", count := [ 7, 2, 5, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 5, 11 ], mathmode := "Text", name := "P", next := 291132, root := ~, start := 291128, stop := 291131 ), rec( content := "\n\n \ If ", count := [ 7, 2, 5, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 5, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 11 ], mathmode := "Text", name := "A", next := 291155, root := ~, start := 291141, stop := 291154 ), rec( content := " is a mu\ ltidigraph then the automorphism group is returned\n as the direct product \ of a group of permutations on the set of vertices of\n ", count := [ 7, 2, 5, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 5, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 11 ], mathmode := "Text", name := "A", next := 291311, root := ~, start := 291297, stop := 291310 ), rec( content := " with a \ group of permutations on the set of edges of\n ", count := [ 7, 2, 5, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 5, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 11 ], mathmode := "Text", name := "A", next := 291382, root := ~, start := 291368, stop := 291381 ), rec( content := ". These \ groups can be accessed using ", count := [ 7, 2, 5, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "ref\ ", Label := "for a domain and a positive integer", Oper := "Projection" ), content := 0, count := [ 7, 2, 5, 11 ], mathmode := "Text", name := "Ref", next := 291508, root := ~, start := 291419, stop := 291507 ), rec( content := " on the\\ n returned group.", count := [ 7, 2, 5, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "P", next := 291539, root := ~, start := 291535, stop := 291538 ), rec( content := "\n\n \ By default, the automorphism group is found using ", count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\ oftware/bliss/", count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "URL", next := 81, root := ~, start := 17, stop := 80 ) ], count := [ 7, 2, 5, 12 ], name := "Alt", next := 87, root := ~, start := 1, stop := 86 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "bliss", count := [ 7, 2, 5, 12 ], name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 12 ], name := "Package", next := 131, root := ~, start := 107 , stop := 130 ) ], count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "Alt", next := 137, root := ~, start := 87, stop := 136 ), rec( content := " by Tomm\ i Junttila\n and Petteri Kaski. If ", count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\ github.com/gap-packages/NautyTracesInterface", count := [ 7, 2, 5, 12 ], mathm\ ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 12 ], mathmode := \ "Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], count := [ 7, 2, 5, 12 ], name := "Alt", next := 117, root := ~, start := 1, stop := 116 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "NautyTracesInterface", count := [ 7, 2\ , 5, 12 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 12 ], name := "Pac\ kage", next := 176, root := ~, start := 137, stop := 175 ) ], count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "Alt", next := 182, root := ~, start := 117, stop := 181 ), rec( content := " is avai\ lable, then ", count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\ ma1.it/", count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "URL", next := 74, root := ~, start := 17, stop := 73 ) ], count := [ 7, 2, 5, 12 ], name := "Alt", next := 80, root := ~, start := 1, stop := 79 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "nauty", count := [ 7, 2, 5, 12 ], name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 12 ], name := "Package", next := 124, root := ~, start := 100 , stop := 123 ) ], count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "Alt", next := 130, root := ~, start := 80, stop := 129 ), rec( content := " by\n \ Brendan Mckay and Adolfo Piperno can be used instead; see\n ", count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "BlissAu\ tomorphismGroup", Label := "for a digraph and homogenous list" ), content := 0, count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "Ref", next := 291850, root := ~, start := 291766, stop := 291849 ), rec( content := ",\n " , count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "NautyAu\ tomorphismGroup" ), content := 0, count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "Ref", next := 291892, root := ~, start := 291856, stop := 291891 ), rec( content := ", ", count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sUseBliss" ), content := 0, count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "Ref", next := 291924, root := ~, start := 291894, stop := 291923 ), rec( content := ",\n a\ nd ", count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sUseNauty" ), content := 0, count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "Ref", next := 291964, root := ~, start := 291934, stop := 291963 ), rec( content := ".\n\n " , count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> cycle := CycleDigraph(9);\n\nga\ p> G := AutomorphismGroup(cycle);;\ngap> IsCyclic(G) and Size(G) = 9;\ntrue\ng\ ap> colours := [[1, 4, 7], [2, 5, 8], [3, 6, 9]];;\ngap> H := AutomorphismGrou\ p(cycle, colours);;\ngap> Size(H);\n3\ngap> H = AutomorphismGroup(cycle, [1, 2\ , 3, 1, 2, 3, 1, 2, 3]);\ntrue\ngap> H = SubgroupByProperty(G, p -> OnTuplesSe\ ts(colours, p) = colours);\ntrue\ngap> IsTrivial(AutomorphismGroup(cycle, [1, \ 1, 2, 2, 2, 2, 2, 2, 2]));\ntrue", count := [ 7, 2, 5, 13 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 13 ], mathmode := "Text", name := "Example", next := 292486, root := ~, start := 291969, stop := 292485 ), rec( content := "\n ", count := [ 7, 2, 5, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "Description", next := 292503, root := ~, start := 289433, stop := 292502 ) ], count := [ 7, 2, 5, 1 ], mathmode := "Text", name := "ManSection", next := 292517, root := ~, start := 289264, stop := 292516 ), rec( content := "\n\n ", count := [ 7, 2, 5, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, vert_co\ lours, edge_colours", Label := "for a digraph, homogeneous list, and list", Name := "AutomorphismGro\ up" ), content := 0, count := [ 7, 2, 6, 2 ], mathmode := "Text", name := "Oper", next := 292670, root := ~, start := 292538, stop := 292669 ), rec( attributes := rec( ), content := [ rec( content := "A permuta\ tion group.", count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "Returns", next := 292712, root := ~, start := 292673, stop := 292711 ), rec( attributes := rec( ), content := [ rec( content := "\n\n T\ his operation computes the automorphism group of a vertex- and/or\n edge-co\ loured digraph.\n A coloured digraph can be specified by its underlying dig\ raph\n ", count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "A", next := 292912, root := ~, start := 292898, stop := 292911 ), rec( content := " and col\ ourings ", count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ert_colours", count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "A", next := 292947, root := ~, start := 292928, stop := 292946 ), rec( content := ", ", count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dge_colours", count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "A", next := 292968, root := ~, start := 292949, stop := 292967 ), rec( content := ".\n L\ et ", count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "C", next := 292986, root := ~, start := 292978, stop := 292985 ), rec( content := " be the \ number of vertices of ", count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "A", next := 293030, root := ~, start := 293016, stop := 293029 ), rec( content := ". The co\ lourings\n must have the following forms:\n\n ", count := [ 7, 2, 6, 3 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "\n ", count := [ 7, 2, 6, 5 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "vert_colours", count := [ 7, 2, 6, 5 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 5 ], mathmode := \ "Text", name := "A", next := 293134, root := ~, start := 293115, stop := 29313\ 3 ), rec( content := " must be ", count := [ 7, 2, 6, 5 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "fail", count := [ 7, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", r\ oot := ~ ) ], count := [ 7, 2, 6, 5 ], mathmode := "Text", name := "K", next :\ = 293154, root := ~, start := 293143, stop := 293153 ), rec( content := " or a\ list of ", count := [ 7, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "n", count :\ = [ 7, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :\ = [ 7, 2, 6, 5 ], mathmode := "Text", name := "C", next := 293176, root := ~, star\ t := 293168, stop := 293175 ), rec( content := " integers,\n where ", coun\ t := [ 7, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "vert_colours", count := [ 7, \ 2, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, \ 2, 6, 5 ], mathmode := "Text", name := "A", next := 293220, root := ~, start :\ = 293201, stop := 293219 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "[i]", count := [ 7, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", r\ oot := ~ ) ], count := [ 7, 2, 6, 5 ], mathmode := "Text", name := "C", next :\ = 293230, root := ~, start := 293220, stop := 293229 ), rec( content := " is t\ he colour of vertex ", count := [ 7, 2, 6, 5 ], mathmode := "Text", name := "P\ CDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := \ "i", count := [ 7, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ \ ) ], count := [ 7, 2, 6, 5 ], mathmode := "Text", name := "C", next := 293263, root\ := ~, start := 293255, stop := 293262 ), rec( content := ",\n using th\ e colours ", count := [ 7, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "[1 .. m]", \ count := [ 7, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 7, 2, 6, 5 ], mathmode := "Text", name := "C", next := 293306, root := \ ~, start := 293291, stop := 293305 ), rec( content := " for some ", count := [ \ 7, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribut\ es := rec( ), content := [ rec( content := "m <= n", count := [ 7, 2, 6, 5 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 5 ], math\ mode := "Text", name := "C", next := 293332, root := ~, start := 293316, stop \ := 293331 ), rec( content := ";\n ", count := [ 7, 2, 6, 5 ], mathmode :=\ "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 5 ], name := "Ite\ m", next := 293347, root := ~, start := 293100, stop := 293346 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n ", count := [ 7, 2, 6, 7 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "edge_colours", count := [ 7, 2, 6, 7 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 7 ], mathmode := \ "Text", name := "A", next := 293388, root := ~, start := 293369, stop := 29338\ 7 ), rec( content := " must be ", count := [ 7, 2, 6, 7 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "fail", count := [ 7, 2, 6, 7 ], mathmode := "Text", name := "PCDATA", r\ oot := ~ ) ], count := [ 7, 2, 6, 7 ], mathmode := "Text", name := "K", next :\ = 293408, root := ~, start := 293397, stop := 293407 ), rec( content := " or a\ list of ", count := [ 7, 2, 6, 7 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "n", count :\ = [ 7, 2, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :\ = [ 7, 2, 6, 7 ], mathmode := "Text", name := "C", next := 293430, root := ~, star\ t := 293422, stop := 293429 ), rec( content := " lists of\n integers of\ the same shape as ", count := [ 7, 2, 6, 7 ], mathmode := "Text", name := "PC\ DATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\ OutNeighbours(digraph)", count := [ 7, 2, 6, 7 ], mathmode := "Text", name := \ "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 7 ], mathmode := "Text", name := \ "C", next := 293507, root := ~, start := 293478, stop := 293506 ), rec( conten\ t := ", where\n ", count := [ 7, 2, 6, 7 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content \ := "edge_colours", count := [ 7, 2, 6, 7 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 7, 2, 6, 7 ], mathmode := "Text", name := "A", next\ := 293542, root := ~, start := 293523, stop := 293541 ), rec( attributes := re\ c( ), content := [ rec( content := "[i][j]", count := [ 7, 2, 6, 7 ], mathmod\ e := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 7 ], mathmod\ e := "Text", name := "C", next := 293555, root := ~, start := 293542, stop := \ 293554 ), rec( content := " is the colour of the edge\n ", count := [ 7\ , 2, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribute\ s := rec( ), content := [ rec( content := "OutNeighbours(digraph)[i][j]", cou\ nt := [ 7, 2, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 7, 2, 6, 7 ], mathmode := "Text", name := "C", next := 293625, root := \ ~, start := 293590, stop := 293624 ), rec( content := ", using the colours ", coun\ t := [ 7, 2, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "[1 .. k]", count := [ 7, 2, 6\ , 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6\ , 7 ], mathmode := "Text", name := "C", next := 293660, root := ~, start := 29\ 3645, stop := 293659 ), rec( content := "\n for some ", count := [ 7, 2\ , 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "k <= n", count := [ 7, 2, 6, 7 ], mat\ hmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 7 ], math\ mode := "Text", name := "C", next := 293694, root := ~, start := 293678, stop \ := 293693 ), rec( content := ";\n ", count := [ 7, 2, 6, 7 ], mathmode :=\ "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 7 ], name := "Ite\ m", next := 293709, root := ~, start := 293354, stop := 293708 ) ], count := [ 7, 2, 6, 4 ], mathmode := "Text", name := "List", next := 293721, root := ~, start := 293087, stop := 293720 ), rec( content := "\n\n \ Giving ", count := [ 7, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ert_colours", count := [ 7, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 9 ], mathmode := "Text", name := "A", next := 293753, root := ~, start := 293734, stop := 293752 ), rec( content := " [", count := [ 7, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ dge_colours", count := [ 7, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 9 ], mathmode := "Text", name := "A", next := 293774, root := ~, start := 293755, stop := 293773 ), rec( content := "] as ", count := [ 7, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 7, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 9 ], mathmode := "Text", name := "C", next := 293790, root := ~, start := 293779, stop := 293789 ), rec( content := " is\n \ equivalent to setting all vertices [edges] to be the same colour. ", count := [ 7, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "P", next := 293868, root := ~, start := 293864, stop := 293867 ), rec( content := "\n\n \ Unlike ", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Automor\ phismGroup", Label := "for a digraph" ), content := 0, count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "Ref", next := 293934, root := ~, start := 293881, stop := 293933 ), rec( content := ", it is\\ n possible to obtain the automorphism group of an edge-coloured multidigrap\ h\n (see ", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsMulti\ Digraph" ), content := 0, count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "Ref", next := 294059, root := ~, start := 294030, stop := 294058 ), rec( content := ") when n\ o two edges share the same\n source, range, and colour.\n\n The ", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "a\ utomorphism group", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "E", next := 294159, root := ~, start := 294134, stop := 294158 ), rec( content := " of a ve\ rtex/edge-coloured digraph\n ", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "A", next := 294212, root := ~, start := 294198, stop := 294211 ), rec( content := " with co\ louring ", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ ", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "A", next := 294236, root := ~, start := 294228, stop := 294235 ), rec( content := " is the \ group consisting of its\n vertex/edge-colour preserving automorphisms; an\n\ ", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "a\ utomorphism", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "E", next := 294343, root := ~, start := 294324, stop := 294342 ), rec( content := " of ", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "A", next := 294361, root := ~, start := 294347, stop := 294360 ), rec( content := " is an i\ somorphism of vertex/edge-coloured\n digraphs from ", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "A", next := 294436, root := ~, start := 294422, stop := 294435 ), rec( content := " to itse\ lf. This group is equal to the\n subgroup of ", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "A\ utomorphismGroup(", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root \ := ~ ) ], count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "A", next := 2945\ 27, root := ~, start := 294513, stop := 294526 ), rec( content := ")", count := [ 7, 2, 6, 10 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "C", next := 294532, root := ~, start := 294492, stop := 294531 ), rec( content := " consist\ ing of those\n automorphisms that preserve the colouring specified by ", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olours", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "A", next := 294626, root := ~, start := 294612, stop := 294625 ), rec( content := ". See\n \ ", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Automor\ phismGroup", Label := "for a digraph" ), content := 0, count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "Ref", next := 294690, root := ~, start := 294636, stop := 294689 ), rec( content := ", and se\ e ", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for di\ graphs and homogeneous lists", Oper := "IsomorphismDigraphs" ), content := 0, count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "Ref", next := 294783, root := ~, start := 294700, stop := 294782 ), rec( content := "\n fo\ r more information about isomorphisms of coloured digraphs. ", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 6, 11 ], mathmode := "Text", name := "P", next := 294854, root := ~, start := 294850, stop := 294853 ), rec( content := "\n\n \ If ", count := [ 7, 2, 6, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 6, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 11 ], mathmode := "Text", name := "A", next := 294877, root := ~, start := 294863, stop := 294876 ), rec( content := " is not \ a multidigraph then the automorphism group is\n returned as a group of perm\ utations on the set of vertices of\n ", count := [ 7, 2, 6, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 6, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 11 ], mathmode := "Text", name := "A", next := 295015, root := ~, start := 295001, stop := 295014 ), rec( content := ". ", count := [ 7, 2, 6, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 6, 12 ], mathmode := "Text", name := "P", next := 295021, root := ~, start := 295017, stop := 295020 ), rec( content := "\n\n \ If ", count := [ 7, 2, 6, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 6, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 12 ], mathmode := "Text", name := "A", next := 295044, root := ~, start := 295030, stop := 295043 ), rec( content := " is a mu\ ltidigraph then the automorphism group is returned\n as the direct product \ of a group of permutations on the set of vertices of\n ", count := [ 7, 2, 6, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 6, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 12 ], mathmode := "Text", name := "A", next := 295200, root := ~, start := 295186, stop := 295199 ), rec( content := " with a \ group of permutations on the set of edges of\n ", count := [ 7, 2, 6, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 6, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 12 ], mathmode := "Text", name := "A", next := 295271, root := ~, start := 295257, stop := 295270 ), rec( content := ". These \ groups can be accessed using ", count := [ 7, 2, 6, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "ref\ ", Label := "for a domain and a positive integer", Oper := "Projection" ), content := 0, count := [ 7, 2, 6, 12 ], mathmode := "Text", name := "Ref", next := 295397, root := ~, start := 295308, stop := 295396 ), rec( content := " on the\\ n returned group.", count := [ 7, 2, 6, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "P", next := 295428, root := ~, start := 295424, stop := 295427 ), rec( content := "\n\n \ By default, the automorphism group is found using ", count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\ oftware/bliss/", count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "URL", next := 81, root := ~, start := 17, stop := 80 ) ], count := [ 7, 2, 6, 13 ], name := "Alt", next := 87, root := ~, start := 1, stop := 86 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "bliss", count := [ 7, 2, 6, 13 ], name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 13 ], name := "Package", next := 131, root := ~, start := 107 , stop := 130 ) ], count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "Alt", next := 137, root := ~, start := 87, stop := 136 ), rec( content := " by Tomm\ i Junttila\n and Petteri Kaski. If ", count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\ github.com/gap-packages/NautyTracesInterface", count := [ 7, 2, 6, 13 ], mathm\ ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 13 ], mathmode := \ "Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], count := [ 7, 2, 6, 13 ], name := "Alt", next := 117, root := ~, start := 1, stop := 116 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "NautyTracesInterface", count := [ 7, 2\ , 6, 13 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 13 ], name := "Pac\ kage", next := 176, root := ~, start := 137, stop := 175 ) ], count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "Alt", next := 182, root := ~, start := 117, stop := 181 ), rec( content := " is avai\ lable, then ", count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\ ma1.it/", count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "URL", next := 74, root := ~, start := 17, stop := 73 ) ], count := [ 7, 2, 6, 13 ], name := "Alt", next := 80, root := ~, start := 1, stop := 79 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "nauty", count := [ 7, 2, 6, 13 ], name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 13 ], name := "Package", next := 124, root := ~, start := 100 , stop := 123 ) ], count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "Alt", next := 130, root := ~, start := 80, stop := 129 ), rec( content := " by\n \ Brendan Mckay and Adolfo Piperno can be used instead; see\n ", count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "BlissAu\ tomorphismGroup", Label := "for a digraph, homogenous list, and list" ), content := 0, count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "Ref", next := 295748, root := ~, start := 295656, stop := 295747 ), rec( content := ",\n \ ", count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( Attr := "NautyAu\ tomorphismGroup" ), content := 0, count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "Ref", next := 295791, root := ~, start := 295755, stop := 295790 ), rec( content := ", ", count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sUseBliss" ), content := 0, count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "Ref", next := 295823, root := ~, start := 295793, stop := 295822 ), rec( content := ", and\n \ ", count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sUseNauty" ), content := 0, count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "Ref", next := 295864, root := ~, start := 295834, stop := 295863 ), rec( content := ".\n\n " , count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> cycle := CycleDigraph(12);\n\n\ gap> vert_colours := List([1 .. 12], x -> x mod 3 + 1);;\ngap> edge_colours :=\ List([1 .. 12], x -> [x mod 2 + 1]);;\ngap> Size(AutomorphismGroup(cycle));\n\ 12\ngap> Size(AutomorphismGroup(cycle, vert_colours));\n4\ngap> Size(Automorph\ ismGroup(cycle, fail, edge_colours));\n6\ngap> Size(AutomorphismGroup(cycle, v\ ert_colours, edge_colours));\n2\ngap> IsTrivial(AutomorphismGroup(cycle,\n> ve\ rt_colours, List([1 .. 12], x -> [x mod 4 + 1])));\ntrue\n", count := [ 7, 2, 6, 14 ], name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 6, 14 ], mathmode := "Text", name := "Example", next := 296411, root := ~, start := 295869, stop := 296410 ), rec( content := "\n ", count := [ 7, 2, 6, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "Description", next := 296428, root := ~, start := 292715, stop := 296427 ) ], count := [ 7, 2, 6, 1 ], mathmode := "Text", name := "ManSection", next := 296442, root := ~, start := 292523, stop := 296441 ), rec( content := "\n\n ", count := [ 7, 2, 6, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Label := "for a digraph" , Name := "BlissCanonicalL\ abelling" ), content := 0, count := [ 7, 2, 7, 2 ], mathmode := "Text", name := "Attr", next := 296537, root := ~, start := 296463, stop := 296536 ), rec( attributes := rec( Arg := "digraph", Label := "for a digraph" , Name := "NautyCanonicalL\ abelling" ), content := 0, count := [ 7, 2, 7, 4 ], mathmode := "Text", name := "Attr", next := 296614, root := ~, start := 296540, stop := 296613 ), rec( attributes := rec( ), content := [ rec( content := "A permuta\ tion, or a list of two permutations.", count := [ 7, 2, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 5 ], mathmode := "Text", name := "Returns", next := 296681, root := ~, start := 296617, stop := 296680 ), rec( attributes := rec( ), content := [ rec( content := "\n A f\ unction ", count := [ 7, 2, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ \rho", count := [ 7, 2, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 5 ], mathmode := "Text", name := "M", next := 296724, root := ~, start := 296713, stop := 296723 ), rec( content := " that ma\ ps a digraph to a digraph is a ", count := [ 7, 2, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ anonical\n representative map", count := [ 7, 2, 7, 5 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 5 ], mathmode := "Text", name := "E", next := 296804, root := ~, start := 296763, stop := 296803 ), rec( content := " if the \ following two conditions hold for all\n digraphs ", count := [ 7, 2, 7, 5 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 7, 2, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 5 ], mathmode := "Text", name := "M", next := 296871, root := ~, start := 296863, stop := 296870 ), rec( content := " and ", count := [ 7, 2, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "H\ ", count := [ 7, 2, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 5 ], mathmode := "Text", name := "M", next := 296884, root := ~, start := 296876, stop := 296883 ), rec( content := ": ", count := [ 7, 2, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 7, 6 ], mathmode := "Text", name := "P", next := 296890, root := ~, start := 296886, stop := 296889 ), rec( content := "\n\n \ ", count := [ 7, 2, 7, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "\n ", count := [ 7, 2, 7, 8 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "\\rho(G)", count := [ 7, 2, 7, 8 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 8 ], mathmode := "Tex\ t", name := "M", next := 296938, root := ~, start := 296924, stop := 296937 ), rec( cont\ ent := " and ", count := [ 7, 2, 7, 8 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "G", count :\ = [ 7, 2, 7, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :\ = [ 7, 2, 7, 8 ], mathmode := "Text", name := "M", next := 296951, root := ~, star\ t := 296943, stop := 296950 ), rec( content := " are isomorphic as digraphs; a\ nd\n ", count := [ 7, 2, 7, 8 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 2, 7, 8 ], name := "Item", next := 296997, root := ~, start := 296\ 909, stop := 296996 ), rec( attributes := rec( ), content := [ rec( content :\ = "\n ", count := [ 7, 2, 7, 10 ], mathmode := "Text", name := "PCDATA" , root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\rho(G)=\\\ rho(H)", count := [ 7, 2, 7, 10 ], mathmode := "Text", name := "PCDATA", root \ := ~ ) ], count := [ 7, 2, 7, 10 ], mathmode := "Text", name := "M", next := 2\ 97041, root := ~, start := 297019, stop := 297040 ), rec( content := " if and \ only if ", count := [ 7, 2, 7, 10 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "G", count :\ = [ 7, 2, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count \ := [ 7, 2, 7, 10 ], mathmode := "Text", name := "M", next := 297065, root := ~ , star\ t := 297057, stop := 297064 ), rec( content := " and ", count := [ 7, 2, 7, 10\ ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(\ ), content := [ rec( content := "H", count := [ 7, 2, 7, 10 ], mathmode := "\ Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 10 ], mathmode := \ "Text", name := "M", next := 297078, root := ~, start := 297070, stop := 29707\ 7 ), rec( content := " are\n isomorphic as digraphs.\n ", count :=\ [ 7, 2, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 10 ], name := "Ite\ m", next := 297128, root := ~, start := 297004, stop := 297127 ) ], count := [ 7, 2, 7, 7 ], mathmode := "Text", name := "List", next := 297140, root := ~, start := 296896, stop := 297139 ), rec( content := "\n\n \ A ", count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ anonical labelling", count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "E", next := 297174, root := ~, start := 297148, stop := 297173 ), rec( content := " of a di\ graph ", count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "M", next := 297196, root := ~, start := 297188, stop := 297195 ), rec( content := " (under \ ", count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ \rho", count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "M", next := 297215, root := ~, start := 297204, stop := 297214 ), rec( content := ") is an\\ n isomorphism of ", count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "M", next := 297250, root := ~, start := 297242, stop := 297249 ), rec( content := " onto it\ s ", count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ anonical representative", count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "E", next := 297291, root := ~, start := 297260, stop := 297290 ), rec( content := ",\n " , count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ \rho(G)", count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "M", next := 297311, root := ~, start := 297297, stop := 297310 ), rec( content := ". See " , count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for di\ graphs", Oper := "IsomorphismDigraphs" ), content := 0, count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "Ref", next := 297373, root := ~, start := 297318, stop := 297372 ), rec( content := "\n fo\ r more information about isomorphisms of digraphs. ", count := [ 7, 2, 7, 12 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "P", next := 297435, root := ~, start := 297431, stop := 297434 ), rec( content := "\n\n \ ", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "B\ lissCanonicalLabelling", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "C", next := 297471, root := ~, start := 297441, stop := 297470 ), rec( content := " returns\ a canonical labelling of the digraph\n ", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "A", next := 297535, root := ~, start := 297521, stop := 297534 ), rec( content := " found u\ sing ", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\ oftware/bliss/", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "URL", next := 81, root := ~, start := 17, stop := 80 ) ], count := [ 7, 2, 7, 13 ], name := "Alt", next := 87, root := ~, start := 1, stop := 86 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "bliss", count := [ 7, 2, 7, 13 ], name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 13 ], name := "Package", next := 131, root := ~, start := 107 , stop := 130 ) ], count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "Alt", next := 137, root := ~, start := 87, stop := 136 ), rec( content := " by Tomm\ i Junttila and Petteri Kaski.\n ", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "N\ autyCanonicalLabelling", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "C", next := 297627, root := ~, start := 297597, stop := 297626 ), rec( content := " returns\ a canonical labelling of the digraph\n ", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "A", next := 297691, root := ~, start := 297677, stop := 297690 ), rec( content := " found u\ sing ", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\ ma1.it/", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "URL", next := 74, root := ~, start := 17, stop := 73 ) ], count := [ 7, 2, 7, 13 ], name := "Alt", next := 80, root := ~, start := 1, stop := 79 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "nauty", count := [ 7, 2, 7, 13 ], name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 13 ], name := "Package", next := 124, root := ~, start := 100 , stop := 123 ) ], count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "Alt", next := 130, root := ~, start := 80, stop := 129 ), rec( content := " by Bren\ dan McKay and Adolfo Piperno.\n Note that the canonical labellings returned\ by ", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\ oftware/bliss/", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "URL", next := 81, root := ~, start := 17, stop := 80 ) ], count := [ 7, 2, 7, 13 ], name := "Alt", next := 87, root := ~, start := 1, stop := 86 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "bliss", count := [ 7, 2, 7, 13 ], name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 13 ], name := "Package", next := 131, root := ~, start := 107 , stop := 130 ) ], count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "Alt", next := 137, root := ~, start := 87, stop := 136 ), rec( content := " and ", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\ ma1.it/", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "URL", next := 74, root := ~, start := 17, stop := 73 ) ], count := [ 7, 2, 7, 13 ], name := "Alt", next := 80, root := ~, start := 1, stop := 79 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "nauty", count := [ 7, 2, 7, 13 ], name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 13 ], name := "Package", next := 124, root := ~, start := 100 , stop := 123 ) ], count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "Alt", next := 130, root := ~, start := 80, stop := 129 ), rec( content := " are not\ \n usually the same (and may depend of the version used).", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 7, 14 ], mathmode := "Text", name := "P", next := 297890, root := ~, start := 297886, stop := 297889 ), rec( content := "\n\n \ ", count := [ 7, 2, 7, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "B\ lissCanonicalLabelling", count := [ 7, 2, 7, 14 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 7, 14 ], mathmode := "Text", name := "C", next := 297926, root := ~, start := 297896, stop := 297925 ), rec( content := " can onl\ y be computed if ", count := [ 7, 2, 7, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 7, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 14 ], mathmode := "Text", name := "A", next := 297965, root := ~, start := 297951, stop := 297964 ), rec( content := " has\n \ no multiple edges; see ", count := [ 7, 2, 7, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsMulti\ Digraph" ), content := 0, count := [ 7, 2, 7, 14 ], mathmode := "Text", name := "Ref", next := 298026, root := ~, start := 297997, stop := 298025 ), rec( content := ". ", count := [ 7, 2, 7, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 7, 15 ], mathmode := "Text", name := "P", next := 298032, root := ~, start := 298028, stop := 298031 ), rec( content := "\n\n \ ", count := [ 7, 2, 7, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> digraph1 := DigraphFromDiSparse6String(\".ImNS_AiB?qRN\");\n\ngap> BlissCanonicalLabelling(digraph1);\n(1\ ,9,5,7)(3,6,4,10)\ngap> p := (1, 2, 7, 5)(3, 9)(6, 10, 8);;\ngap> digraph2 := \ OnDigraphs(digraph1, p);\n\ngap> \ digraph1 = digraph2;\nfalse\ngap> OnDigraphs(digraph1, BlissCanonicalLabelling\ (digraph1)) =\n> OnDigraphs(digraph2, BlissCanonicalLabelling(digraph2));\n\ true", count := [ 7, 2, 7, 16 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 16 ], mathmode := "Text", name := "Example", next := 298528, root := ~, start := 298038, stop := 298527 ), rec( content := "\n ", count := [ 7, 2, 7, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 5 ], mathmode := "Text", name := "Description", next := 298545, root := ~, start := 296684, stop := 298544 ) ], count := [ 7, 2, 7, 1 ], mathmode := "Text", name := "ManSection", next := 298559, root := ~, start := 296448, stop := 298558 ), rec( content := "\n\n ", count := [ 7, 2, 7, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, colours\ ", Label := "for a digraph and a list", Name := "BlissCanonicalLabelling" ), content := 0, count := [ 7, 2, 8, 2 ], mathmode := "Text", name := "Oper", next := 298678, root := ~, start := 298580, stop := 298677 ), rec( attributes := rec( Arg := "digraph, colours\ ", Label := "for a digraph and a list", Name := "NautyCanonicalLabelling" ), content := 0, count := [ 7, 2, 8, 4 ], mathmode := "Text", name := "Oper", next := 298779, root := ~, start := 298681, stop := 298778 ), rec( attributes := rec( ), content := [ rec( content := "A permuta\ tion.", count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "Returns", next := 298815, root := ~, start := 298782, stop := 298814 ), rec( attributes := rec( ), content := [ rec( content := "\n A f\ unction ", count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ \rho", count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "M", next := 298858, root := ~, start := 298847, stop := 298857 ), rec( content := " that ma\ ps a coloured digraph to a coloured digraph is\n a ", count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ anonical representative map", count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "E", next := 298954, root := ~, start := 298919, stop := 298953 ), rec( content := " if the \ following two conditions hold\n for all coloured digraphs ", count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "M", next := 299030, root := ~, start := 299022, stop := 299029 ), rec( content := " and ", count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "H\ ", count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "M", next := 299043, root := ~, start := 299035, stop := 299042 ), rec( content := ":\n\n \ ", count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "\n ", count := [ 7, 2, 8, 7 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "\\rho(G)", count := [ 7, 2, 8, 7 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 7 ], mathmode := "Tex\ t", name := "M", next := 299092, root := ~, start := 299078, stop := 299091 ), rec( cont\ ent := " and ", count := [ 7, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "G", count :\ = [ 7, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :\ = [ 7, 2, 8, 7 ], mathmode := "Text", name := "M", next := 299105, root := ~, star\ t := 299097, stop := 299104 ), rec( content := " are isomorphic as coloured di\ graphs; and\n ", count := [ 7, 2, 8, 7 ], mathmode := "Text", name := "PC\ DATA", root := ~ ) ], count := [ 7, 2, 8, 7 ], name := "Item", next := 299160, root := ~, start := 299\ 063, stop := 299159 ), rec( attributes := rec( ), content := [ rec( content :\ = "\n ", count := [ 7, 2, 8, 9 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\rho(G)=\\\ rho(H)", count := [ 7, 2, 8, 9 ], mathmode := "Text", name := "PCDATA", root :\ = ~ ) ], count := [ 7, 2, 8, 9 ], mathmode := "Text", name := "M", next := 299\ 204, root := ~, start := 299182, stop := 299203 ), rec( content := " if and on\ ly if ", count := [ 7, 2, 8, 9 ], mathmode := "Text", name := "PCDATA", root :\ = ~ ), rec( attributes := rec( ), content := [ rec( content := "G", count := \ [ 7, 2, 8, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ \ 7, 2, 8, 9 ], mathmode := "Text", name := "M", next := 299228, root := ~, star\ t := 299220, stop := 299227 ), rec( content := " and ", count := [ 7, 2, 8, 9 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "H", count := [ 7, 2, 8, 9 ], mathmode := "Text", nam\ e := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 9 ], mathmode := "Text", name\ := "M", next := 299241, root := ~, start := 299233, stop := 299240 ), rec( cont\ ent := " are\n isomorphic as coloured digraphs.\n ", count := [ 7,\ 2, 8, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 9 ], name := "Ite\ m", next := 299300, root := ~, start := 299167, stop := 299299 ) ], count := [ 7, 2, 8, 6 ], mathmode := "Text", name := "List", next := 299312, root := ~, start := 299050, stop := 299311 ), rec( content := "\n\n \ A ", count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ anonical labelling", count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "E", next := 299346, root := ~, start := 299320, stop := 299345 ), rec( content := " of a co\ loured digraph ", count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "M", next := 299377, root := ~, start := 299369, stop := 299376 ), rec( content := " (under\\ n ", count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ \rho", count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "M", next := 299400, root := ~, start := 299389, stop := 299399 ), rec( content := ") is an \ isomorphism of ", count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "M", next := 299431, root := ~, start := 299423, stop := 299430 ), rec( content := " onto it\ s ", count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ anonical\n representative", count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "E", next := 299478, root := ~, start := 299441, stop := 299477 ), rec( content := ", ", count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ \rho(G)", count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "M", next := 299494, root := ~, start := 299480, stop := 299493 ), rec( content := ". See " , count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for di\ graphs and homogeneous lists", Oper := "IsomorphismDigraphs" ), content := 0, count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "Ref", next := 299584, root := ~, start := 299501, stop := 299583 ), rec( content := " for mor\ e information about\n isomorphisms of coloured digraphs. ", count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "P", next := 299655, root := ~, start := 299651, stop := 299654 ), rec( content := "\n\n \ A coloured digraph can be specified by its underlying digraph ", count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "A", next := 299737, root := ~, start := 299723, stop := 299736 ), rec( content := "\n an\ d its colouring ", count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olours", count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "A", next := 299774, root := ~, start := 299760, stop := 299773 ), rec( content := ". Let " , count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "C", next := 299789, root := ~, start := 299781, stop := 299788 ), rec( content := " be the \ number of vertices of\n ", count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "A", next := 299837, root := ~, start := 299823, stop := 299836 ), rec( content := ". The co\ louring ", count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olours", count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "A", next := 299867, root := ~, start := 299853, stop := 299866 ), rec( content := " may hav\ e one of the following\n two forms: ", count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 8, 13 ], mathmode := "Text", name := "P", next := 299917, root := ~, start := 299913, stop := 299916 ), rec( content := "\n\n \ ", count := [ 7, 2, 8, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "\n a list of ", count := [ 7, 2\ , 8, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes \ := rec( ), content := [ rec( content := "n", count := [ 7, 2, 8, 15 ], mathmo\ de := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 15 ], mathm\ ode := "Text", name := "C", next := 299969, root := ~, start := 299961, stop :\ = 299968 ), rec( content := " integers, where ", count := [ 7, 2, 8, 15 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "colours", count := [ 7, 2, 8, 15 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 15 ], mathmode := "Te\ xt", name := "A", next := 300000, root := ~, start := 299986, stop := 299999 ) , rec( attr\ ibutes := rec( ), content := [ rec( content := "[i]", count := [ 7, 2, 8, 15 \ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 15\ ], mathmode := "Text", name := "C", next := 300010, root := ~, start := 30000\ 0, stop := 300009 ), rec( content := " is the\n colour of vertex ", coun\ t := [ 7, 2, 8, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "i", count := [ 7, 2, 8, 15 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 15 ] , math\ mode := "Text", name := "C", next := 300051, root := ~, start := 300043, stop \ := 300050 ), rec( content := ", using the colours ", count := [ 7, 2, 8, 15 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "[1 .. m]", count := [ 7, 2, 8, 15 ], mathmode := "Te\ xt", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 15 ], mathmode := "T\ ext", name := "C", next := 300086, root := ~, start := 300071, stop := 300085 ), rec( cont\ ent := " for some\n ", count := [ 7, 2, 8, 15 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "m <= n", count := [ 7, 2, 8, 15 ], mathmode := "Text", name := "PCDATA"\ , root := ~ ) ], count := [ 7, 2, 8, 15 ], mathmode := "Text", name := "C", next\ := 300120, root := ~, start := 300104, stop := 300119 ), rec( content := "; o\ r\n ", count := [ 7, 2, 8, 15 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 2, 8, 15 ], name := "Item", next := 300138, root := ~, start := 299\ 936, stop := 300137 ), rec( attributes := rec( ), content := [ rec( content :\ = "\n a list of non-empty disjoint lists whose union is\n ", coun\ t := [ 7, 2, 8, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "DigraphVertices(", count := [\ 7, 2, 8, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attrib\ utes := rec( ), content := [ rec( content := "digraph", count := [ 7, 2, 8, 1\ 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, \ 17 ], mathmode := "Text", name := "A", next := 300251, root := ~, start := 300\ 237, stop := 300250 ), rec( content := ")", count := [ 7, 2, 8, 17 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 17 ], mathmod\ e := "Text", name := "C", next := 300256, root := ~, start := 300218, stop := \ 300255 ), rec( content := ", such that\n ", count := [ 7, 2, 8, 17 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "colours", count := [ 7, 2, 8, 17 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 17 ], mathmode := "Te\ xt", name := "A", next := 300290, root := ~, start := 300276, stop := 300289 ) , rec( attr\ ibutes := rec( ), content := [ rec( content := "[i]", count := [ 7, 2, 8, 17 \ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 17\ ], mathmode := "Text", name := "C", next := 300300, root := ~, start := 30029\ 0, stop := 300299 ), rec( content := " is the list of all vertices with colour\ \n ", count := [ 7, 2, 8, 17 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "i", count :\ = [ 7, 2, 8, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count \ := [ 7, 2, 8, 17 ], mathmode := "Text", name := "C", next := 300357, root := ~ , star\ t := 300349, stop := 300356 ), rec( content := ".\n ", count := [ 7, 2, 8\ , 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 17 ], name := "Ite\ m", next := 300372, root := ~, start := 300145, stop := 300371 ) ], count := [ 7, 2, 8, 14 ], mathmode := "Text", name := "List", next := 300384, root := ~, start := 299923, stop := 300383 ), rec( content := "\n\n \ If ", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "A", next := 300407, root := ~, start := 300393, stop := 300406 ), rec( content := " and ", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olours", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "A", next := 300426, root := ~, start := 300412, stop := 300425 ), rec( content := " togethe\ r form a coloured digraph,\n ", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "B\ lissCanonicalLabelling", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "C", next := 300495, root := ~, start := 300465, stop := 300494 ), rec( content := " returns\ a canonical labelling of the digraph\n ", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "A", next := 300559, root := ~, start := 300545, stop := 300558 ), rec( content := " found u\ sing ", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\ oftware/bliss/", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "URL", next := 81, root := ~, start := 17, stop := 80 ) ], count := [ 7, 2, 8, 19 ], name := "Alt", next := 87, root := ~, start := 1, stop := 86 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "bliss", count := [ 7, 2, 8, 19 ], name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 19 ], name := "Package", next := 131, root := ~, start := 107 , stop := 130 ) ], count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "Alt", next := 137, root := ~, start := 87, stop := 136 ), rec( content := " by Tomm\ i Junttila and Petteri Kaski.\n Similarly, ", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "N\ autyCanonicalLabelling", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "C", next := 300662, root := ~, start := 300632, stop := 300661 ), rec( content := " returns\ a canonical labelling of\n the digraph ", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "A", next := 300726, root := ~, start := 300712, stop := 300725 ), rec( content := " found u\ sing ", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\ ma1.it/", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "URL", next := 74, root := ~, start := 17, stop := 73 ) ], count := [ 7, 2, 8, 19 ], name := "Alt", next := 80, root := ~, start := 1, stop := 79 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "nauty", count := [ 7, 2, 8, 19 ], name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 19 ], name := "Package", next := 124, root := ~, start := 100 , stop := 123 ) ], count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "Alt", next := 130, root := ~, start := 80, stop := 129 ), rec( content := " by Bren\ dan McKay and Adolfo\n Piperno. Note that the canonical labellings returne\ d by ", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\ oftware/bliss/", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "URL", next := 81, root := ~, start := 17, stop := 80 ) ], count := [ 7, 2, 8, 19 ], name := "Alt", next := 87, root := ~, start := 1, stop := 86 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "bliss", count := [ 7, 2, 8, 19 ], name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 19 ], name := "Package", next := 131, root := ~, start := 107 , stop := 130 ) ], count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "Alt", next := 137, root := ~, start := 87, stop := 136 ), rec( content := " and\n \ ", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\ ma1.it/", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "URL", next := 74, root := ~, start := 17, stop := 73 ) ], count := [ 7, 2, 8, 19 ], name := "Alt", next := 80, root := ~, start := 1, stop := 79 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "nauty", count := [ 7, 2, 8, 19 ], name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 19 ], name := "Package", next := 124, root := ~, start := 100 , stop := 123 ) ], count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "Alt", next := 130, root := ~, start := 80, stop := 129 ), rec( content := " are not\ usually the same (and may depend of the version used).", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "P", next := 300926, root := ~, start := 300922, stop := 300925 ), rec( content := "\n\n \ ", count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "B\ lissCanonicalLabelling", count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "C", next := 300962, root := ~, start := 300932, stop := 300961 ), rec( content := " can onl\ y be computed if ", count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "A", next := 301001, root := ~, start := 300987, stop := 301000 ), rec( content := " has\n \ no multiple edges; see ", count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsMulti\ Digraph" ), content := 0, count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "Ref", next := 301062, root := ~, start := 301033, stop := 301061 ), rec( content := ". The ca\ nonical\n labelling of ", count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "A", next := 301109, root := ~, start := 301095, stop := 301108 ), rec( content := " is give\ n as a permutation of its vertices.\n The canonical representative of ", count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "A", next := 301203, root := ~, start := 301189, stop := 301202 ), rec( content := " can be \ created from\n ", count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "A", next := 301242, root := ~, start := 301228, stop := 301241 ), rec( content := " and its\ canonical labelling ", count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ ", count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "C", next := 301279, root := ~, start := 301271, stop := 301278 ), rec( content := " by usin\ g the\n operation ", count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for a \ digraph and a perm", Oper := "OnDigraphs" ), content := 0, count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "Ref", next := 301365, root := ~, start := 301307, stop := 301364 ), rec( content := ":\n " , count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ ap> OnDigraphs(digraph, p);", count := [ 7, 2, 8, 21 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 21 ], mathmode := "Text", name := "Log", next := 301410, root := ~, start := 301371, stop := 301409 ), rec( content := "\n\n \ The colouring of the canonical representative can easily be\n constructed. \ A vertex ", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "C", next := 301510, root := ~, start := 301502, stop := 301509 ), rec( content := " (in ", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "A", next := 301529, root := ~, start := 301515, stop := 301528 ), rec( content := ") has co\ lour ", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "C", next := 301550, root := ~, start := 301542, stop := 301549 ), rec( content := " if\n \ and only if the vertex ", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ^ p", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "C", next := 301593, root := ~, start := 301581, stop := 301592 ), rec( content := " (in the\ canonical representative) has\n colour ", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "C", next := 301651, root := ~, start := 301643, stop := 301650 ), rec( content := ", where \ ", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "p\ ", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "C", next := 301667, root := ~, start := 301659, stop := 301666 ), rec( content := " is the \ permutation of the canonical\n labelling that acts on the vertices of ", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "A", next := 301761, root := ~, start := 301747, stop := 301760 ), rec( content := ". In par\ ticular, if\n ", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olours", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "A", next := 301799, root := ~, start := 301785, stop := 301798 ), rec( content := " has the\ first form that is described above, then the\n colouring of the canonical \ representative is given by:\n\n ", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ ap> List(DigraphVertices(digraph), i -> colours[i / p]);", count := [ 7, 2, 8, 23 ], name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 8, 23 ], mathmode := "Text", name := "Log", next := 301985, root := ~, start := 301917, stop := 301984 ), rec( content := "\n\n \ On the other hand, if ", count := [ 7, 2, 8, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olours", count := [ 7, 2, 8, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 24 ], mathmode := "Text", name := "A", next := 302027, root := ~, start := 302013, stop := 302026 ), rec( content := " has the\ second form above, then the\n canonical representative has colouring:\n\n \ ", count := [ 7, 2, 8, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ ap> OnTuplesSets(colours, p);", count := [ 7, 2, 8, 25 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 25 ], mathmode := "Text", name := "Log", next := 302154, root := ~, start := 302113, stop := 302153 ), rec( content := "\n\n \ ", count := [ 7, 2, 8, 26 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := 0, count := [ 7, 2, 8, 27 ], mathmode := "Text", name := "P", next := 302164, root := ~, start := 302160, stop := 302163 ), rec( content := "\n\n \ ", count := [ 7, 2, 8, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> digraph := DigraphFromDiSparse6String(\".ImNS_AiB?qRN\");\n\ngap> colours := [[1, 2, 8, 9, 10], [3, 4, 5,\ 6, 7]];;\ngap> p := BlissCanonicalLabelling(digraph, colours);\n(1,5,8,4,10,3\ ,9)(6,7)\ngap> OnDigraphs(digraph, p);\n\ngap> OnTuplesSets(colours, p);\n[ [ 1, 2, 3, 4, 5 ], [ 6, 7, 8, 9, 10\ ] ]\ngap> colours := [1, 1, 1, 1, 2, 3, 1, 3, 2, 1];;\ngap> p := BlissCanonic\ alLabelling(digraph, colours);\n(1,6,9,7)(3,4,5,8,10)\ngap> OnDigraphs(digraph\ , p);\n\ngap> List(DigraphVertice\ s(digraph), i -> colours[i / p]);\n[ 1, 1, 1, 1, 1, 1, 2, 2, 3, 3 ]", count := [ 7, 2, 8, 28 ], name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 8, 28 ], mathmode := "Text", name := "Example", next := 302875, root := ~, start := 302170, stop := 302874 ), rec( content := "\n ", count := [ 7, 2, 8, 29 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "Description", next := 302892, root := ~, start := 298818, stop := 302891 ) ], count := [ 7, 2, 8, 1 ], mathmode := "Text", name := "ManSection", next := 302906, root := ~, start := 298565, stop := 302905 ), rec( content := "\n\n ", count := [ 7, 2, 8, 29 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "BlissCanonicalD\ igraph" ), content := 0, count := [ 7, 2, 9, 2 ], mathmode := "Text", name := "Attr", next := 302977, root := ~, start := 302927, stop := 302976 ), rec( attributes := rec( Arg := "digraph", Name := "NautyCanonicalD\ igraph" ), content := 0, count := [ 7, 2, 9, 4 ], mathmode := "Text", name := "Attr", next := 303030, root := ~, start := 302980, stop := 303029 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 7, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 9, 5 ], mathmode := "Text", name := "Returns", next := 303062, root := ~, start := 303033, stop := 303061 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ attribute ", count := [ 7, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "B\ lissCanonicalLabelling", count := [ 7, 2, 9, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 9, 5 ], mathmode := "Text", name := "C", next := 303127, root := ~, start := 303097, stop := 303126 ), rec( content := " returns\ the canonical\n representative found by applying ", count := [ 7, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "BlissCa\ nonicalLabelling", Label := "for a digraph" ), content := 0, count := [ 7, 2, 9, 5 ], mathmode := "Text", name := "Ref", next := 303252, root := ~, start := 303187, stop := 303251 ), rec( content := ". The di\ graph returned is canonical in the sense\n that\n\n ", count := [ 7, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "\n ", count := [ 7, 2, 9, 7 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "BlissCanonicalDigraph(", count := [ 7, 2, 9, 7 ], ma\ thmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), c\ ontent := [ rec( content := "digraph", count := [ 7, 2, 9, 7 ], mathmode := "T\ ext", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 9, 7 ], mathmode := "T\ ext", name := "A", next := 303382, root := ~, start := 303368, stop := 303381 \ ), rec( content := ")", count := [ 7, 2, 9, 7 ], mathmode := "Text", name := "\ PCDATA", root := ~ ) ], count := [ 7, 2, 9, 7 ], mathmode := "Text", name := "\ C", next := 303387, root := ~, start := 303343, stop := 303386 ), rec( content\ := " and ", count := [ 7, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "digraph", c\ ount := [ 7, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 7, 2, 9, 7 ], mathmode := "Text", name := "A", next := 303406, root := \ ~, start := 303392, stop := 303405 ), rec( content := " are\n isomorphi\ c as digraphs; and\n ", count := [ 7, 2, 9, 7 ], mathmode := "Text", name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 9, 7 ], name := "Item", next := 3034\ 60, root := ~, start := 303328, stop := 303459 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "\n If ", count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "\ PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content :=\ "gr", count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "PCDATA", root := \ ~ ) ], count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "C", next := 30349\ 4, root := ~, start := 303485, stop := 303493 ), rec( content := " is any digr\ aph then ", count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "BlissCanoni\ calDigraph(gr)", count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "PCDATA"\ , root := ~ ) ], count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "C", next\ := 303547, root := ~, start := 303515, stop := 303546 ), rec( content := "\n \ and ", count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "BlissCanoni\ calDigraph(", count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "PCDATA", r\ oot := ~ ), rec( attributes := rec( ), content := [ rec( content := "digraph"\ , count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ]\ , count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "A", next := 303599, ro\ ot := ~, start := 303585, stop := 303598 ), rec( content := ")", count := [ 7,\ 2, 9, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7,\ 2, 9, 9 ], mathmode := "Text", name := "C", next := 303604, root := ~, start \ := 303560, stop := 303603 ), rec( content := " are equal if and only\n \ if ", count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "PCDATA", root := ~\ ), rec( attributes := rec( ), content := [ rec( content := "gr", count := [ \ 7, 2, 9, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ \ 7, 2, 9, 9 ], mathmode := "Text", name := "C", next := 303647, root := ~, star\ t := 303638, stop := 303646 ), rec( content := " and ", count := [ 7, 2, 9, 9 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "digraph", count := [ 7, 2, 9, 9 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 9, 9 ], mathmode := "Text\ ", name := "A", next := 303666, root := ~, start := 303652, stop := 303665 ), rec( cont\ ent := " are isomorphic as digraphs.\n ", count := [ 7, 2, 9, 9 ], mathmo\ de := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 9, 9 ], name := "Ite\ m", next := 303708, root := ~, start := 303467, stop := 303707 ) ], count := [ 7, 2, 9, 6 ], mathmode := "Text", name := "List", next := 303720, root := ~, start := 303315, stop := 303719 ), rec( content := "\n\n \ Analogously, the attribute ", count := [ 7, 2, 9, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "N\ autyCanonicalLabelling", count := [ 7, 2, 9, 11 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 9, 11 ], mathmode := "Text", name := "C", next := 303783, root := ~, start := 303753, stop := 303782 ), rec( content := " returns\ the\n canonical representative found by applying ", count := [ 7, 2, 9, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "NautyCa\ nonicalLabelling", Label := "for a digraph" ), content := 0, count := [ 7, 2, 9, 11 ], mathmode := "Text", name := "Ref", next := 303908, root := ~, start := 303843, stop := 303907 ), rec( content := ".\n " , count := [ 7, 2, 9, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 9, 12 ], mathmode := "Text", name := "P", next := 303918, root := ~, start := 303914, stop := 303917 ), rec( content := "\n\n \ If the argument ", count := [ 7, 2, 9, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 9, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 9, 12 ], mathmode := "Text", name := "A", next := 303954, root := ~, start := 303940, stop := 303953 ), rec( content := " is muta\ ble, then the return value of\n this attribute is recomputed every time it \ is called. \n\n ", count := [ 7, 2, 9, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> digraph := Digraph([[1], [2, 3], [3], [1, 2, 3]]);\n\ngap> canon := BlissCanonicalDigraph(digraph);\n\ngap> OutNeighbours(canon);\n[ [ 1 ], \ [ 2 ], [ 3, 2 ], [ 1, 3, 2 ] ]\n", count := [ 7, 2, 9, 13 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 9, 13 ], mathmode := "Text", name := "Example", next := 304347, root := ~, start := 304056, stop := 304346 ), rec( content := "\n ", count := [ 7, 2, 9, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 9, 5 ], mathmode := "Text", name := "Description", next := 304364, root := ~, start := 303065, stop := 304363 ) ], count := [ 7, 2, 9, 1 ], mathmode := "Text", name := "ManSection", next := 304378, root := ~, start := 302912, stop := 304377 ), rec( content := "\n\n ", count := [ 7, 2, 9, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphGroup" ) , content := 0, count := [ 7, 2, 10, 2 ], mathmode := "Text", name := "Attr", next := 304440, root := ~, start := 304399, stop := 304439 ), rec( attributes := rec( ), content := [ rec( content := "A permuta\ tion group.", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "Returns", next := 304482, root := ~, start := 304443, stop := 304481 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "A", next := 304520, root := ~, start := 304506, stop := 304519 ), rec( content := " is immu\ table and was created knowing a subgroup of\n its automorphism group, then \ this group is stored in the attribute\n ", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphGroup", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "C", next := 304666, root := ~, start := 304647, stop := 304665 ), rec( content := ". If ", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "A", next := 304685, root := ~, start := 304671, stop := 304684 ), rec( content := " is muta\ ble, or was not created\n knowing a subgroup of its automorphism group, the\ n ", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphGroup", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "C", next := 304791, root := ~, start := 304772, stop := 304790 ), rec( content := "\n re\ turns the entire automorphism group of ", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "A", next := 304851, root := ~, start := 304837, stop := 304850 ), rec( content := ". \n \ Note that if ", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "A", next := 304888, root := ~, start := 304874, stop := 304887 ), rec( content := " is muta\ ble, then the automorphism group is\n recomputed every time this function i\ s called.\n ", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 10, 4 ], mathmode := "Text", name := "P", next := 304991, root := ~, start := 304987, stop := 304990 ), rec( content := "\n\n \ Note that certain other constructor operations such as ", count := [ 7, 2, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "CayleyD\ igraph" ), content := 0, count := [ 7, 2, 10, 4 ], mathmode := "Text", name := "Ref", next := 305086, root := ~, start := 305053, stop := 305085 ), rec( content := ", ", count := [ 7, 2, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Biparti\ teDoubleDigraph" ), content := 0, count := [ 7, 2, 10, 4 ], mathmode := "Text", name := "Ref", next := 305124, root := ~, start := 305088, stop := 305123 ), rec( content := ", and ", count := [ 7, 2, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "DoubleD\ igraph" ), content := 0, count := [ 7, 2, 10, 4 ], mathmode := "Text", name := "Ref", next := 305163, root := ~, start := 305130, stop := 305162 ), rec( content := ", may no\ t require a group as one of the arguments,\n but use the standard construct\ or method using a group, and hence set the\n ", count := [ 7, 2, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphGroup", count := [ 7, 2, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 10, 4 ], mathmode := "Text", name := "C", next := 305314, root := ~, start := 305295, stop := 305313 ), rec( content := " attribu\ te for the resulting digraph.\n\n ", count := [ 7, 2, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> n := 4;;\ngap> adj := function(x, y)\n> return (((x - y) mod n) = 1\ ) or (((x - y) mod n) = n - 1);\n> end;;\ngap> group := CyclicGroup(IsPermG\ roup, n);\nGroup([ (1,2,3,4) ])\ngap> D := Digraph(IsMutableDigraph, group, [1\ .. n], \\^, adj);\n\ngap> HasDigrap\ hGroup(D);\nfalse\ngap> DigraphGroup(D);\nGroup([ (2,4), (1,2)(3,4) ])\ngap> A\ utomorphismGroup(D);\nGroup([ (2,4), (1,2)(3,4) ])\ngap> D := Digraph(group, [\ 1 .. n], \\^, adj);\n\ngap> HasDig\ raphGroup(D);\ntrue\ngap> DigraphGroup(D);\nGroup([ (1,2,3,4) ])\ngap> D := Do\ ubleDigraph(D);\n\ngap> HasDigrap\ hGroup(D);\ntrue\ngap> DigraphGroup(D);\nGroup([ (1,2,3,4)(5,6,7,8), (1,5)(2,6\ )(3,7)(4,8) ])\ngap> AutomorphismGroup(D) =\n> Group([(6, 8), (5, 7), (4, 6), \ (3, 5), (2, 4),\n> (1, 2)(3, 4)(5, 6)(7, 8)]);\ntrue\ngap> D := Digraph\ ([[2, 3], [], []]);\n\ngap> HasDig\ raphGroup(D);\nfalse\ngap> HasAutomorphismGroup(D);\nfalse\ngap> DigraphGroup(\ D);\nGroup([ (2,3) ])\ngap> HasAutomorphismGroup(D);\ntrue\ngap> group := Dihe\ dralGroup(8);\n\ngap> D := CayleyDigraph\ (group);\n\ngap> HasDigraphGroup(\ D);\ntrue\ngap> GeneratorsOfGroup(DigraphGroup(D));\n[ (1,2)(3,8)(4,6)(5,7), (\ 1,3,4,7)(2,5,6,8), (1,4)(2,6)(3,7)(5,8) ]", count := [ 7, 2, 10, 5 ], name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 10, 5 ], mathmode := "Text", name := "Example", next := 306784, root := ~, start := 305357, stop := 306783 ), rec( content := "\n ", count := [ 7, 2, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "Description", next := 306801, root := ~, start := 304485, stop := 306800 ) ], count := [ 7, 2, 10, 1 ], mathmode := "Text", name := "ManSection", next := 306815, root := ~, start := 304384, stop := 306814 ), rec( content := "\n\n ", count := [ 7, 2, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphOrbits" ), content := 0, count := [ 7, 2, 11, 2 ], mathmode := "Text", name := "Attr", next := 306878, root := ~, start := 306836, stop := 306877 ), rec( attributes := rec( ), content := [ rec( content := "\n An \ immutable list of lists of integers.\n ", count := [ 7, 2, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 11, 3 ], mathmode := "Text", name := "Returns", next := 306947, root := ~, start := 306881, stop := 306946 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 7, 2, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphOrbits", count := [ 7, 2, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 11, 3 ], mathmode := "Text", name := "C", next := 306988, root := ~, start := 306968, stop := 306987 ), rec( content := " returns\ the orbits of the action of the\n ", count := [ 7, 2, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Group" ), content := 0, count := [ 7, 2, 11, 3 ], mathmode := "Text", name := "Ref", next := 307059, root := ~, start := 307033, stop := 307058 ), rec( content := " on the \ set of vertices of ", count := [ 7, 2, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 11, 3 ], mathmode := "Text", name := "A", next := 307100, root := ~, start := 307086, stop := 307099 ), rec( content := ".\n\n \ ", count := [ 7, 2, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> G := Group([(2, 3)(7, 8, 9), (1, 2, 3)(4, 5, 6)(8, 9)]);;\ngap> D := Edg\ eOrbitsDigraph(G, [1, 2]);\n\ngap>\ DigraphOrbits(D);\n[ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 7, 8, 9 ] ]\ngap> D := Digra\ phMutableCopy(D);\n\ngap> DigraphOrb\ its(D);\n[ [ 1, 2, 3 ], [ 4, 5, 6, 7, 8, 9 ] ]\n", count := [ 7, 2, 11, 4 ], name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 11, 4 ], mathmode := "Text", name := "Example", next := 307489, root := ~, start := 307107, stop := 307488 ), rec( content := "\n ", count := [ 7, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 11, 3 ], mathmode := "Text", name := "Description", next := 307506, root := ~, start := 306950, stop := 307505 ) ], count := [ 7, 2, 11, 1 ], mathmode := "Text", name := "ManSection", next := 307520, root := ~, start := 306821, stop := 307519 ), rec( content := "\n\n ", count := [ 7, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphOrbitRep\ s" ), content := 0, count := [ 7, 2, 12, 2 ], mathmode := "Text", name := "Attr", next := 307586, root := ~, start := 307541, stop := 307585 ), rec( attributes := rec( ), content := [ rec( content := "\n An \ immutable list of integers.\n ", count := [ 7, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 12, 3 ], mathmode := "Text", name := "Returns", next := 307646, root := ~, start := 307589, stop := 307645 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 7, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphOrbitReps", count := [ 7, 2, 12, 3 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 7, 2, 12, 3 ], mathmode := "Text", name := "C", next := 307690, root := ~, start := 307667, stop := 307689 ), rec( content := " returns\ a list of orbit representatives\n of the action of the ", count := [ 7, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Group" ), content := 0, count := [ 7, 2, 12, 3 ], mathmode := "Text", name := "Ref", next := 307782, root := ~, start := 307756, stop := 307781 ), rec( content := " on the \ set of vertices of\n ", count := [ 7, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 12, 3 ], mathmode := "Text", name := "A", next := 307827, root := ~, start := 307813, stop := 307826 ), rec( content := ".\n\n \ ", count := [ 7, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CayleyDigraph(AlternatingGroup(4));\n\ngap> DigraphOrbitReps(D);\n[ 1 ]\ngap> D := DigraphMutableCo\ py(D);\n\ngap> DigraphOrbitReps(D)\ ;\n[ 1 ]\ngap> D := DigraphFromDigraph6String(\"&IGO??S?`?_@?a?CK?O\");\n\ngap> DigraphOrbitReps(D);\n[ 1, 2, \ 3, 4, 5, 6, 7, 8, 9, 10 ]\ngap> DigraphOrbitReps(DigraphMutableCopy(D));\n[ 1,\ 2, 3, 4, 5, 6, 7, 8, 9, 10 ]\n", count := [ 7, 2, 12, 4 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 12, 4 ], mathmode := "Text", name := "Example", next := 308348, root := ~, start := 307834, stop := 308347 ), rec( content := "\n ", count := [ 7, 2, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 12, 3 ], mathmode := "Text", name := "Description", next := 308365, root := ~, start := 307649, stop := 308364 ) ], count := [ 7, 2, 12, 1 ], mathmode := "Text", name := "ManSection", next := 308379, root := ~, start := 307526, stop := 308378 ), rec( content := "\n\n ", count := [ 7, 2, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphSchreier\ Vector" ), content := 0, count := [ 7, 2, 13, 2 ], mathmode := "Text", name := "Attr", next := 308450, root := ~, start := 308400, stop := 308449 ), rec( attributes := rec( ), content := [ rec( content := "\n An \ immutable list of integers.\n ", count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "Returns", next := 308510, root := ~, start := 308453, stop := 308509 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphSchreierVector", count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "C", next := 308559, root := ~, start := 308531, stop := 308558 ), rec( content := " returns\ the so-called ", count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "S\ chreier vector", count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "E", next := 308604, root := ~, start := 308582, stop := 308603 ), rec( content := "\n of\ the action of the ", count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Group" ), content := 0, count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "Ref", next := 308656, root := ~, start := 308630, stop := 308655 ), rec( content := " on the \ set of vertices of\n ", count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "A", next := 308701, root := ~, start := 308687, stop := 308700 ), rec( content := ". The Sc\ hreier vector is a list ", count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ch", count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "C", next := 308743, root := ~, start := 308733, stop := 308742 ), rec( content := " of inte\ gers with\n length ", count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphNrVertices(", count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "PCDATA", root \ := ~ ) ], count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "A", next := 3088\ 07, root := ~, start := 308793, stop := 308806 ), rec( content := ")", count := [ 7, 2, 13, 3 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "C", next := 308812, root := ~, start := 308772, stop := 308811 ), rec( content := " where:\\ n ", count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( attributes := rec( ), content := [ rec( content :\ = "sch[i] < 0:", count := [ 7, 2, 13, 4 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 7, 2, 13, 4 ], mathmode := "Text", name := "C", next\ := 308864, root := ~, start := 308843, stop := 308863 ) ], count := [ 7, 2, 13, 4 ], name := "Mar\ k", next := 308871, root := ~, start := 308837, stop := 308870 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n implies that ", count := [ \ 7, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\ tes := rec( ), content := [ rec( content := "i", count := [ 7, 2, 13, 5 ], ma\ thmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 13, 5 ], math\ mode := "Text", name := "C", next := 308914, root := ~, start := 308906, stop \ := 308913 ), rec( content := " is an orbit representative and\n ", coun\ t := [ 7, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "DigraphOrbitReps(", count := \ [ 7, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attri\ butes := rec( ), content := [ rec( content := "digraph", count := [ 7, 2, 13,\ 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 13\ , 5 ], mathmode := "Text", name := "A", next := 308988, root := ~, start := 30\ 8974, stop := 308987 ), rec( content := ")[-sch[i]] = i", count := [ 7, 2, 13,\ 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 13\ , 5 ], mathmode := "Text", name := "C", next := 309006, root := ~, start := 30\ 8954, stop := 309005 ), rec( content := ".\n ", count := [ 7, 2, 13, 5 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 13, 5 ], name := "Ite\ m", next := 309021, root := ~, start := 308878, stop := 309020 ), rec( attributes :\ = rec( ), content := [ rec( attributes := rec( ), content := [ rec( content \ := "sch[i] > 0:", count := [ 7, 2, 13, 6 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 7, 2, 13, 6 ], mathmode := "Text", name := "C", next\ := 309056, root := ~, start := 309035, stop := 309055 ) ], count := [ 7, 2, 13, 6 ], name := "Mar\ k", next := 309063, root := ~, start := 309029, stop := 309062 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n implies that ", count := [ \ 7, 2, 13, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\ tes := rec( ), content := [ rec( content := "i / gens[sch[i]]", count := [ 7,\ 2, 13, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7\ , 2, 13, 7 ], mathmode := "Text", name := "C", next := 309121, root := ~, star\ t := 309098, stop := 309120 ), rec( content := "\n is one step closer t\ o the root (or representative) of the tree, where\n ", count := [ 7, 2,\ 13, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "gens", count := [ 7, 2, 13, 7 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 13, 7 ], math\ mode := "Text", name := "C", next := 309219, root := ~, start := 309208, stop \ := 309218 ), rec( content := " is the generators of ", count := [ 7, 2, 13, 7 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "DigraphGroup(", count := [ 7, 2, 13, 7 ], mathmode :\ = "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content :\ = [ rec( content := "digraph", count := [ 7, 2, 13, 7 ], mathmode := "Text", n\ ame := "PCDATA", root := ~ ) ], count := [ 7, 2, 13, 7 ], mathmode := "Text", \ name := "A", next := 309271, root := ~, start := 309257, stop := 309270 ), rec\ ( content := ")", count := [ 7, 2, 13, 7 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 7, 2, 13, 7 ], mathmode := "Text", name := "C", next\ := 309276, root := ~, start := 309241, stop := 309275 ), rec( content := ".\n\ ", count := [ 7, 2, 13, 7 ], mathmode := "Text", name := "PCDATA", root \ := ~ ) ], count := [ 7, 2, 13, 7 ], name := "Item", next := 309291, root := ~, start := 309\ 070, stop := 309290 ) ], count := [ 7, 2, 13, 4 ], mathmode := "Text", name := "List", next := 309303, root := ~, start := 308824, stop := 309302 ), rec( content := "\n\n \ ", count := [ 7, 2, 13, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> n := 4;;\ngap> adj := function(x, y)\n> return (((x - y) mod n) = 1\ ) or (((x - y) mod n) = n - 1);\n> end;;\ngap> group := CyclicGroup(IsPermG\ roup, n);\nGroup([ (1,2,3,4) ])\ngap> D := Digraph(IsMutableDigraph, group, [1\ .. n], \\^, adj);\n\ngap> sch := Di\ graphSchreierVector(D);\n[ -1, 2, 2, 1 ]\ngap> D := CayleyDigraph(AlternatingG\ roup(4));\n\ngap> sch := Digraph\ SchreierVector(D);\n[ -1, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1 ]\ngap> DigraphOrbit\ Reps(D);\n[ 1 ]\ngap> gens := GeneratorsOfGroup(DigraphGroup(D));\n[ (1,5,7)(2\ ,4,8)(3,6,9)(10,11,12), (1,2,3)(4,7,10)(5,9,11)(6,8,12) ]\ngap> 10 / gens[sch[\ 10]];\n7\ngap> 7 / gens[sch[7]];\n5\ngap> 5 / gens[sch[5]];\n1", count := [ 7, 2, 13, 10 ] , name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 13, 10 ], mathmode := "Text", name := "Example", next := 310080, root := ~, start := 309309, stop := 310079 ), rec( content := "\n ", count := [ 7, 2, 13, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "Description", next := 310097, root := ~, start := 308513, stop := 310096 ) ], count := [ 7, 2, 13, 1 ], mathmode := "Text", name := "ManSection", next := 310111, root := ~, start := 308385, stop := 310110 ), rec( content := "\n\n ", count := [ 7, 2, 13, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, v", Name := "DigraphStabiliz\ er" ), content := 0, count := [ 7, 2, 14, 2 ], mathmode := "Text", name := "Oper", next := 310181, root := ~, start := 310132, stop := 310180 ), rec( attributes := rec( ), content := [ rec( content := "\n A p\ ermutation group.\n ", count := [ 7, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 14, 3 ], mathmode := "Text", name := "Returns", next := 310231, root := ~, start := 310184, stop := 310230 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 7, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphStabilizer", count := [ 7, 2, 14, 3 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 7, 2, 14, 3 ], mathmode := "Text", name := "C", next := 310276, root := ~, start := 310252, stop := 310275 ), rec( content := " returns\ the stabilizer of the vertex ", count := [ 7, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 7, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 14, 3 ], mathmode := "Text", name := "A", next := 310322, root := ~, start := 310314, stop := 310321 ), rec( content := "\n un\ der of the action of the ", count := [ 7, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Group" ), content := 0, count := [ 7, 2, 14, 3 ], mathmode := "Text", name := "Ref", next := 310380, root := ~, start := 310354, stop := 310379 ), rec( content := " on the \ set of\n vertices of ", count := [ 7, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 14, 3 ], mathmode := "Text", name := "A", next := 310425, root := ~, start := 310411, stop := 310424 ), rec( content := ".\n\n \ ", count := [ 7, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := DigraphFromDigraph6String(\"&GYHPQgWTIIPW\");\n\ngap> DigraphStabilizer(D, 8);\nGroup(())\ngap> Digr\ aphStabilizer(D, 2);\nGroup(())\ngap> D := DigraphMutableCopy(D);\n\ngap> DigraphStabilizer(D, 8);\nGroup(())\nga\ p> DigraphStabilizer(D, 2);\nGroup(())\n", count := [ 7, 2, 14, 4 ], name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 14, 4 ], mathmode := "Text", name := "Example", next := 310801, root := ~, start := 310432, stop := 310800 ), rec( content := "\n ", count := [ 7, 2, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 14, 3 ], mathmode := "Text", name := "Description", next := 310818, root := ~, start := 310234, stop := 310817 ) ], count := [ 7, 2, 14, 1 ], mathmode := "Text", name := "ManSection", next := 310832, root := ~, start := 310117, stop := 310831 ), rec( content := "\n\n ", count := [ 7, 2, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph1, digrap\ h2", Label := "for digraphs", Name := "IsIsomorphicDigraph" ), content := 0, count := [ 7, 2, 15, 2 ], mathmode := "Text", name := "Oper", next := 310933, root := ~, start := 310853, stop := 310932 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "K", next := 310956, root := ~, start := 310945, stop := 310955 ), rec( content := " or ", count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "K", next := 310972, root := ~, start := 310960, stop := 310971 ), rec( content := ".", count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "Returns", next := 310983, root := ~, start := 310936, stop := 310982 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s operation returns ", count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "K", next := 311038, root := ~, start := 311027, stop := 311037 ), rec( content := " if ther\ e exists an isomorphism from the\n digraph ", count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "A", next := 311106, root := ~, start := 311091, stop := 311105 ), rec( content := " to the \ digraph ", count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "A", next := 311137, root := ~, start := 311122, stop := 311136 ), rec( content := ". See " , count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for di\ graphs", Oper := "IsomorphismDigraphs" ), content := 0, count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "Ref", next := 311205, root := ~, start := 311144, stop := 311204 ), rec( content := " for mor\ e information\n about isomorphisms of digraphs. ", count := [ 7, 2, 15, 3 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "P", next := 311267, root := ~, start := 311263, stop := 311266 ), rec( content := "\n\n \ By default, an isomorphism is found using the canonical labellings of the\n \ digraphs obtained from ", count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\ oftware/bliss/", count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "URL", next := 81, root := ~, start := 17, stop := 80 ) ], count := [ 7, 2, 15, 4 ], name := "Alt", next := 87, root := ~, start := 1, stop := 86 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "bliss", count := [ 7, 2, 15, 4 ], name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 15, 4 ], name := "Package", next := 131, root := ~, start := 107 , stop := 130 ) ], count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "Alt", next := 137, root := ~, start := 87, stop := 136 ), rec( content := " by Tomm\ i Junttila\n and Petteri Kaski. If ", count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\ github.com/gap-packages/NautyTracesInterface", count := [ 7, 2, 15, 4 ], mathm\ ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 15, 4 ], mathmode := \ "Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], count := [ 7, 2, 15, 4 ], name := "Alt", next := 117, root := ~, start := 1, stop := 116 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "NautyTracesInterface", count := [ 7, 2\ , 15, 4 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 15, 4 ], name := "Pac\ kage", next := 176, root := ~, start := 137, stop := 175 ) ], count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "Alt", next := 182, root := ~, start := 117, stop := 181 ), rec( content := " is avai\ lable, then ", count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\ ma1.it/", count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "URL", next := 74, root := ~, start := 17, stop := 73 ) ], count := [ 7, 2, 15, 4 ], name := "Alt", next := 80, root := ~, start := 1, stop := 79 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "nauty", count := [ 7, 2, 15, 4 ], name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 15, 4 ], name := "Package", next := 124, root := ~, start := 100 , stop := 123 ) ], count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "Alt", next := 130, root := ~, start := 80, stop := 129 ), rec( content := " by\n \ Brendan Mckay and Adolfo Piperno can be used instead; see\n ", count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sUseBliss" ), content := 0, count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "Ref", next := 311575, root := ~, start := 311545, stop := 311574 ), rec( content := ", and ", count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sUseNauty" ), content := 0, count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "Ref", next := 311611, root := ~, start := 311581, stop := 311610 ), rec( content := ".\n\n \ ", count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> digraph1 := CycleDigraph(4);\n\ \ngap> digraph2 := CycleDigraph(5);\n\ \ngap> IsIsomorphicDigraph(digraph1, digraph2);\nfalse\ngap> digraph2 := Digra\ phReverse(digraph1);\n\ngap> IsIso\ morphicDigraph(digraph1, digraph2);\ntrue\ngap> digraph1 := Digraph([[3], [], \ []]);\n\ngap> digraph2 := Digraph([\ [], [], [2]]);\n\ngap> IsIsomorphic\ Digraph(digraph1, digraph2);\ntrue", count := [ 7, 2, 15, 5 ], name := "PCDATA\ ", root := ~ ) ], count := [ 7, 2, 15, 5 ], mathmode := "Text", name := "Example", next := 312213, root := ~, start := 311618, stop := 312212 ), rec( content := "\n ", count := [ 7, 2, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "Description", next := 312230, root := ~, start := 310986, stop := 312229 ) ], count := [ 7, 2, 15, 1 ], mathmode := "Text", name := "ManSection", next := 312244, root := ~, start := 310838, stop := 312243 ), rec( content := "\n\n ", count := [ 7, 2, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph1, digrap\ h2, colours1, colours2", Label := "for digraphs and homogeneous lists", Name := "IsIsomorphicDig\ raph" ), content := 0, count := [ 7, 2, 16, 2 ], mathmode := "Text", name := "Oper", next := 312391, root := ~, start := 312265, stop := 312390 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "K", next := 312414, root := ~, start := 312403, stop := 312413 ), rec( content := " or ", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "K", next := 312430, root := ~, start := 312418, stop := 312429 ), rec( content := ".", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "Returns", next := 312441, root := ~, start := 312394, stop := 312440 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s operation tests for isomorphism of coloured digraphs. A coloured\n digra\ ph can be specified by its underlying digraph ", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "A", next := 312603, root := ~, start := 312588, stop := 312602 ), rec( content := " and its\ \n colouring ", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olours1", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "A", next := 312641, root := ~, start := 312626, stop := 312640 ), rec( content := ". Let " , count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "C", next := 312656, root := ~, start := 312648, stop := 312655 ), rec( content := " be the \ number of vertices of\n ", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "A", next := 312705, root := ~, start := 312690, stop := 312704 ), rec( content := ". The co\ louring ", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olours1", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "A", next := 312736, root := ~, start := 312721, stop := 312735 ), rec( content := " may hav\ e one of the following\n two forms:\n\n ", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "\n a list of ", count := [ 7, 2\ , 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes \ := rec( ), content := [ rec( content := "n", count := [ 7, 2, 16, 5 ], mathmo\ de := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 5 ], mathm\ ode := "Text", name := "C", next := 312833, root := ~, start := 312825, stop :\ = 312832 ), rec( content := " integers, where ", count := [ 7, 2, 16, 5 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "colours", count := [ 7, 2, 16, 5 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 5 ], mathmode := "Te\ xt", name := "A", next := 312864, root := ~, start := 312850, stop := 312863 ) , rec( attr\ ibutes := rec( ), content := [ rec( content := "[i]", count := [ 7, 2, 16, 5 \ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 5\ ], mathmode := "Text", name := "C", next := 312874, root := ~, start := 31286\ 4, stop := 312873 ), rec( content := " is the\n colour of vertex ", coun\ t := [ 7, 2, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "i", count := [ 7, 2, 16, 5 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 5 ] , math\ mode := "Text", name := "C", next := 312915, root := ~, start := 312907, stop \ := 312914 ), rec( content := ", using the colours ", count := [ 7, 2, 16, 5 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "[1 .. m]", count := [ 7, 2, 16, 5 ], mathmode := "Te\ xt", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 5 ], mathmode := "T\ ext", name := "C", next := 312950, root := ~, start := 312935, stop := 312949 ), rec( cont\ ent := " for some\n ", count := [ 7, 2, 16, 5 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "m <= n", count := [ 7, 2, 16, 5 ], mathmode := "Text", name := "PCDATA"\ , root := ~ ) ], count := [ 7, 2, 16, 5 ], mathmode := "Text", name := "C", next\ := 312984, root := ~, start := 312968, stop := 312983 ), rec( content := "; o\ r\n ", count := [ 7, 2, 16, 5 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 2, 16, 5 ], name := "Item", next := 313002, root := ~, start := 312\ 800, stop := 313001 ), rec( attributes := rec( ), content := [ rec( content :\ = "\n a list of non-empty disjoint lists whose union is\n ", coun\ t := [ 7, 2, 16, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "DigraphVertices(", count := [\ 7, 2, 16, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attrib\ utes := rec( ), content := [ rec( content := "digraph", count := [ 7, 2, 16, \ 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16,\ 7 ], mathmode := "Text", name := "A", next := 313115, root := ~, start := 313\ 101, stop := 313114 ), rec( content := ")", count := [ 7, 2, 16, 7 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 7 ], mathmod\ e := "Text", name := "C", next := 313120, root := ~, start := 313082, stop := \ 313119 ), rec( content := ", such that\n ", count := [ 7, 2, 16, 7 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "colours", count := [ 7, 2, 16, 7 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 7 ], mathmode := "Te\ xt", name := "A", next := 313154, root := ~, start := 313140, stop := 313153 ) , rec( attr\ ibutes := rec( ), content := [ rec( content := "[i]", count := [ 7, 2, 16, 7 \ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 7\ ], mathmode := "Text", name := "C", next := 313164, root := ~, start := 31315\ 4, stop := 313163 ), rec( content := " is the list of all vertices with colour\ \n ", count := [ 7, 2, 16, 7 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "i", count :\ = [ 7, 2, 16, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count \ := [ 7, 2, 16, 7 ], mathmode := "Text", name := "C", next := 313221, root := ~ , star\ t := 313213, stop := 313220 ), rec( content := ".\n ", count := [ 7, 2, 1\ 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 7 ], name := "Ite\ m", next := 313236, root := ~, start := 313009, stop := 313235 ) ], count := [ 7, 2, 16, 4 ], mathmode := "Text", name := "List", next := 313248, root := ~, start := 312787, stop := 313247 ), rec( content := "\n\n \ If ", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "A", next := 313272, root := ~, start := 313257, stop := 313271 ), rec( content := " and ", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "A", next := 313292, root := ~, start := 313277, stop := 313291 ), rec( content := " are dig\ raphs without multiple edges,\n and ", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olours1", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "A", next := 313353, root := ~, start := 313338, stop := 313352 ), rec( content := " and ", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olours2", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "A", next := 313373, root := ~, start := 313358, stop := 313372 ), rec( content := " are col\ ourings of ", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "A", next := 313407, root := ~, start := 313392, stop := 313406 ), rec( content := "\n an\ d ", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "A", next := 313431, root := ~, start := 313416, stop := 313430 ), rec( content := ", respec\ tively, then this operation returns ", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "K", next := 313486, root := ~, start := 313475, stop := 313485 ), rec( content := "\n if\ there exists an isomorphism between these two coloured digraphs. See\n ", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for di\ graphs and homogeneous lists", Oper := "IsomorphismDigraphs" ), content := 0, count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "Ref", next := 313651, root := ~, start := 313568, stop := 313650 ), rec( content := " for mor\ e information about isomorphisms of coloured digraphs. ", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "P", next := 313718, root := ~, start := 313714, stop := 313717 ), rec( content := "\n\n \ By default, an isomorphism is found using the canonical labellings of the\n \ digraphs obtained from ", count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\ oftware/bliss/", count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "URL\ ", next := 81, root := ~, start := 17, stop := 80 ) ], count := [ 7, 2, 16, 10 ], name := "Alt", next := 87, root := ~, start := 1, stop := 86 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "bliss", count := [ 7, 2, 16, 10 ], name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 10 ], name := "Package", next := 131, root := ~, start := 107 , stop := 130 ) ], count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "Alt", next := 137, root := ~, start := 87, stop := 136 ), rec( content := " by Tomm\ i Junttila\n and Petteri Kaski. If ", count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\ github.com/gap-packages/NautyTracesInterface", count := [ 7, 2, 16, 10 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 10 ], mathmode := \ "Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], count := [ 7, 2, 16, 10 ], name := "Alt", next := 117, root := ~, start := 1, stop := 116 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "NautyTracesInterface", count := [ 7, 2\ , 16, 10 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 10 ], name := "Pac\ kage", next := 176, root := ~, start := 137, stop := 175 ) ], count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "Alt", next := 182, root := ~, start := 117, stop := 181 ), rec( content := " is avai\ lable, then ", count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\ ma1.it/", count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "URL", next := 74, root := ~, start := 17, stop := 73 ) ], count := [ 7, 2, 16, 10 ], name := "Alt", next := 80, root := ~, start := 1, stop := 79 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "nauty", count := [ 7, 2, 16, 10 ], name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 10 ], name := "Package", next := 124, root := ~, start := 100 , stop := 123 ) ], count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "Alt", next := 130, root := ~, start := 80, stop := 129 ), rec( content := " by\n \ Brendan Mckay and Adolfo Piperno can be used instead; see\n ", count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sUseBliss" ), content := 0, count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "Ref", next := 314026, root := ~, start := 313996, stop := 314025 ), rec( content := ", and ", count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sUseNauty" ), content := 0, count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "Ref", next := 314062, root := ~, start := 314032, stop := 314061 ), rec( content := ".\n\n \ ", count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> digraph1 := ChainDigraph(4);\n\ \ngap> digraph2 := ChainDigraph(3);\n\ \ngap> IsIsomorphicDigraph(digraph1, digraph2,\n> [[1, 4], [2, 3]], [[1, 2], \ [3]]);\nfalse\ngap> digraph2 := DigraphReverse(digraph1);\n\ngap> IsIsomorphicDigraph(digraph1, digraph2,\n> [1\ , 1, 1, 1], [1, 1, 1, 1]);\ntrue\ngap> IsIsomorphicDigraph(digraph1, digraph2,\ \n> [1, 2, 2, 1], [1, 2, 2, 1]);\ntrue\ngap> IsIsomorphicDigraph(digraph1, di\ graph2,\n> [1, 1, 2, 2], [1, 1, 2, 2]);\nfalse", count := [ 7, 2, 16, 11 ], name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 16, 11 ], mathmode := "Text", name := "Example", next := 314675, root := ~, start := 314069, stop := 314674 ), rec( content := "\n ", count := [ 7, 2, 16, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "Description", next := 314692, root := ~, start := 312444, stop := 314691 ) ], count := [ 7, 2, 16, 1 ], mathmode := "Text", name := "ManSection", next := 314706, root := ~, start := 312250, stop := 314705 ), rec( content := "\n\n ", count := [ 7, 2, 16, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph1, digrap\ h2", Label := "for digraphs", Name := "IsomorphismDigraphs" ), content := 0, count := [ 7, 2, 17, 2 ], mathmode := "Text", name := "Oper", next := 314807, root := ~, start := 314727, stop := 314806 ), rec( attributes := rec( ), content := [ rec( content := " A permut\ ation, or a pair of permutations, or ", count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "K", next := 314876, root := ~, start := 314865, stop := 314875 ), rec( content := ".", count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "Returns", next := 314887, root := ~, start := 314810, stop := 314886 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s operation returns an isomorphism between the digraphs ", count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "A", next := 314982, root := ~, start := 314967, stop := 314981 ), rec( content := "\n an\ d ", count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "A", next := 315006, root := ~, start := 314991, stop := 315005 ), rec( content := " if one \ exists, else this operation returns ", count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "K", next := 315061, root := ~, start := 315050, stop := 315060 ), rec( content := ".\n " , count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "P", next := 315071, root := ~, start := 315067, stop := 315070 ), rec( content := "\n\n \ An ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ somorphism", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "E", next := 315098, root := ~, start := 315080, stop := 315097 ), rec( content := " from a \ digraph ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "A", next := 315129, root := ~, start := 315114, stop := 315128 ), rec( content := " to a di\ graph\n ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "A", next := 315162, root := ~, start := 315147, stop := 315161 ), rec( content := " is a bi\ jection ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "C", next := 315186, root := ~, start := 315178, stop := 315185 ), rec( content := " from th\ e vertices of\n ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "A", next := 315227, root := ~, start := 315212, stop := 315226 ), rec( content := " to the \ vertices of ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "A", next := 315262, root := ~, start := 315247, stop := 315261 ), rec( content := " with th\ e following\n property: for all vertices ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "C", next := 315321, root := ~, start := 315313, stop := 315320 ), rec( content := " and ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "C", next := 315334, root := ~, start := 315326, stop := 315333 ), rec( content := " of ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "A", next := 315353, root := ~, start := 315338, stop := 315352 ), rec( content := ",\n " , count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ i, j]", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "C", next := 315372, root := ~, start := 315359, stop := 315371 ), rec( content := " is an e\ dge of ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "A", next := 315402, root := ~, start := 315387, stop := 315401 ), rec( content := " if and \ only if ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ i ^ p, j\n ^ p]", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "C", next := 315445, root := ~, start := 315418, stop := 315444 ), rec( content := " is an e\ dge of ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "A", next := 315475, root := ~, start := 315460, stop := 315474 ), rec( content := ". ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 17, 5 ], mathmode := "Text", name := "P", next := 315481, root := ~, start := 315477, stop := 315480 ), rec( content := "\n\n \ If there exists such an isomorphism, then this operation returns one.\n The\ form of this isomorphism is a permutation ", count := [ 7, 2, 17, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ ", count := [ 7, 2, 17, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 5 ], mathmode := "Text", name := "C", next := 315615, root := ~, start := 315607, stop := 315614 ), rec( content := " of the \ vertices of\n ", count := [ 7, 2, 17, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 2, 17, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 5 ], mathmode := "Text", name := "A", next := 315654, root := ~, start := 315639, stop := 315653 ), rec( content := " such th\ at ", count := [ 7, 2, 17, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "P", next := 315669, root := ~, start := 315665, stop := 315668 ), rec( content := "\n\n \ ", count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "O\ nDigraphs(", count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "digraph1", count := [ 7, 2, 17, 6 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 6 ], mathmode := \ "Text", name := "A", next := 315704, root := ~, start := 315689, stop := 31570\ 3 ), rec( content := ", p) = digraph2", count := [ 7, 2, 17, 6 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "C", next := 315723, root := ~, start := 315675, stop := 315722 ), rec( content := ".\n\n \ By default, an isomorphism is found using the canonical labellings of the\n \ digraphs obtained from ", count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\ oftware/bliss/", count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "URL", next := 81, root := ~, start := 17, stop := 80 ) ], count := [ 7, 2, 17, 6 ], name := "Alt", next := 87, root := ~, start := 1, stop := 86 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "bliss", count := [ 7, 2, 17, 6 ], name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 6 ], name := "Package", next := 131, root := ~, start := 107 , stop := 130 ) ], count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "Alt", next := 137, root := ~, start := 87, stop := 136 ), rec( content := " by Tomm\ i Junttila\n and Petteri Kaski. If ", count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\ github.com/gap-packages/NautyTracesInterface", count := [ 7, 2, 17, 6 ], mathm\ ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 6 ], mathmode := \ "Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], count := [ 7, 2, 17, 6 ], name := "Alt", next := 117, root := ~, start := 1, stop := 116 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "NautyTracesInterface", count := [ 7, 2\ , 17, 6 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 6 ], name := "Pac\ kage", next := 176, root := ~, start := 137, stop := 175 ) ], count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "Alt", next := 182, root := ~, start := 117, stop := 181 ), rec( content := " is avai\ lable, then ", count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\ ma1.it/", count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "URL", next := 74, root := ~, start := 17, stop := 73 ) ], count := [ 7, 2, 17, 6 ], name := "Alt", next := 80, root := ~, start := 1, stop := 79 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "nauty", count := [ 7, 2, 17, 6 ], name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 6 ], name := "Package", next := 124, root := ~, start := 100 , stop := 123 ) ], count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "Alt", next := 130, root := ~, start := 80, stop := 129 ), rec( content := " by\n \ Brendan Mckay and Adolfo Piperno can be used instead; see\n ", count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sUseBliss" ), content := 0, count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "Ref", next := 316032, root := ~, start := 316002, stop := 316031 ), rec( content := ", and ", count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sUseNauty" ), content := 0, count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "Ref", next := 316068, root := ~, start := 316038, stop := 316067 ), rec( content := ".\n\n \ ", count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> digraph1 := CycleDigraph(4);\n\ \ngap> digraph2 := CycleDigraph(5);\n\ \ngap> IsomorphismDigraphs(digraph1, digraph2);\nfail\ngap> digraph1 := Comple\ teBipartiteDigraph(10, 5);\n\ngap> digraph2 := CompleteBipartiteDigraph(5, 10);\n\ngap> p := I\ somorphismDigraphs(digraph1, digraph2);\n(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10\ ,15)\ngap> OnDigraphs(digraph1, p) = digraph2;\ntrue\n", count := [ 7, 2, 17, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 17, 7 ], mathmode := "Text", name := "Example", next := 316691, root := ~, start := 316075, stop := 316690 ), rec( content := "\n ", count := [ 7, 2, 17, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "Description", next := 316708, root := ~, start := 314890, stop := 316707 ) ], count := [ 7, 2, 17, 1 ], mathmode := "Text", name := "ManSection", next := 316722, root := ~, start := 314712, stop := 316721 ), rec( content := "\n\n ", count := [ 7, 2, 17, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph1, digrap\ h2, colours1, colours2", Label := "for digraphs and homogeneous lists", Name := "IsomorphismDigr\ aphs" ), content := 0, count := [ 7, 2, 18, 2 ], mathmode := "Text", name := "Oper", next := 316869, root := ~, start := 316743, stop := 316868 ), rec( attributes := rec( ), content := [ rec( content := " A permut\ ation, or ", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "K", next := 316911, root := ~, start := 316900, stop := 316910 ), rec( content := ".", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "Returns", next := 316922, root := ~, start := 316872, stop := 316921 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s operation searches for an isomorphism between coloured digraphs. A\n col\ oured digraph can be specified by its underlying digraph ", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "A", next := 317095, root := ~, start := 317080, stop := 317094 ), rec( content := "\n an\ d its colouring ", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olours1", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "A", next := 317133, root := ~, start := 317118, stop := 317132 ), rec( content := ". Let " , count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "C", next := 317148, root := ~, start := 317140, stop := 317147 ), rec( content := " be the \ number of vertices\n of ", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "A", next := 317197, root := ~, start := 317182, stop := 317196 ), rec( content := ". The co\ louring ", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olours1", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "A", next := 317228, root := ~, start := 317213, stop := 317227 ), rec( content := " may hav\ e one of the\n following two forms:\n\n ", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "\n a list of ", count := [ 7, 2\ , 18, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes \ := rec( ), content := [ rec( content := "n", count := [ 7, 2, 18, 5 ], mathmo\ de := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 5 ], mathm\ ode := "Text", name := "C", next := 317325, root := ~, start := 317317, stop :\ = 317324 ), rec( content := " integers, where ", count := [ 7, 2, 18, 5 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "colours", count := [ 7, 2, 18, 5 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 5 ], mathmode := "Te\ xt", name := "A", next := 317356, root := ~, start := 317342, stop := 317355 ) , rec( attr\ ibutes := rec( ), content := [ rec( content := "[i]", count := [ 7, 2, 18, 5 \ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 5\ ], mathmode := "Text", name := "C", next := 317366, root := ~, start := 31735\ 6, stop := 317365 ), rec( content := " is the\n colour of vertex ", coun\ t := [ 7, 2, 18, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "i", count := [ 7, 2, 18, 5 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 5 ] , math\ mode := "Text", name := "C", next := 317407, root := ~, start := 317399, stop \ := 317406 ), rec( content := ", using the colours ", count := [ 7, 2, 18, 5 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "[1 .. m]", count := [ 7, 2, 18, 5 ], mathmode := "Te\ xt", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 5 ], mathmode := "T\ ext", name := "C", next := 317442, root := ~, start := 317427, stop := 317441 ), rec( cont\ ent := " for some\n ", count := [ 7, 2, 18, 5 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "m <= n", count := [ 7, 2, 18, 5 ], mathmode := "Text", name := "PCDATA"\ , root := ~ ) ], count := [ 7, 2, 18, 5 ], mathmode := "Text", name := "C", next\ := 317476, root := ~, start := 317460, stop := 317475 ), rec( content := "; o\ r\n ", count := [ 7, 2, 18, 5 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 2, 18, 5 ], name := "Item", next := 317494, root := ~, start := 317\ 292, stop := 317493 ), rec( attributes := rec( ), content := [ rec( content :\ = "\n a list of non-empty disjoint lists whose union is\n ", coun\ t := [ 7, 2, 18, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "DigraphVertices(", count := [\ 7, 2, 18, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attrib\ utes := rec( ), content := [ rec( content := "digraph", count := [ 7, 2, 18, \ 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18,\ 7 ], mathmode := "Text", name := "A", next := 317607, root := ~, start := 317\ 593, stop := 317606 ), rec( content := ")", count := [ 7, 2, 18, 7 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 7 ], mathmod\ e := "Text", name := "C", next := 317612, root := ~, start := 317574, stop := \ 317611 ), rec( content := ", such that\n ", count := [ 7, 2, 18, 7 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "colours", count := [ 7, 2, 18, 7 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 7 ], mathmode := "Te\ xt", name := "A", next := 317646, root := ~, start := 317632, stop := 317645 ) , rec( attr\ ibutes := rec( ), content := [ rec( content := "[i]", count := [ 7, 2, 18, 7 \ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 7\ ], mathmode := "Text", name := "C", next := 317656, root := ~, start := 31764\ 6, stop := 317655 ), rec( content := " is the list of all vertices with colour\ \n ", count := [ 7, 2, 18, 7 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "i", count :\ = [ 7, 2, 18, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count \ := [ 7, 2, 18, 7 ], mathmode := "Text", name := "C", next := 317713, root := ~ , star\ t := 317705, stop := 317712 ), rec( content := ".\n ", count := [ 7, 2, 1\ 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 7 ], name := "Ite\ m", next := 317728, root := ~, start := 317501, stop := 317727 ) ], count := [ 7, 2, 18, 4 ], mathmode := "Text", name := "List", next := 317740, root := ~, start := 317279, stop := 317739 ), rec( content := "\n\n \ An ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ somorphism", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "E", next := 317767, root := ~, start := 317749, stop := 317766 ), rec( content := " between\ coloured digraphs is an isomorphism between\n the underlying digraphs that\ preserves the colourings. See ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for di\ graphs", Oper := "IsomorphismDigraphs" ), content := 0, count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "Ref", next := 317944, root := ~, start := 317884, stop := 317943 ), rec( content := " for mor\ e information\n about isomorphisms of digraphs. More precisely, let ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "C", next := 318030, root := ~, start := 318022, stop := 318029 ), rec( content := " be an\n\ isomorphism of digraphs from the digraph ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "A", next := 318097, root := ~, start := 318082, stop := 318096 ), rec( content := " (with c\ olouring\n ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olours1", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "A", next := 318133, root := ~, start := 318118, stop := 318132 ), rec( content := ") to the\ digraph ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "A", next := 318165, root := ~, start := 318150, stop := 318164 ), rec( content := " (with c\ olouring\n ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olours2", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "A", next := 318201, root := ~, start := 318186, stop := 318200 ), rec( content := "), and l\ et ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "C", next := 318220, root := ~, start := 318212, stop := 318219 ), rec( content := " be the \ permutation of the vertices of\n ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "A", next := 318278, root := ~, start := 318263, stop := 318277 ), rec( content := " that co\ rresponds to ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "C", next := 318307, root := ~, start := 318299, stop := 318306 ), rec( content := ". Then \ ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "f\ ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "C", next := 318323, root := ~, start := 318315, stop := 318322 ), rec( content := " preserv\ es the\n colourings of ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "A", next := 318371, root := ~, start := 318356, stop := 318370 ), rec( content := " and ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "A", next := 318391, root := ~, start := 318376, stop := 318390 ), rec( content := " – and\ hence is an\n isomorphism of coloured digraphs – if ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "colours1", count := [ 7, 2, 18, 9 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 9 ], mathmode := \ "Text", name := "A", next := 318474, root := ~, start := 318459, stop := 31847\ 3 ), rec( content := "[i] =\n ", count := [ 7, 2, 18, 9 ], mathmode := "T\ ext", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "colours2", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "A", next := 3185\ 01, root := ~, start := 318486, stop := 318500 ), rec( content := "[i ^ p]", count := [ 7, 2, 18, 9 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "C", next := 318512, root := ~, start := 318456, stop := 318511 ), rec( content := " for all\ vertices ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "C", next := 318538, root := ~, start := 318530, stop := 318537 ), rec( content := " in ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "A", next := 318557, root := ~, start := 318542, stop := 318556 ), rec( content := ".\n " , count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 18, 10 ], mathmode := "Text", name := "P", next := 318567, root := ~, start := 318563, stop := 318566 ), rec( content := "\n\n \ This operation returns such an isomorphism if one exists, else it returns\n \ ", count := [ 7, 2, 18, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 7, 2, 18, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 10 ], mathmode := "Text", name := "K", next := 318662, root := ~, start := 318651, stop := 318661 ), rec( content := ". ", count := [ 7, 2, 18, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "P", next := 318668, root := ~, start := 318664, stop := 318667 ), rec( content := "\n\n \ By default, an isomorphism is found using the canonical labellings of the\n \ digraphs obtained from ", count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\ oftware/bliss/", count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "URL\ ", next := 81, root := ~, start := 17, stop := 80 ) ], count := [ 7, 2, 18, 11 ], name := "Alt", next := 87, root := ~, start := 1, stop := 86 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "bliss", count := [ 7, 2, 18, 11 ], name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 11 ], name := "Package", next := 131, root := ~, start := 107 , stop := 130 ) ], count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "Alt", next := 137, root := ~, start := 87, stop := 136 ), rec( content := " by Tomm\ i Junttila\n and Petteri Kaski. If ", count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\ github.com/gap-packages/NautyTracesInterface", count := [ 7, 2, 18, 11 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 11 ], mathmode := \ "Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], count := [ 7, 2, 18, 11 ], name := "Alt", next := 117, root := ~, start := 1, stop := 116 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "NautyTracesInterface", count := [ 7, 2\ , 18, 11 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 11 ], name := "Pac\ kage", next := 176, root := ~, start := 137, stop := 175 ) ], count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "Alt", next := 182, root := ~, start := 117, stop := 181 ), rec( content := " is avai\ lable, then ", count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\ ma1.it/", count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "URL", next := 74, root := ~, start := 17, stop := 73 ) ], count := [ 7, 2, 18, 11 ], name := "Alt", next := 80, root := ~, start := 1, stop := 79 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "nauty", count := [ 7, 2, 18, 11 ], name\ := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 11 ], name := "Package", next := 124, root := ~, start := 100 , stop := 123 ) ], count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "Alt", next := 130, root := ~, start := 80, stop := 129 ), rec( content := " by\n \ Brendan Mckay and Adolfo Piperno can be used instead; see\n ", count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sUseBliss" ), content := 0, count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "Ref", next := 318976, root := ~, start := 318946, stop := 318975 ), rec( content := ", and ", count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ sUseNauty" ), content := 0, count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "Ref", next := 319012, root := ~, start := 318982, stop := 319011 ), rec( content := ".\n\n \ ", count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> digraph1 := ChainDigraph(4);\n\ \ngap> digraph2 := ChainDigraph(3);\n\ \ngap> IsomorphismDigraphs(digraph1, digraph2,\n> [[1, 4], [2, 3]], [[1, 2], \ [3]]);\nfail\ngap> digraph2 := DigraphReverse(digraph1);\n\ngap> colours1 := [1, 1, 1, 1];;\ngap> colours2 := [1\ , 1, 1, 1];;\ngap> p := IsomorphismDigraphs(digraph1, digraph2, colours1, colo\ urs2);\n(1,4)(2,3)\ngap> OnDigraphs(digraph1, p) = digraph2;\ntrue\ngap> List(\ DigraphVertices(digraph1), i -> colours1[i ^ p]) = colours2;\ntrue\ngap> colou\ rs1 := [1, 1, 2, 2];;\ngap> colours2 := [2, 2, 1, 1];;\ngap> p := IsomorphismD\ igraphs(digraph1, digraph2, colours1, colours2);\n(1,4)(2,3)\ngap> OnDigraphs(\ digraph1, p) = digraph2;\ntrue\ngap> List(DigraphVertices(digraph1), i -> colo\ urs1[i ^ p]) = colours2;\ntrue\ngap> IsomorphismDigraphs(digraph1, digraph2,\n\ > [1, 1, 2, 2], [1, 1, 2, 2]);\nfail", count := [ 7, 2, 18, 12 ], name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 18, 12 ], mathmode := "Text", name := "Example", next := 319995, root := ~, start := 319019, stop := 319994 ), rec( content := "\n ", count := [ 7, 2, 18, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "Description", next := 320012, root := ~, start := 316925, stop := 320011 ) ], count := [ 7, 2, 18, 1 ], mathmode := "Text", name := "ManSection", next := 320026, root := ~, start := 316728, stop := 320025 ), rec( content := "\n\n ", count := [ 7, 2, 18, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "RepresentativeO\ utNeighbours" ), content := 0, count := [ 7, 2, 19, 2 ], mathmode := "Text", name := "Attr", next := 320103, root := ~, start := 320047, stop := 320102 ), rec( attributes := rec( ), content := [ rec( content := "An immuta\ ble list of lists.", count := [ 7, 2, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 19, 3 ], mathmode := "Text", name := "Returns", next := 320152, root := ~, start := 320106, stop := 320151 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function returns the list ", count := [ 7, 2, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ ut", count := [ 7, 2, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 19, 3 ], mathmode := "Text", name := "C", next := 320214, root := ~, start := 320204, stop := 320213 ), rec( content := " of ", count := [ 7, 2, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ ut-neighbours", count := [ 7, 2, 19, 3 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 7, 2, 19, 3 ], mathmode := "Text", name := "E", next := 320239, root := ~, start := 320218, stop := 320238 ), rec( content := " of each\ \n representative of the orbits of the action of ", count := [ 7, 2, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Group" ), content := 0, count := [ 7, 2, 19, 3 ], mathmode := "Text", name := "Ref", next := 320324, root := ~, start := 320298, stop := 320323 ), rec( content := " on\n \ the vertex set of the digraph ", count := [ 7, 2, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 19, 3 ], mathmode := "Text", name := "A", next := 320376, root := ~, start := 320362, stop := 320375 ), rec( content := ". ", count := [ 7, 2, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "P", next := 320382, root := ~, start := 320378, stop := 320381 ), rec( content := "\n\n \ More specifically, if ", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "r\ eps", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "C", next := 320421, root := ~, start := 320410, stop := 320420 ), rec( content := " is the \ list of orbit representatives,\n then a vertex ", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "C", next := 320486, root := ~, start := 320478, stop := 320485 ), rec( content := " appears\ in ", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ ut[i]", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "C", next := 320511, root := ~, start := 320498, stop := 320510 ), rec( content := " each ti\ me\n there exists an edge with source ", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "r\ eps[i]", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "C", next := 320573, root := ~, start := 320559, stop := 320572 ), rec( content := " and ran\ ge ", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ ", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "C", next := 320592, root := ~, start := 320584, stop := 320591 ), rec( content := " in\n \ ", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "A", next := 320614, root := ~, start := 320600, stop := 320613 ), rec( content := ".\n " , count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 19, 5 ], mathmode := "Text", name := "P", next := 320624, root := ~, start := 320620, stop := 320623 ), rec( content := "\n\n \ If ", count := [ 7, 2, 19, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ Group" ), content := 0, count := [ 7, 2, 19, 5 ], mathmode := "Text", name := "Ref", next := 320659, root := ~, start := 320633, stop := 320658 ), rec( content := " is triv\ ial, then ", count := [ 7, 2, 19, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "OutNeig\ hbours" ), content := 0, count := [ 7, 2, 19, 5 ], mathmode := "Text", name := "Ref", next := 320704, root := ~, start := 320677, stop := 320703 ), rec( content := "\n is\ returned.\n\n ", count := [ 7, 2, 19, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([\n> [2, 1, 3, 4, 5], [3, 5], [2], [1, 2, 3, 5], [1, 2, 3,\ 4]]);\n\ngap> DigraphGroup(D);\n\ Group(())\ngap> RepresentativeOutNeighbours(D);\n[ [ 2, 1, 3, 4, 5 ], [ 3, 5 ]\ , [ 2 ], [ 1, 2, 3, 5 ], [ 1, 2, 3, 4 ] ]\ngap> D := Digraph(IsMutableDigraph,\ [\n> [2, 1, 3, 4, 5], [3, 5], [2], [1, 2, 3, 5], [1, 2, 3, 4]]);\n\ngap> DigraphGroup(D);\nGroup(())\ngap> Repr\ esentativeOutNeighbours(D);\n[ [ 2, 1, 3, 4, 5 ], [ 3, 5 ], [ 2 ], [ 1, 2, 3, \ 5 ], [ 1, 2, 3, 4 ] ]\ngap> D := DigraphFromDigraph6String(\"&GYHPQgWTIIPW\");\ \n\ngap> G := DigraphGroup(D);;\n\ gap> GeneratorsOfGroup(G);\n[ (1,2)(3,4)(5,6)(7,8), (1,3,2,4)(5,7,6,8), (1,5)(\ 2,6)(3,8)(4,7) ]\ngap> Set(RepresentativeOutNeighbours(D), Set);\n[ [ 2, 3, 5 \ ] ]", count := [ 7, 2, 19, 6 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 19, 6 ], mathmode := "Text", name := "Example", next := 321597, root := ~, start := 320727, stop := 321596 ), rec( content := "\n ", count := [ 7, 2, 19, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 19, 3 ], mathmode := "Text", name := "Description", next := 321614, root := ~, start := 320155, stop := 321613 ) ], count := [ 7, 2, 19, 1 ], mathmode := "Text", name := "ManSection", next := 321628, root := ~, start := 320032, stop := 321627 ), rec( content := "\n\n ", count := [ 7, 2, 19, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "src, ran, x", Label := "for digraphs a\ nd transformation or permutation", Name := "IsDigraphIsomorphism" ), content := 0, count := [ 7, 2, 20, 2 ], mathmode := "Text", name := "Oper", next := 321766, root := ~, start := 321649, stop := 321765 ), rec( attributes := rec( Arg := "src, ran, x, col\ 1, col2", Name := "IsDigraphIsomorphism" ), content := 0, count := [ 7, 2, 20, 4 ], mathmode := "Text", name := "Oper", next := 321834, root := ~, start := 321769, stop := 321833 ), rec( attributes := rec( Arg := "digraph, x", Label := "for a digraph \ and a transformation or permutation", Name := "IsDigraphAutomorphism" ), content := 0, count := [ 7, 2, 20, 6 ], mathmode := "Text", name := "Oper", next := 321957, root := ~, start := 321837, stop := 321956 ), rec( attributes := rec( Arg := "digraph, x, col" , Name := "IsDigraphAutomo\ rphism" ), content := 0, count := [ 7, 2, 20, 8 ], mathmode := "Text", name := "Oper", next := 322018, root := ~, start := 321960, stop := 322017 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "K", next := 322041, root := ~, start := 322030, stop := 322040 ), rec( content := " or ", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "K", next := 322057, root := ~, start := 322045, stop := 322056 ), rec( content := ".", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "Returns", next := 322068, root := ~, start := 322021, stop := 322067 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sDigraphIsomorphism", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "C", next := 322116, root := ~, start := 322089, stop := 322115 ), rec( content := " returns\ ", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "K", next := 322136, root := ~, start := 322125, stop := 322135 ), rec( content := " if the \ permutation or\n transformation ", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "A", next := 322186, root := ~, start := 322178, stop := 322185 ), rec( content := " is an i\ somorphism from the digraph ", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ rc", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "A", next := 322232, root := ~, start := 322222, stop := 322231 ), rec( content := " to\n \ the digraph ", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "r\ an", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "A", next := 322262, root := ~, start := 322252, stop := 322261 ), rec( content := ".\n " , count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 20, 10 ], mathmode := "Text", name := "P", next := 322272, root := ~, start := 322268, stop := 322271 ), rec( content := "\n\n \ ", count := [ 7, 2, 20, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sDigraphAutomorphism", count := [ 7, 2, 20, 10 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 20, 10 ], mathmode := "Text", name := "C", next := 322306, root := ~, start := 322278, stop := 322305 ), rec( content := " returns\ ", count := [ 7, 2, 20, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 7, 2, 20, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 10 ], mathmode := "Text", name := "K", next := 322326, root := ~, start := 322315, stop := 322325 ), rec( content := " if the \ permutation or\n transformation ", count := [ 7, 2, 20, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ", count := [ 7, 2, 20, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 10 ], mathmode := "Text", name := "A", next := 322376, root := ~, start := 322368, stop := 322375 ), rec( content := " is an a\ utomorphism of the digraph ", count := [ 7, 2, 20, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 20, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 10 ], mathmode := "Text", name := "A", next := 322425, root := ~, start := 322411, stop := 322424 ), rec( content := ".\n " , count := [ 7, 2, 20, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 20, 11 ], mathmode := "Text", name := "P", next := 322435, root := ~, start := 322431, stop := 322434 ), rec( content := "\n\n \ A permutation or transformation ", count := [ 7, 2, 20, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ", count := [ 7, 2, 20, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 11 ], mathmode := "Text", name := "A", next := 322481, root := ~, start := 322473, stop := 322480 ), rec( content := " is an " , count := [ 7, 2, 20, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ somorphism", count := [ 7, 2, 20, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 11 ], mathmode := "Text", name := "E", next := 322506, root := ~, start := 322488, stop := 322505 ), rec( content := " from a\\ n digraph ", count := [ 7, 2, 20, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ rc", count := [ 7, 2, 20, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 11 ], mathmode := "Text", name := "A", next := 322536, root := ~, start := 322526, stop := 322535 ), rec( content := " to a di\ graph ", count := [ 7, 2, 20, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "r\ an", count := [ 7, 2, 20, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 11 ], mathmode := "Text", name := "A", next := 322560, root := ~, start := 322550, stop := 322559 ), rec( content := " if the \ following hold:\n ", count := [ 7, 2, 20, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "\n ", count := [ 7, 2, 20, 13 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "x", count := [ 7, 2, 20, 13 ], mathmode := "Text", n\ ame := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 13 ], mathmode := "Text", name\ := "A", next := 322624, root := ~, start := 322616, stop := 322623 ), rec( cont\ ent := " is a bijection from the vertices of ", count := [ 7, 2, 20, 13 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "src", count := [ 7, 2, 20, 13 ], mathmode := "Text",\ name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 13 ], mathmode := "Text\ ", name := "A", next := 322671, root := ~, start := 322661, stop := 322670 ), rec( cont\ ent := " to those of\n ", count := [ 7, 2, 20, 13 ], mathmode := "Text" , name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "ran", count := [ 7, 2, 20, 13 ], mathmode := "Text", name := "PCDATA", \ root := ~ ) ], count := [ 7, 2, 20, 13 ], mathmode := "Text", name := "A", next\ := 322702, root := ~, start := 322692, stop := 322701 ), rec( content := ";\n\ ", count := [ 7, 2, 20, 13 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 2, 20, 13 ], name := "Item", next := 322717, root := ~, start := 322\ 601, stop := 322716 ), rec( attributes := rec( ), content := [ rec( content :\ = "\n ", count := [ 7, 2, 20, 15 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[u ^\ ", count := [ 7, 2, 20, 15 ], mathmode := "Text", name := "PCDATA", root := ~\ ), rec( attributes := rec( ), content := [ rec( content := "x", count := [ 7\ , 2, 20, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [\ 7, 2, 20, 15 ], mathmode := "Text", name := "A", next := 322755, root := ~, s\ tart := 322747, stop := 322754 ), rec( content := ", v ^ ", count := [ 7, 2, 2\ 0, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :=\ rec( ), content := [ rec( content := "x", count := [ 7, 2, 20, 15 ], mathmod\ e := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 15 ], mathm\ ode := "Text", name := "A", next := 322769, root := ~, start := 322761, stop :\ = 322768 ), rec( content := "]", count := [ 7, 2, 20, 15 ], mathmode := "Text"\ , name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 15 ], mathmode := "Tex\ t", name := "C", next := 322774, root := ~, start := 322739, stop := 322773 ), rec( cont\ ent := " is an edge of\n ", count := [ 7, 2, 20, 15 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ re\ c( content := "ran", count := [ 7, 2, 20, 15 ], mathmode := "Text", name := "P\ CDATA", root := ~ ) ], count := [ 7, 2, 20, 15 ], mathmode := "Text", name := \ "A", next := 322807, root := ~, start := 322797, stop := 322806 ), rec( conten\ t := " if and only if ", count := [ 7, 2, 20, 15 ], mathmode := "Text", name :\ = "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content\ := "[u, v]", count := [ 7, 2, 20, 15 ], mathmode := "Text", name := "PCDATA",\ root := ~ ) ], count := [ 7, 2, 20, 15 ], mathmode := "Text", name := "C", next\ := 322836, root := ~, start := 322823, stop := 322835 ), rec( content := " is\ an\n edge of ", count := [ 7, 2, 20, 15 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content \ := "src", count := [ 7, 2, 20, 15 ], mathmode := "Text", name := "PCDATA", roo\ t := ~ ) ], count := [ 7, 2, 20, 15 ], mathmode := "Text", name := "A", next :\ = 322869, root := ~, start := 322859, stop := 322868 ), rec( content := "; and\ \n ", count := [ 7, 2, 20, 15 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 2, 20, 15 ], name := "Item", next := 322888, root := ~, start := 322\ 724, stop := 322887 ), rec( attributes := rec( ), content := [ rec( content :\ = "\n ", count := [ 7, 2, 20, 17 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x", \ count := [ 7, 2, 20, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ] , coun\ t := [ 7, 2, 20, 17 ], mathmode := "Text", name := "A", next := 322918, root :\ = ~, start := 322910, stop := 322917 ), rec( content := " fixes every ", count\ := [ 7, 2, 20, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "i", count := [ 7, 2, 20, 17 ]\ , mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 17\ ], mathmode := "Text", name := "C", next := 322939, root := ~, start := 32293\ 1, stop := 322938 ), rec( content := " which is not a vertex of ", count := [ \ 7, 2, 20, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attrib\ utes := rec( ), content := [ rec( content := "src", count := [ 7, 2, 20, 17 ]\ , mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 17\ ], mathmode := "Text", name := "A", next := 322975, root := ~, start := 32296\ 5, stop := 322974 ), rec( content := ".\n ", count := [ 7, 2, 20, 17 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 17 ], name := "Ite\ m", next := 322990, root := ~, start := 322895, stop := 322989 ) ], count := [ 7, 2, 20, 12 ], mathmode := "Text", name := "List", next := 323002, root := ~, start := 322588, stop := 323001 ), rec( content := "\n Se\ e also ", count := [ 7, 2, 20, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Automor\ phismGroup", Label := "for a digraph" ), content := 0, count := [ 7, 2, 20, 19 ], mathmode := "Text", name := "Ref", next := 323076, root := ~, start := 323016, stop := 323075 ), rec( content := ".", count := [ 7, 2, 20, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 20, 20 ], mathmode := "Text", name := "P", next := 323081, root := ~, start := 323077, stop := 323080 ), rec( content := "\n \n\ If ", count := [ 7, 2, 20, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ ol1", count := [ 7, 2, 20, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 20 ], mathmode := "Text", name := "A", next := 323105, root := ~, start := 323094, stop := 323104 ), rec( content := " and ", count := [ 7, 2, 20, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ ol2", count := [ 7, 2, 20, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 20 ], mathmode := "Text", name := "A", next := 323121, root := ~, start := 323110, stop := 323120 ), rec( content := ", or ", count := [ 7, 2, 20, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ ol", count := [ 7, 2, 20, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 20 ], mathmode := "Text", name := "A", next := 323136, root := ~, start := 323126, stop := 323135 ), rec( content := ", are gi\ ven, then they must\n represent vertex colourings; see \n ", count := [ 7, 2, 20, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for a \ digraph and a homogeneous list", Oper := "AutomorphismGroup" ), content := 0, count := [ 7, 2, 20, 20 ], mathmode := "Text", name := "Ref", next := 323282, root := ~, start := 323206, stop := 323281 ), rec( content := " \n f\ or details of the permissible values for\n these arguments. The homomorphis\ m must then also have the property:\n \n ", count := [ 7, 2, 20, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "\n ", count := [ 7, 2, 20, 22 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "col1[i] = col2[i ^ x]", count := [ 7, 2, 20, 22 ], m\ athmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 22 ], math\ mode := "Text", name := "C", next := 323465, root := ~, start := 323437, stop \ := 323464 ), rec( content := " for all vertices ", count := [ 7, 2, 20, 22 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "i", count := [ 7, 2, 20, 22 ], mathmode := "Text", n\ ame := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 22 ], mathmode := "Text", name\ := "C", next := 323491, root := ~, start := 323483, stop := 323490 ), rec( cont\ ent := " of ", count := [ 7, 2, 20, 22 ], mathmode := "Text", name := "PCDATA" , root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "src", count\ := [ 7, 2, 20, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 7, 2, 20, 22 ], mathmode := "Text", name := "A", next := 323505, root :\ = ~, start := 323495, stop := 323504 ), rec( content := ",\n for ", coun\ t := [ 7, 2, 20, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "IsDigraphIsomorphism", count \ := [ 7, 2, 20, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 7, 2, 20, 22 ], mathmode := "Text", name := "C", next := 323546, root :\ = ~, start := 323519, stop := 323545 ), rec( content := ". ", count := [ 7, 2,\ 20, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 22 ] , name := "Ite\ m", next := 323555, root := ~, start := 323422, stop := 323554 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n ", count := [ 7, 2, 20, 24 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "col[i] = col[i ^ x]", count := [ 7, 2, 20, 24 ], mat\ hmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 24 ], math\ mode := "Text", name := "C", next := 323603, root := ~, start := 323577, stop \ := 323602 ), rec( content := " for all vertices ", count := [ 7, 2, 20, 24 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "i", count := [ 7, 2, 20, 24 ], mathmode := "Text", n\ ame := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 24 ], mathmode := "Text", name\ := "C", next := 323629, root := ~, start := 323621, stop := 323628 ), rec( cont\ ent := " of ", count := [ 7, 2, 20, 24 ], mathmode := "Text", name := "PCDATA" , root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "digraph", c\ ount := [ 7, 2, 20, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 7, 2, 20, 24 ], mathmode := "Text", name := "A", next := 323647, root :\ = ~, start := 323633, stop := 323646 ), rec( content := ",\n for ", coun\ t := [ 7, 2, 20, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "IsDigraphAutomorphism", count\ := [ 7, 2, 20, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 7, 2, 20, 24 ], mathmode := "Text", name := "C", next := 323689, root :\ = ~, start := 323661, stop := 323688 ), rec( content := ". ", count := [ 7, 2,\ 20, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 24 ] , name := "Ite\ m", next := 323698, root := ~, start := 323562, stop := 323697 ) ], count := [ 7, 2, 20, 21 ], mathmode := "Text", name := "List", next := 323710, root := ~, start := 323409, stop := 323709 ), rec( content := "\n\n \ For some digraphs, it can be faster to use ", count := [ 7, 2, 20, 26 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sDigraphAutomorphism", count := [ 7, 2, 20, 26 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 20, 26 ], mathmode := "Text", name := "C", next := 323787, root := ~, start := 323759, stop := 323786 ), rec( content := "\n th\ an to test membership in the automorphism group of ", count := [ 7, 2, 20, 26 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 20, 26 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 26 ], mathmode := "Text", name := "A", next := 323859, root := ~, start := 323845, stop := 323858 ), rec( content := ".\n\n \ ", count := [ 7, 2, 20, 26 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> src := Digraph([[1], [1, 2], [1, 3]]);\n\ngap> IsDigraphAutomorphism(src, (1, 2, 3));\nfalse\ngap> IsDigra\ phAutomorphism(src, (2, 3));\ntrue\ngap> IsDigraphAutomorphism(src, (2, 3), [2\ , 1, 1]);\ntrue\ngap> IsDigraphAutomorphism(src, (2, 3), [2, 2, 1]);\nfalse\ng\ ap> IsDigraphAutomorphism(src, (2, 3)(4, 5));\nfalse\ngap> IsDigraphAutomorphi\ sm(src, (1, 4));\nfalse\ngap> IsDigraphAutomorphism(src, ());\ntrue\ngap> ran \ := Digraph([[2, 1], [2], [2, 3]]);\n\ngap> IsDigraphIsomorphism(src, ran, (1, 2));\ntrue\ngap> IsDigraphIsomorph\ ism(ran, src, (1, 2));\ntrue\ngap> IsDigraphIsomorphism(ran, src, (1, 2));\ntr\ ue\ngap> IsDigraphIsomorphism(src, Digraph([[3], [1, 3], [2]]), (1, 2, 3));\nf\ alse\ngap> IsDigraphIsomorphism(src, ran, (1, 2), [1, 2, 3], [2, 1, 3]);\ntrue\ \ngap> IsDigraphIsomorphism(src, ran, (1, 2), [1, 2, 2], [2, 1, 3]);\nfalse\n" , count := [ 7, 2, 20, 27 ] , name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 20, 27 ], mathmode := "Text", name := "Example", next := 324802, root := ~, start := 323866, stop := 324801 ), rec( content := "\n ", count := [ 7, 2, 20, 28 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "Description", next := 324819, root := ~, start := 322071, stop := 324818 ) ], count := [ 7, 2, 20, 1 ], mathmode := "Text", name := "ManSection", next := 324833, root := ~, start := 321634, stop := 324832 ), rec( content := "\n\n ", count := [ 7, 2, 20, 28 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, list", Name := "IsDigraphColour\ ing" ), content := 0, count := [ 7, 2, 21, 2 ], mathmode := "Text", name := "Oper", next := 324911, root := ~, start := 324858, stop := 324910 ), rec( attributes := rec( Arg := "digraph, t", Label := "for a transfor\ mation", Name := "IsDigraphColouring" ), content := 0, count := [ 7, 2, 21, 4 ], mathmode := "Text", name := "Oper", next := 325002, root := ~, start := 324916, stop := 325001 ), rec( attributes := rec( ), content := [ rec( content := " ", count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "K", next := 325028, root := ~, start := 325017, stop := 325027 ), rec( content := " or ", count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "K", next := 325044, root := ~, start := 325032, stop := 325043 ), rec( content := ". ", count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "Returns", next := 325056, root := ~, start := 325007, stop := 325055 ), rec( attributes := rec( ), content := [ rec( content := "\n T\ he operation ", count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sDigraphColouring", count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "C", next := 325120, root := ~, start := 325095, stop := 325119 ), rec( content := " verifie\ s whether or not \n the list ", count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "A", next := 325172, root := ~, start := 325161, stop := 325171 ), rec( content := " describ\ es a proper colouring of the digraph \n ", count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "A", next := 325238, root := ~, start := 325224, stop := 325237 ), rec( content := ". \n \ ", count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "P", next := 325251, root := ~, start := 325247, stop := 325250 ), rec( content := "\n\n \ A list ", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "A", next := 325277, root := ~, start := 325266, stop := 325276 ), rec( content := " describ\ es a ", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ roper colouring", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "E", next := 325313, root := ~, start := 325290, stop := 325312 ), rec( content := " of a di\ graph\n ", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "A", next := 325347, root := ~, start := 325333, stop := 325346 ), rec( content := " if ", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "A", next := 325362, root := ~, start := 325351, stop := 325361 ), rec( content := " consist\ s of positive integers, the length of\n ", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "A", next := 325425, root := ~, start := 325414, stop := 325424 ), rec( content := " equals \ the number of vertices in ", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "A", next := 325473, root := ~, start := 325459, stop := 325472 ), rec( content := ", and fo\ r any\n vertices ", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ , v", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "C", next := 325513, root := ~, start := 325502, stop := 325512 ), rec( content := " of ", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "A", next := 325531, root := ~, start := 325517, stop := 325530 ), rec( content := " if ", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "C", next := 325543, root := ~, start := 325535, stop := 325542 ), rec( content := " and ", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "C", next := 325556, root := ~, start := 325548, stop := 325555 ), rec( content := " are adj\ acent,\n then ", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "list", count := [ 7, 2, 21, 6 ], mathm\ ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 6 ], mathmode := \ "Text", name := "A", next := 325596, root := ~, start := 325585, stop := 32559\ 5 ), rec( content := "[u] >< ", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ist", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := \ ~ ) ], count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "A", next := 3256\ 20, root := ~, start := 325609, stop := 325619 ), rec( content := "[v]", count := [ 7, 2, 21, 6 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "C", next := 325627, root := ~, start := 325582, stop := 325626 ), rec( content := ".\n \ ", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "P", next := 325639, root := ~, start := 325635, stop := 325638 ), rec( content := "\n\n \ A transformation ", count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ ", count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "A", next := 325672, root := ~, start := 325664, stop := 325671 ), rec( content := " describ\ es a proper colouring of a digraph\n ", count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "A", next := 325735, root := ~, start := 325721, stop := 325734 ), rec( content := ", if ", count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ mageListOfTransformation(", count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ ", count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 7 ], mathmode := \ "Text", name := "A", next := 325777, root := ~, start := 325769, stop := 32577\ 6 ), rec( content := ",\n DigraphNrVertices(", count := [ 7, 2, 21, 7 ], mathmode := \ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( cont\ ent := "digraph", count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "A", next := 3258\ 17, root := ~, start := 325803, stop := 325816 ), rec( content := "))", count := [ 7, 2, 21, 7 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "C", next := 325823, root := ~, start := 325740, stop := 325822 ), rec( content := " is a pr\ oper colouring of \n ", count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "A", next := 325870, root := ~, start := 325856, stop := 325869 ), rec( content := ". ", count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 2, 21, 8 ], mathmode := "Text", name := "P", next := 325876, root := ~, start := 325872, stop := 325875 ), rec( content := "\n\n \ See also ", count := [ 7, 2, 21, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "IsDigra\ phHomomorphism" ), content := 0, count := [ 7, 2, 21, 8 ], mathmode := "Text", name := "Ref", next := 325928, root := ~, start := 325893, stop := 325927 ), rec( content := ".\n \ \n ", count := [ 7, 2, 21, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := JohnsonDigraph(5, 3);\n\ngap> IsDigraphColouring(D, [1, 2, 3, 3, 2, 1, 4, 5, 6, 7]);\ntru\ e\ngap> IsDigraphColouring(D, [1, 2, 3, 3, 2, 1, 2, 5, 6, 7]);\nfalse\ngap> Is\ DigraphColouring(D, [1, 2, 3, 3, 2, 1, 2, 5, 6, -1]);\nfalse\ngap> IsDigraphCo\ louring(D, [1, 2, 3]);\nfalse\ngap> IsDigraphColouring(D, IdentityTransformati\ on);\ntrue\n", count := [ 7, 2, 21, 9 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 9 ], mathmode := "Text", name := "Example", next := 326364, root := ~, start := 325943, stop := 326363 ), rec( content := "\n ", count := [ 7, 2, 21, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "Description", next := 326383, root := ~, start := 325061, stop := 326382 ) ], count := [ 7, 2, 21, 1 ], mathmode := "Text", name := "ManSection", next := 326399, root := ~, start := 324841, stop := 326398 ), rec( content := "\n\n ", count := [ 7, 2, 21, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 0, 1 ], mathmode := "Text", name := "Section", next := 326413, root := ~, start := 282491, stop := 326412 ) , rec( content := "\n\n ", count := [ 7, 2, 21, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Homomorphisms of \ digraphs", count := [ 7, 3, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 0, 2 ], mathmode := "Text", name := "Heading", next := 326470, root := ~, start := 326426, stop := 326469 ), rec( content := "\n\n The following me\ thods exist to find homomorphisms between digraphs.\n If an argument to one\ of these methods is a digraph with multiple edges,\n then the multiplicity\ of edges will be ignored in order to perform the\n calculation; the digrap\ h will be treated as if it has no multiple edges.\n\n ", count := [ 7, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "D1, D2, hook, us\ er_param, max_results, hint, injective, image, partial_map, colors1, colors2[,\ order, aut_grp]", Name := "HomomorphismDigraphsFinder" ), content := 0, count := [ 7, 3, 1, 2 ], mathmode := "Text", name := "Func", next := 326951, root := ~, start := 326793, stop := 326950 ), rec( attributes := rec( ), content := [ rec( content := "The argum\ ent ", count := [ 7, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ser_param", count := [ 7, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 3 ], mathmode := "Text", name := "A", next := 326993, root := ~, start := 326976, stop := 326992 ), rec( content := ".", count := [ 7, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 3 ], mathmode := "Text", name := "Returns", next := 327004, root := ~, start := 326954, stop := 327003 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function finds homomorphisms from the digraph ", count := [ 7, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 1", count := [ 7, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 3 ], mathmode := "Text", name := "A", next := 327085, root := ~, start := 327076, stop := 327084 ), rec( content := " to the \ digraph\n ", count := [ 7, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 2", count := [ 7, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 3 ], mathmode := "Text", name := "A", next := 327114, root := ~, start := 327105, stop := 327113 ), rec( content := " subject\ to the conditions imposed by the other arguments as\n described below.", count := [ 7, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "P", next := 327199, root := ~, start := 327195, stop := 327198 ), rec( content := "\n\n \ If ", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "C", next := 327216, root := ~, start := 327208, stop := 327215 ), rec( content := " and ", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ ", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "C", next := 327229, root := ~, start := 327221, stop := 327228 ), rec( content := " are hom\ omorphisms found by\n ", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "H\ omomorphismDigraphsFinder", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "C", next := 327294, root := ~, start := 327261, stop := 327293 ), rec( content := ", then " , count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "C", next := 327309, root := ~, start := 327301, stop := 327308 ), rec( content := " cannot \ be obtained from\n ", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ ", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "C", next := 327346, root := ~, start := 327338, stop := 327345 ), rec( content := " by righ\ t multiplying by an automorphism of ", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 2", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "A", next := 327399, root := ~, start := 327390, stop := 327398 ), rec( content := " in\n \ ", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "a\ ut_grp", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "A", next := 327421, root := ~, start := 327407, stop := 327420 ), rec( content := ".\n\n \ ", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( attributes := rec( ), content := [ rec( content :\ = "hook", count := [ 7, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root \ := ~ ) ], count := [ 7, 3, 1, 5 ], mathmode := "Text", name := "A", next := 32\ 7458, root := ~, start := 327447, stop := 327457 ) ], count := [ 7, 3, 1, 5 ], name := "Mar\ k", next := 327465, root := ~, start := 327441, stop := 327464 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n This argument should be a f\ unction or ", count := [ 7, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "fail", coun\ t := [ 7, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 7, 3, 1, 6 ], mathmode := "Text", name := "K", next := 327536, root := \ ~, start := 327525, stop := 327535 ), rec( content := ".", count := [ 7, 3, 1,\ 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\ c( ), content := 0, count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "P", next\ := 327541, root := ~, start := 327537, stop := 327540 ), rec( content := "\n\ \n If ", count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "hook", coun\ t := [ 7, 3, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 7, 3, 1, 7 ], mathmode := "Text", name := "A", next := 327565, root := \ ~, start := 327554, stop := 327564 ), rec( content := " is a function, then it\ must have two arguments\n ", count := [ 7, 3, 1, 7 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ re\ c( content := "user_param", count := [ 7, 3, 1, 7 ], mathmode := "Text", name \ := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 7 ], mathmode := "Text", name \ := "A", next := 327638, root := ~, start := 327621, stop := 327637 ), rec( cont\ ent := " (see below) and a transformation ", count := [ 7, 3, 1, 7 ], mathmode\ := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content\ := [ rec( content := "t", count := [ 7, 3, 1, 7 ], mathmode := "Text", name :\ = "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 7 ], mathmode := "Text", name :\ = "C", next := 327680, root := ~, start := 327672, stop := 327679 ), rec( cont\ ent := ". The\n function ", count := [ 7, 3, 1, 7 ], mathmode := "Text" , name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attri\ butes := rec( ), content := [ rec( content := "hook", count := [ 7, 3, 1, 7 ]\ , mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 7 ]\ , mathmode := "Text", name := "A", next := 327717, root := ~, start := 327706,\ stop := 327716 ), rec( content := "(", count := [ 7, 3, 1, 7 ], mathmode := "\ Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [\ rec( content := "user_param", count := [ 7, 3, 1, 7 ], mathmode := "Text", na\ me := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 7 ], mathmode := "Text", na\ me := "A", next := 327735, root := ~, start := 327718, stop := 327734 ), rec( \ content := ", t)", count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "C", next\ := 327743, root := ~, start := 327703, stop := 327742 ), rec( content := " is\ called every time\n a new homomorphism ", count := [ 7, 3, 1, 7 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "t", count := [ 7, 3, 1, 7 ], mathmode := "Text", nam\ e := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 7 ], mathmode := "Text", name\ := "C", next := 327800, root := ~, start := 327792, stop := 327799 ), rec( cont\ ent := " is found by\n ", count := [ 7, 3, 1, 7 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "HomomorphismDigraphsFinder", count := [ 7, 3, 1, 7 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 7 ], mathmode := "Text\ ", name := "C", next := 327854, root := ~, start := 327821, stop := 327853 ), rec( cont\ ent := ". If the function returns ", count := [ 7, 3, 1, 7 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ re\ c( content := "true", count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "PC\ DATA", root := ~ ) ], count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "K" , next\ := 327891, root := ~, start := 327880, stop := 327890 ), rec( content := ",\n\ then ", count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "Homomorphis\ mDigraphsFinder", count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "C", next\ := 327939, root := ~, start := 327906, stop := 327938 ), rec( content := " st\ ops and does not find any\n further homomorphisms. This feature might b\ e useful if you are\n searching for a homomorphism that satisfies some \ condition that you\n cannot specify via the other arguments to\n \ ", count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attr\ ibutes := rec( ), content := [ rec( content := "HomomorphismDigraphsFinder", \ count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 7, 3, 1, 7 ], mathmode := "Text", name := "C", next := 328206, root := \ ~, start := 328173, stop := 328205 ), rec( content := ".\n ", count := [ \ 7, 3, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribut\ es := rec( ), content := 0, count := [ 7, 3, 1, 8 ], mathmode := "Text", name\ := "P", next := 328220, root := ~, start := 328216, stop := 328219 ), rec( cont\ ent := "\n\n If ", count := [ 7, 3, 1, 8 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content \ := "hook", count := [ 7, 3, 1, 8 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 3, 1, 8 ], mathmode := "Text", name := "A", next := 3\ 28244, root := ~, start := 328233, stop := 328243 ), rec( content := " is ", coun\ t := [ 7, 3, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "fail", count := [ 7, 3, 1, 8 \ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 8 ] , math\ mode := "Text", name := "K", next := 328259, root := ~, start := 328248, stop \ := 328258 ), rec( content := ", then a default function is used which\n \ simply adds every new homomorphism found by\n ", count := [ 7, 3, 1, 8\ ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(\ ), content := [ rec( content := "HomomorphismDigraphsFinder", count := [ 7, \ 3, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, \ 3, 1, 8 ], mathmode := "Text", name := "C", next := 328392, root := ~, start :\ = 328359, stop := 328391 ), rec( content := " to ", count := [ 7, 3, 1, 8 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "user_param", count := [ 7, 3, 1, 8 ], mathmode := "T\ ext", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 8 ], mathmode := "T\ ext", name := "A", next := 328413, root := ~, start := 328396, stop := 328412 ), rec( cont\ ent := ", which must be a\n mutable list in this case.\n ", count \ := [ 7, 3, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 6 ], name := "Ite\ m", next := 328479, root := ~, start := 327472, stop := 328478 ), rec( attributes :\ = rec( ), content := [ rec( attributes := rec( ), content := [ rec( content \ := "user_param", count := [ 7, 3, 1, 9 ], mathmode := "Text", name := "PCDATA"\ , root := ~ ) ], count := [ 7, 3, 1, 9 ], mathmode := "Text", name := "A", next\ := 328510, root := ~, start := 328493, stop := 328509 ) ], count := [ 7, 3, 1, 9 ], name := "Mar\ k", next := 328517, root := ~, start := 328487, stop := 328516 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n If ", count := [ 7, 3, 1, 1\ 0 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec\ ( ), content := [ rec( content := "hook", count := [ 7, 3, 1, 10 ], mathmode \ := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 10 ], mathmode\ := "Text", name := "A", next := 328553, root := ~, start := 328542, stop := 3\ 28552 ), rec( content := " is a function, then ", count := [ 7, 3, 1, 10 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "user_param", count := [ 7, 3, 1, 10 ], mathmode := "\ Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 10 ], mathmode := \ "Text", name := "A", next := 328591, root := ~, start := 328574, stop := 32859\ 0 ), rec( content := " can be any ", count := [ 7, 3, 1, 10 ], mathmode := "Te\ xt", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ r\ ec( content := "GAP", count := [ 7, 3, 1, 10 ], mathmode := "Text", name := "P\ CDATA", root := ~ ) ], count := [ 7, 3, 1, 10 ], mathmode := "Text", name := "\ Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := "\n\ object. The object ", count := [ 7, 3, 1, 10 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "user_param", count := [ 7, 3, 1, 10 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 1, 10 ], mathmode := "Text", name := "A" , next\ := 328653, root := ~, start := 328636, stop := 328652 ), rec( content := " is\ used as the first argument of\n the function ", count := [ 7, 3, 1, 10\ ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(\ ), content := [ rec( content := "hook", count := [ 7, 3, 1, 10 ], mathmode :\ = "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 10 ], mathmode \ := "Text", name := "A", next := 328719, root := ~, start := 328708, stop := 32\ 8718 ), rec( content := ". For example, ", count := [ 7, 3, 1, 10 ], mathmode \ := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content \ := [ rec( content := "user_param", count := [ 7, 3, 1, 10 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 10 ], mathmode := "Tex\ t", name := "A", next := 328751, root := ~, start := 328734, stop := 328750 ), rec( cont\ ent := " might be a\n transformation semigroup, and ", count := [ 7, 3,\ 1, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( attributes := rec( ), content := [ rec( content \ := "hook", count := [ 7, 3, 1, 10 ], mathmode := "Text", name := "PCDATA", roo\ t := ~ ) ], count := [ 7, 3, 1, 10 ], mathmode := "Text", name := "A", next :=\ 328815, root := ~, start := 328804, stop := 328814 ), rec( content := "(", co\ unt := [ 7, 3, 1, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec\ ( attributes := rec( ), content := [ rec( content := "user_param", count := [\ 7, 3, 1, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := \ [ 7, 3, 1, 10 ], mathmode := "Text", name := "A", next := 328833, root := ~, s\ tart := 328816, stop := 328832 ), rec( content := ", t)", count := [ 7, 3, 1, \ 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1,\ 10 ], mathmode := "Text", name := "C", next := 328841, root := ~, start := 32\ 8801, stop := 328840 ), rec( content := "\n might set ", count := [ 7, \ 3, 1, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes\ := rec( ), content := [ rec( content := "user_param", count := [ 7, 3, 1, 10\ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 1\ 0 ], mathmode := "Text", name := "A", next := 328877, root := ~, start := 3288\ 60, stop := 328876 ), rec( content := " to be the closure of ", count := [ 7, \ 3, 1, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes\ := rec( ), content := [ rec( content := "user_param", count := [ 7, 3, 1, 10\ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 1\ 0 ], mathmode := "Text", name := "A", next := 328916, root := ~, start := 3288\ 99, stop := 328915 ), rec( content := " and\n ", count := [ 7, 3, 1, 10\ ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(\ ), content := [ rec( content := "t", count := [ 7, 3, 1, 10 ], mathmode := "\ Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 10 ], mathmode := \ "Text", name := "C", next := 328937, root := ~, start := 328929, stop := 32893\ 6 ), rec( content := ". ", count := [ 7, 3, 1, 10 ], mathmode := "Text", name \ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ \ 7, 3, 1, 11 ], mathmode := "Text", name := "P", next := 328943, root := ~, star\ t := 328939, stop := 328942 ), rec( content := "\n\n If the value of ", coun\ t := [ 7, 3, 1, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "hook", count := [ 7, 3, 1, 11\ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 1\ 1 ], mathmode := "Text", name := "A", next := 328980, root := ~, start := 3289\ 69, stop := 328979 ), rec( content := " is ", count := [ 7, 3, 1, 11 ], mathmo\ de := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), conte\ nt := [ rec( content := "fail", count := [ 7, 3, 1, 11 ], mathmode := "Text", \ name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 11 ], mathmode := "Text", name\ := "K", next := 328995, root := ~, start := 328984, stop := 328994 ), rec( cont\ ent := ", then the value of\n ", count := [ 7, 3, 1, 11 ], mathmode := \ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ \ rec( content := "user_param", count := [ 7, 3, 1, 11 ], mathmode := "Text", na\ me := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 11 ], mathmode := "Text", name\ := "A", next := 329040, root := ~, start := 329023, stop := 329039 ), rec( cont\ ent := " must be a mutable list.\n ", count := [ 7, 3, 1, 11 ], mathmode \ := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 10 ], name := "Ite\ m", next := 329078, root := ~, start := 328524, stop := 329077 ), rec( attributes :\ = rec( ), content := [ rec( attributes := rec( ), content := [ rec( content \ := "max_results", count := [ 7, 3, 1, 12 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 7, 3, 1, 12 ], mathmode := "Text", name := "A", next\ := 329110, root := ~, start := 329092, stop := 329109 ) ], count := [ 7, 3, 1, 12 ], name := "Mar\ k", next := 329117, root := ~, start := 329086, stop := 329116 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n This argument should be a p\ ositive integer or ", count := [ 7, 3, 1, 13 ], mathmode := "Text", name := "P\ CDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := \ "infinity", count := [ 7, 3, 1, 13 ], mathmode := "Text", name := "PCDATA", ro\ ot := ~ ) ], count := [ 7, 3, 1, 13 ], mathmode := "Text", name := "K", next :\ = 329200, root := ~, start := 329185, stop := 329199 ), rec( content := ".\n \ ", count := [ 7, 3, 1, 13 ], mathmode := "Text", name := "PCDATA", root \ := ~ ), rec( attributes := rec( ), content := [ rec( content := "Homomorphism\ DigraphsFinder", count := [ 7, 3, 1, 13 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 7, 3, 1, 13 ], mathmode := "Text", name := "C", next\ := 329243, root := ~, start := 329210, stop := 329242 ), rec( content := " wi\ ll return after it has found\n ", count := [ 7, 3, 1, 13 ], mathmode :=\ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content :=\ [ rec( content := "max_results", count := [ 7, 3, 1, 13 ], mathmode := "Text"\ , name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 13 ], mathmode := "Text\ ", name := "A", next := 329301, root := ~, start := 329283, stop := 329300 ), rec( cont\ ent := " homomorphisms or the search is complete, whichever\n happens f\ irst.\n ", count := [ 7, 3, 1, 13 ], mathmode := "Text", name := "PCDATA" , root\ := ~ ) ], count := [ 7, 3, 1, 13 ], name := "Item", next := 329389, root := ~, start := 329\ 124, stop := 329388 ), rec( attributes := rec( ), content := [ rec( attribute\ s := rec( ), content := [ rec( content := "hint", count := [ 7, 3, 1, 14 ], m\ athmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 14 ], math\ mode := "Text", name := "A", next := 329414, root := ~, start := 329403, stop \ := 329413 ) ], count := [ 7, 3, 1, 14 ], name := "Mark", next := 329421, root := ~, start := 329\ 397, stop := 329420 ), rec( attributes := rec( ), content := [ rec( content :\ = "\n This argument should be a positive integer or ", count := [ 7, 3,\ 1, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "fail", count := [ 7, 3, 1, 15 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 15 ], math\ mode := "Text", name := "K", next := 329500, root := ~, start := 329489, stop \ := 329499 ), rec( content := ". ", count := [ 7, 3, 1, 15 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, coun\ t := [ 7, 3, 1, 16 ], mathmode := "Text", name := "P", next := 329506, root :=\ ~, start := 329502, stop := 329505 ), rec( content := "\n\n If ", coun\ t := [ 7, 3, 1, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "hint", count := [ 7, 3, 1, 16\ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 1\ 6 ], mathmode := "Text", name := "A", next := 329530, root := ~, start := 3295\ 19, stop := 329529 ), rec( content := " is a positive integer, then only homor\ phisms of rank\n ", count := [ 7, 3, 1, 16 ], mathmode := "Text", name \ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conten\ t := "hint", count := [ 7, 3, 1, 16 ], mathmode := "Text", name := "PCDATA", r\ oot := ~ ) ], count := [ 7, 3, 1, 16 ], mathmode := "Text", name := "A", next \ := 329603, root := ~, start := 329592, stop := 329602 ), rec( content := " are\ found.", count := [ 7, 3, 1, 16 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 1, 17 ], math\ mode := "Text", name := "P", next := 329618, root := ~, start := 329614, stop \ := 329617 ), rec( content := "\n\n If ", count := [ 7, 3, 1, 17 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "hint", count := [ 7, 3, 1, 17 ], mathmode := "Text",\ name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 17 ], mathmode := "Text" , name\ := "A", next := 329642, root := ~, start := 329631, stop := 329641 ), rec( cont\ ent := " is ", count := [ 7, 3, 1, 17 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "fail", coun\ t := [ 7, 3, 1, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 7, 3, 1, 17 ], mathmode := "Text", name := "K", next := 329657, root :=\ ~, start := 329646, stop := 329656 ), rec( content := ", then no restriction \ is put on the rank\n of homomorphisms found.\n ", count := [ 7, 3,\ 1, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 15 ], name := "Ite\ m", next := 329743, root := ~, start := 329428, stop := 329742 ), rec( attributes :\ = rec( ), content := [ rec( attributes := rec( ), content := [ rec( content \ := "injective", count := [ 7, 3, 1, 18 ], mathmode := "Text", name := "PCDATA"\ , root := ~ ) ], count := [ 7, 3, 1, 18 ], mathmode := "Text", name := "A", next\ := 329773, root := ~, start := 329757, stop := 329772 ) ], count := [ 7, 3, 1, 18 ], name := "Mar\ k", next := 329780, root := ~, start := 329751, stop := 329779 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n This argument should be ", coun\ t := [ 7, 3, 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "0", count := [ 7, 3, 1, 19 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 19 ] , math\ mode := "Text", name := "C", next := 329834, root := ~, start := 329826, stop \ := 329833 ), rec( content := ", ", count := [ 7, 3, 1, 19 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec\ ( content := "1", count := [ 7, 3, 1, 19 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 7, 3, 1, 19 ], mathmode := "Text", name := "C", next\ := 329844, root := ~, start := 329836, stop := 329843 ), rec( content := ", o\ r ", count := [ 7, 3, 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~\ ), rec( attributes := rec( ), content := [ rec( content := "2", count := [ 7\ , 3, 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ \ 7, 3, 1, 19 ], mathmode := "Text", name := "C", next := 329857, root := ~, star\ t := 329849, stop := 329856 ), rec( content := ". If it is\n ", count \ := [ 7, 3, 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "2", count := [ 7, 3, 1, 19 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 19 ] , math\ mode := "Text", name := "C", next := 329885, root := ~, start := 329877, stop \ := 329884 ), rec( content := ", then only embeddings are found, if it is ", coun\ t := [ 7, 3, 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "1", count := [ 7, 3, 1, 19 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 19 ] , math\ mode := "Text", name := "C", next := 329936, root := ~, start := 329928, stop \ := 329935 ), rec( content := ", then only\n injective homomorphisms are\ found, and if it is ", count := [ 7, 3, 1, 19 ], mathmode := "Text", name := \ "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content :\ = "0", count := [ 7, 3, 1, 19 ], mathmode := "Text", name := "PCDATA", root :=\ ~ ) ], count := [ 7, 3, 1, 19 ], mathmode := "Text", name := "C", next := 330\ 012, root := ~, start := 330004, stop := 330011 ), rec( content := " there are\ no\n restrictions imposed by this argument.\n ", count := [ 7, \ 3, 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes\ := rec( ), content := 0, count := [ 7, 3, 1, 20 ], mathmode := "Text", name \ := "P", next := 330085, root := ~, start := 330081, stop := 330084 ), rec( cont\ ent := "\n\n For backwards compatibility, ", count := [ 7, 3, 1, 20 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "injective", count := [ 7, 3, 1, 20 ], mathmode := "T\ ext", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 20 ], mathmode := "\ Text", name := "A", next := 330140, root := ~, start := 330124, stop := 330139\ ), rec( content := " can also be ", count := [ 7, 3, 1, 20 ], mathmode := "Te\ xt", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ r\ ec( content := "false", count := [ 7, 3, 1, 20 ], mathmode := "Text", name := \ "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 20 ], mathmode := "Text", name :=\ "K", next := 330165, root := ~, start := 330153, stop := 330164 ), rec( conte\ nt := "\n or ", count := [ 7, 3, 1, 20 ], mathmode := "Text", name := "\ PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content :=\ "true", count := [ 7, 3, 1, 20 ], mathmode := "Text", name := "PCDATA", root \ := ~ ) ], count := [ 7, 3, 1, 20 ], mathmode := "Text", name := "K", next := 3\ 30188, root := ~, start := 330177, stop := 330187 ), rec( content := " which c\ orrespond to the values ", count := [ 7, 3, 1, 20 ], mathmode := "Text", name \ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conten\ t := "0", count := [ 7, 3, 1, 20 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 3, 1, 20 ], mathmode := "Text", name := "C", next := \ 330228, root := ~, start := 330220, stop := 330227 ), rec( content := " and ", coun\ t := [ 7, 3, 1, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "1", count := [ 7, 3, 1, 20 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 20 ] , math\ mode := "Text", name := "C", next := 330241, root := ~, start := 330233, stop \ := 330240 ), rec( content := "\n described in the previous paragraph, r\ espectively. \n ", count := [ 7, 3, 1, 20 ], mathmode := "Text", name := \ "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 19 ], name := "Item", next := 3303\ 15, root := ~, start := 329787, stop := 330314 ), rec( attributes := rec( ), content := [ rec( attr\ ibutes := rec( ), content := [ rec( content := "image", count := [ 7, 3, 1, 2\ 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, \ 21 ], mathmode := "Text", name := "A", next := 330341, root := ~, start := 330\ 329, stop := 330340 ) ], count := [ 7, 3, 1, 21 ], name := "Mark", next := 3303\ 48, root := ~, start := 330323, stop := 330347 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "\n This argument should be a subset of the vertices of the grap\ h ", count := [ 7, 3, 1, 22 ], mathmode := "Text", name := "PCDATA", root := ~\ ), rec( attributes := rec( ), content := [ rec( content := "D2", count := [ \ 7, 3, 1, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ \ 7, 3, 1, 22 ], mathmode := "Text", name := "A", next := 330441, root := ~, star\ t := 330432, stop := 330440 ), rec( content := ".\n ", count := [ 7, 3,\ 1, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "HomomorphismDigraphsFinder", count :=\ [ 7, 3, 1, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :\ = [ 7, 3, 1, 22 ], mathmode := "Text", name := "C", next := 330484, root := ~, star\ t := 330451, stop := 330483 ), rec( content := " only finds homomorphisms from\ \n ", count := [ 7, 3, 1, 22 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "D1", count \ := [ 7, 3, 1, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count\ := [ 7, 3, 1, 22 ], mathmode := "Text", name := "A", next := 330532, root := \ ~, start := 330523, stop := 330531 ), rec( content := " to the subgraph of ", coun\ t := [ 7, 3, 1, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "D2", count := [ 7, 3, 1, 22 ]\ , mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 22 ] , math\ mode := "Text", name := "A", next := 330561, root := ~, start := 330552, stop \ := 330560 ), rec( content := " induced by the vertices\n ", count := [ \ 7, 3, 1, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\ tes := rec( ), content := [ rec( content := "image", count := [ 7, 3, 1, 22 ]\ , mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 22 ] , math\ mode := "Text", name := "A", next := 330606, root := ~, start := 330594, stop \ := 330605 ), rec( content := ".\n ", count := [ 7, 3, 1, 22 ], mathmode :\ = "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 22 ], name := "Ite\ m", next := 330621, root := ~, start := 330355, stop := 330620 ), rec( attributes :\ = rec( ), content := [ rec( attributes := rec( ), content := [ rec( content \ := "partial_map", count := [ 7, 3, 1, 23 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 7, 3, 1, 23 ], mathmode := "Text", name := "A", next\ := 330653, root := ~, start := 330635, stop := 330652 ) ], count := [ 7, 3, 1, 23 ], name := "Mar\ k", next := 330660, root := ~, start := 330629, stop := 330659 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n This argument should be a p\ artial map from ", count := [ 7, 3, 1, 24 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D1\ ", count := [ 7, 3, 1, 24 ], mathmode := "Text", name := "PCDATA", root := ~ )\ ], count := [ 7, 3, 1, 24 ], mathmode := "Text", name := "A", next := 330734, root\ := ~, start := 330725, stop := 330733 ), rec( content := " to ", count := [ 7\ , 3, 1, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribut\ es := rec( ), content := [ rec( content := "D2", count := [ 7, 3, 1, 24 ], ma\ thmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 24 ], math\ mode := "Text", name := "A", next := 330747, root := ~, start := 330738, stop \ := 330746 ), rec( content := ",\n that is, a (not necessarily dense) li\ st of vertices of the digraph\n ", count := [ 7, 3, 1, 24 ], mathmode :\ = "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content :\ = [ rec( content := "D2", count := [ 7, 3, 1, 24 ], mathmode := "Text", name :\ = "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 24 ], mathmode := "Text", name \ := "A", next := 330841, root := ~, start := 330832, stop := 330840 ), rec( cont\ ent := " of length no greater than the number vertices in the digraph\n \ ", count := [ 7, 3, 1, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "D1", count := [ 7, 3, 1, 24 ]\ , mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 24 ] , math\ mode := "Text", name := "A", next := 330920, root := ~, start := 330911, stop \ := 330919 ), rec( content := ". ", count := [ 7, 3, 1, 24 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec\ ( content := "HomomorphismDigraphsFinder", count := [ 7, 3, 1, 24 ], mathmode \ := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 24 ], mathmode\ := "Text", name := "C", next := 330955, root := ~, start := 330922, stop := 3\ 30954 ), rec( content := " only finds homomorphisms\n extending ", coun\ t := [ 7, 3, 1, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "partial_map", count := [ 7, 3\ , 1, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, \ 3, 1, 24 ], mathmode := "Text", name := "A", next := 331017, root := ~, start \ := 330999, stop := 331016 ), rec( content := " (if any).\n ", count := [ \ 7, 3, 1, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 24 ], name := "Ite\ m", next := 331041, root := ~, start := 330667, stop := 331040 ), rec( attributes :\ = rec( ), content := [ rec( attributes := rec( ), content := [ rec( content \ := "colors1", count := [ 7, 3, 1, 25 ], mathmode := "Text", name := "PCDATA", \ root := ~ ) ], count := [ 7, 3, 1, 25 ], mathmode := "Text", name := "A", next\ := 331075, root := ~, start := 331061, stop := 331074 ) ], count := [ 7, 3, 1, 25 ], name := "Mar\ k", next := 331082, root := ~, start := 331055, stop := 331081 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n This should be a list repre\ senting possible colours of vertices in the\n digraph ", count := [ 7, \ 3, 1, 26 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes\ := rec( ), content := [ rec( content := "D1", count := [ 7, 3, 1, 26 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 26 ], math\ mode := "Text", name := "A", next := 331200, root := ~, start := 331191, stop \ := 331199 ), rec( content := "; see \n ", count := [ 7, 3, 1, 26 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label :\ = "for a digraph and a homogeneous list", Oper := "AutomorphismGroup" ), conte\ nt := 0, count := [ 7, 3, 1, 26 ], mathmode := "Text", name := "Ref", next := \ 331302, root := ~, start := 331215, stop := 331301 ), rec( content := " \n \ for details of the permissible values for this argument.\n ", count :\ = [ 7, 3, 1, 26 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 26 ], name := "Ite\ m", next := 331382, root := ~, start := 331089, stop := 331381 ), rec( attributes :\ = rec( ), content := [ rec( attributes := rec( ), content := [ rec( content \ := "colors2", count := [ 7, 3, 1, 27 ], mathmode := "Text", name := "PCDATA", \ root := ~ ) ], count := [ 7, 3, 1, 27 ], mathmode := "Text", name := "A", next\ := 331416, root := ~, start := 331402, stop := 331415 ) ], count := [ 7, 3, 1, 27 ], name := "Mar\ k", next := 331423, root := ~, start := 331396, stop := 331422 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n This should be a list repre\ senting possible colours of vertices in the\n digraph ", count := [ 7, \ 3, 1, 28 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes\ := rec( ), content := [ rec( content := "D2", count := [ 7, 3, 1, 28 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 28 ], math\ mode := "Text", name := "A", next := 331541, root := ~, start := 331532, stop \ := 331540 ), rec( content := "; see \n ", count := [ 7, 3, 1, 28 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label :\ = "for a digraph and a homogeneous list", Oper := "AutomorphismGroup" ), conte\ nt := 0, count := [ 7, 3, 1, 28 ], mathmode := "Text", name := "Ref", next := \ 331643, root := ~, start := 331556, stop := 331642 ), rec( content := " \n \ for details of the permissible values for this argument.\n ", count :\ = [ 7, 3, 1, 28 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 28 ], name := "Ite\ m", next := 331723, root := ~, start := 331430, stop := 331722 ), rec( attributes :\ = rec( ), content := [ rec( attributes := rec( ), content := [ rec( content \ := "order", count := [ 7, 3, 1, 29 ], mathmode := "Text", name := "PCDATA", ro\ ot := ~ ) ], count := [ 7, 3, 1, 29 ], mathmode := "Text", name := "A", next :\ = 331748, root := ~, start := 331736, stop := 331747 ) ], count := [ 7, 3, 1, 29 ], name := "Mar\ k", next := 331755, root := ~, start := 331730, stop := 331754 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n The optional argument ", coun\ t := [ 7, 3, 1, 30 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "order", count := [ 7, 3, 1, 3\ 0 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, \ 30 ], mathmode := "Text", name := "A", next := 331811, root := ~, start := 331\ 799, stop := 331810 ), rec( content := " specifies the order the\n vert\ ices in ", count := [ 7, 3, 1, 30 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "D1", count \ := [ 7, 3, 1, 30 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count\ := [ 7, 3, 1, 30 ], mathmode := "Text", name := "A", next := 331865, root := \ ~, start := 331856, stop := 331864 ), rec( content := " appear in the search f\ or homomorphisms. \n The value of this parameter can have a large impac\ t\n on the runtime of the function. It seems in many cases to be a good\ \n idea for this to be the ", count := [ 7, 3, 1, 30 ], mathmode := "Te\ xt", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "DigraphWe\ lshPowellOrder" ), content := 0, count := [ 7, 3, 1, 30 ], mathmode := "Text", name\ := "Ref", next := 332112, root := ~, start := 332075, stop := 332111 ), rec( cont\ ent := ", i.e.\n vertices ordered from highest to lowest degree.\n \ ", count := [ 7, 3, 1, 30 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 30 ], name := "Ite\ m", next := 332188, root := ~, start := 331762, stop := 332187 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n The optional argument ", coun\ t := [ 7, 3, 1, 32 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "aut_grp", count := [ 7, 3, 1,\ 32 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1\ , 32 ], mathmode := "Text", name := "A", next := 332246, root := ~, start := 3\ 32232, stop := 332245 ), rec( content := " should be a subgroup of the\n \ automorphism group of ", count := [ 7, 3, 1, 32 ], mathmode := "Text", name \ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conten\ t := "D2", count := [ 7, 3, 1, 32 ], mathmode := "Text", name := "PCDATA", roo\ t := ~ ) ], count := [ 7, 3, 1, 32 ], mathmode := "Text", name := "A", next :=\ 332314, root := ~, start := 332305, stop := 332313 ), rec( content := ". This\ function returns unique\n representatives of the homomorphisms found u\ p to right multiplication\n by ", count := [ 7, 3, 1, 32 ], mathmode :=\ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content :=\ [ rec( content := "aut_grp", count := [ 7, 3, 1, 32 ], mathmode := "Text", na\ me := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 32 ], mathmode := "Text", name\ := "A", next := 332448, root := ~, start := 332434, stop := 332447 ), rec( cont\ ent := ". If this argument is not specific, it defaults to the\n full a\ utomorphism group of ", count := [ 7, 3, 1, 32 ], mathmode := "Text", name := \ "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content :\ = "D2", count := [ 7, 3, 1, 32 ], mathmode := "Text", name := "PCDATA", root :\ = ~ ) ], count := [ 7, 3, 1, 32 ], mathmode := "Text", name := "A", next := 33\ 2547, root := ~, start := 332538, stop := 332546 ), rec( content := ", which m\ ay be costly to calculate.\n ", count := [ 7, 3, 1, 32 ], mathmode := "Te\ xt", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 32 ], name := "Item" , next := 3325\ 96, root := ~, start := 332195, stop := 332595 ) ], count := [ 7, 3, 1, 5 ], mathmode := "Text", name := "List", next := 332608, root := ~, start := 327428, stop := 332607 ), rec( content := "\n\n \ ", count := [ 7, 3, 1, 34 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := ChainDigraph(10);\n\ngap>\ D := DigraphSymmetricClosure(D);\n\ngap> HomomorphismDigraphsFinder(D, D, fail, [], infinity, 2, 0,\ \n> [3, 4], [], fail, fail);\n[ Transformation( [ 3, 4, 3, 4, 3, 4, 3, 4, 3, 4\ ] ), \n Transformation( [ 4, 3, 4, 3, 4, 3, 4, 3, 4, 3 ] ) ]\ngap> D2 := Com\ pleteDigraph(6);;\ngap> HomomorphismDigraphsFinder(D, D2, fail, [], 1, fail, 0\ ,\n> [1 .. 6], [1, 2, 1], fail, fail);\n[ Transformation( [ 1, 2, 1, 3, 4, 5, \ 6, 1, 2, 1 ] ) ]\ngap> func := function(user_param, t)\n> Add(user_param, t * \ user_param[1]);\n> end;;\ngap> HomomorphismDigraphsFinder(D, D2, func, [Transf\ ormation([2, 2])],\n> 3, fail, 0, [1 .. 6], [1, 2, 1], fail, fail);\n[ Transfo\ rmation( [ 2, 2 ] ), \n Transformation( [ 2, 2, 2, 3, 4, 5, 6, 2, 2, 2 ] ), \ \n Transformation( [ 2, 2, 2, 3, 4, 5, 6, 2, 2, 3 ] ), \n Transformation( [ \ 2, 2, 2, 3, 4, 5, 6, 2, 2, 4 ] ) ]\ngap> HomomorphismDigraphsFinder(NullDigrap\ h(2), NullDigraph(3), fail,\n> [], infinity, fail, 1, [1, 2, 3], fail, fail, f\ ail, fail,\n> Group(()));\n[ IdentityTransformation, Transformation( [ 1, 3, 3\ ] ), \n Transformation( [ 2, 1 ] ), Transformation( [ 2, 3, 3 ] ), \n Trans\ formation( [ 3, 1, 3 ] ), Transformation( [ 3, 2, 3 ] ) ]\ngap> HomomorphismDi\ graphsFinder(NullDigraph(2), NullDigraph(3), fail,\n> [], infinity, fail, 1, [\ 1, 2, 3], fail, fail, fail, fail,\n> Group((1, 2)));\n[ IdentityTransformation\ , Transformation( [ 1, 3, 3 ] ), \n Transformation( [ 3, 1, 3 ] ) ]", count := [ 7, 3, 1, 35 ], name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 1, 35 ], mathmode := "Text", name := "Example", next := 334163, root := ~, start := 332614, stop := 334162 ), rec( content := "\n ", count := [ 7, 3, 1, 36 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 3 ], mathmode := "Text", name := "Description", next := 334180, root := ~, start := 327007, stop := 334179 ) ], count := [ 7, 3, 1, 1 ], mathmode := "Text", name := "ManSection", next := 334194, root := ~, start := 326778, stop := 334193 ), rec( content := "\n\n ", count := [ 7, 3, 1, 36 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph1, digrap\ h2", Name := "DigraphHomomorphism" ), content := 0, count := [ 7, 3, 2, 2 ], mathmode := "Text", name := "Oper", next := 334274, root := ~, start := 334215, stop := 334273 ), rec( attributes := rec( ), content := [ rec( content := " A transf\ ormation, or ", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "K", next := 334319, root := ~, start := 334308, stop := 334318 ), rec( content := ".", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "Returns", next := 334330, root := ~, start := 334277, stop := 334329 ), rec( attributes := rec( ), content := [ rec( content := "\n A h\ omomorphism from ", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "A", next := 334386, root := ~, start := 334371, stop := 334385 ), rec( content := " to ", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "A", next := 334405, root := ~, start := 334390, stop := 334404 ), rec( content := " is a ma\ pping from\n the vertex set of ", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "A", next := 334461, root := ~, start := 334446, stop := 334460 ), rec( content := " to a su\ bset of the vertices of\n ", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "A", next := 334512, root := ~, start := 334497, stop := 334511 ), rec( content := ", such t\ hat every pair of vertices ", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ i,j]", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "C", next := 334559, root := ~, start := 334547, stop := 334558 ), rec( content := " which h\ as\n an edge ", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ->j", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "C", next := 334593, root := ~, start := 334582, stop := 334592 ), rec( content := " is mapp\ ed to a pair of vertices ", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ a,b]", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "C", next := 334638, root := ~, start := 334626, stop := 334637 ), rec( content := " which\n\ has an edge ", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "a\ ->b", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "C", next := 334672, root := ~, start := 334661, stop := 334671 ), rec( content := ". Note \ that non-adjacent vertices can still be\n mapped to adjacent vertices. ", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 2, 4 ], mathmode := "Text", name := "P", next := 334757, root := ~, start := 334753, stop := 334756 ), rec( content := "\n\n \ ", count := [ 7, 3, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphHomomorphism", count := [ 7, 3, 2, 4 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 2, 4 ], mathmode := "Text", name := "C", next := 334789, root := ~, start := 334763, stop := 334788 ), rec( content := " returns\ a single homomorphism between\n ", count := [ 7, 3, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 3, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 2, 4 ], mathmode := "Text", name := "A", next := 334847, root := ~, start := 334832, stop := 334846 ), rec( content := " and ", count := [ 7, 3, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 3, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 2, 4 ], mathmode := "Text", name := "A", next := 334867, root := ~, start := 334852, stop := 334866 ), rec( content := " if it e\ xists, otherwise it returns\n ", count := [ 7, 3, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 7, 3, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 2, 4 ], mathmode := "Text", name := "K", next := 334918, root := ~, start := 334907, stop := 334917 ), rec( content := ".\n", count := [ 7, 3, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr1 := ChainDigraph(3);;\ngap> gr2 := Digraph([[3, 5], [2], [3, 1], [], \ [4]]);\n\ngap> DigraphHomomorphism\ (gr1, gr1);\nIdentityTransformation\ngap> map := DigraphHomomorphism(gr1, gr2)\ ;\nTransformation( [ 3, 1, 5, 4, 5 ] )\ngap> IsDigraphHomomorphism(gr1, gr2, m\ ap);\ntrue\n", count := [ 7, 3, 2, 5 ], name := "PCDATA", root := ~ ) ], count := [ 7, 3, 2, 5 ], mathmode := "Text", name := "Example", next := 335266, root := ~, start := 334920, stop := 335265 ), rec( content := "\n ", count := [ 7, 3, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "Description", next := 335283, root := ~, start := 334333, stop := 335282 ) ], count := [ 7, 3, 2, 1 ], mathmode := "Text", name := "ManSection", next := 335297, root := ~, start := 334200, stop := 335296 ), rec( content := "\n\n ", count := [ 7, 3, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph1, digrap\ h2", Name := "HomomorphismsDigraphs" ), content := 0, count := [ 7, 3, 3, 2 ], mathmode := "Text", name := "Oper", next := 335379, root := ~, start := 335318, stop := 335378 ), rec( attributes := rec( Arg := "digraph1, digrap\ h2", Name := "HomomorphismsDigraphsRepresentatives" ), content := 0, count := [ 7, 3, 3, 4 ], mathmode := "Text", name := "Oper", next := 335458, root := ~, start := 335382, stop := 335457 ), rec( attributes := rec( ), content := [ rec( content := " A list o\ f transformations.", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "Returns", next := 335507, root := ~, start := 335461, stop := 335506 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "H\ omomorphismsDigraphsRepresentatives", count := [ 7, 3, 3, 5 ], mathmode := "Te\ xt", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "C", next := 335571, root := ~, start := 335528, stop := 335570 ), rec( content := " finds e\ very\n ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ Homomorphism" ), content := 0, count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "Ref", next := 335621, root := ~, start := 335588, stop := 335620 ), rec( content := " between\ ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "A", next := 335645, root := ~, start := 335630, stop := 335644 ), rec( content := " and\n \ ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "A", next := 335669, root := ~, start := 335654, stop := 335668 ), rec( content := ", up to \ right multiplication by an element of the\n ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Automor\ phismGroup", Label := "for a digraph" ), content := 0, count := [ 7, 3, 3, 5 ] , mathmode := "Text", name := "Ref", next := 335776, root := ~, start := 335723, stop := 335775 ), rec( content := " of ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "A", next := 335795, root := ~, start := 335780, stop := 335794 ), rec( content := ".\n I\ n other words, every homomorphism ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "C", next := 335844, root := ~, start := 335836, stop := 335843 ), rec( content := " between\ ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "A", next := 335868, root := ~, start := 335853, stop := 335867 ), rec( content := " and\n \ ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "A", next := 335892, root := ~, start := 335877, stop := 335891 ), rec( content := " can be \ written as the composition ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ = g * x", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "C", next := 335943, root := ~, start := 335927, stop := 335942 ), rec( content := ",\n w\ here ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "g\ ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "C", next := 335963, root := ~, start := 335955, stop := 335962 ), rec( content := " is one \ of the ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "H\ omomorphismsDigraphsRepresentatives", count := [ 7, 3, 3, 5 ], mathmode := "Te\ xt", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "C", next := 336021, root := ~, start := 335978, stop := 336020 ), rec( content := "\n an\ d ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "C", next := 336038, root := ~, start := 336030, stop := 336037 ), rec( content := " is an a\ utomorphism of ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "A", next := 336076, root := ~, start := 336061, stop := 336075 ), rec( content := ".\n " , count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 3, 6 ], mathmode := "Text", name := "P", next := 336086, root := ~, start := 336082, stop := 336085 ), rec( content := "\n\n \ ", count := [ 7, 3, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "H\ omomorphismsDigraphs", count := [ 7, 3, 3, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 3, 6 ], mathmode := "Text", name := "C", next := 336120, root := ~, start := 336092, stop := 336119 ), rec( content := " returns\ all homomorphisms between\n ", count := [ 7, 3, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 3, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 3, 6 ], mathmode := "Text", name := "A", next := 336174, root := ~, start := 336159, stop := 336173 ), rec( content := " and ", count := [ 7, 3, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 3, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 3, 6 ], mathmode := "Text", name := "A", next := 336194, root := ~, start := 336179, stop := 336193 ), rec( content := ".\n " , count := [ 7, 3, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr1 := ChainDigraph(3);;\ngap> gr2 := Digraph([[3, 5], [2], [3, 1], [], \ [4]]);\n\ngap> HomomorphismsDigrap\ hs(gr1, gr2);\n[ Transformation( [ 1, 3, 1 ] ), Transformation( [ 1, 3, 3 ] ),\ \n Transformation( [ 1, 5, 4, 4, 5 ] ), Transformation( [ 2, 2, 2 ] ), \n T\ ransformation( [ 3, 1, 3 ] ), Transformation( [ 3, 1, 5, 4, 5 ] ), \n Transfo\ rmation( [ 3, 3, 1 ] ), Transformation( [ 3, 3, 3 ] ) ]\ngap> HomomorphismsDig\ raphsRepresentatives(gr1, CompleteDigraph(3));\n[ Transformation( [ 2, 1 ] ), \ Transformation( [ 2, 1, 2 ] ) ]\n", count := [ 7, 3, 3, 7 ], name := "PCDATA", root := ~ ) ], count := [ 7, 3, 3, 7 ], mathmode := "Text", name := "Example", next := 336800, root := ~, start := 336200, stop := 336799 ), rec( content := "\n ", count := [ 7, 3, 3, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "Description", next := 336817, root := ~, start := 335510, stop := 336816 ) ], count := [ 7, 3, 3, 1 ], mathmode := "Text", name := "ManSection", next := 336831, root := ~, start := 335303, stop := 336830 ), rec( content := "\n\n ", count := [ 7, 3, 3, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph1, digrap\ h2", Name := "DigraphMonomorphism" ), content := 0, count := [ 7, 3, 4, 2 ], mathmode := "Text", name := "Oper", next := 336911, root := ~, start := 336852, stop := 336910 ), rec( attributes := rec( ), content := [ rec( content := "A transfo\ rmation, or ", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "K", next := 336955, root := ~, start := 336944, stop := 336954 ), rec( content := ".", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "Returns", next := 336966, root := ~, start := 336914, stop := 336965 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphMonomorphism", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "C", next := 337013, root := ~, start := 336987, stop := 337012 ), rec( content := " returns\ a single ", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ njective", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "E", next := 337047, root := ~, start := 337031, stop := 337046 ), rec( content := " ", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ Homomorphism" ), content := 0, count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "Ref", next := 337087, root := ~, start := 337048, stop := 337086 ), rec( content := " between\ ", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "A", next := 337111, root := ~, start := 337096, stop := 337110 ), rec( content := " and ", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "A", next := 337131, root := ~, start := 337116, stop := 337130 ), rec( content := "\n if\ one exists, otherwise it returns ", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "K", next := 337183, root := ~, start := 337172, stop := 337182 ), rec( content := ".\n " , count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr1 := ChainDigraph(3);;\ngap> gr2 := Digraph([[3, 5], [2], [3, 1], [], \ [4]]);\n\ngap> DigraphMonomorphism\ (gr1, gr1);\nIdentityTransformation\ngap> DigraphMonomorphism(gr1, gr2);\nTran\ sformation( [ 3, 1, 5, 4, 5 ] )\n", count := [ 7, 3, 4, 4 ], name := "PCDATA", root := ~ ) ], count := [ 7, 3, 4, 4 ], mathmode := "Text", name := "Example", next := 337480, root := ~, start := 337189, stop := 337479 ), rec( content := "\n ", count := [ 7, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "Description", next := 337497, root := ~, start := 336969, stop := 337496 ) ], count := [ 7, 3, 4, 1 ], mathmode := "Text", name := "ManSection", next := 337511, root := ~, start := 336837, stop := 337510 ), rec( content := "\n\n ", count := [ 7, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph1, digrap\ h2", Name := "MonomorphismsDigraphs" ), content := 0, count := [ 7, 3, 5, 2 ], mathmode := "Text", name := "Oper", next := 337593, root := ~, start := 337532, stop := 337592 ), rec( attributes := rec( Arg := "digraph1, digrap\ h2", Name := "MonomorphismsDigraphsRepresentatives" ), content := 0, count := [ 7, 3, 5, 4 ], mathmode := "Text", name := "Oper", next := 337672, root := ~, start := 337596, stop := 337671 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ transformations.", count := [ 7, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 5, 5 ], mathmode := "Text", name := "Returns", next := 337720, root := ~, start := 337675, stop := 337719 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ se operations behave the same as ", count := [ 7, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Homomor\ phismsDigraphs" ), content := 0, count := [ 7, 3, 5, 5 ], mathmode := "Text", name := "Ref", next := 337812, root := ~, start := 337777, stop := 337811 ), rec( content := " and\n \ ", count := [ 7, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Homomor\ phismsDigraphsRepresentatives" ), content := 0, count := [ 7, 3, 5, 5 ], mathmode := "Text", name := "Ref", next := 337871, root := ~, start := 337821, stop := 337870 ), rec( content := ", except\ they only return\n ", count := [ 7, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ njective", count := [ 7, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 5, 5 ], mathmode := "Text", name := "E", next := 337917, root := ~, start := 337901, stop := 337916 ), rec( content := " homomor\ phisms.\n ", count := [ 7, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr1 := ChainDigraph(3);;\ngap> gr2 := Digraph([[3, 5], [2], [3, 1], [], \ [4]]);\n\ngap> MonomorphismsDigrap\ hs(gr1, gr2);\n[ Transformation( [ 1, 5, 4, 4, 5 ] ), \n Transformation( [ 3,\ 1, 5, 4, 5 ] ) ]\ngap> MonomorphismsDigraphsRepresentatives(gr1, CompleteDigr\ aph(3));\n[ Transformation( [ 2, 1 ] ) ]\n", count := [ 7, 3, 5, 6 ], name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 5, 6 ], mathmode := "Text", name := "Example", next := 338314, root := ~, start := 337937, stop := 338313 ), rec( content := "\n ", count := [ 7, 3, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 5, 5 ], mathmode := "Text", name := "Description", next := 338331, root := ~, start := 337723, stop := 338330 ) ], count := [ 7, 3, 5, 1 ], mathmode := "Text", name := "ManSection", next := 338345, root := ~, start := 337517, stop := 338344 ), rec( content := "\n\n ", count := [ 7, 3, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph1, digrap\ h2", Name := "DigraphEpimorphism" ), content := 0, count := [ 7, 3, 6, 2 ], mathmode := "Text", name := "Oper", next := 338424, root := ~, start := 338366, stop := 338423 ), rec( attributes := rec( ), content := [ rec( content := "A transfo\ rmation, or ", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "K", next := 338468, root := ~, start := 338457, stop := 338467 ), rec( content := ".", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "Returns", next := 338479, root := ~, start := 338427, stop := 338478 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphEpimorphism", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "C", next := 338525, root := ~, start := 338500, stop := 338524 ), rec( content := " returns\ a single ", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ urjective", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "E", next := 338560, root := ~, start := 338543, stop := 338559 ), rec( content := " ", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ Homomorphism" ), content := 0, count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "Ref", next := 338600, root := ~, start := 338561, stop := 338599 ), rec( content := " between\ ", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "A", next := 338624, root := ~, start := 338609, stop := 338623 ), rec( content := " and ", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "A", next := 338644, root := ~, start := 338629, stop := 338643 ), rec( content := "\n if\ one exists, otherwise it returns ", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "K", next := 338696, root := ~, start := 338685, stop := 338695 ), rec( content := ".\n " , count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr1 := DigraphReverse(ChainDigraph(4));\n\ngap> gr2 := DigraphRemoveEdge(CompleteDigraph(3), [1, 2]);\n\ngap> DigraphEpimorphism(gr2, gr1);\ \nfail\ngap> DigraphEpimorphism(gr1, gr2);\nTransformation( [ 3, 1, 2, 3 ] )\n\ ", count := [ 7, 3, 6, 4 ], name := "PCDATA", root := ~ ) ], count := [ 7, 3, 6, 4 ], mathmode := "Text", name := "Example", next := 339036, root := ~, start := 338702, stop := 339035 ), rec( content := "\n ", count := [ 7, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "Description", next := 339053, root := ~, start := 338482, stop := 339052 ) ], count := [ 7, 3, 6, 1 ], mathmode := "Text", name := "ManSection", next := 339067, root := ~, start := 338351, stop := 339066 ), rec( content := "\n\n ", count := [ 7, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph1, digrap\ h2", Name := "EpimorphismsDigraphs" ), content := 0, count := [ 7, 3, 7, 2 ], mathmode := "Text", name := "Oper", next := 339148, root := ~, start := 339088, stop := 339147 ), rec( attributes := rec( Arg := "digraph1, digrap\ h2", Name := "EpimorphismsDigraphsRepresentatives" ), content := 0, count := [ 7, 3, 7, 4 ], mathmode := "Text", name := "Oper", next := 339226, root := ~, start := 339151, stop := 339225 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ transformations.", count := [ 7, 3, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 7, 5 ], mathmode := "Text", name := "Returns", next := 339274, root := ~, start := 339229, stop := 339273 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ se operations behave the same as ", count := [ 7, 3, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Homomor\ phismsDigraphs" ), content := 0, count := [ 7, 3, 7, 5 ], mathmode := "Text", name := "Ref", next := 339366, root := ~, start := 339331, stop := 339365 ), rec( content := " and\n \ ", count := [ 7, 3, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Homomor\ phismsDigraphsRepresentatives" ), content := 0, count := [ 7, 3, 7, 5 ], mathmode := "Text", name := "Ref", next := 339425, root := ~, start := 339375, stop := 339424 ), rec( content := ", except\ they only return\n ", count := [ 7, 3, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ urjective", count := [ 7, 3, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 7, 5 ], mathmode := "Text", name := "E", next := 339472, root := ~, start := 339455, stop := 339471 ), rec( content := " homomor\ phisms.\n ", count := [ 7, 3, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr1 := DigraphReverse(ChainDigraph(4));\n\ngap> gr2 := DigraphSymmetricClosure(CycleDigraph(3));\n\ngap> EpimorphismsDigraphsRepre\ sentatives(gr1, gr2);\n[ Transformation( [ 3, 1, 2, 1 ] ), Transformation( [ 3\ , 1, 2, 3 ] ), \n Transformation( [ 2, 1, 2, 3 ] ) ]\ngap> EpimorphismsDigrap\ hs(gr1, gr2);\n[ Transformation( [ 1, 2, 1, 3 ] ), Transformation( [ 1, 2, 3, \ 1 ] ), \n Transformation( [ 1, 2, 3, 2 ] ), Transformation( [ 1, 3, 1, 2 ] ),\ \n Transformation( [ 1, 3, 2, 1 ] ), Transformation( [ 1, 3, 2, 3 ] ), \n T\ ransformation( [ 2, 1, 2, 3 ] ), Transformation( [ 2, 1, 3, 1 ] ), \n Transfo\ rmation( [ 2, 1, 3, 2 ] ), Transformation( [ 2, 3, 1, 2 ] ), \n Transformatio\ n( [ 2, 3, 1, 3 ] ), Transformation( [ 2, 3, 2, 1 ] ), \n Transformation( [ 3\ , 1, 2, 1 ] ), Transformation( [ 3, 1, 2, 3 ] ), \n Transformation( [ 3, 1, 3\ , 2 ] ), Transformation( [ 3, 2, 1, 2 ] ), \n Transformation( [ 3, 2, 1, 3 ] \ ), Transformation( [ 3, 2, 3, 1 ] ) ]\n", count := [ 7, 3, 7, 6 ], name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 7, 6 ], mathmode := "Text", name := "Example", next := 340559, root := ~, start := 339492, stop := 340558 ), rec( content := "\n ", count := [ 7, 3, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 7, 5 ], mathmode := "Text", name := "Description", next := 340576, root := ~, start := 339277, stop := 340575 ) ], count := [ 7, 3, 7, 1 ], mathmode := "Text", name := "ManSection", next := 340590, root := ~, start := 339073, stop := 340589 ), rec( content := "\n\n ", count := [ 7, 3, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph1, digrap\ h2", Name := "DigraphEmbedding" ), content := 0, count := [ 7, 3, 8, 2 ], mathmode := "Text", name := "Oper", next := 340667, root := ~, start := 340611, stop := 340666 ), rec( attributes := rec( ), content := [ rec( content := " A transf\ ormation, or ", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "K", next := 340712, root := ~, start := 340701, stop := 340711 ), rec( content := ".", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "Returns", next := 340723, root := ~, start := 340670, stop := 340722 ), rec( attributes := rec( ), content := [ rec( content := "\n An \ embedding of a digraph ", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "A", next := 340785, root := ~, start := 340770, stop := 340784 ), rec( content := " into an\ other digraph\n ", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "A", next := 340826, root := ~, start := 340811, stop := 340825 ), rec( content := " is a ", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ Monomorphism" ), content := 0, count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "Ref", next := 340865, root := ~, start := 340832, stop := 340864 ), rec( content := " from ", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "A", next := 340886, root := ~, start := 340871, stop := 340885 ), rec( content := "\n to\ ", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "A", next := 340909, root := ~, start := 340894, stop := 340908 ), rec( content := " which h\ as the additional property that a pair of\n vertices ", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ i, j]", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "C", next := 340985, root := ~, start := 340972, stop := 340984 ), rec( content := " which h\ ave no edge ", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ -> j", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "C", next := 341018, root := ~, start := 341005, stop := 341017 ), rec( content := " in ", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "A", next := 341037, root := ~, start := 341022, stop := 341036 ), rec( content := " are\n\n\ mapped to a pair of vertices ", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ a, b]", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "C", next := 341089, root := ~, start := 341076, stop := 341088 ), rec( content := " which h\ ave no edge ", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "a\ ->b", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "C", next := 341120, root := ~, start := 341109, stop := 341119 ), rec( content := " in\n \ ", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "A", next := 341143, root := ~, start := 341128, stop := 341142 ), rec( content := ".", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "P", next := 341148, root := ~, start := 341144, stop := 341147 ), rec( content := "\n\n \ In other words, an embedding ", count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ ", count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "C", next := 341191, root := ~, start := 341183, stop := 341190 ), rec( content := " is an i\ somorphism from\n ", count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph1", count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "A", next := 341234, root := ~, start := 341219, stop := 341233 ), rec( content := " to the \ ", count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Induced\ Subdigraph" ), content := 0, count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "Ref", next := 341273, root := ~, start := 341242, stop := 341272 ), rec( content := " of ", count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph2", count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "A", next := 341292, root := ~, start := 341277, stop := 341291 ), rec( content := "\n on\ the image of ", count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ ", count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "C", next := 341321, root := ~, start := 341313, stop := 341320 ), rec( content := ". ", count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 8, 5 ], mathmode := "Text", name := "P", next := 341327, root := ~, start := 341323, stop := 341326 ), rec( content := "\n\n \ ", count := [ 7, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphEmbedding", count := [ 7, 3, 8, 5 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 7, 3, 8, 5 ], mathmode := "Text", name := "C", next := 341356, root := ~, start := 341333, stop := 341355 ), rec( content := " returns\ a single embedding if one exists, otherwise\n it returns ", count := [ 7, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 7, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 8, 5 ], mathmode := "Text", name := "K", next := 341435, root := ~, start := 341424, stop := 341434 ), rec( content := ".\n " , count := [ 7, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := ChainDigraph(3);\n\ngap> \ DigraphEmbedding(gr, CompleteDigraph(4));\nfail\ngap> DigraphEmbedding(gr, Dig\ raph([[3], [1, 4], [1], [3]]));\nTransformation( [ 2, 4, 3, 4 ] )\n", count := [ 7, 3, 8, 6 ], name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 8, 6 ], mathmode := "Text", name := "Example", next := 341689, root := ~, start := 341441, stop := 341688 ), rec( content := "\n ", count := [ 7, 3, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "Description", next := 341706, root := ~, start := 340726, stop := 341705 ) ], count := [ 7, 3, 8, 1 ], mathmode := "Text", name := "ManSection", next := 341720, root := ~, start := 340596, stop := 341719 ), rec( content := "\n\n ", count := [ 7, 3, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "D1, D2", Name := "EmbeddingsDigra\ phs" ), content := 0, count := [ 7, 3, 9, 2 ], mathmode := "Text", name := "Oper", next := 341787, root := ~, start := 341741, stop := 341786 ), rec( attributes := rec( Arg := "D1, D2", Name := "EmbeddingsDigra\ phsRepresentatives" ), content := 0, count := [ 7, 3, 9, 4 ], mathmode := "Text", name := "Oper", next := 341851, root := ~, start := 341790, stop := 341850 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ transformations.", count := [ 7, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 9, 5 ], mathmode := "Text", name := "Returns", next := 341899, root := ~, start := 341854, stop := 341898 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ se operations behave the same as ", count := [ 7, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Homomor\ phismsDigraphs" ), content := 0, count := [ 7, 3, 9, 5 ], mathmode := "Text", name := "Ref", next := 341991, root := ~, start := 341956, stop := 341990 ), rec( content := " and\n \ ", count := [ 7, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Homomor\ phismsDigraphsRepresentatives" ), content := 0, count := [ 7, 3, 9, 5 ], mathmode := "Text", name := "Ref", next := 342050, root := ~, start := 342000, stop := 342049 ), rec( content := ", except\ they only return\n embeddings of ", count := [ 7, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 1", count := [ 7, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 9, 5 ], mathmode := "Text", name := "A", next := 342103, root := ~, start := 342094, stop := 342102 ), rec( content := " into ", count := [ 7, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ 2", count := [ 7, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 9, 5 ], mathmode := "Text", name := "A", next := 342118, root := ~, start := 342109, stop := 342117 ), rec( content := ".", count := [ 7, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 9, 6 ], mathmode := "Text", name := "P", next := 342123, root := ~, start := 342119, stop := 342122 ), rec( content := "\n\n \ See also ", count := [ 7, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "IsDigra\ phEmbedding" ), content := 0, count := [ 7, 3, 9, 6 ], mathmode := "Text", name := "Ref", next := 342170, root := ~, start := 342138, stop := 342169 ), rec( content := ".\n " , count := [ 7, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D1 := NullDigraph(2);\n\ngap> D\ 2 := CycleDigraph(5);\n\ngap> Embeddi\ ngsDigraphsRepresentatives(D1, D2);\n[ Transformation( [ 1, 3, 3 ] ), Transfor\ mation( [ 1, 4, 3, 4 ] ) ]\ngap> EmbeddingsDigraphs(D1, D2);\n[ Transformation\ ( [ 1, 3, 3 ] ), Transformation( [ 1, 4, 3, 4 ] ), \n Transformation( [ 2, 4,\ 4, 5, 1 ] ), \n Transformation( [ 2, 5, 4, 5, 1 ] ), \n Transformation( [ 3\ , 1, 5, 1, 2 ] ), \n Transformation( [ 3, 5, 5, 1, 2 ] ), \n Transformation(\ [ 4, 1, 1, 2, 3 ] ), \n Transformation( [ 4, 2, 1, 2, 3 ] ), \n Transformat\ ion( [ 5, 2, 2, 3, 4 ] ), \n Transformation( [ 5, 3, 2, 3, 4 ] ) ]\n", count := [ 7, 3, 9, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 9, 7 ], mathmode := "Text", name := "Example", next := 342884, root := ~, start := 342176, stop := 342883 ), rec( content := "\n ", count := [ 7, 3, 9, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 9, 5 ], mathmode := "Text", name := "Description", next := 342901, root := ~, start := 341902, stop := 342900 ) ], count := [ 7, 3, 9, 1 ], mathmode := "Text", name := "ManSection", next := 342915, root := ~, start := 341726, stop := 342914 ), rec( content := "\n\n ", count := [ 7, 3, 9, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "src, ran, x", Label := "for digraphs a\ nd a permutation or transformation", Name := "IsDigraphHomomorphism" ), content := 0, count := [ 7, 3, 10, 2 ], mathmode := "Text", name := "Oper", next := 343056, root := ~, start := 342936, stop := 343055 ), rec( attributes := rec( Arg := "src, ran, x, col\ 1, col2", Name := "IsDigraphHomomorphism" ), content := 0, count := [ 7, 3, 10, 4 ], mathmode := "Text", name := "Oper", next := 343125, root := ~, start := 343059, stop := 343124 ), rec( attributes := rec( Arg := "src, ran, x", Label := "for digraphs a\ nd a permutation or transformation", Name := "IsDigraphEpimorphism" ), content := 0, count := [ 7, 3, 10, 6 ], mathmode := "Text", name := "Oper", next := 343246, root := ~, start := 343128, stop := 343245 ), rec( attributes := rec( Arg := "src, ran, x, col\ 1, col2", Name := "IsDigraphEpimorphism" ), content := 0, count := [ 7, 3, 10, 8 ], mathmode := "Text", name := "Oper", next := 343314, root := ~, start := 343249, stop := 343313 ), rec( attributes := rec( Arg := "src, ran, x", Label := "for digraphs a\ nd a permutation or transformation", Name := "IsDigraphMonomorphism" ), content := 0, count := [ 7, 3, 10, 10 ], mathmode := "Text", name := "Oper", next := 343436, root := ~, start := 343317, stop := 343435 ), rec( attributes := rec( Arg := "src, ran, x, col\ 1, col2", Name := "IsDigraphMonomorphism" ), content := 0, count := [ 7, 3, 10, 12 ], mathmode := "Text", name := "Oper", next := 343505, root := ~, start := 343439, stop := 343504 ), rec( attributes := rec( Arg := "digraph, x", Label := "for digraphs a\ nd a permutation or transformation", Name := "IsDigraphEndomorphism" ), content := 0, count := [ 7, 3, 10, 14 ], mathmode := "Text", name := "Oper", next := 343626, root := ~, start := 343508, stop := 343625 ), rec( attributes := rec( Arg := "digraph, x, col" , Name := "IsDigraphEndomo\ rphism" ), content := 0, count := [ 7, 3, 10, 16 ], mathmode := "Text", name := "Oper", next := 343687, root := ~, start := 343629, stop := 343686 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "K", next := 343710, root := ~, start := 343699, stop := 343709 ), rec( content := " or ", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "K", next := 343726, root := ~, start := 343714, stop := 343725 ), rec( content := ".", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "Returns", next := 343737, root := ~, start := 343690, stop := 343736 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sDigraphHomomorphism", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "C", next := 343786, root := ~, start := 343758, stop := 343785 ), rec( content := " returns\ ", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "K", next := 343806, root := ~, start := 343795, stop := 343805 ), rec( content := " if the \ permutation\n or transformation ", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "A", next := 343856, root := ~, start := 343848, stop := 343855 ), rec( content := " is a ho\ momorphism from the digraph\n ", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ rc", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "A", next := 343906, root := ~, start := 343896, stop := 343905 ), rec( content := " to the \ digraph ", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "r\ an", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "A", next := 343932, root := ~, start := 343922, stop := 343931 ), rec( content := ".\n " , count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "P", next := 343942, root := ~, start := 343938, stop := 343941 ), rec( content := "\n\n \ ", count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sDigraphEpimorphism", count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "C", next := 343975, root := ~, start := 343948, stop := 343974 ), rec( content := " returns\ ", count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "K", next := 343995, root := ~, start := 343984, stop := 343994 ), rec( content := " if the \ permutation\n or transformation ", count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ", count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "A", next := 344045, root := ~, start := 344037, stop := 344044 ), rec( content := " is a su\ rjective homomorphism from the digraph\n ", count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ rc", count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "A", next := 344106, root := ~, start := 344096, stop := 344105 ), rec( content := " to the \ digraph ", count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "r\ an", count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "A", next := 344132, root := ~, start := 344122, stop := 344131 ), rec( content := ".\n " , count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "P", next := 344142, root := ~, start := 344138, stop := 344141 ), rec( content := "\n\n \ ", count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sDigraphMonomorphism", count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "C", next := 344176, root := ~, start := 344148, stop := 344175 ), rec( content := " returns\ ", count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "K", next := 344196, root := ~, start := 344185, stop := 344195 ), rec( content := " if the \ permutation\n or transformation ", count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ", count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "A", next := 344246, root := ~, start := 344238, stop := 344245 ), rec( content := " is an i\ njective homomorphism from the digraph\n ", count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ rc", count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "A", next := 344307, root := ~, start := 344297, stop := 344306 ), rec( content := " to the \ digraph ", count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "r\ an", count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "A", next := 344333, root := ~, start := 344323, stop := 344332 ), rec( content := ".\n " , count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 10, 20 ], mathmode := "Text", name := "P", next := 344343, root := ~, start := 344339, stop := 344342 ), rec( content := "\n\n \ ", count := [ 7, 3, 10, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sDigraphEndomorphism", count := [ 7, 3, 10, 20 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 10, 20 ], mathmode := "Text", name := "C", next := 344377, root := ~, start := 344349, stop := 344376 ), rec( content := " returns\ ", count := [ 7, 3, 10, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 7, 3, 10, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 20 ], mathmode := "Text", name := "K", next := 344397, root := ~, start := 344386, stop := 344396 ), rec( content := " if the \ permutation\n or transformation ", count := [ 7, 3, 10, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ", count := [ 7, 3, 10, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 20 ], mathmode := "Text", name := "A", next := 344447, root := ~, start := 344439, stop := 344446 ), rec( content := " is an e\ ndomorphism of the digraph\n ", count := [ 7, 3, 10, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 3, 10, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 20 ], mathmode := "Text", name := "A", next := 344500, root := ~, start := 344486, stop := 344499 ), rec( content := ".\n " , count := [ 7, 3, 10, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 10, 21 ], mathmode := "Text", name := "P", next := 344510, root := ~, start := 344506, stop := 344509 ), rec( content := "\n\n \ A permutation or transformation ", count := [ 7, 3, 10, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ", count := [ 7, 3, 10, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 21 ], mathmode := "Text", name := "A", next := 344556, root := ~, start := 344548, stop := 344555 ), rec( content := " is a ", count := [ 7, 3, 10, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "h\ omomorphism", count := [ 7, 3, 10, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 21 ], mathmode := "Text", name := "E", next := 344581, root := ~, start := 344562, stop := 344580 ), rec( content := " from a\\ n digraph ", count := [ 7, 3, 10, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ rc", count := [ 7, 3, 10, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 21 ], mathmode := "Text", name := "A", next := 344611, root := ~, start := 344601, stop := 344610 ), rec( content := " to a di\ graph ", count := [ 7, 3, 10, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "r\ an", count := [ 7, 3, 10, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 21 ], mathmode := "Text", name := "A", next := 344635, root := ~, start := 344625, stop := 344634 ), rec( content := " if the \ following hold:\n ", count := [ 7, 3, 10, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "\n ", count := [ 7, 3, 10, 23 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "[u ^ ", count := [ 7, 3, 10, 23 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec\ ( content := "x", count := [ 7, 3, 10, 23 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 7, 3, 10, 23 ], mathmode := "Text", name := "A"\ , next := 344707, root := ~, start := 344699, stop := 344706 ), rec( content :\ = ", v ^ ", count := [ 7, 3, 10, 23 ], mathmode := "Text", name := "PCDATA", r\ oot := ~ ), rec( attributes := rec( ), content := [ rec( content := "x", coun\ t := [ 7, 3, 10, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], co\ unt := [ 7, 3, 10, 23 ], mathmode := "Text", name := "A", next := 344721, root\ := ~, start := 344713, stop := 344720 ), rec( content := "]", count := [ 7, 3\ , 10, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7,\ 3, 10, 23 ], mathmode := "Text", name := "C", next := 344726, root := ~, star\ t := 344691, stop := 344725 ), rec( content := " is an edge of\n ", coun\ t := [ 7, 3, 10, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "ran", count := [ 7, 3, 10, 23\ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, \ 23 ], mathmode := "Text", name := "A", next := 344759, root := ~, start := 344\ 749, stop := 344758 ), rec( content := " whenever ", count := [ 7, 3, 10, 23 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "[u, v]", count := [ 7, 3, 10, 23 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 23 ], mathmode := "T\ ext", name := "C", next := 344782, root := ~, start := 344769, stop := 344781 ), rec( cont\ ent := " is an\n edge of ", count := [ 7, 3, 10, 23 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ re\ c( content := "src", count := [ 7, 3, 10, 23 ], mathmode := "Text", name := "P\ CDATA", root := ~ ) ], count := [ 7, 3, 10, 23 ], mathmode := "Text", name := \ "A", next := 344815, root := ~, start := 344805, stop := 344814 ), rec( conten\ t := "; and ", count := [ 7, 3, 10, 23 ], mathmode := "Text", name := "PCDATA" , root\ := ~ ) ], count := [ 7, 3, 10, 23 ], name := "Item", next := 344828, root := ~, start := 344\ 676, stop := 344827 ), rec( attributes := rec( ), content := [ rec( content :\ = "\n ", count := [ 7, 3, 10, 25 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x", \ count := [ 7, 3, 10, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ) ] , coun\ t := [ 7, 3, 10, 25 ], mathmode := "Text", name := "A", next := 344858, root :\ = ~, start := 344850, stop := 344857 ), rec( content := " fixes every ", count\ := [ 7, 3, 10, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "i", count := [ 7, 3, 10, 25 ]\ , mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 25\ ], mathmode := "Text", name := "C", next := 344879, root := ~, start := 34487\ 1, stop := 344878 ), rec( content := " which is not a vertex of ", count := [ \ 7, 3, 10, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attrib\ utes := rec( ), content := [ rec( content := "src", count := [ 7, 3, 10, 25 ]\ , mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 25\ ], mathmode := "Text", name := "A", next := 344915, root := ~, start := 34490\ 5, stop := 344914 ), rec( content := ".\n ", count := [ 7, 3, 10, 25 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 25 ], name := "Ite\ m", next := 344930, root := ~, start := 344835, stop := 344929 ) ], count := [ 7, 3, 10, 22 ], mathmode := "Text", name := "List", next := 344942, root := ~, start := 344663, stop := 344941 ), rec( content := "\n Se\ e also ", count := [ 7, 3, 10, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Generat\ orsOfEndomorphismMonoid" ), content := 0, count := [ 7, 3, 10, 27 ], mathmode := "Text", name := "Ref", next := 345000, root := ~, start := 344956, stop := 344999 ), rec( content := ".", count := [ 7, 3, 10, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 10, 28 ], mathmode := "Text", name := "P", next := 345005, root := ~, start := 345001, stop := 345004 ), rec( content := "\n\n\n \ If ", count := [ 7, 3, 10, 28 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ ol1", count := [ 7, 3, 10, 28 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 28 ], mathmode := "Text", name := "A", next := 345026, root := ~, start := 345015, stop := 345025 ), rec( content := " and ", count := [ 7, 3, 10, 28 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ ol2", count := [ 7, 3, 10, 28 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 28 ], mathmode := "Text", name := "A", next := 345042, root := ~, start := 345031, stop := 345041 ), rec( content := ", or ", count := [ 7, 3, 10, 28 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ ol", count := [ 7, 3, 10, 28 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 28 ], mathmode := "Text", name := "A", next := 345057, root := ~, start := 345047, stop := 345056 ), rec( content := ", are gi\ ven, then they must\n represent vertex colourings; see \n ", count := [ 7, 3, 10, 28 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for a \ digraph and a homogeneous list", Oper := "AutomorphismGroup" ), content := 0, count := [ 7, 3, 10, 28 ], mathmode := "Text", name := "Ref", next := 345203, root := ~, start := 345127, stop := 345202 ), rec( content := " \n f\ or details of the permissible values for these argument. The\n homomorphism\ must then also have the property:\n \n ", count := [ 7, 3, 10, 28 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "\n ", count := [ 7, 3, 10, 30 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "col[i] = col[i ^ x]", count := [ 7, 3, 10, 30 ], mat\ hmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 30 ], math\ mode := "Text", name := "C", next := 345383, root := ~, start := 345357, stop \ := 345382 ), rec( content := " for all vertices ", count := [ 7, 3, 10, 30 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "i", count := [ 7, 3, 10, 30 ], mathmode := "Text", n\ ame := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 30 ], mathmode := "Text", name\ := "C", next := 345409, root := ~, start := 345401, stop := 345408 ), rec( cont\ ent := " of ", count := [ 7, 3, 10, 30 ], mathmode := "Text", name := "PCDATA" , root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "digraph", c\ ount := [ 7, 3, 10, 30 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 7, 3, 10, 30 ], mathmode := "Text", name := "A", next := 345427, root :\ = ~, start := 345413, stop := 345426 ), rec( content := ",\n in the cas\ e of ", count := [ 7, 3, 10, 30 ], mathmode := "Text", name := "PCDATA", root \ := ~ ), rec( attributes := rec( ), content := [ rec( content := "IsDigraphEnd\ omorphism", count := [ 7, 3, 10, 30 ], mathmode := "Text", name := "PCDATA", r\ oot := ~ ) ], count := [ 7, 3, 10, 30 ], mathmode := "Text", name := "C", next\ := 345480, root := ~, start := 345452, stop := 345479 ), rec( content := ".", coun\ t := [ 7, 3, 10, 30 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 30 ] , name := "Ite\ m", next := 345488, root := ~, start := 345342, stop := 345487 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n ", count := [ 7, 3, 10, 32 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "col1[i] = col2[i ^ x]", count := [ 7, 3, 10, 32 ], m\ athmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 32 ], math\ mode := "Text", name := "C", next := 345538, root := ~, start := 345510, stop \ := 345537 ), rec( content := " for all vertices ", count := [ 7, 3, 10, 32 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "i", count := [ 7, 3, 10, 32 ], mathmode := "Text", n\ ame := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 32 ], mathmode := "Text", name\ := "C", next := 345564, root := ~, start := 345556, stop := 345563 ), rec( cont\ ent := " of ", count := [ 7, 3, 10, 32 ], mathmode := "Text", name := "PCDATA" , root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "src", count\ := [ 7, 3, 10, 32 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 7, 3, 10, 32 ], mathmode := "Text", name := "A", next := 345578, root :\ = ~, start := 345568, stop := 345577 ), rec( content := ",\n in the cas\ es of the other operations.", count := [ 7, 3, 10, 32 ], mathmode := "Text", name\ := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 32 ], name := "Item", next := 3456\ 32, root := ~, start := 345495, stop := 345631 ) ], count := [ 7, 3, 10, 29 ], mathmode := "Text", name := "List", next := 345644, root := ~, start := 345329, stop := 345643 ), rec( content := "\n\n \ See also ", count := [ 7, 3, 10, 34 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ sRespectsColouring" ), content := 0, count := [ 7, 3, 10, 34 ], mathmode := "Text", name := "Ref", next := 345698, root := ~, start := 345659, stop := 345697 ), rec( content := ".\n \\ n ", count := [ 7, 3, 10, 34 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> src := Digraph([[1], [1, 2], [1, 3]]);\n\ngap> ran := Digraph([[1], [1, 2]]);\n\ngap> IsDigraphHomomorphism(src, ran, Transformation([1, 2, \ 2]));\ntrue\ngap> IsDigraphHomomorphism(src, ran, Transformation([2, 1, 2]));\ \nfalse\ngap> IsDigraphHomomorphism(src, ran, Transformation([3, 3, 3]));\nfal\ se\ngap> IsDigraphHomomorphism(src, src, Transformation([3, 3, 3]));\ntrue\nga\ p> IsDigraphHomomorphism(src, ran, Transformation([1, 2, 2]),\n> \ [1, 2, 2], [1, 2]);\ntrue\ngap> IsDigraphHomomorphism(src, ran, Tr\ ansformation([1, 2, 2]),\n> [2, 1, 1], [1, 2]);\nfals\ e\ngap> IsDigraphEndomorphism(src, Transformation([3, 3, 3]));\ntrue\ngap> IsD\ igraphEndomorphism(src, Transformation([3, 3, 3]), [1, 1, 1]);\ntrue\ngap> IsD\ igraphEndomorphism(src, Transformation([3, 3, 3]), [1, 1, 2]);\nfalse\ngap> Is\ DigraphEpimorphism(src, ran, Transformation([3, 3, 3]));\nfalse\ngap> IsDigrap\ hMonomorphism(src, ran, Transformation([1, 2, 2]));\nfalse\ngap> IsDigraphEpim\ orphism(src, ran, Transformation([1, 2, 2]));\ntrue\ngap> IsDigraphMonomorphis\ m(ran, src, ());\ntrue", count := [ 7, 3, 10, 35 ], name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 35 ], mathmode := "Text", name := "Example", next := 346900, root := ~, start := 345709, stop := 346899 ), rec( content := "\n ", count := [ 7, 3, 10, 36 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "Description", next := 346917, root := ~, start := 343740, stop := 346916 ) ], count := [ 7, 3, 10, 1 ], mathmode := "Text", name := "ManSection", next := 346931, root := ~, start := 342921, stop := 346930 ), rec( content := "\n\n ", count := [ 7, 3, 10, 36 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "src, ran, x", Label := "for digraphs a\ nd a permutation or transformation", Name := "IsDigraphEmbedding" ), content := 0, count := [ 7, 3, 11, 2 ], mathmode := "Text", name := "Oper", next := 347068, root := ~, start := 346952, stop := 347067 ), rec( attributes := rec( Arg := "src, ran, x, col\ 1, col2", Name := "IsDigraphEmbedding" ), content := 0, count := [ 7, 3, 11, 4 ], mathmode := "Text", name := "Oper", next := 347134, root := ~, start := 347071, stop := 347133 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "K", next := 347157, root := ~, start := 347146, stop := 347156 ), rec( content := " or ", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "K", next := 347173, root := ~, start := 347161, stop := 347172 ), rec( content := ".", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "Returns", next := 347184, root := ~, start := 347137, stop := 347183 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sDigraphEmbedding", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "C", next := 347230, root := ~, start := 347205, stop := 347229 ), rec( content := " returns\ ", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "K", next := 347250, root := ~, start := 347239, stop := 347249 ), rec( content := " if the \ permutation\n or transformation ", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "A", next := 347300, root := ~, start := 347292, stop := 347299 ), rec( content := " is a em\ bedding of the digraph\n ", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ rc", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "A", next := 347345, root := ~, start := 347335, stop := 347344 ), rec( content := " into th\ e digraph ", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "r\ an", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "A", next := 347373, root := ~, start := 347363, stop := 347372 ), rec( content := ", while \ respecting the colourings\n ", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ ol1", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "A", next := 347422, root := ~, start := 347411, stop := 347421 ), rec( content := " and ", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ ol2", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "A", next := 347438, root := ~, start := 347427, stop := 347437 ), rec( content := " if give\ n.\n ", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "P", next := 347457, root := ~, start := 347453, stop := 347456 ), rec( content := "\n\n \ A permutation or transformation ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "A", next := 347503, root := ~, start := 347495, stop := 347502 ), rec( content := " is a ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ mbedding", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "E", next := 347525, root := ~, start := 347509, stop := 347524 ), rec( content := " of a di\ graph\n ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ rc", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "A", next := 347553, root := ~, start := 347543, stop := 347552 ), rec( content := " into a \ digraph ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "r\ an", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "A", next := 347579, root := ~, start := 347569, stop := 347578 ), rec( content := " if ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "A", next := 347591, root := ~, start := 347583, stop := 347590 ), rec( content := " is a mo\ nomorphism from\n ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ rc", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "A", next := 347629, root := ~, start := 347619, stop := 347628 ), rec( content := " to ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "r\ an", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "A", next := 347643, root := ~, start := 347633, stop := 347642 ), rec( content := " and the\ inverse of ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "A", next := 347671, root := ~, start := 347663, stop := 347670 ), rec( content := " is a mo\ nomorphism from\n the subdigraph of ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "r\ an", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "A", next := 347727, root := ~, start := 347717, stop := 347726 ), rec( content := " induced\ by the image of ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "A", next := 347760, root := ~, start := 347752, stop := 347759 ), rec( content := " to\n \ ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ rc", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "A", next := 347778, root := ~, start := 347768, stop := 347777 ), rec( content := ".\n\n \ See also ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "IsDigra\ phHomomorphism" ), content := 0, count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "Ref", next := 347829, root := ~, start := 347794, stop := 347828 ), rec( content := ".", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 11, 7 ], mathmode := "Text", name := "P", next := 347834, root := ~, start := 347830, stop := 347833 ), rec( content := "\n\n \ ", count := [ 7, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> src := Digraph([[1], [1, 2]]);\n\ngap> ran := Digraph([[1], [1, 2], [1, 3]]);\n\ngap> IsDigraphMonomorphism(src, ran, ());\ntrue\ngap> IsDig\ raphEmbedding(src, ran, ());\ntrue\ngap> IsDigraphEmbedding(src, ran, (), [2, \ 1], [2, 1, 1]);\ntrue\ngap> IsDigraphEmbedding(src, ran, (), [2, 1], [1, 2, 1]\ );\nfalse\ngap> ran := Digraph([[1, 2], [1, 2], [1, 3]]);\n\ngap> IsDigraphMonomorphism(src, ran, IdentityTransf\ ormation);\ntrue\ngap> IsDigraphEmbedding(src, ran, IdentityTransformation);\n\ false", count := [ 7, 3, 11, 8 ], name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 8 ], mathmode := "Text", name := "Example", next := 348483, root := ~, start := 347840, stop := 348482 ), rec( content := "\n ", count := [ 7, 3, 11, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "Description", next := 348500, root := ~, start := 347187, stop := 348499 ) ], count := [ 7, 3, 11, 1 ], mathmode := "Text", name := "ManSection", next := 348514, root := ~, start := 346937, stop := 348513 ), rec( content := "\n\n ", count := [ 7, 3, 11, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "src, ran, x, col\ 1, col2", Name := "DigraphsRespectsColouring" ), content := 0, count := [ 7, 3, 12, 2 ], mathmode := "Text", name := "Oper", next := 348609, root := ~, start := 348539, stop := 348608 ), rec( attributes := rec( ), content := [ rec( content := " ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "K", next := 348635, root := ~, start := 348624, stop := 348634 ), rec( content := " or ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "K", next := 348651, root := ~, start := 348639, stop := 348650 ), rec( content := ". ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "Returns", next := 348663, root := ~, start := 348614, stop := 348662 ), rec( attributes := rec( ), content := [ rec( content := "\n T\ he operation ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphsRespectsColouring", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "C", next := 348734, root := ~, start := 348702, stop := 348733 ), rec( content := " verifie\ s whether or not \n the permutation or transformation ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "A", next := 348808, root := ~, start := 348800, stop := 348807 ), rec( content := " respect\ s the vertex colourings\n ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ ol1", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "A", next := 348857, root := ~, start := 348846, stop := 348856 ), rec( content := " and ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ ol2", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "A", next := 348873, root := ~, start := 348862, stop := 348872 ), rec( content := " of the \ digraphs ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ rc", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "A", next := 348900, root := ~, start := 348890, stop := 348899 ), rec( content := " and ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "r\ ange", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "A", next := 348917, root := ~, start := 348905, stop := 348916 ), rec( content := ".\n \ That is, ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphsRespectsColouring", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "C", next := 348966, root := ~, start := 348934, stop := 348965 ), rec( content := " returns\ ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "K", next := 348986, root := ~, start := 348975, stop := 348985 ), rec( content := " if and \ only if for\n all vertices ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "C", next := 349033, root := ~, start := 349025, stop := 349032 ), rec( content := " of ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ rc", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "A", next := 349047, root := ~, start := 349037, stop := 349046 ), rec( content := ", ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ ol1[i] = col2[i ^ x]", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "C", next := 349077, root := ~, start := 349049, stop := 349076 ), rec( content := ".\n \ ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 12, 4 ], mathmode := "Text", name := "P", next := 349089, root := ~, start := 349085, stop := 349088 ), rec( content := "\n\n \ ", count := [ 7, 3, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> src := Digraph([[1], [1, 2]]);\n\ngap> ran := Digraph([[1], [1, 2], [1, 3]]);\n\ngap> DigraphsRespectsColouring(src, ran, (1, 2), [2, 1], [1\ , 2, 1]);\ntrue\ngap> DigraphsRespectsColouring(src, ran, (1, 2), [2, 1], [2, \ 1, 1]);\nfalse\n", count := [ 7, 3, 12, 5 ], name := "PCDATA", root := ~ ) ], count := [ 7, 3, 12, 5 ], mathmode := "Text", name := "Example", next := 349448, root := ~, start := 349097, stop := 349447 ), rec( content := "\n ", count := [ 7, 3, 12, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "Description", next := 349467, root := ~, start := 348668, stop := 349466 ) ], count := [ 7, 3, 12, 1 ], mathmode := "Text", name := "ManSection", next := 349483, root := ~, start := 348522, stop := 349482 ), rec( content := "\n\n ", count := [ 7, 3, 12, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph[, colors\ ][, limit]", Name := "GeneratorsOfEndomorphismMonoid" ), content := 0, count := [ 7, 3, 13, 2 ], mathmode := "Text", name := "Func", next := 349582, root := ~, start := 349504, stop := 349581 ), rec( attributes := rec( Arg := "digraph", Name := "GeneratorsOfEnd\ omorphismMonoidAttr" ), content := 0, count := [ 7, 3, 13, 4 ], mathmode := "Text", name := "Attr", next := 349648, root := ~, start := 349585, stop := 349647 ), rec( attributes := rec( ), content := [ rec( content := " A list o\ f transformations.", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "Returns", next := 349697, root := ~, start := 349651, stop := 349696 ), rec( attributes := rec( ), content := [ rec( content := "\n An \ endomorphism of ", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "A", next := 349751, root := ~, start := 349737, stop := 349750 ), rec( content := " is a ho\ momorphism\n ", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ Homomorphism" ), content := 0, count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "Ref", next := 349807, root := ~, start := 349774, stop := 349806 ), rec( content := " from ", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "A", next := 349827, root := ~, start := 349813, stop := 349826 ), rec( content := " back to\ itself.\n\n ", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ eneratorsOfEndomorphismMonoid", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "C", next := 349886, root := ~, start := 349849, stop := 349885 ), rec( content := ", called\ with a single argument,\n returns a generating set for the monoid of all e\ ndomorphisms of\n ", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "A", next := 350005, root := ~, start := 349991, stop := 350004 ), rec( content := ". If ", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "A", next := 350024, root := ~, start := 350010, stop := 350023 ), rec( content := " belong\ s to ", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "Ref", next := 350075, root := ~, start := 350037, stop := 350074 ), rec( content := ", then t\ he value of\n ", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ eneratorsOfEndomorphismMonoid", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "C", next := 350136, root := ~, start := 350099, stop := 350135 ), rec( content := " will no\ t be recomputed on future\n calls.", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 13, 6 ], mathmode := "Text", name := "P", next := 350184, root := ~, start := 350180, stop := 350183 ), rec( content := "\n\n \ If the ", count := [ 7, 3, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olors", count := [ 7, 3, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 6 ], mathmode := "Text", name := "A", next := 350210, root := ~, start := 350197, stop := 350209 ), rec( content := " argumen\ t is specified, then\n ", count := [ 7, 3, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ eneratorsOfEndomorphismMonoid", count := [ 7, 3, 13, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 13, 6 ], mathmode := "Text", name := "C", next := 350280, root := ~, start := 350243, stop := 350279 ), rec( content := " will re\ turn a generating\n set for the monoid of endomorphisms which respect the g\ iven colouring.\n The colouring ", count := [ 7, 3, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olors", count := [ 7, 3, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 6 ], mathmode := "Text", name := "A", next := 350412, root := ~, start := 350399, stop := 350411 ), rec( content := " can be \ in one of two forms: ", count := [ 7, 3, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 13, 7 ], mathmode := "Text", name := "P", next := 350445, root := ~, start := 350441, stop := 350444 ), rec( content := "\n\n \ ", count := [ 7, 3, 13, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "\n A list of positive integers \ of size the number of vertices of\n ", count := [ 7, 3, 13, 9 ], mathmo\ de := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), conte\ nt := [ rec( content := "digraph", count := [ 7, 3, 13, 9 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 9 ], mathmode := "Tex\ t", name := "A", next := 350563, root := ~, start := 350549, stop := 350562 ), rec( cont\ ent := ", where ", count := [ 7, 3, 13, 9 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "co\ lors", count := [ 7, 3, 13, 9 ], mathmode := "Text", name := "PCDATA", root :=\ ~ ) ], count := [ 7, 3, 13, 9 ], mathmode := "Text", name := "A", next := 350\ 584, root := ~, start := 350571, stop := 350583 ), rec( attributes := rec( ), cont\ ent := [ rec( content := "[i]", count := [ 7, 3, 13, 9 ], mathmode := "Text", \ name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 9 ], mathmode := "Text", name\ := "C", next := 350594, root := ~, start := 350584, stop := 350593 ), rec( cont\ ent := " is the colour of vertex\n ", count := [ 7, 3, 13, 9 ], mathmod\ e := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), conten\ t := [ rec( content := "i", count := [ 7, 3, 13, 9 ], mathmode := "Text", name\ := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 9 ], mathmode := "Text", name\ := "C", next := 350635, root := ~, start := 350627, stop := 350634 ), rec( cont\ ent := ".\n ", count := [ 7, 3, 13, 9 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 13, 9 ], name := "Item", next := 350650, root := ~, start := 350\ 464, stop := 350649 ), rec( attributes := rec( ), content := [ rec( content :\ = "\n A list of lists, such that ", count := [ 7, 3, 13, 11 ], mathmode\ := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content\ := [ rec( content := "colors", count := [ 7, 3, 13, 11 ], mathmode := "Text",\ name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 11 ], mathmode := "Text\ ", name := "A", next := 350712, root := ~, start := 350699, stop := 350711 ), rec( attr\ ibutes := rec( ), content := [ rec( content := "[i]", count := [ 7, 3, 13, 11\ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, \ 11 ], mathmode := "Text", name := "C", next := 350722, root := ~, start := 350\ 712, stop := 350721 ), rec( content := " is a list of all\n vertices wi\ th colour ", count := [ 7, 3, 13, 11 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "i", count :\ = [ 7, 3, 13, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count\ := [ 7, 3, 13, 11 ], mathmode := "Text", name := "C", next := 350777, root :=\ ~, start := 350769, stop := 350776 ), rec( content := ".\n ", count := [ \ 7, 3, 13, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 11 ] , name := "Ite\ m", next := 350792, root := ~, start := 350657, stop := 350791 ) ], count := [ 7, 3, 13, 8 ], mathmode := "Text", name := "List", next := 350804, root := ~, start := 350451, stop := 350803 ), rec( content := "\n\n \ If the ", count := [ 7, 3, 13, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ imit", count := [ 7, 3, 13, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 13 ], mathmode := "Text", name := "A", next := 350829, root := ~, start := 350817, stop := 350828 ), rec( content := " argumen\ t is specified, then it will return only the\n first ", count := [ 7, 3, 13, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ imit", count := [ 7, 3, 13, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 13 ], mathmode := "Text", name := "A", next := 350904, root := ~, start := 350892, stop := 350903 ), rec( content := " homomor\ phisms, where ", count := [ 7, 3, 13, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ imit", count := [ 7, 3, 13, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 13 ], mathmode := "Text", name := "A", next := 350938, root := ~, start := 350926, stop := 350937 ), rec( content := " must be\ a positive\n integer or ", count := [ 7, 3, 13, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nfinity", count := [ 7, 3, 13, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 13 ], mathmode := "Text", name := "C", next := 350988, root := ~, start := 350973, stop := 350987 ), rec( content := ". ", count := [ 7, 3, 13, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 13, 14 ], mathmode := "Text", name := "P", next := 350994, root := ~, start := 350990, stop := 350993 ), rec( content := "\n\n \ ", count := [ 7, 3, 13, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := Digraph(List([1 .. 3], x -> [1 .. 3]));;\ngap> GeneratorsOfEndomor\ phismMonoid(gr);\n[ Transformation( [ 1, 3, 2 ] ), Transformation( [ 2, 1 ] ),\ \n IdentityTransformation, Transformation( [ 1, 2, 1 ] ), \n Transformation\ ( [ 1, 2, 2 ] ), Transformation( [ 1, 1, 2 ] ), \n Transformation( [ 1, 1, 1 \ ] ) ]\ngap> GeneratorsOfEndomorphismMonoid(gr, 3);\n[ Transformation( [ 1, 3, \ 2 ] ), Transformation( [ 2, 1 ] ), \n IdentityTransformation ]\ngap> gr := Co\ mpleteDigraph(3);;\ngap> GeneratorsOfEndomorphismMonoid(gr);\n[ Transformation\ ( [ 2, 3, 1 ] ), Transformation( [ 2, 1 ] ), \n IdentityTransformation ]\ngap\ > GeneratorsOfEndomorphismMonoid(gr, [1, 2, 2]);\n[ Transformation( [ 1, 3, 2 \ ] ), IdentityTransformation ]\ngap> GeneratorsOfEndomorphismMonoid(gr, [[1], [\ 2, 3]]);\n[ Transformation( [ 1, 3, 2 ] ), IdentityTransformation ]\n", count := [ 7, 3, 13, 15 ] , name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 13, 15 ], mathmode := "Text", name := "Example", next := 351863, root := ~, start := 351000, stop := 351862 ), rec( content := "\n ", count := [ 7, 3, 13, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "Description", next := 351880, root := ~, start := 349700, stop := 351879 ) ], count := [ 7, 3, 13, 1 ], mathmode := "Text", name := "ManSection", next := 351894, root := ~, start := 349489, stop := 351893 ), rec( content := "\n\n ", count := [ 7, 3, 13, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, n", Label := "for a digraph \ and a number of colours", Name := "DigraphColouring" ), content := 0, count := [ 7, 3, 14, 2 ], mathmode := "Text", name := "Oper", next := 352013, root := ~, start := 351915, stop := 352012 ), rec( attributes := rec( ), content := [ rec( content := " A transf\ ormation, or ", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "K", next := 352058, root := ~, start := 352047, stop := 352057 ), rec( content := ".", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "Returns", next := 352069, root := ~, start := 352016, stop := 352068 ), rec( attributes := rec( ), content := [ rec( content := "\n A " , count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ roper colouring", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "E", next := 352115, root := ~, start := 352092, stop := 352114 ), rec( content := " of a di\ graph is a labelling of its vertices in\n such a way that adjacent vertices\ have different labels. A ", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ roper\n ", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA" , root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "n", count := [ 7, 3, 14, 3 ], mathmod\ e := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 14, 3 ], mathmode := \ "Text", name := "C", next := 352250, root := ~, start := 352242, stop := 35224\ 9 ), rec( content := "-colouring", count := [ 7, 3, 14, 3 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "E", next := 352264, root := ~, start := 352226, stop := 352263 ), rec( content := " is a pr\ oper colouring that uses exactly ", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "C", next := 352313, root := ~, start := 352305, stop := 352312 ), rec( content := "\n co\ lours. Equivalently, a proper (", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "C", next := 352360, root := ~, start := 352352, stop := 352359 ), rec( content := "-)colour\ ing of a digraph can be\n defined to be a ", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ Epimorphism" ), content := 0, count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "Ref", next := 352444, root := ~, start := 352412, stop := 352443 ), rec( content := " from a \ digraph onto the\n complete digraph (with ", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "C", next := 352504, root := ~, start := 352496, stop := 352503 ), rec( content := " vertice\ s); see ", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Complet\ eDigraph" ), content := 0, count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "Ref", next := 352555, root := ~, start := 352520, stop := 352554 ), rec( content := ". Note \ that a digraph with loops (", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "Digraph\ HasLoops" ), content := 0, count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "Ref", next := 352625, root := ~, start := 352590, stop := 352624 ), rec( content := ") does n\ ot have a proper ", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "C", next := 352658, root := ~, start := 352650, stop := 352657 ), rec( content := "-colouri\ ng for\n any value ", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "C", next := 352695, root := ~, start := 352687, stop := 352694 ), rec( content := ".\n " , count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "P", next := 352705, root := ~, start := 352701, stop := 352704 ), rec( content := "\n\n \ If ", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "A", next := 352728, root := ~, start := 352714, stop := 352727 ), rec( content := " is a di\ graph and ", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "A", next := 352754, root := ~, start := 352746, stop := 352753 ), rec( content := " is a no\ n-negative integer, then\n ", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphColouring(", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "di\ graph", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root :\ = ~ ) ], count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "A", next := 3528\ 25, root := ~, start := 352811, stop := 352824 ), rec( content := ", ", count := [ 7, 3, 14, 4 ], mathmode := \ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( cont\ ent := "n", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "A", next := 3528\ 35, root := ~, start := 352827, stop := 352834 ), rec( content := ")", count := [ 7, 3, 14, 4 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "C", next := 352840, root := ~, start := 352791, stop := 352839 ), rec( content := " returns\ an epimorphism\n from ", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "A", next := 352887, root := ~, start := 352873, stop := 352886 ), rec( content := " onto th\ e complete digraph with ", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "A", next := 352927, root := ~, start := 352919, stop := 352926 ), rec( content := " vertice\ s if one\n exists, else it returns ", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "K", next := 352983, root := ~, start := 352972, stop := 352982 ), rec( content := ". ", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 14, 5 ], mathmode := "Text", name := "P", next := 352989, root := ~, start := 352985, stop := 352988 ), rec( content := "\n\n \ See also ", count := [ 7, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ GreedyColouring", Label := "for a digraph" ), content := 0, count := [ 7, 3, 14, 5 ], mathmode := "Text", name := "Ref", next := 353062, root := ~, start := 353004, stop := 353061 ), rec( content := " and \n \ ", count := [ 7, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 14, 6 ], mathmode := "Text", name := "P", next := 353076, root := ~, start := 353072, stop := 353075 ), rec( content := "\n\n \ Note that a digraph with at least two vertices has a 2-colouring if and only\n\ if it is bipartite, see ", count := [ 7, 3, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsBipar\ titeDigraph" ), content := 0, count := [ 7, 3, 14, 6 ], mathmode := "Text", name := "Ref", next := 353219, root := ~, start := 353187, stop := 353218 ), rec( content := ".\n\n \ ", count := [ 7, 3, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> DigraphColouring(CompleteDigraph(5), 4);\nfail\ngap> DigraphColouring(Ch\ ainDigraph(10), 1);\nfail\ngap> D := ChainDigraph(10);;\ngap> t := DigraphColo\ uring(D, 2);\nTransformation( [ 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ] )\ngap> IsDigra\ phColouring(D, t); \ntrue\ngap> DigraphGreedyColouring(D);\nTransformation( [ \ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1 ] )\n", count := [ 7, 3, 14, 7 ], name := "PCDATA\ ", root := ~ ) ], count := [ 7, 3, 14, 7 ], mathmode := "Text", name := "Example", next := 353592, root := ~, start := 353226, stop := 353591 ), rec( content := "\n ", count := [ 7, 3, 14, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "Description", next := 353609, root := ~, start := 352072, stop := 353608 ) ], count := [ 7, 3, 14, 1 ], mathmode := "Text", name := "ManSection", next := 353623, root := ~, start := 351900, stop := 353622 ), rec( content := "\n\n ", count := [ 7, 3, 14, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, order", Label := "for a digraph \ and vertex order", Name := "DigraphGreedyColouring" ), content := 0, count := [ 7, 3, 15, 2 ], mathmode := "Text", name := "Oper", next := 353759, root := ~, start := 353644, stop := 353758 ), rec( attributes := rec( Arg := "digraph, func", Label := "for a digraph \ and vertex order function", Name := "DigraphGreedyColouring" ), content := 0, count := [ 7, 3, 15, 4 ], mathmode := "Text", name := "Oper", next := 353885, root := ~, start := 353762, stop := 353884 ), rec( attributes := rec( Arg := "digraph", Label := "for a digraph" , Name := "DigraphGreedyCo\ louring" ), content := 0, count := [ 7, 3, 15, 6 ], mathmode := "Text", name := "Attr", next := 353979, root := ~, start := 353888, stop := 353978 ), rec( attributes := rec( ), content := [ rec( content := " A transf\ ormation, or ", count := [ 7, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 7, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 15, 7 ], mathmode := "Text", name := "K", next := 354024, root := ~, start := 354013, stop := 354023 ), rec( content := ".", count := [ 7, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 15, 7 ], mathmode := "Text", name := "Returns", next := 354035, root := ~, start := 353982, stop := 354034 ), rec( attributes := rec( ), content := [ rec( content := "\n A " , count := [ 7, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ roper colouring", count := [ 7, 3, 15, 7 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 7, 3, 15, 7 ], mathmode := "Text", name := "E", next := 354081, root := ~, start := 354058, stop := 354080 ), rec( content := " of a di\ graph is a labelling of its vertices in\n such a way that adjacent vertices\ have different labels. Note that a digraph \n with loops (", count := [ 7, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "Digraph\ HasLoops" ), content := 0, count := [ 7, 3, 15, 7 ], mathmode := "Text", name := "Ref", next := 354256, root := ~, start := 354227, stop := 354255 ), rec( content := ") does n\ ot have any proper \n colouring.\n ", count := [ 7, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "P", next := 354307, root := ~, start := 354303, stop := 354306 ), rec( content := "\n \n\ If ", count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "A", next := 354334, root := ~, start := 354320, stop := 354333 ), rec( content := " is a di\ graph and ", count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ rder", count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "A", next := 354364, root := ~, start := 354352, stop := 354363 ), rec( content := " is a de\ nse list consisting \n of all of the vertices of ", count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "A", next := 354437, root := ~, start := 354423, stop := 354436 ), rec( content := " (in any\ order), then \n ", count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphGreedyColouring", count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "C", next := 354494, root := ~, start := 354465, stop := 354493 ), rec( content := "\n us\ es a greedy algorithm with the specified order to obtain some proper\n colo\ uring of ", count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "A", next := 354601, root := ~, start := 354587, stop := 354600 ), rec( content := ", which \ may not use the minimal number of\n colours. ", count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "P", next := 354660, root := ~, start := 354656, stop := 354659 ), rec( content := "\n \n\ If ", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "A", next := 354687, root := ~, start := 354673, stop := 354686 ), rec( content := " is a di\ graph and ", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ unc", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "A", next := 354716, root := ~, start := 354705, stop := 354715 ), rec( content := " is a fu\ nction whose argument \n is a digraph, and that returns a dense list ", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ rder", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "A", next := 354807, root := ~, start := 354795, stop := 354806 ), rec( content := ", then \\ n ", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphGreedyColouring(", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", root \ := ~ ) ], count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "A", next := 3548\ 59, root := ~, start := 354845, stop := 354858 ), rec( content := ", ", count := [ 7, 3, 15, 9 ], mathmode := \ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( cont\ ent := "func", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "A", next := 3548\ 72, root := ~, start := 354861, stop := 354871 ), rec( content := ")", count := [ 7, 3, 15, 9 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "C", next := 354877, root := ~, start := 354819, stop := 354876 ), rec( content := " returns\ \n ", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphGreedyColouring(", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", root \ := ~ ) ], count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "A", next := 3549\ 30, root := ~, start := 354916, stop := 354929 ), rec( content := ", ", count := [ 7, 3, 15, 9 ], mathmode := \ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( cont\ ent := "func", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "A", next := 3549\ 43, root := ~, start := 354932, stop := 354942 ), rec( content := "(", count := [ 7, 3, 15, 9 ], mathmode := \ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( cont\ ent := "digraph", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "A", next := 3549\ 58, root := ~, start := 354944, stop := 354957 ), rec( content := "))", count := [ 7, 3, 15, 9 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "C", next := 354964, root := ~, start := 354890, stop := 354963 ), rec( content := ".\n " , count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 15, 10 ], mathmode := "Text", name := "P", next := 354974, root := ~, start := 354970, stop := 354973 ), rec( content := "\n\n \ If the optional second argument (either a list or a function), is not \n sp\ ecified, then ", count := [ 7, 3, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ WelshPowellOrder" ), content := 0, count := [ 7, 3, 15, 10 ], mathmode := "Text", name := "Ref", next := 355108, root := ~, start := 355071, stop := 355107 ), rec( content := " is used\ by default. \n ", count := [ 7, 3, 15, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 15, 11 ], mathmode := "Text", name := "P", next := 355138, root := ~, start := 355134, stop := 355137 ), rec( content := "\n \n\ See also\n ", count := [ 7, 3, 15, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for a \ digraph and a number of colours", Oper := "DigraphColouring" ), content := 0, count := [ 7, 3, 15, 11 ], mathmode := "Text", name := "Ref", next := 355247, root := ~, start := 355161, stop := 355246 ), rec( content := ".\n " , count := [ 7, 3, 15, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 15, 12 ], mathmode := "Text", name := "P", next := 355257, root := ~, start := 355253, stop := 355256 ), rec( content := "\n\n \ ", count := [ 7, 3, 15, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> DigraphGreedyColouring(ChainDigraph(10));\nTransformation( [ 2, 1, 2, 1,\ 2, 1, 2, 1, 2, 1 ] )\ngap> DigraphGreedyColouring(ChainDigraph(10), [1 .. 10]\ );\nTransformation( [ 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ] )\n", count := [ 7, 3, 15, 13 ] , name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 15, 13 ], mathmode := "Text", name := "Example", next := 355502, root := ~, start := 355263, stop := 355501 ), rec( content := "\n ", count := [ 7, 3, 15, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 15, 7 ], mathmode := "Text", name := "Description", next := 355519, root := ~, start := 354038, stop := 355518 ) ], count := [ 7, 3, 15, 1 ], mathmode := "Text", name := "ManSection", next := 355533, root := ~, start := 353629, stop := 355532 ), rec( content := "\n\n ", count := [ 7, 3, 15, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DigraphWelshPow\ ellOrder" ), content := 0, count := [ 7, 3, 16, 2 ], mathmode := "Text", name := "Attr", next := 355606, root := ~, start := 355554, stop := 355605 ), rec( attributes := rec( ), content := [ rec( content := " A list o\ f the vertices.", count := [ 7, 3, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 16, 3 ], mathmode := "Text", name := "Returns", next := 355652, root := ~, start := 355609, stop := 355651 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 7, 3, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphWelshPowellOrder", count := [ 7, 3, 16, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 16, 3 ], mathmode := "Text", name := "C", next := 355703, root := ~, start := 355673, stop := 355702 ), rec( content := " returns\ a list of all of the vertices of \n the digraph ", count := [ 7, 3, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 3, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 16, 3 ], mathmode := "Text", name := "A", next := 355776, root := ~, start := 355762, stop := 355775 ), rec( content := " ordered\ according to the sum of the number of \n out- and in-neighbours, from high\ est to lowest. \n ", count := [ 7, 3, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 16, 4 ], mathmode := "Text", name := "P", next := 355885, root := ~, start := 355881, stop := 355884 ), rec( content := "\n\n \ ", count := [ 7, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> DigraphWelshPowellOrder(Digraph([[4], [9], [9], [], \n> \ [4, 6, 9], [1], [], [], \n> \ [4, 5], [4, 5]]));\n[ 5, 9, 4, 1, 6, 10, 2, 3, 7, 8 ]\n", count := [ 7, 3, 16, 5 ], name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 16, 5 ], mathmode := "Text", name := "Example", next := 356135, root := ~, start := 355891, stop := 356134 ), rec( content := "\n ", count := [ 7, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 16, 3 ], mathmode := "Text", name := "Description", next := 356152, root := ~, start := 355655, stop := 356151 ) ], count := [ 7, 3, 16, 1 ], mathmode := "Text", name := "ManSection", next := 356166, root := ~, start := 355539, stop := 356165 ), rec( content := "\n\n ", count := [ 7, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "ChromaticNumber\ " ), content := 0, count := [ 7, 3, 17, 2 ], mathmode := "Text", name := "Attr", next := 356231, root := ~, start := 356187, stop := 356230 ), rec( attributes := rec( ), content := [ rec( content := " A non-ne\ gative integer.", count := [ 7, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 17, 3 ], mathmode := "Text", name := "Returns", next := 356277, root := ~, start := 356234, stop := 356276 ), rec( attributes := rec( ), content := [ rec( content := "\n A " , count := [ 7, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ roper colouring", count := [ 7, 3, 17, 3 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 7, 3, 17, 3 ], mathmode := "Text", name := "E", next := 356323, root := ~, start := 356300, stop := 356322 ), rec( content := " of a di\ graph is a labelling of its\n vertices in such a way that adjacent vertices\ have different labels.\n Equivalently, a proper digraph colouring can be d\ efined to be a ", count := [ 7, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ Epimorphism" ), content := 0, count := [ 7, 3, 17, 3 ], mathmode := "Text", name := "Ref", next := 356538, root := ~, start := 356500, stop := 356537 ), rec( content := " from a \ digraph onto a complete digraph. ", count := [ 7, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "P", next := 356583, root := ~, start := 356579, stop := 356582 ), rec( content := "\n\n \ If ", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "A", next := 356606, root := ~, start := 356592, stop := 356605 ), rec( content := " is a di\ graph without loops (see ", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "Digraph\ HasLoops" ), content := 0, count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "Ref", next := 356674, root := ~, start := 356639, stop := 356673 ), rec( content := ", then " , count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "C\ hromaticNumber", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "C", next := 356703, root := ~, start := 356681, stop := 356702 ), rec( content := " returns\ the least\n non-negative integer ", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "C", next := 356755, root := ~, start := 356747, stop := 356754 ), rec( content := " such th\ at there is a proper colouring of\n ", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "A", next := 356815, root := ~, start := 356801, stop := 356814 ), rec( content := " with ", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "C", next := 356829, root := ~, start := 356821, stop := 356828 ), rec( content := " colours\ . In other words, for a digraph with at\n least one vertex, ", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "C\ hromaticNumber", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "C", next := 356922, root := ~, start := 356900, stop := 356921 ), rec( content := " returns\ the least number ", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "C", next := 356956, root := ~, start := 356948, stop := 356955 ), rec( content := "\n su\ ch that ", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphColouring(", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "di\ graph", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root :\ = ~ ) ], count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "A", next := 3570\ 05, root := ~, start := 356991, stop := 357004 ), rec( content := ", n)", count := [ 7, 3, 17, 4 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "C", next := 357013, root := ~, start := 356971, stop := 357012 ), rec( content := " does no\ t return\n ", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "K", next := 357045, root := ~, start := 357034, stop := 357044 ), rec( content := ". See ", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for a \ digraph and a number of colours", Oper := "DigraphColouring" ), content := 0, count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "Ref", next := 357133, root := ~, start := 357051, stop := 357132 ), rec( content := ".\n\n \ ", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> ChromaticNumber(NullDigraph(10));\n1\ngap> ChromaticNumber(CompleteDigra\ ph(10));\n10\ngap> ChromaticNumber(CompleteBipartiteDigraph(5, 5));\n2\ngap> C\ hromaticNumber(Digraph([[], [3], [5], [2, 3], [4]]));\n3\ngap> ChromaticNumber\ (NullDigraph(0));\n0\ngap> D := PetersenGraph(IsMutableDigraph);\n\ngap> ChromaticNumber(D);\n3\n", count := [ 7, 3, 17, 5 ], name := "PCD\ ATA", root := ~ ) ], count := [ 7, 3, 17, 5 ], mathmode := "Text", name := "Example", next := 357532, root := ~, start := 357140, stop := 357531 ), rec( content := "\n ", count := [ 7, 3, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 17, 3 ], mathmode := "Text", name := "Description", next := 357549, root := ~, start := 356280, stop := 357548 ) ], count := [ 7, 3, 17, 1 ], mathmode := "Text", name := "ManSection", next := 357563, root := ~, start := 356172, stop := 357562 ), rec( content := "\n\n ", count := [ 7, 3, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "D", Name := "DigraphCore" ), content := 0, count := [ 7, 3, 18, 2 ], mathmode := "Text", name := "Attr", next := 357626, root := ~, start := 357588, stop := 357625 ), rec( attributes := rec( ), content := [ rec( content := "A list of\ positive integers.", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "Returns", next := 357678, root := ~, start := 357631, stop := 357677 ), rec( attributes := rec( ), content := [ rec( content := "\n I\ f ", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ ", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "A", next := 357714, root := ~, start := 357706, stop := 357713 ), rec( content := " is a di\ graph, then ", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphCore", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "C", next := 357752, root := ~, start := 357734, stop := 357751 ), rec( content := " returns\ a list of vertices\n corresponding to the ", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ ore", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "C", next := 357818, root := ~, start := 357807, stop := 357817 ), rec( content := " of ", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ ", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "A", next := 357830, root := ~, start := 357822, stop := 357829 ), rec( content := ". In par\ ticular, the subdigraph\n of ", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ ", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "A", next := 357879, root := ~, start := 357871, stop := 357878 ), rec( content := " induced\ by this list is isomorphic to the core of ", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ ", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "A", next := 357938, root := ~, start := 357930, stop := 357937 ), rec( content := ".", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "P", next := 357943, root := ~, start := 357939, stop := 357942 ), rec( content := "\n\n \ The ", count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ ore", count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "E", next := 357964, root := ~, start := 357953, stop := 357963 ), rec( content := " of a di\ graph ", count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ ", count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "C", next := 357986, root := ~, start := 357978, stop := 357985 ), rec( content := " is the \ minimal subdigraph ", count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "C\ ", count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "A", next := 358021, root := ~, start := 358013, stop := 358020 ), rec( content := " of\n \ ", count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ ", count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "C", next := 358037, root := ~, start := 358029, stop := 358036 ), rec( content := " which i\ s a homomorphic image of ", count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ ", count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "C", next := 358078, root := ~, start := 358070, stop := 358077 ), rec( content := ". The co\ re of a digraph \n is unique up to isomorphism.\n ", count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := DigraphSymmetricClosure(CycleDigraph(8));\n\ngap> DigraphCore(D);\n[ 1, 2 ]\ngap> D := Pet\ ersenGraph();\n\ngap> DigraphCor\ e(D);\n[ 1 .. 10 ]\ngap> D := Digraph(IsMutableDigraph, [[3], [3], [4], [5], [\ 2]]);\n\ngap> DigraphCore(D);\n[ 2, \ 3, 4, 5 ]\n", count := [ 7, 3, 18, 5 ], name := "PCDATA", root := ~ ) ], count := [ 7, 3, 18, 5 ], mathmode := "Text", name := "Example", next := 358562, root := ~, start := 358142, stop := 358561 ), rec( content := "\n ", count := [ 7, 3, 18, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "Description", next := 358581, root := ~, start := 357683, stop := 358580 ) ], count := [ 7, 3, 18, 1 ], mathmode := "Text", name := "ManSection", next := 358597, root := ~, start := 357571, stop := 358596 ), rec( content := "\n\n ", count := [ 7, 3, 18, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 0, 1 ], mathmode := "Text", name := "Section", next := 358611, root := ~, start := 326417, stop := 358610 ) , rec( content := "\n\n", count := [ 7, 3, 18, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 0, 0, 1 ], mathmode := "Text", name := "Chapter", next := 358623, root := ~, start := 277589, stop := 358622 ), rec( content := "\n ", count := [ 7, 3, 18, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := " homomorphisms ", count := [ 7, 3, 18, 6 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n ", count := [ 7, 3, 18, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "Finding cliques and independent sets" ), content := [ rec( content := "\n ", count := [ 8, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Finding cliques and indep\ endent sets", count := [ 8, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 2 ], mathmode := "Text", name := "Heading", next := 358762, root := ~, start := 358707, stop := 358761 ) , rec( content := "\n\n In ", count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := ", a ", count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "clique", count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "E", next := 358798, root := ~, start := 358785, stop := 358797 ), rec( content := " of a digraph is a set of mutual\ ly adjacent\n vertices of the digraph, and an ", count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "independent set", count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "E", next := 358900, root := ~, start := 358878, stop := 358899 ), rec( content := " is a set of mutually\n non-a\ djacent vertices of the digraph. A ", count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "maximal clique", count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "E", next := 358987, root := ~, start := 358966, stop := 358986 ), rec( content := " is a clique\n which is not p\ roperly contained in another clique, and a ", count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "maximal\n independen\ t set", count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "E", next := 359097, root := ~, start := 359061, stop := 359096 ), rec( content := " is an independent set which is \ not properly contained\n in another independent set. Using this definition\ in ", count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := ", cliques\n and independent s\ ets are both permitted, but not required, to contain vertices\n at which th\ ere is a loop. Another name for a clique is a ", count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "complete\n subgraph" , count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "E", next := 359405, root := ~, start := 359375, stop := 359404 ), rec( content := ".\n ", count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 0, 0, 4 ], mathmode := "Text", name := "P", next := 359415, root := ~, start := 359411, stop := 359414 ), rec( content := "\n\n ", count := [ 8, 0, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 8, 0, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 4 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " provides extensive functionalit\ y for computing cliques and\n independent sets of a digraph, whether maxima\ l or not. The fundamental\n algorithm used in most of the methods in ", count := [ 8, 0, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 8, 0, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 4 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " to calculate cliques\n and i\ ndependent sets is a version of the Bron-Kerbosch algorithm.\n Calculating \ the cliques and independent sets of a digraph is a well-known\n and hard pr\ oblem, and searching for cliques or independent sets in a\n digraph can be \ very lengthy, even for a digraph with a small number of\n vertices. ", count := [ 8, 0, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 8, 0, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 4 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " uses several strategies to incr\ ease the performance\n of these calculations.\n ", count := [ 8, 0, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 0, 0, 5 ], mathmode := "Text", name := "P", next := 360053, root := ~, start := 360049, stop := 360052 ), rec( content := "\n\n From the definition of c\ liques and independent sets, it follows that the\n presence of loops and mu\ ltiple edges in a digraph is irrelevant to the\n existence of cliques and i\ ndependent sets in the digraph. See ", count := [ 8, 0, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "DigraphHasLoops" ), content := 0, count := [ 8, 0, 0, 5 ], mathmode := "Text", name := "Ref", next := 360309, root := ~, start := 360274, stop := 360308 ), rec( content := " and ", count := [ 8, 0, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsMultiDigraph" ), content := 0, count := [ 8, 0, 0, 5 ], mathmode := "Text", name := "Ref", next := 360342, root := ~, start := 360314, stop := 360341 ), rec( content := " for more\n information about\ these properties. Therefore given a digraph\n ", count := [ 8, 0, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "digraph", count := [ 8, 0, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 5 ], mathmode := "Text", name := "A", next := 360437, root := ~, start := 360423, stop := 360436 ), rec( content := ", the cliques and independent se\ ts of ", count := [ 8, 0, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "digraph", count := [ 8, 0, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 5 ], mathmode := "Text", name := "A", next := 360489, root := ~, start := 360475, stop := 360488 ), rec( content := " are\n equal to the cliques a\ nd independent sets of the digraph:\n\n ", count := [ 8, 0, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 8, 0, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "DigraphRe\ moveLoops(DigraphRemoveAllMultipleEdges(", count := [ 8, 0, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 7 ], mathmode := "Text", name := "C", next := 360645, root := ~, start := 360589, stop := 360644 ), rec( attributes := rec( ), content := [ rec( content := "digraph", count := [ 8, 0, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 7 ], mathmode := "Text", name := "A", next := 360659, root := ~, start := 360645, stop := 360658 ), rec( attributes := rec( ), content := [ rec( content := "))", count := [ 8, 0, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 7 ], mathmode := "Text", name := "C", next := 360668, root := ~, start := 360659, stop := 360667 ), rec( content := ".\n ", count := [ 8, 0, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 7 ], name := "Item", next := 360683, root := ~, start := 360574, stop := 360682 ) ], count := [ 8, 0, 0, 6 ], mathmode := "Text", name := "List", next := 360695, root := ~, start := 360561, stop := 360694 ), rec( content := "\n\n See ", count := [ 8, 0, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "DigraphRemoveLoops" ), content := 0, count := [ 8, 0, 0, 9 ], mathmode := "Text", name := "Ref", next := 360737, root := ~, start := 360705, stop := 360736 ), rec( content := " and ", count := [ 8, 0, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "DigraphRemoveAllMultipleEdges" ), content := 0, count := [ 8, 0, 0, 9 ], mathmode := "Text", name := "Ref", next := 360791, root := ~, start := 360742, stop := 360790 ), rec( content := " for more information about thes\ e\n attributes. Furthermore, the cliques of this digraph are equal to the\ \n cliques of the digraph formed by removing any edge ", count := [ 8, 0, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[u,v]", count := [ 8, 0, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 9 ], mathmode := "Text", name := "C", next := 360967, root := ~, start := 360955, stop := 360966 ), rec( content := " for which\n the correspondin\ g reverse edge ", count := [ 8, 0, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[v,u]", count := [ 8, 0, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 9 ], mathmode := "Text", name := "C", next := 361025, root := ~, start := 361013, stop := 361024 ), rec( content := " is not present. Therefore,\n \ overall, the cliques of ", count := [ 8, 0, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "digraph", count := [ 8, 0, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 9 ], mathmode := "Text", name := "A", next := 361096, root := ~, start := 361082, stop := 361095 ), rec( content := " are equal to the cliques of the\ \n symmetric digraph:\n\n ", count := [ 8, 0, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 8, 0, 0, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "MaximalSy\ mmetricSubdigraphWithoutLoops(", count := [ 8, 0, 0, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 11 ], mathmode := "Text", name := "C", next := 361231, root := ~, start := 361185, stop := 361230 ), rec( attributes := rec( ), content := [ rec( content := "digraph", count := [ 8, 0, 0, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 11 ], mathmode := "Text", name := "A", next := 361245, root := ~, start := 361231, stop := 361244 ), rec( attributes := rec( ), content := [ rec( content := ")", count := [ 8, 0, 0, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 11 ], mathmode := "Text", name := "C", next := 361253, root := ~, start := 361245, stop := 361252 ), rec( content := ".\n ", count := [ 8, 0, 0, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 11 ], name := "Item", next := 361268, root := ~, start := 361170, stop := 361267 ) ], count := [ 8, 0, 0, 10 ], mathmode := "Text", name := "List", next := 361280, root := ~, start := 361157, stop := 361279 ), rec( content := "\n\n See ", count := [ 8, 0, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "MaximalSymmetricSubdigraphWitho\ utLoops" ), content := 0, count := [ 8, 0, 0, 13 ], mathmode := "Text", name := "Ref", next := 361342, root := ~, start := 361290, stop := 361341 ), rec( content := " for more\n information about\ this. The ", count := [ 8, 0, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "AutomorphismGroup", Label := "for a digraph" ), content := 0, count := [ 8, 0, 0, 13 ], mathmode := "Text", name := "Ref", next := 361444, root := ~, start := 361384, stop := 361443 ), rec( content := " of this symmetric digraph conta\ ins the\n automorphism group of ", count := [ 8, 0, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "digraph", count := [ 8, 0, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 13 ], mathmode := "Text", name := "A", next := 361524, root := ~, start := 361510, stop := 361523 ), rec( content := " as a subgroup. By performing t\ he\n search for maximal cliques with the help of this larger automorphism g\ roup\n to reduce the search space, the computation time may be reduced. Th\ e\n functions and attributes which return representatives of cliques of\n \ ", count := [ 8, 0, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "digraph", count := [ 8, 0, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 13 ], mathmode := "Text", name := "A", next := 361802, root := ~, start := 361788, stop := 361801 ), rec( content := " will return orbit representativ\ es of cliques under the\n action of the automorphism group of the ", count := [ 8, 0, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "maximal symmetric subdigr\ aph\n without loops", count := [ 8, 0, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 13 ], mathmode := "Text", name := "E", next := 361957, root := ~, start := 361902, stop := 361956 ), rec( content := " on sets of vertices.", count := [ 8, 0, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 0, 0, 14 ], mathmode := "Text", name := "P", next := 361982, root := ~, start := 361978, stop := 361981 ), rec( content := "\n\n The independent sets of \ a digraph are equal to the independent sets of the\n ", count := [ 8, 0, 0, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "DigraphSymmetricClosure" ), content := 0, count := [ 8, 0, 0, 14 ], mathmode := "Text", name := "Ref", next := 362104, root := ~, start := 362067, stop := 362103 ), rec( content := ". Therefore, overall, the indep\ endent\n sets of ", count := [ 8, 0, 0, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "digraph", count := [ 8, 0, 0, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 14 ], mathmode := "Text", name := "A", next := 362169, root := ~, start := 362155, stop := 362168 ), rec( content := " are equal to the independent se\ ts of the symmetric\n digraph:\n\n ", count := [ 8, 0, 0, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 8, 0, 0, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "DigraphSy\ mmetricClosure(DigraphRemoveLoops(DigraphRemoveAllMultipleEdges(\n ", count := [ 8, 0, 0, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 16 ], mathmode := "Text", name := "C", next := 362356, root := ~, start := 362267, stop := 362355 ), rec( attributes := rec( ), content := [ rec( content := "digraph", count := [ 8, 0, 0, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 16 ], mathmode := "Text", name := "A", next := 362370, root := ~, start := 362356, stop := 362369 ), rec( attributes := rec( ), content := [ rec( content := ")))", count := [ 8, 0, 0, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 16 ], mathmode := "Text", name := "C", next := 362380, root := ~, start := 362370, stop := 362379 ), rec( content := ".\n ", count := [ 8, 0, 0, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 16 ], name := "Item", next := 362395, root := ~, start := 362252, stop := 362394 ) ], count := [ 8, 0, 0, 15 ], mathmode := "Text", name := "List", next := 362407, root := ~, start := 362239, stop := 362406 ), rec( content := "\n\n Again, the automorphism \ group of this symmetric digraph contains the\n automorphism group of ", count := [ 8, 0, 0, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "digraph", count := [ 8, 0, 0, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 18 ], mathmode := "Text", name := "A", next := 362522, root := ~, start := 362508, stop := 362521 ), rec( content := ". Since a search for independent\ sets\n is equal to a search for cliques in the ", count := [ 8, 0, 0, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "DigraphDual" ), content := 0, count := [ 8, 0, 0, 18 ], mathmode := "Text", name := "Ref", next := 362629, root := ~, start := 362604, stop := 362628 ), rec( content := ", the\n methods used in ", count := [ 8, 0, 0, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 8, 0, 0, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 18 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " usually transform a search for \ independent sets\n into a search for cliques, as described above. The func\ tions and\n attributes which return representatives of independent sets of\ \n ", count := [ 8, 0, 0, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "digraph", count := [ 8, 0, 0, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 18 ], mathmode := "Text", name := "A", next := 362869, root := ~, start := 362855, stop := 362868 ), rec( content := " will return orbit representativ\ es of independent sets under\n the action of the automorphism group of the \ ", count := [ 8, 0, 0, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "symmetric closure", count := [ 8, 0, 0, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 18 ], mathmode := "Text", name := "E", next := 363002, root := ~, start := 362978, stop := 363001 ), rec( content := " of the\n digraph formed by r\ emoving loops and multiple edges.", count := [ 8, 0, 0, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 0, 0, 19 ], mathmode := "Text", name := "P", next := 363070, root := ~, start := 363066, stop := 363069 ), rec( content := "\n\n Please note that in ", count := [ 8, 0, 0, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 8, 0, 0, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 19 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := ", cliques and independent sets a\ re not\n required to be maximal. Some authors use the word clique to mean\n\ ", count := [ 8, 0, 0, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "maximal", count := [ 8, 0, 0, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 19 ], mathmode := "Text", name := "E", next := 363232, root := ~, start := 363218, stop := 363231 ), rec( content := " clique, and some authors use th\ e phrase independent set to\n mean ", count := [ 8, 0, 0, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "maximal", count := [ 8, 0, 0, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 19 ], mathmode := "Text", name := "E", next := 363315, root := ~, start := 363301, stop := 363314 ), rec( content := " independent set, but please not\ e that ", count := [ 8, 0, 0, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 8, 0, 0, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 19 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " does\n not use this definiti\ on.\n ", count := [ 8, 0, 0, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 0, 0, 20 ], mathmode := "Text", name := "P", next := 363407, root := ~, start := 363403, stop := 363406 ), rec( content := "\n\n ", count := [ 8, 0, 0, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Finding cliques", count := [ 8, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 0, 2 ], mathmode := "Text", name := "Heading", next := 363454, root := ~, start := 363420, stop := 363453 ), rec( content := "\n ", count := [ 8, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, l", Name := "IsClique" ), content := 0, count := [ 8, 1, 1, 2 ], mathmode := "Text", name := "Oper", next := 363512, root := ~, start := 363472, stop := 363511 ), rec( attributes := rec( Arg := "digraph, l", Name := "IsMaximalClique\ " ), content := 0, count := [ 8, 1, 1, 4 ], mathmode := "Text", name := "Oper", next := 363560, root := ~, start := 363513, stop := 363559 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "K", next := 363581, root := ~, start := 363570, stop := 363580 ), rec( content := " or ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "K", next := 363597, root := ~, start := 363585, stop := 363596 ), rec( content := ".", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "Returns", next := 363608, root := ~, start := 363561, stop := 363607 ), rec( attributes := rec( ), content := [ rec( content := "\n If ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "A", next := 363642, root := ~, start := 363628, stop := 363641 ), rec( content := " is a di\ graph and ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "A", next := 363668, root := ~, start := 363660, stop := 363667 ), rec( content := " is a du\ plicate-free list of\n vertices of ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "A", next := 363725, root := ~, start := 363711, stop := 363724 ), rec( content := ", then\n\ ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sClique(", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "C", next := 363750, root := ~, start := 363734, stop := 363749 ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "A", next := 363764, root := ~, start := 363750, stop := 363763 ), rec( attributes := rec( ), content := [ rec( content := ",\ ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "C", next := 363772, root := ~, start := 363764, stop := 363771 ), rec( attributes := rec( ), content := [ rec( content := "l\ ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "A", next := 363780, root := ~, start := 363772, stop := 363779 ), rec( attributes := rec( ), content := [ rec( content := ")\ ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "C", next := 363788, root := ~, start := 363780, stop := 363787 ), rec( content := " returns\ ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "K", next := 363808, root := ~, start := 363797, stop := 363807 ), rec( content := "\n if\ ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "l\ ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "A", next := 363824, root := ~, start := 363816, stop := 363823 ), rec( content := " is a ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ lique", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "E", next := 363843, root := ~, start := 363830, stop := 363842 ), rec( content := " of ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "A", next := 363861, root := ~, start := 363847, stop := 363860 ), rec( content := " and ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "K", next := 363878, root := ~, start := 363866, stop := 363877 ), rec( content := " if it i\ s\n not. Similarly,\n ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sMaximalClique(", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "C", next := 363936, root := ~, start := 363913, stop := 363935 ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "A", next := 363950, root := ~, start := 363936, stop := 363949 ), rec( attributes := rec( ), content := [ rec( content := ",\ ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "C", next := 363958, root := ~, start := 363950, stop := 363957 ), rec( attributes := rec( ), content := [ rec( content := "l\ ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "A", next := 363966, root := ~, start := 363958, stop := 363965 ), rec( attributes := rec( ), content := [ rec( content := ")\ ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "C", next := 363974, root := ~, start := 363966, stop := 363973 ), rec( content := " returns\ \n ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "K", next := 363998, root := ~, start := 363987, stop := 363997 ), rec( content := " if ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "A", next := 364010, root := ~, start := 364002, stop := 364009 ), rec( content := " is a ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ aximal clique", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "E", next := 364037, root := ~, start := 364016, stop := 364036 ), rec( content := " of ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "A", next := 364055, root := ~, start := 364041, stop := 364054 ), rec( content := " and\n \ ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "K", next := 364076, root := ~, start := 364064, stop := 364075 ), rec( content := " if it i\ s not. ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 1, 1, 6 ], mathmode := "Text", name := "P", next := 364096, root := ~, start := 364092, stop := 364095 ), rec( content := "\n\n \ A ", count := [ 8, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ lique", count := [ 8, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 6 ], mathmode := "Text", name := "E", next := 364117, root := ~, start := 364104, stop := 364116 ), rec( content := " of a di\ graph is a set of mutually adjacent vertices of the\n digraph. A ", count := [ 8, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ aximal clique", count := [ 8, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 6 ], mathmode := "Text", name := "E", next := 364213, root := ~, start := 364192, stop := 364212 ), rec( content := " is a cl\ ique that is not properly\n contained in another clique. A clique is permit\ ted, but not required, to\n contain vertices at which there is a loop.\n \ ", count := [ 8, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CompleteDigraph(4);;\ngap> IsClique(D, [1, 3, 2]);\ntrue\ngap> IsMa\ ximalClique(D, [1, 3, 2]);\nfalse\ngap> IsMaximalClique(D, DigraphVertices(D))\ ;\ntrue\ngap> D := Digraph([[1, 2, 4, 4], [1, 3, 4], [2, 1], [1, 2]]);\n\ngap> IsClique(D, [2, 3, 4]);\nfa\ lse\ngap> IsMaximalClique(D, [1, 2, 4]);\ntrue\ngap> D := CompleteDigraph(IsMu\ tableDigraph, 4);;\ngap> IsClique(D, [1, 3, 2]);\ntrue", count := [ 8, 1, 1, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 8, 1, 1, 7 ], mathmode := "Text", name := "Example", next := 364835, root := ~, start := 364375, stop := 364834 ), rec( content := "\n ", count := [ 8, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "Description", next := 364852, root := ~, start := 363609, stop := 364851 ) ], count := [ 8, 1, 1, 1 ], mathmode := "Text", name := "ManSection", next := 364866, root := ~, start := 363459, stop := 364865 ), rec( content := "\n\n ", count := [ 8, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, hook, u\ ser_param, limit, include,\n exclude, max, size, reps", Name := "CliquesFinder" ), content := 0, count := [ 8, 1, 2, 2 ], mathmode := "Text", name := "Func", next := 364993, root := ~, start := 364887, stop := 364992 ), rec( attributes := rec( ), content := [ rec( content := "The argum\ ent ", count := [ 8, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "u\ ser_param", count := [ 8, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 3 ], mathmode := "Text", name := "A", next := 365035, root := ~, start := 365018, stop := 365034 ), rec( content := ".", count := [ 8, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 3 ], mathmode := "Text", name := "Returns", next := 365046, root := ~, start := 364996, stop := 365045 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function finds cliques of the digraph ", count := [ 8, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 3 ], mathmode := "Text", name := "A", next := 365124, root := ~, start := 365110, stop := 365123 ), rec( content := " subject\ to the\n conditions imposed by the other arguments as described below. Not\ e\n that a clique is represented by the immutable list of the vertices that\ \n it contains.\n ", count := [ 8, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 1, 2, 4 ], mathmode := "Text", name := "P", next := 365312, root := ~, start := 365308, stop := 365311 ), rec( content := "\n\n \ Let ", count := [ 8, 1, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 8, 1, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 4 ], mathmode := "Text", name := "C", next := 365330, root := ~, start := 365322, stop := 365329 ), rec( content := " denote \ the automorphism group of the maximal symmetric\n subdigraph of ", count := [ 8, 1, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 1, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 4 ], mathmode := "Text", name := "A", next := 365418, root := ~, start := 365404, stop := 365417 ), rec( content := " without\ loops (see ", count := [ 8, 1, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Automor\ phismGroup", Label := "for a digraph" ), content := 0, count := [ 8, 1, 2, 4 ] , mathmode := "Text", name := "Ref", next := 365497, root := ~, start := 365438, stop := 365496 ), rec( content := " and ", count := [ 8, 1, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Maximal\ SymmetricSubdigraphWithoutLoops" ), content := 0, count := [ 8, 1, 2, 4 ], mathmode := "Text", name := "Ref", next := 365560, root := ~, start := 365502, stop := 365559 ), rec( content := ").\n\n \ ", count := [ 8, 1, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( attributes := rec( ), content := [ rec( content :\ = "hook", count := [ 8, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root \ := ~ ) ], count := [ 8, 1, 2, 5 ], mathmode := "Text", name := "A", next := 36\ 5598, root := ~, start := 365587, stop := 365597 ) ], count := [ 8, 1, 2, 5 ], name := "Mar\ k", next := 365605, root := ~, start := 365581, stop := 365604 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n This argument should be a f\ unction or ", count := [ 8, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "fail", coun\ t := [ 8, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 8, 1, 2, 6 ], mathmode := "Text", name := "K", next := 365676, root := \ ~, start := 365665, stop := 365675 ), rec( content := ".", count := [ 8, 1, 2,\ 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\ c( ), content := 0, count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "P", next\ := 365681, root := ~, start := 365677, stop := 365680 ), rec( content := "\n\ \n If ", count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "hook", coun\ t := [ 8, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 8, 1, 2, 7 ], mathmode := "Text", name := "A", next := 365705, root := \ ~, start := 365694, stop := 365704 ), rec( content := " is a function, then it\ should have two arguments\n ", count := [ 8, 1, 2, 7 ], mathmode := "T\ ext", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ \ rec( content := "user_param", count := [ 8, 1, 2, 7 ], mathmode := "Text", nam\ e := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 7 ], mathmode := "Text", name\ := "A", next := 365780, root := ~, start := 365763, stop := 365779 ), rec( cont\ ent := " (see below) and a clique ", count := [ 8, 1, 2, 7 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ re\ c( content := "c", count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "C", next\ := 365814, root := ~, start := 365806, stop := 365813 ), rec( content := ". T\ he function\n ", count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "\ PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes\ := rec( ), content := [ rec( content := "hook", count := [ 8, 1, 2, 7 ], mat\ hmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 7 ], mat\ hmode := "Text", name := "A", next := 365851, root := ~, start := 365840, stop\ := 365850 ), rec( content := "(", count := [ 8, 1, 2, 7 ], mathmode := "Text"\ , name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec(\ content := "user_param", count := [ 8, 1, 2, 7 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 7 ], mathmode := "Text", name :=\ "A", next := 365869, root := ~, start := 365852, stop := 365868 ), rec( conte\ nt := ", c)", count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", r\ oot := ~ ) ], count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "C", next :\ = 365877, root := ~, start := 365837, stop := 365876 ), rec( content := " is c\ alled every time a new\n clique ", count := [ 8, 1, 2, 7 ], mathmode :=\ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content :=\ [ rec( content := "c", count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "\ PCDATA", root := ~ ) ], count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "\ C", next := 365928, root := ~, start := 365920, stop := 365927 ), rec( content\ := " is found by ", count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "C\ liquesFinder", count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", \ root := ~ ) ], count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "C", next \ := 365961, root := ~, start := 365941, stop := 365960 ), rec( content := ".", coun\ t := [ 8, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := 0, count := [ 8, 1, 2, 8 ], mathmode := "Text", name\ := "P", next := 365966, root := ~, start := 365962, stop := 365965 ), rec( cont\ ent := "\n\n If ", count := [ 8, 1, 2, 8 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content \ := "hook", count := [ 8, 1, 2, 8 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 8, 1, 2, 8 ], mathmode := "Text", name := "A", next := 3\ 65990, root := ~, start := 365979, stop := 365989 ), rec( content := " is ", coun\ t := [ 8, 1, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "fail", count := [ 8, 1, 2, 8 \ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 8 ] , math\ mode := "Text", name := "K", next := 366005, root := ~, start := 365994, stop \ := 366004 ), rec( content := ", then a default function is used that\n \ simply adds every new clique found by ", count := [ 8, 1, 2, 8 ], mathmode := \ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ \ rec( content := "CliquesFinder", count := [ 8, 1, 2, 8 ], mathmode := "Text", \ name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 8 ], mathmode := "Text", name\ := "C", next := 366110, root := ~, start := 366090, stop := 366109 ), rec( cont\ ent := " to\n ", count := [ 8, 1, 2, 8 ], mathmode := "Text", name := "\ PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content :=\ "user_param", count := [ 8, 1, 2, 8 ], mathmode := "Text", name := "PCDATA", \ root := ~ ) ], count := [ 8, 1, 2, 8 ], mathmode := "Text", name := "A", next \ := 366139, root := ~, start := 366122, stop := 366138 ), rec( content := ", wh\ ich must be a list in this case.\n ", count := [ 8, 1, 2, 8 ], mathmode :\ = "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 6 ], name := "Ite\ m", next := 366189, root := ~, start := 365612, stop := 366188 ), rec( attributes :\ = rec( ), content := [ rec( attributes := rec( ), content := [ rec( content \ := "user_param", count := [ 8, 1, 2, 9 ], mathmode := "Text", name := "PCDATA"\ , root := ~ ) ], count := [ 8, 1, 2, 9 ], mathmode := "Text", name := "A", next\ := 366220, root := ~, start := 366203, stop := 366219 ) ], count := [ 8, 1, 2, 9 ], name := "Mar\ k", next := 366227, root := ~, start := 366197, stop := 366226 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n If ", count := [ 8, 1, 2, 1\ 0 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec\ ( ), content := [ rec( content := "hook", count := [ 8, 1, 2, 10 ], mathmode \ := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], mathmode\ := "Text", name := "A", next := 366263, root := ~, start := 366252, stop := 3\ 66262 ), rec( content := " is a function, then ", count := [ 8, 1, 2, 10 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "user_param", count := [ 8, 1, 2, 10 ], mathmode := "\ Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], mathmode := \ "Text", name := "A", next := 366301, root := ~, start := 366284, stop := 36630\ 0 ), rec( content := " can be any ", count := [ 8, 1, 2, 10 ], mathmode := "Te\ xt", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ r\ ec( content := "GAP", count := [ 8, 1, 2, 10 ], mathmode := "Text", name := "P\ CDATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], mathmode := "Text", name := "\ Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := "\n\ object. The object ", count := [ 8, 1, 2, 10 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "user_param", count := [ 8, 1, 2, 10 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], mathmode := "Text", name := "A" , next\ := 366363, root := ~, start := 366346, stop := 366362 ), rec( content := " is\ used as the first argument for\n the function ", count := [ 8, 1, 2, 1\ 0 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec\ ( ), content := [ rec( content := "hook", count := [ 8, 1, 2, 10 ], mathmode \ := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], mathmode\ := "Text", name := "A", next := 366430, root := ~, start := 366419, stop := 3\ 66429 ), rec( content := ". For example, ", count := [ 8, 1, 2, 10 ], mathmode\ := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content\ := [ rec( content := "user_param", count := [ 8, 1, 2, 10 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], mathmode := "Te\ xt", name := "A", next := 366462, root := ~, start := 366445, stop := 366461 ) , rec( cont\ ent := " might be a\n list, and ", count := [ 8, 1, 2, 10 ], mathmode :\ = "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content :\ = [ rec( attributes := rec( ), content := [ rec( content := "hook", count := \ [ 8, 1, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :=\ [ 8, 1, 2, 10 ], mathmode := "Text", name := "A", next := 366506, root := ~, \ start := 366495, stop := 366505 ), rec( content := "(", count := [ 8, 1, 2, 10\ ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(\ ), content := [ rec( content := "user_param", count := [ 8, 1, 2, 10 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], mat\ hmode := "Text", name := "A", next := 366524, root := ~, start := 366507, stop\ := 366523 ), rec( content := ", c)", count := [ 8, 1, 2, 10 ], mathmode := "T\ ext", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], mathmode := "\ Text", name := "C", next := 366532, root := ~, start := 366492, stop := 366531\ ), rec( content := " might add the size\n of the clique ", count := [ \ 8, 1, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\ tes := rec( ), content := [ rec( content := "c", count := [ 8, 1, 2, 10 ], ma\ thmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], math\ mode := "Text", name := "C", next := 366582, root := ~, start := 366574, stop \ := 366581 ), rec( content := " to the list ", count := [ 8, 1, 2, 10 ], mathmo\ de := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), conte\ nt := [ rec( content := "user_param", count := [ 8, 1, 2, 10 ], mathmode := "T\ ext", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], mathmode := "\ Text", name := "A", next := 366612, root := ~, start := 366595, stop := 366611\ ), rec( content := ". ", count := [ 8, 1, 2, 10 ], mathmode := "Text", name :\ = "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ \ 8, 1, 2, 11 ], mathmode := "Text", name := "P", next := 366618, root := ~, star\ t := 366614, stop := 366617 ), rec( content := "\n\n If the value of ", coun\ t := [ 8, 1, 2, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "hook", count := [ 8, 1, 2, 11\ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 1\ 1 ], mathmode := "Text", name := "A", next := 366655, root := ~, start := 3666\ 44, stop := 366654 ), rec( content := " is ", count := [ 8, 1, 2, 11 ], mathmo\ de := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), conte\ nt := [ rec( content := "fail", count := [ 8, 1, 2, 11 ], mathmode := "Text", \ name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 11 ], mathmode := "Text", name\ := "K", next := 366670, root := ~, start := 366659, stop := 366669 ), rec( cont\ ent := ", then the value of\n ", count := [ 8, 1, 2, 11 ], mathmode := \ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ \ rec( content := "user_param", count := [ 8, 1, 2, 11 ], mathmode := "Text", na\ me := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 11 ], mathmode := "Text", name\ := "A", next := 366715, root := ~, start := 366698, stop := 366714 ), rec( cont\ ent := " must be a list.\n ", count := [ 8, 1, 2, 11 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], name := "Item", next := 3667\ 45, root := ~, start := 366234, stop := 366744 ), rec( attributes := rec( ), content := [ rec( attr\ ibutes := rec( ), content := [ rec( content := "limit", count := [ 8, 1, 2, 1\ 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, \ 12 ], mathmode := "Text", name := "A", next := 366771, root := ~, start := 366\ 759, stop := 366770 ) ], count := [ 8, 1, 2, 12 ], name := "Mark", next := 3667\ 78, root := ~, start := 366753, stop := 366777 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "\n This argument should be a positive integer or ", count := [ \ 8, 1, 2, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\ tes := rec( ), content := [ rec( content := "infinity", count := [ 8, 1, 2, 1\ 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, \ 13 ], mathmode := "Text", name := "K", next := 366861, root := ~, start := 366\ 846, stop := 366860 ), rec( content := ".\n ", count := [ 8, 1, 2, 13 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "CliquesFinder", count := [ 8, 1, 2, 13 ], mathmode :\ = "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 13 ], mathmode \ := "Text", name := "C", next := 366891, root := ~, start := 366871, stop := 36\ 6890 ), rec( content := " will return after it has found\n ", count := [ \ 8, 1, 2, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\ tes := rec( ), content := [ rec( content := "limit", count := [ 8, 1, 2, 13 ]\ , mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 13 ] , math\ mode := "Text", name := "A", next := 366943, root := ~, start := 366931, stop \ := 366942 ), rec( content := " cliques or the search is complete.\n ", coun\ t := [ 8, 1, 2, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 13 ], name := "Ite\ m", next := 366992, root := ~, start := 366785, stop := 366991 ), rec( attributes :\ = rec( ), content := [ rec( attributes := rec( ), content := [ rec( content \ := "include", count := [ 8, 1, 2, 14 ], mathmode := "Text", name := "PCDATA", \ root := ~ ) ], count := [ 8, 1, 2, 14 ], mathmode := "Text", name := "A", next\ := 367020, root := ~, start := 367006, stop := 367019 ), rec( content := " an\ d ", count := [ 8, 1, 2, 14 ], mathmode := "Text", name := "PCDATA", root := ~\ ), rec( attributes := rec( ), content := [ rec( content := "exclude", count \ := [ 8, 1, 2, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count\ := [ 8, 1, 2, 14 ], mathmode := "Text", name := "A", next := 367039, root := \ ~, start := 367025, stop := 367038 ) ], count := [ 8, 1, 2, 14 ], name := "Mar\ k", next := 367046, root := ~, start := 367000, stop := 367045 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n These arguments should each\ be a (possibly empty) duplicate-free list\n of vertices of ", count :=\ [ 8, 1, 2, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "digraph", count := [ 8, 1, 2,\ 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2\ , 15 ], mathmode := "Text", name := "A", next := 367175, root := ~, start := 3\ 67161, stop := 367174 ), rec( content := " (i.e. positive integers less than t\ he\n number of vertices of ", count := [ 8, 1, 2, 15 ], mathmode := "Te\ xt", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ r\ ec( content := "digraph", count := [ 8, 1, 2, 15 ], mathmode := "Text", name :\ = "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 15 ], mathmode := "Text", name \ := "A", next := 367258, root := ~, start := 367244, stop := 367257 ), rec( cont\ ent := "). ", count := [ 8, 1, 2, 15 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 1, 2, 16 ], math\ mode := "Text", name := "P", next := 367265, root := ~, start := 367261, stop \ := 367264 ), rec( content := "\n\n ", count := [ 8, 1, 2, 16 ], mathmod\ e := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), conten\ t := [ rec( content := "CliquesFinder", count := [ 8, 1, 2, 16 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 16 ], mathmode :=\ "Text", name := "C", next := 367295, root := ~, start := 367275, stop := 3672\ 94 ), rec( content := " will only look for cliques containing all of the\n \ vertices in ", count := [ 8, 1, 2, 16 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "in\ clude", count := [ 8, 1, 2, 16 ], mathmode := "Text", name := "PCDATA", root :\ = ~ ) ], count := [ 8, 1, 2, 16 ], mathmode := "Text", name := "A", next := 36\ 7379, root := ~, start := 367365, stop := 367378 ), rec( content := " and cont\ aining none of the vertices in\n ", count := [ 8, 1, 2, 16 ], mathmode \ := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content \ := [ rec( content := "exclude", count := [ 8, 1, 2, 16 ], mathmode := "Text", \ name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 16 ], mathmode := "Text", name\ := "A", next := 367441, root := ~, start := 367427, stop := 367440 ), rec( cont\ ent := ". ", count := [ 8, 1, 2, 16 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 1, 2, 17 ], math\ mode := "Text", name := "P", next := 367447, root := ~, start := 367443, stop \ := 367446 ), rec( content := "\n\n Note that the search may be much mor\ e efficient if each of these lists\n is invariant under the action of " , coun\ t := [ 8, 1, 2, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "G", count := [ 8, 1, 2, 17 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 17 ] , math\ mode := "Text", name := "C", next := 367577, root := ~, start := 367569, stop \ := 367576 ), rec( content := " on sets of vertices.\n ", count := [ 8, 1,\ 2, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 15 ], name := "Ite\ m", next := 367612, root := ~, start := 367053, stop := 367611 ), rec( attributes :\ = rec( ), content := [ rec( attributes := rec( ), content := [ rec( content \ := "max", count := [ 8, 1, 2, 18 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 8, 1, 2, 18 ], mathmode := "Text", name := "A", next := \ 367636, root := ~, start := 367626, stop := 367635 ) ], count := [ 8, 1, 2, 18 ], name := "Mar\ k", next := 367643, root := ~, start := 367620, stop := 367642 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n This argument should be ", coun\ t := [ 8, 1, 2, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "true", count := [ 8, 1, 2, 19\ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 1\ 9 ], mathmode := "Text", name := "K", next := 367700, root := ~, start := 3676\ 89, stop := 367699 ), rec( content := " or ", count := [ 8, 1, 2, 19 ], mathmo\ de := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), conte\ nt := [ rec( content := "false", count := [ 8, 1, 2, 19 ], mathmode := "Text",\ name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 19 ], mathmode := "Text" , name\ := "K", next := 367716, root := ~, start := 367704, stop := 367715 ), rec( cont\ ent := ". If ", count := [ 8, 1, 2, 19 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "max"\ , count := [ 8, 1, 2, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ] , coun\ t := [ 8, 1, 2, 19 ], mathmode := "Text", name := "A", next := 367732, root :=\ ~, start := 367722, stop := 367731 ), rec( content := " is\n true then\ ", count := [ 8, 1, 2, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "CliquesFinder", count := [ 8,\ 1, 2, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8\ , 1, 2, 19 ], mathmode := "Text", name := "C", next := 367774, root := ~, star\ t := 367754, stop := 367773 ), rec( content := " will only search for ", count\ := [ 8, 1, 2, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "maximal", count := [ 8, 1, 2,\ 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2\ , 19 ], mathmode := "Text", name := "E", next := 367810, root := ~, start := 3\ 67796, stop := 367809 ), rec( content := "\n cliques. If ", count := [ \ 8, 1, 2, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\ tes := rec( ), content := [ rec( content := "max", count := [ 8, 1, 2, 19 ], \ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 19 ], math\ mode := "Text", name := "K", next := 367841, root := ~, start := 367831, stop \ := 367840 ), rec( content := " is ", count := [ 8, 1, 2, 19 ], mathmode := "Te\ xt", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ r\ ec( content := "false", count := [ 8, 1, 2, 19 ], mathmode := "Text", name := \ "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 19 ], mathmode := "Text", name :=\ "K", next := 367857, root := ~, start := 367845, stop := 367856 ), rec( conte\ nt := " then non-maximal cliques may be\n found.\n ", count := [ 8\ , 1, 2, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 19 ], name := "Ite\ m", next := 367918, root := ~, start := 367650, stop := 367917 ), rec( attributes :\ = rec( ), content := [ rec( attributes := rec( ), content := [ rec( content \ := "size", count := [ 8, 1, 2, 20 ], mathmode := "Text", name := "PCDATA", roo\ t := ~ ) ], count := [ 8, 1, 2, 20 ], mathmode := "Text", name := "A", next :=\ 367943, root := ~, start := 367932, stop := 367942 ) ], count := [ 8, 1, 2, 20 ], name := "Mar\ k", next := 367950, root := ~, start := 367926, stop := 367949 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n This argument should be ", coun\ t := [ 8, 1, 2, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "fail", count := [ 8, 1, 2, 21\ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 2\ 1 ], mathmode := "Text", name := "K", next := 368007, root := ~, start := 3679\ 96, stop := 368006 ), rec( content := " or a positive integer.\n If ", coun\ t := [ 8, 1, 2, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "size", count := [ 8, 1, 2, 21\ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 2\ 1 ], mathmode := "Text", name := "A", next := 368053, root := ~, start := 3680\ 42, stop := 368052 ), rec( content := " is a positive integer then ", count :=\ [ 8, 1, 2, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "CliquesFinder", count := [ 8,\ 1, 2, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8\ , 1, 2, 21 ], mathmode := "Text", name := "C", next := 368101, root := ~, star\ t := 368081, stop := 368100 ), rec( content := " will\n only search for\ cliques that contain precisely ", count := [ 8, 1, 2, 21 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec\ ( content := "size", count := [ 8, 1, 2, 21 ], mathmode := "Text", name := "PC\ DATA", root := ~ ) ], count := [ 8, 1, 2, 21 ], mathmode := "Text", name := "A\ ", next := 368173, root := ~, start := 368162, stop := 368172 ), rec( content \ := " vertices.\n If ", count := [ 8, 1, 2, 21 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "size", count := [ 8, 1, 2, 21 ], mathmode := "Text", name := "PCDATA", \ root := ~ ) ], count := [ 8, 1, 2, 21 ], mathmode := "Text", name := "A", next\ := 368206, root := ~, start := 368195, stop := 368205 ), rec( content := " is\ ", count := [ 8, 1, 2, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "fail", count := [ 8, 1, 2, 21\ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 2\ 1 ], mathmode := "Text", name := "K", next := 368221, root := ~, start := 3682\ 10, stop := 368220 ), rec( content := " then cliques of any size may be found.\ \n ", count := [ 8, 1, 2, 21 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 8, 1, 2, 21 ], name := "Item", next := 368274, root := ~, start := 367\ 957, stop := 368273 ), rec( attributes := rec( ), content := [ rec( attribute\ s := rec( ), content := [ rec( content := "reps", count := [ 8, 1, 2, 22 ], m\ athmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 22 ], math\ mode := "Text", name := "A", next := 368299, root := ~, start := 368288, stop \ := 368298 ) ], count := [ 8, 1, 2, 22 ], name := "Mark", next := 368306, root := ~, start := 368\ 282, stop := 368305 ), rec( attributes := rec( ), content := [ rec( content :\ = "\n This argument should be ", count := [ 8, 1, 2, 23 ], mathmode := \ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ \ rec( content := "true", count := [ 8, 1, 2, 23 ], mathmode := "Text", name := \ "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 23 ], mathmode := "Text", name :=\ "K", next := 368363, root := ~, start := 368352, stop := 368362 ), rec( conte\ nt := " or ", count := [ 8, 1, 2, 23 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "false", cou\ nt := [ 8, 1, 2, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 8, 1, 2, 23 ], mathmode := "Text", name := "K", next := 368379, root :=\ ~, start := 368367, stop := 368378 ), rec( content := ".", count := [ 8, 1, 2\ , 23 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\ c( ), content := 0, count := [ 8, 1, 2, 24 ], mathmode := "Text", name := "P" , next\ := 368384, root := ~, start := 368380, stop := 368383 ), rec( content := "\n\ \n If ", count := [ 8, 1, 2, 24 ], mathmode := "Text", name := "PCDATA" , root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "reps", coun\ t := [ 8, 1, 2, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 8, 1, 2, 24 ], mathmode := "Text", name := "A", next := 368408, root :=\ ~, start := 368397, stop := 368407 ), rec( content := " is ", count := [ 8, 1\ , 2, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes \ := rec( ), content := [ rec( content := "true", count := [ 8, 1, 2, 24 ], mat\ hmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 24 ], math\ mode := "Text", name := "K", next := 368423, root := ~, start := 368412, stop \ := 368422 ), rec( content := " then the arguments ", count := [ 8, 1, 2, 24 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "include", count := [ 8, 1, 2, 24 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 24 ], mathmode := "Te\ xt", name := "A", next := 368457, root := ~, start := 368443, stop := 368456 ) , rec( cont\ ent := " and\n ", count := [ 8, 1, 2, 24 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content \ := "exclude", count := [ 8, 1, 2, 24 ], mathmode := "Text", name := "PCDATA", \ root := ~ ) ], count := [ 8, 1, 2, 24 ], mathmode := "Text", name := "A", next\ := 368484, root := ~, start := 368470, stop := 368483 ), rec( content := " ar\ e each required to be invariant under the action of\n ", count := [ 8, \ 1, 2, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes\ := rec( ), content := [ rec( content := "G", count := [ 8, 1, 2, 24 ], mathm\ ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 24 ], math\ mode := "Text", name := "C", next := 368555, root := ~, start := 368547, stop \ := 368554 ), rec( content := " on sets of vertices. In this case, ", count :=\ [ 8, 1, 2, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "CliquesFinder", count := [ 8,\ 1, 2, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8\ , 1, 2, 24 ], mathmode := "Text", name := "C", next := 368612, root := ~, star\ t := 368592, stop := 368611 ), rec( content := " will\n find representa\ tives of the orbits of the desired cliques under the\n action of ", coun\ t := [ 8, 1, 2, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "G", count := [ 8, 1, 2, 24 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 24 ] , math\ mode := "Text", name := "C", next := 368720, root := ~, start := 368712, stop \ := 368719 ), rec( content := ", ", count := [ 8, 1, 2, 24 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec\ ( content := "although representatives may be returned that\n are in \ the same orbit", count := [ 8, 1, 2, 24 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 8, 1, 2, 24 ], mathmode := "Text", name := "E", next\ := 368806, root := ~, start := 368722, stop := 368805 ), rec( content := ".\n\ If ", count := [ 8, 1, 2, 24 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "reps", coun\ t := [ 8, 1, 2, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 8, 1, 2, 24 ], mathmode := "Text", name := "A", next := 368830, root :=\ ~, start := 368819, stop := 368829 ), rec( content := " is false then ", coun\ t := [ 8, 1, 2, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "CliquesFinder", count := [ 8,\ 1, 2, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8\ , 1, 2, 24 ], mathmode := "Text", name := "C", next := 368865, root := ~, star\ t := 368845, stop := 368864 ), rec( content := " will not take this into\n \ consideration.", count := [ 8, 1, 2, 24 ], mathmode := "Text", name := "PC\ DATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 1,\ 2, 25 ], mathmode := "Text", name := "P", next := 368916, root := ~, start :=\ 368912, stop := 368915 ), rec( content := "\n\n For a digraph such tha\ t ", count := [ 8, 1, 2, 25 ], mathmode := "Text", name := "PCDATA", root := ~\ ), rec( attributes := rec( ), content := [ rec( content := "G", count := [ 8\ , 1, 2, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ \ 8, 1, 2, 25 ], mathmode := "Text", name := "C", next := 368958, root := ~, star\ t := 368950, stop := 368957 ), rec( content := " is non-trivial, the search fo\ r\n clique representatives can be much more efficient than the search f\ or\n all cliques.\n ", count := [ 8, 1, 2, 25 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 23 ], name := "Item", next := 3691\ 02, root := ~, start := 368313, stop := 369101 ) ], count := [ 8, 1, 2, 5 ], mathmode := "Text", name := "List", next := 369114, root := ~, start := 365568, stop := 369113 ), rec( content := "\n\n \ This function uses a version of the Bron-Kerbosch algorithm.\n ", count := [ 8, 1, 2, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CompleteDigraph(5);\n\n\ gap> user_param := [];;\ngap> f := function(a, b) # Calculate size of clique\ \n> AddSet(user_param, Size(b));\n> end;;\ngap> CliquesFinder(D, f, user_par\ am, infinity, [], [], false, fail,\n> true);\n[ 1, 2, 3, 4, 5\ ]\ngap> CliquesFinder(D, fail, [], 5, [2, 4], [3], false, fail, false);\n[ [ \ 2, 4 ], [ 1, 2, 4 ], [ 2, 4, 5 ], [ 1, 2, 4, 5 ] ]\ngap> CliquesFinder(D, fail\ , [], 2, [2, 4], [3], false, fail, false);\n[ [ 2, 4 ], [ 1, 2, 4 ] ]\ngap> Cl\ iquesFinder(D, fail, [], infinity, [], [], true, 5, false);\n[ [ 1, 2, 3, 4, 5\ ] ]\ngap> CliquesFinder(D, fail, [], infinity, [1, 3], [], false, 3, false);\ \n[ [ 1, 2, 3 ], [ 1, 3, 4 ], [ 1, 3, 5 ] ]\ngap> CliquesFinder(D, fail, [], i\ nfinity, [1, 3], [], true, 3, false);\n[ ]\ngap> D := CompleteDigraph(IsMutab\ leDigraph, 5);\n\ngap> user_param :\ = [];;\ngap> f := function(a, b) # Calculate size of clique\n> AddSet(user_\ param, Size(b));\n> end;;\ngap> CliquesFinder(D, f, user_param, infinity, [], \ [], false, fail,\n> true);\n[ 1, 2, 3, 4, 5 ]\ngap> CliquesFi\ nder(D, fail, [], 5, [2, 4], [3], false, fail, false);\n[ [ 2, 4 ], [ 1, 2, 4 \ ], [ 2, 4, 5 ], [ 1, 2, 4, 5 ] ]\ngap> CliquesFinder(D, fail, [], 2, [2, 4], [\ 3], false, fail, false);\n[ [ 2, 4 ], [ 1, 2, 4 ] ]\ngap> CliquesFinder(D, fai\ l, [], infinity, [], [], true, 5, false);\n[ [ 1, 2, 3, 4, 5 ] ]\ngap> Cliques\ Finder(D, fail, [], infinity, [1, 3], [], false, 3, false);\n[ [ 1, 2, 3 ], [ \ 1, 3, 4 ], [ 1, 3, 5 ] ]\ngap> CliquesFinder(D, fail, [], infinity, [1, 3], []\ , true, 3, false);\n[ ]", count := [ 8, 1, 2, 28 ], name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 28 ], mathmode := "Text", name := "Example", next := 370839, root := ~, start := 369185, stop := 370838 ), rec( content := "\n ", count := [ 8, 1, 2, 29 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 3 ], mathmode := "Text", name := "Description", next := 370856, root := ~, start := 365049, stop := 370855 ) ], count := [ 8, 1, 2, 1 ], mathmode := "Text", name := "ManSection", next := 370870, root := ~, start := 364872, stop := 370869 ), rec( content := "\n\n ", count := [ 8, 1, 2, 29 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph[, includ\ e[, exclude[, size]]]", Name := "DigraphClique" ), content := 0, count := [ 8, 1, 3, 2 ], mathmode := "Text", name := "Func", next := 370963, root := ~, start := 370891, stop := 370962 ), rec( attributes := rec( Arg := "digraph[, includ\ e[, exclude[,\n size]]]", Name := "DigraphMaximalClique" ), content := 0, count := [ 8, 1, 3, 4 ], mathmode := "Text", name := "Func", next := 371049, root := ~, start := 370966, stop := 371048 ), rec( attributes := rec( ), content := [ rec( content := "An immuta\ ble list of positive integers, or ", count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "K", next := 371115, root := ~, start := 371104, stop := 371114 ), rec( content := ".", count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "Returns", next := 371126, root := ~, start := 371052, stop := 371125 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "A", next := 371164, root := ~, start := 371150, stop := 371163 ), rec( content := " is a di\ graph, then these functions returns a clique\n of ", count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "A", next := 371238, root := ~, start := 371224, stop := 371237 ), rec( content := " if one \ exists that satisfies the arguments, else it\n returns ", count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "K", next := 371314, root := ~, start := 371303, stop := 371313 ), rec( content := ". A cli\ que is defined by the set of vertices that it\n contains; see ", count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "IsCliqu\ e" ), content := 0, count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "Ref", next := 371408, root := ~, start := 371386, stop := 371407 ), rec( content := " and ", count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "IsMaxim\ alClique" ), content := 0, count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "Ref", next := 371442, root := ~, start := 371413, stop := 371441 ), rec( content := ".", count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "P", next := 371447, root := ~, start := 371443, stop := 371446 ), rec( content := "\n\n \ The optional arguments ", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nclude", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "A", next := 371490, root := ~, start := 371476, stop := 371489 ), rec( content := " and ", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ xclude", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "A", next := 371509, root := ~, start := 371495, stop := 371508 ), rec( content := " must ea\ ch be a\n (possibly empty) duplicate-free list of vertices of ", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "A", next := 371595, root := ~, start := 371581, stop := 371594 ), rec( content := ", and\n \ the optional argument ", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ize", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "A", next := 371638, root := ~, start := 371627, stop := 371637 ), rec( content := " must be\ a positive integer. By default,\n ", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nclude", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "A", next := 371698, root := ~, start := 371684, stop := 371697 ), rec( content := " and ", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ xclude", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "A", next := 371717, root := ~, start := 371703, stop := 371716 ), rec( content := " are emp\ ty. These functions will search for\n a clique of ", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "A", next := 371791, root := ~, start := 371777, stop := 371790 ), rec( content := " that in\ cludes the vertices of ", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nclude", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "A", next := 371836, root := ~, start := 371822, stop := 371835 ), rec( content := "\n bu\ t does not include any vertices in ", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ xclude", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "A", next := 371892, root := ~, start := 371878, stop := 371891 ), rec( content := "; if the\ argument\n ", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ize", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "A", next := 371925, root := ~, start := 371914, stop := 371924 ), rec( content := " is supp\ lied, then additionally the clique will be required to\n contain precisely \ ", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ize", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "A", next := 372021, root := ~, start := 372010, stop := 372020 ), rec( content := " vertice\ s.", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 1, 3, 7 ], mathmode := "Text", name := "P", next := 372035, root := ~, start := 372031, stop := 372034 ), rec( content := "\n\n \ If ", count := [ 8, 1, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nclude", count := [ 8, 1, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 7 ], mathmode := "Text", name := "A", next := 372058, root := ~, start := 372044, stop := 372057 ), rec( content := " is not \ a clique, then these functions return ", count := [ 8, 1, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 8, 1, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 7 ], mathmode := "Text", name := "K", next := 372115, root := ~, start := 372104, stop := 372114 ), rec( content := ".\n O\ therwise, the functions behave in the following way, depending on the\n num\ ber of arguments:\n\n ", count := [ 8, 1, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "One or two arguments", count := [ 8, 1\ , 3, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 8 ], name := "Mar\ k", next := 372268, root := ~, start := 372235, stop := 372267 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n If one or two arguments are\ supplied, then ", count := [ 8, 1, 3, 9 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Dig\ raphClique", count := [ 8, 1, 3, 9 ], mathmode := "Text", name := "PCDATA", ro\ ot := ~ ) ], count := [ 8, 1, 3, 9 ], mathmode := "Text", name := "C", next :=\ 372353, root := ~, start := 372333, stop := 372352 ), rec( content := " and\n\ ", count := [ 8, 1, 3, 9 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "DigraphMaxi\ malClique", count := [ 8, 1, 3, 9 ], mathmode := "Text", name := "PCDATA", roo\ t := ~ ) ], count := [ 8, 1, 3, 9 ], mathmode := "Text", name := "C", next := \ 372393, root := ~, start := 372366, stop := 372392 ), rec( content := " greedi\ ly enlarge the clique ", count := [ 8, 1, 3, 9 ], mathmode := "Text", name := \ "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content :\ = "include", count := [ 8, 1, 3, 9 ], mathmode := "Text", name := "PCDATA", ro\ ot := ~ ) ], count := [ 8, 1, 3, 9 ], mathmode := "Text", name := "A", next :=\ 372436, root := ~, start := 372422, stop := 372435 ), rec( content := "\n \ until it can not continue. The result is guaranteed to be a maximal\n \ clique. This may or may not return an answer more quickly than using\n \ ", count := [ 8, 1, 3, 9 ], mathmode := "Text", name := "PCDATA", root := \ ~ ), rec( attributes := rec( Func := "DigraphMaximalCliques" ), content := 0, coun\ t := [ 8, 1, 3, 9 ], mathmode := "Text", name := "Ref", next := 372634, root :\ = ~, start := 372599, stop := 372633 ), rec( content := ". with a limit of 1.\ \n ", count := [ 8, 1, 3, 9 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 8, 1, 3, 9 ], name := "Item", next := 372669, root := ~, start := 372\ 275, stop := 372668 ), rec( attributes := rec( ), content := [ rec( content :\ = "Three arguments", count := [ 8, 1, 3, 10 ], mathmode := "Text", name := "PC\ DATA", root := ~ ) ], count := [ 8, 1, 3, 10 ], name := "Mark", next := 372704 , root := ~, start := 372\ 676, stop := 372703 ), rec( attributes := rec( ), content := [ rec( content :\ = "\n If three arguments are supplied, then ", count := [ 8, 1, 3, 11 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "DigraphClique", count := [ 8, 1, 3, 11 ], mathmode :\ = "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 11 ], mathmode \ := "Text", name := "C", next := 372784, root := ~, start := 372764, stop := 37\ 2783 ), rec( content := " greedily\n enlarges the clique ", count := [ \ 8, 1, 3, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\ tes := rec( ), content := [ rec( content := "include", count := [ 8, 1, 3, 11\ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 1\ 1 ], mathmode := "Text", name := "A", next := 372836, root := ~, start := 3728\ 22, stop := 372835 ), rec( content := " until it can not continue, although\n \ this clique may not be maximal.", count := [ 8, 1, 3, 11 ], mathmode :=\ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content :=\ 0, count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "P", next := 372916, root\ := ~, start := 372912, stop := 372915 ), rec( content := "\n\n Given t\ hree arguments, ", count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Di\ graphMaximalClique", count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "PC\ DATA", root := ~ ) ], count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "C\ ", next := 372976, root := ~, start := 372949, stop := 372975 ), rec( content \ := " returns the maximal\n clique returned by ", count := [ 8, 1, 3, 12\ ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(\ ), content := [ rec( content := "DigraphMaximalCliques(", count := [ 8, 1, 3\ , 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, \ 3, 12 ], mathmode := "Text", name := "C", next := 373053, root := ~, start := \ 373024, stop := 373052 ), rec( attributes := rec( ), content := [ rec( conten\ t := "digraph", count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "PCDATA"\ , root := ~ ) ], count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "A", next\ := 373067, root := ~, start := 373053, stop := 373066 ), rec( attributes := re\ c( ), content := [ rec( content := ",\n ", count := [ 8, 1, 3, 12 ], m\ athmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 12 ], math\ mode := "Text", name := "C", next := 373084, root := ~, start := 373067, stop \ := 373083 ), rec( attributes := rec( ), content := [ rec( content := "include\ ", count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "PCDATA", root := ~ )\ ], count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "A", next := 373098, root\ := ~, start := 373084, stop := 373097 ), rec( attributes := rec( ), content \ := [ rec( content := ", ", count := [ 8, 1, 3, 12 ], mathmode := "Text", name \ := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 12 ], mathmode := "Text", name\ := "C", next := 373107, root := ~, start := 373098, stop := 373106 ), rec( attr\ ibutes := rec( ), content := [ rec( content := "exclude", count := [ 8, 1, 3,\ 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3\ , 12 ], mathmode := "Text", name := "A", next := 373121, root := ~, start := 3\ 73107, stop := 373120 ), rec( attributes := rec( ), content := [ rec( content\ := ", 1)", count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "PCDATA", ro\ ot := ~ ) ], count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "C", next :\ = 373132, root := ~, start := 373121, stop := 373131 ), rec( content := " if o\ ne exists,\n else ", count := [ 8, 1, 3, 12 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "fail", count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "PCDATA", \ root := ~ ) ], count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "K", next\ := 373172, root := ~, start := 373161, stop := 373171 ), rec( content := ".\n\ ", count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "PCDATA", root \ := ~ ) ], count := [ 8, 1, 3, 11 ], name := "Item", next := 373187, root := ~, start := 372\ 711, stop := 373186 ), rec( attributes := rec( ), content := [ rec( content :\ = "Four arguments", count := [ 8, 1, 3, 13 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 8, 1, 3, 13 ], name := "Mark", next := 373221, root := ~, start := 373\ 194, stop := 373220 ), rec( attributes := rec( ), content := [ rec( content :\ = "\n If four arguments are supplied, then ", count := [ 8, 1, 3, 14 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "DigraphClique", count := [ 8, 1, 3, 14 ], mathmode :\ = "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 14 ], mathmode \ := "Text", name := "C", next := 373300, root := ~, start := 373280, stop := 37\ 3299 ), rec( content := " returns the\n clique returned by ", count := [ \ 8, 1, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\ tes := rec( ), content := [ rec( content := "DigraphCliques(", count := [ 8, \ 1, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8,\ 1, 3, 14 ], mathmode := "Text", name := "C", next := 373362, root := ~, start\ := 373340, stop := 373361 ), rec( attributes := rec( ), content := [ rec( co\ ntent := "digraph", count := [ 8, 1, 3, 14 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 8, 1, 3, 14 ], mathmode := "Text", name := "A" , next\ := 373376, root := ~, start := 373362, stop := 373375 ), rec( attributes := re\ c( ), content := [ rec( content := ",\n ", count := [ 8, 1, 3, 14 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 14 ] , math\ mode := "Text", name := "C", next := 373395, root := ~, start := 373376, stop \ := 373394 ), rec( attributes := rec( ), content := [ rec( content := "include\ ", count := [ 8, 1, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ )\ ], count := [ 8, 1, 3, 14 ], mathmode := "Text", name := "A", next := 373409, root\ := ~, start := 373395, stop := 373408 ), rec( attributes := rec( ), content \ := [ rec( content := ", ", count := [ 8, 1, 3, 14 ], mathmode := "Text", name \ := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 14 ], mathmode := "Text", name\ := "C", next := 373418, root := ~, start := 373409, stop := 373417 ), rec( attr\ ibutes := rec( ), content := [ rec( content := "exclude", count := [ 8, 1, 3,\ 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3\ , 14 ], mathmode := "Text", name := "A", next := 373432, root := ~, start := 3\ 73418, stop := 373431 ), rec( attributes := rec( ), content := [ rec( content\ := ", 1,\n ", count := [ 8, 1, 3, 14 ], mathmode := "Text", name := "P\ CDATA", root := ~ ) ], count := [ 8, 1, 3, 14 ], mathmode := "Text", name := "\ C", next := 373452, root := ~, start := 373432, stop := 373451 ), rec( attribu\ tes := rec( ), content := [ rec( content := "size", count := [ 8, 1, 3, 14 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 14 ] , math\ mode := "Text", name := "A", next := 373463, root := ~, start := 373452, stop \ := 373462 ), rec( attributes := rec( ), content := [ rec( content := ")", cou\ nt := [ 8, 1, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 8, 1, 3, 14 ], mathmode := "Text", name := "C", next := 373471, root :=\ ~, start := 373463, stop := 373470 ), rec( content := " if one exists, else " , coun\ t := [ 8, 1, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "fail", count := [ 8, 1, 3, 14\ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 1\ 4 ], mathmode := "Text", name := "K", next := 373503, root := ~, start := 3734\ 92, stop := 373502 ), rec( content := ". This clique may\n not be maxim\ al.", count := [ 8, 1, 3, 14 ], mathmode := "Text", name := "PCDATA", root := \ ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 1, 3, 15 ], mathm\ ode := "Text", name := "P", next := 373548, root := ~, start := 373544, stop :\ = 373547 ), rec( content := " Given four arguments, ", count := [ 8, 1, 3, 15 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "DigraphMaximalClique", count := [ 8, 1, 3, 15 ], mat\ hmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 15 ], math\ mode := "Text", name := "C", next := 373598, root := ~, start := 373571, stop \ := 373597 ), rec( content := "\n returns the maximal clique returned by\ \n ", count := [ 8, 1, 3, 15 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "DigraphMaxi\ malCliques(", count := [ 8, 1, 3, 15 ], mathmode := "Text", name := "PCDATA", \ root := ~ ) ], count := [ 8, 1, 3, 15 ], mathmode := "Text", name := "C", next\ := 373683, root := ~, start := 373654, stop := 373682 ), rec( attributes := re\ c( ), content := [ rec( content := "digraph", count := [ 8, 1, 3, 15 ], mathm\ ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 15 ], math\ mode := "Text", name := "A", next := 373697, root := ~, start := 373683, stop \ := 373696 ), rec( attributes := rec( ), content := [ rec( content := ", ", co\ unt := [ 8, 1, 3, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 8, 1, 3, 15 ], mathmode := "Text", name := "C", next := 373706, root :=\ ~, start := 373697, stop := 373705 ), rec( attributes := rec( ), content := [ \ rec( content := "include", count := [ 8, 1, 3, 15 ], mathmode := "Text", name \ := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 15 ], mathmode := "Text", name\ := "A", next := 373720, root := ~, start := 373706, stop := 373719 ), rec( attr\ ibutes := rec( ), content := [ rec( content := ",\n ", count := [ 8, 1\ , 3, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, \ 1, 3, 15 ], mathmode := "Text", name := "C", next := 373737, root := ~, start \ := 373720, stop := 373736 ), rec( attributes := rec( ), content := [ rec( con\ tent := "exclude", count := [ 8, 1, 3, 15 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 8, 1, 3, 15 ], mathmode := "Text", name := "A", next\ := 373751, root := ~, start := 373737, stop := 373750 ), rec( attributes := re\ c( ), content := [ rec( content := ", 1, ", count := [ 8, 1, 3, 15 ], mathmod\ e := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 15 ], mathmo\ de := "Text", name := "C", next := 373763, root := ~, start := 373751, stop :=\ 373762 ), rec( attributes := rec( ), content := [ rec( content := "size", co\ unt := [ 8, 1, 3, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 8, 1, 3, 15 ], mathmode := "Text", name := "A", next := 373774, root :=\ ~, start := 373763, stop := 373773 ), rec( attributes := rec( ), content := [ \ rec( content := ")", count := [ 8, 1, 3, 15 ], mathmode := "Text", name := "PC\ DATA", root := ~ ) ], count := [ 8, 1, 3, 15 ], mathmode := "Text", name := "C\ ", next := 373782, root := ~, start := 373774, stop := 373781 ), rec( content \ := " if one exists, else\n ", count := [ 8, 1, 3, 15 ], mathmode := "Te\ xt", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ r\ ec( content := "fail", count := [ 8, 1, 3, 15 ], mathmode := "Text", name := "\ PCDATA", root := ~ ) ], count := [ 8, 1, 3, 15 ], mathmode := "Text", name := \ "K", next := 373822, root := ~, start := 373811, stop := 373821 ), rec( conten\ t := ".\n ", count := [ 8, 1, 3, 15 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 8, 1, 3, 14 ], name := "Item", next := 373837, root := ~, start := 373\ 228, stop := 373836 ) ], count := [ 8, 1, 3, 8 ], mathmode := "Text", name := "List", next := 373849, root := ~, start := 372222, stop := 373848 ), rec( content := "\n\n \ ", count := [ 8, 1, 3, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([[2, 3, 4], [1, 3], [1, 2], [1, 5], []]);\n\ngap> IsSymmetricDigraph(D);\nfalse\ngap> Digraph\ Clique(D);\n[ 5 ]\ngap> DigraphMaximalClique(D);\n[ 5 ]\ngap> DigraphClique(D,\ [1, 2]);\n[ 1, 2, 3 ]\ngap> DigraphMaximalClique(D, [1, 3]);\n[ 1, 3, 2 ]\nga\ p> DigraphClique(D, [1], [2]);\n[ 1, 4 ]\ngap> DigraphMaximalClique(D, [1], [3\ , 4]);\nfail\ngap> DigraphClique(D, [1, 5]);\nfail\ngap> DigraphClique(D, [], \ [], 2);\n[ 1, 2 ]\ngap> D := Digraph(IsMutableDigraph,\n> [[2,\ 3, 4], [1, 3], [1, 2], [1, 5], []]);\n\ngap> IsSymmetricDigraph(D);\nfalse\ngap> DigraphClique(D);\n[ 5 ]", count := [ 8, 1, 3, 18 ], name := "PCD\ ATA", root := ~ ) ], count := [ 8, 1, 3, 18 ], mathmode := "Text", name := "Example", next := 374554, root := ~, start := 373855, stop := 374553 ), rec( content := "\n ", count := [ 8, 1, 3, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "Description", next := 374571, root := ~, start := 371129, stop := 374570 ) ], count := [ 8, 1, 3, 1 ], mathmode := "Text", name := "ManSection", next := 374585, root := ~, start := 370876, stop := 374584 ), rec( content := "\n\n ", count := [ 8, 1, 3, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph[, includ\ e[, exclude[, limit[, size]]]]", Name := "DigraphMaximalCliques" ), content := 0, count := [ 8, 1, 4, 2 ], mathmode := "Text", name := "Func", next := 374695, root := ~, start := 374606, stop := 374694 ), rec( attributes := rec( Arg := "digraph[, includ\ e[, exclude[,\n limit[, size]]]]", Name := "DigraphMaximalCliquesReps" ), content := 0, count := [ 8, 1, 4, 4 ], mathmode := "Text", name := "Func", next := 374795, root := ~, start := 374698, stop := 374794 ), rec( attributes := rec( Arg := "digraph[, includ\ e[, exclude[,\n limit[, size]]]]", Name := "DigraphCliques" ), content := 0, count := [ 8, 1, 4, 6 ], mathmode := "Text", name := "Func", next := 374884, root := ~, start := 374798, stop := 374883 ), rec( attributes := rec( Arg := "digraph[, includ\ e[,\n exclude[, limit[, size]]]]", Name := "DigraphCliquesReps" ), content := 0, count := [ 8, 1, 4, 8 ], mathmode := "Text", name := "Func", next := 374977, root := ~, start := 374887, stop := 374976 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphMaximalC\ liquesAttr" ), content := 0, count := [ 8, 1, 4, 10 ], mathmode := "Text", name := "Attr", next := 375034, root := ~, start := 374980, stop := 375033 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphMaximalC\ liquesRepsAttr" ), content := 0, count := [ 8, 1, 4, 12 ], mathmode := "Text", name := "Attr", next := 375095, root := ~, start := 375037, stop := 375094 ), rec( attributes := rec( ), content := [ rec( content := "An immuta\ ble list of lists of positive integers.", count := [ 8, 1, 4, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 13 ], mathmode := "Text", name := "Returns", next := 375165, root := ~, start := 375098, stop := 375164 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 8, 1, 4, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 1, 4, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 13 ], mathmode := "Text", name := "A", next := 375203, root := ~, start := 375189, stop := 375202 ), rec( content := " is digr\ aph, then these functions and attributes use ", count := [ 8, 1, 4, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Cliques\ Finder" ), content := 0, count := [ 8, 1, 4, 13 ], mathmode := "Text", name := "Ref", next := 375289, root := ~, start := 375256, stop := 375288 ), rec( content := " to retu\ rn cliques of ", count := [ 8, 1, 4, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 1, 4, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 13 ], mathmode := "Text", name := "A", next := 375325, root := ~, start := 375311, stop := 375324 ), rec( content := ". A\n \ clique is defined by the set of vertices that it contains; see ", count := [ 8, 1, 4, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "IsCliqu\ e" ), content := 0, count := [ 8, 1, 4, 13 ], mathmode := "Text", name := "Ref", next := 375424, root := ~, start := 375396, stop := 375423 ), rec( content := " and ", count := [ 8, 1, 4, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "IsMaxim\ alClique" ), content := 0, count := [ 8, 1, 4, 13 ], mathmode := "Text", name := "Ref", next := 375458, root := ~, start := 375429, stop := 375457 ), rec( content := ".", count := [ 8, 1, 4, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "P", next := 375463, root := ~, start := 375459, stop := 375462 ), rec( content := "\n\n \ The optional arguments ", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nclude", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "A", next := 375506, root := ~, start := 375492, stop := 375505 ), rec( content := " and ", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ xclude", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "A", next := 375525, root := ~, start := 375511, stop := 375524 ), rec( content := " must ea\ ch be a\n (possibly empty) list of vertices of ", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "A", next := 375596, root := ~, start := 375582, stop := 375595 ), rec( content := ", the op\ tional argument\n ", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ imit", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "A", next := 375636, root := ~, start := 375624, stop := 375635 ), rec( content := " must be\ either a positive integer or ", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nfinity", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "C", next := 375689, root := ~, start := 375674, stop := 375688 ), rec( content := ", and th\ e\n optional argument ", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ize", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "A", next := 375732, root := ~, start := 375721, stop := 375731 ), rec( content := " must be\ a positive integer. If not\n specified, then ", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nclude", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "A", next := 375803, root := ~, start := 375789, stop := 375802 ), rec( content := " and ", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ xclude", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "A", next := 375822, root := ~, start := 375808, stop := 375821 ), rec( content := " are cho\ sen to be empty\n lists, and ", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ imit", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "A", next := 375873, root := ~, start := 375861, stop := 375872 ), rec( content := " is set \ to ", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nfinity", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "C", next := 375899, root := ~, start := 375884, stop := 375898 ), rec( content := ". ", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "P", next := 375905, root := ~, start := 375901, stop := 375904 ), rec( content := "\n\n \ The functions will return as many suitable cliques as possible, up to the\n \ number ", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ imit", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "A", next := 376008, root := ~, start := 375996, stop := 376007 ), rec( content := ". These\ functions will find cliques that contain all\n of the vertices of ", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nclude", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "A", next := 376099, root := ~, start := 376085, stop := 376098 ), rec( content := " but do \ not contain any of the\n vertices of ", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ xclude", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "A", next := 376160, root := ~, start := 376146, stop := 376159 ), rec( content := ". The a\ rgument ", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ize", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "A", next := 376187, root := ~, start := 376176, stop := 376186 ), rec( content := " restric\ ts the search\n to those cliques that contain precisely ", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ize", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "A", next := 376264, root := ~, start := 376253, stop := 376263 ), rec( content := " vertice\ s.\n If the function or attribute has ", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "M\ aximal", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "C", next := 376326, root := ~, start := 376312, stop := 376325 ), rec( content := " in its \ name, then only\n maximal cliques will be returned; otherwise non-maximal c\ liques may be\n returned. ", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 1, 4, 16 ], mathmode := "Text", name := "P", next := 376443, root := ~, start := 376439, stop := 376442 ), rec( content := "\n\n \ Let ", count := [ 8, 1, 4, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 8, 1, 4, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 16 ], mathmode := "Text", name := "C", next := 376461, root := ~, start := 376453, stop := 376460 ), rec( content := " denote \ the automorphism group of maximal symmetric subdigraph\n of ", count := [ 8, 1, 4, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 1, 4, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 16 ], mathmode := "Text", name := "A", next := 376545, root := ~, start := 376531, stop := 376544 ), rec( content := " without\ loops (see ", count := [ 8, 1, 4, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Automor\ phismGroup", Label := "for a digraph" ), content := 0, count := [ 8, 1, 4, 16 ], mathmode := "Text", name := "Ref", next := 376624, root := ~, start := 376565, stop := 376623 ), rec( content := " and ", count := [ 8, 1, 4, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Maximal\ SymmetricSubdigraphWithoutLoops" ), content := 0, count := [ 8, 1, 4, 16 ], mathmode := "Text", name := "Ref", next := 376687, root := ~, start := 376629, stop := 376686 ), rec( content := ").\n\n \ ", count := [ 8, 1, 4, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "Distinct cliques", count := [ 8, 1, 4,\ 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 17 ], name := "Mar\ k", next := 376737, root := ~, start := 376708, stop := 376736 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n ", count := [ 8, 1, 4, 18 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "DigraphMaximalCliques", count := [ 8, 1, 4, 18 ], ma\ thmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 18 ], math\ mode := "Text", name := "C", next := 376787, root := ~, start := 376759, stop \ := 376786 ), rec( content := " and ", count := [ 8, 1, 4, 18 ], mathmode := "T\ ext", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ \ rec( content := "DigraphCliques", count := [ 8, 1, 4, 18 ], mathmode := "Text"\ , name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 18 ], mathmode := "Text\ ", name := "C", next := 376813, root := ~, start := 376792, stop := 376812 ), rec( cont\ ent := " each return a\n duplicate-free list of at most ", count := [ 8\ , 1, 4, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribut\ es := rec( ), content := [ rec( content := "limit", count := [ 8, 1, 4, 18 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 18 ] , math\ mode := "Text", name := "A", next := 376879, root := ~, start := 376867, stop \ := 376878 ), rec( content := " cliques of ", count := [ 8, 1, 4, 18 ], mathmod\ e := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), conten\ t := [ rec( content := "digraph", count := [ 8, 1, 4, 18 ], mathmode := "Text"\ , name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 18 ], mathmode := "Text\ ", name := "A", next := 376905, root := ~, start := 376891, stop := 376904 ), rec( cont\ ent := "\n that satisfy the arguments.", count := [ 8, 1, 4, 18 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := 0, count := [ 8, 1, 4, 19 ], mathmode := "Text", name := "P", next := 3\ 76945, root := ~, start := 376941, stop := 376944 ), rec( content := "\n\n \ The computation may be significantly faster if ", count := [ 8, 1, 4, 19 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "include", count := [ 8, 1, 4, 19 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 19 ], mathmode := "Te\ xt", name := "A", next := 377016, root := ~, start := 377002, stop := 377015 ) , rec( cont\ ent := " and\n ", count := [ 8, 1, 4, 19 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content \ := "exclude", count := [ 8, 1, 4, 19 ], mathmode := "Text", name := "PCDATA", \ root := ~ ) ], count := [ 8, 1, 4, 19 ], mathmode := "Text", name := "A", next\ := 377043, root := ~, start := 377029, stop := 377042 ), rec( content := " ar\ e invariant under the action of ", count := [ 8, 1, 4, 19 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec\ ( content := "G", count := [ 8, 1, 4, 19 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 8, 1, 4, 19 ], mathmode := "Text", name := "C", next\ := 377086, root := ~, start := 377078, stop := 377085 ), rec( content := "\n \ on sets of vertices.\n ", count := [ 8, 1, 4, 19 ], mathmode := "T\ ext", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 18 ], name := "Item\ ", next := 377129, root := ~, start := 376744, stop := 377128 ), rec( attributes :\ = rec( ), content := [ rec( content := "Orbit representatives of cliques", coun\ t := [ 8, 1, 4, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 20 ], name := "Mar\ k", next := 377182, root := ~, start := 377137, stop := 377181 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n To use ", count := [ 8, 1, \ 4, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :=\ rec( ), content := [ rec( content := "DigraphMaximalCliquesReps", count := [\ 8, 1, 4, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ \ 8, 1, 4, 21 ], mathmode := "Text", name := "C", next := 377243, root := ~, star\ t := 377211, stop := 377242 ), rec( content := " or ", count := [ 8, 1, 4, 21 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "DigraphCliquesReps", count := [ 8, 1, 4, 21 ], mathm\ ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 21 ], math\ mode := "Text", name := "C", next := 377272, root := ~, start := 377247, stop \ := 377271 ), rec( content := ",\n the arguments ", count := [ 8, 1, 4, \ 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\ c( ), content := [ rec( content := "include", count := [ 8, 1, 4, 21 ], mathm\ ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 21 ], math\ mode := "Text", name := "A", next := 377310, root := ~, start := 377296, stop \ := 377309 ), rec( content := " and ", count := [ 8, 1, 4, 21 ], mathmode := "T\ ext", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ \ rec( content := "exclude", count := [ 8, 1, 4, 21 ], mathmode := "Text", name \ := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 21 ], mathmode := "Text", name\ := "A", next := 377329, root := ~, start := 377315, stop := 377328 ), rec( cont\ ent := " must each be invariant\n under the action of ", count := [ 8, \ 1, 4, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes\ := rec( ), content := [ rec( content := "G", count := [ 8, 1, 4, 21 ], mathm\ ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 21 ], math\ mode := "Text", name := "C", next := 377389, root := ~, start := 377381, stop \ := 377388 ), rec( content := " on sets of vertices.", count := [ 8, 1, 4, 21 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := 0, count := [ 8, 1, 4, 22 ], mathmode := "Text", name := "P", next := 3\ 77414, root := ~, start := 377410, stop := 377413 ), rec( content := "\n\n \ If this is the case, then ", count := [ 8, 1, 4, 22 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "DigraphMaximalCliquesReps", count := [ 8, 1, 4, 22 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 22 ], mathmode := "Tex\ t", name := "C", next := 377482, root := ~, start := 377450, stop := 377481 ), rec( cont\ ent := " and\n ", count := [ 8, 1, 4, 22 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content \ := "DigraphCliquesReps", count := [ 8, 1, 4, 22 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 22 ], mathmode := "Text", name :\ = "C", next := 377520, root := ~, start := 377495, stop := 377519 ), rec( cont\ ent := " each return a duplicate-free list of at most\n ", count := [ 8\ , 1, 4, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribut\ es := rec( ), content := [ rec( content := "limit", count := [ 8, 1, 4, 22 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 22 ] , math\ mode := "Text", name := "A", next := 377586, root := ~, start := 377574, stop \ := 377585 ), rec( content := " orbits representatives (under the action of ", coun\ t := [ 8, 1, 4, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "G", count := [ 8, 1, 4, 22 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 22 ] , math\ mode := "Text", name := "C", next := 377639, root := ~, start := 377631, stop \ := 377638 ), rec( content := " on\n sets vertices) of cliques of ", coun\ t := [ 8, 1, 4, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "digraph", count := [ 8, 1, 4,\ 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4\ , 22 ], mathmode := "Text", name := "A", next := 377694, root := ~, start := 3\ 77680, stop := 377693 ), rec( content := " that satisfy the\n arguments\ .", count := [ 8, 1, 4, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := 0, count := [ 8, 1, 4, 23 ], mathmode := "Text", name\ := "P", next := 377734, root := ~, start := 377730, stop := 377733 ), rec( cont\ ent := "\n\n The representatives are not guaranteed to be in distinct o\ rbits.\n However, if fewer than ", count := [ 8, 1, 4, 23 ], mathmode :\ = "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content :\ = [ rec( content := "lim", count := [ 8, 1, 4, 23 ], mathmode := "Text", name \ := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 23 ], mathmode := "Text", name\ := "A", next := 377850, root := ~, start := 377840, stop := 377849 ), rec( cont\ ent := " results are returned, then there\n will be at least one repres\ entative from each orbit of maximal cliques.\n ", count := [ 8, 1, 4, 23 ] , math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 21 ], name := "Ite\ m", next := 377977, root := ~, start := 377189, stop := 377976 ) ], count := [ 8, 1, 4, 17 ], mathmode := "Text", name := "List", next := 377989, root := ~, start := 376695, stop := 377988 ), rec( content := "\n\n \ ", count := [ 8, 1, 4, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := Digraph([\n> [2, 3], [1, 3], [1, 2, 4], [3, 5, 6], [4, 6], [4, 5]])\ ;\n\ngap> IsSymmetricDigraph(D);\ \ntrue\ngap> G := AutomorphismGroup(D);\nGroup([ (5,6), (1,2), (1,5)(2,6)(3,4)\ ])\ngap> DigraphMaximalCliques(D);\n[ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 3, 4 ] ]\ng\ ap> DigraphMaximalCliquesReps(D);\n[ [ 1, 2, 3 ], [ 3, 4 ] ]\ngap> Orbit(G, [1\ , 2, 3], OnSets);\n[ [ 1, 2, 3 ], [ 4, 5, 6 ] ]\ngap> Orbit(G, [3, 4], OnSets)\ ;\n[ [ 3, 4 ] ]\ngap> DigraphMaximalCliquesReps(D, [3, 4], [], 1);\n[ [ 3, 4 ]\ ]\ngap> DigraphMaximalCliques(D, [1, 2], [5, 6], 1, 2);\n[ ]\ngap> DigraphCl\ iques(D, [1], [5, 6], infinity, 2);\n[ [ 1, 2 ], [ 1, 3 ] ]\ngap> D := Digraph\ (IsMutableDigraph, [\n> [2, 3], [1, 3], [1, 2, 4], [3, 5, 6], [4, 6], [4, 5]])\ ;\n\ngap> IsSymmetricDigraph(D);\nt\ rue\ngap> G := AutomorphismGroup(D);\nGroup([ (5,6), (1,2), (1,5)(2,6)(3,4) ])\ \ngap> DigraphMaximalCliques(D);\n[ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 3, 4 ] ]", count := [ 8, 1, 4, 26 ], name := "PCD\ ATA", root := ~ ) ], count := [ 8, 1, 4, 26 ], mathmode := "Text", name := "Example", next := 379004, root := ~, start := 377995, stop := 379003 ), rec( content := "\n ", count := [ 8, 1, 4, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 13 ], mathmode := "Text", name := "Description", next := 379021, root := ~, start := 375168, stop := 379020 ) ], count := [ 8, 1, 4, 1 ], mathmode := "Text", name := "ManSection", next := 379035, root := ~, start := 374591, stop := 379034 ), rec( content := "\n\n ", count := [ 8, 1, 4, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "CliqueNumber" ) , content := 0, count := [ 8, 1, 5, 2 ], mathmode := "Text", name := "Attr", next := 379097, root := ~, start := 379056, stop := 379096 ), rec( attributes := rec( ), content := [ rec( content := "A non-neg\ ative integer.", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "Returns", next := 379142, root := ~, start := 379100, stop := 379141 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "A", next := 379180, root := ~, start := 379166, stop := 379179 ), rec( content := " is a di\ graph, then ", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "C\ liqueNumber(", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := "digraph", count := [ 8, 1, 5, 3 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 5, 3 ], mathmode := \ "Text", name := "A", next := 379230, root := ~, start := 379216, stop := 37922\ 9 ), rec( content := ")", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "C", next := 379235, root := ~, start := 379200, stop := 379234 ), rec( content := "\n re\ turns the largest integer ", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "C", next := 379276, root := ~, start := 379268, stop := 379275 ), rec( content := " such th\ at ", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "A", next := 379301, root := ~, start := 379287, stop := 379300 ), rec( content := " contain\ s a\n clique with ", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "C", next := 379337, root := ~, start := 379329, stop := 379336 ), rec( content := " vertice\ s as an induced subdigraph.\n ", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 1, 5, 4 ], mathmode := "Text", name := "P", next := 379381, root := ~, start := 379377, stop := 379380 ), rec( content := "\n\n \ A ", count := [ 8, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ lique", count := [ 8, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 5, 4 ], mathmode := "Text", name := "E", next := 379402, root := ~, start := 379389, stop := 379401 ), rec( content := " of a di\ graph is a set of mutually adjacent vertices of the\n digraph. Loops and mu\ ltiple edges are ignored for the purpose of\n determining the clique number\ of a digraph. \n ", count := [ 8, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CompleteDigraph(4);;\ngap> CliqueNumber(D);\n4\ngap> D := Digraph([\ [1, 2, 4, 4], [1, 3, 4], [2, 1], [1, 2]]);\n\ngap> CliqueNumber(D);\n3\ngap> D := CompleteDigraph(IsMutabl\ eDigraph, 4);;\ngap> CliqueNumber(D);\n4", count := [ 8, 1, 5, 5 ], name := "PCD\ ATA", root := ~ ) ], count := [ 8, 1, 5, 5 ], mathmode := "Text", name := "Example", next := 379880, root := ~, start := 379584, stop := 379879 ), rec( content := "\n", count := [ 8, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "Description", next := 379895, root := ~, start := 379145, stop := 379894 ) ], count := [ 8, 1, 5, 1 ], mathmode := "Text", name := "ManSection", next := 379909, root := ~, start := 379041, stop := 379908 ), rec( content := "\n\n ", count := [ 8, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 0, 1 ], mathmode := "Text", name := "Section", next := 379923, root := ~, start := 363411, stop := 379922 ) , rec( content := "\n\n ", count := [ 8, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Finding independe\ nt sets", count := [ 8, 2, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 0, 2 ], mathmode := "Text", name := "Heading", next := 379979, root := ~, start := 379936, stop := 379978 ), rec( content := "\n ", count := [ 8, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, l", Name := "IsIndependentSe\ t" ), content := 0, count := [ 8, 2, 1, 2 ], mathmode := "Text", name := "Oper", next := 380047, root := ~, start := 379999, stop := 380046 ), rec( attributes := rec( Arg := "digraph, l", Name := "IsMaximalIndepe\ ndentSet" ), content := 0, count := [ 8, 2, 1, 4 ], mathmode := "Text", name := "Oper", next := 380105, root := ~, start := 380050, stop := 380104 ), rec( attributes := rec( ), content := [ rec( attributes := rec( ) , content := [ rec( content := "t\ rue", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "K", next := 380128, root := ~, start := 380117, stop := 380127 ), rec( content := " or ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "K", next := 380144, root := ~, start := 380132, stop := 380143 ), rec( content := ".", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "Returns", next := 380155, root := ~, start := 380108, stop := 380154 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "A", next := 380193, root := ~, start := 380179, stop := 380192 ), rec( content := " is a di\ graph and ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "A", next := 380219, root := ~, start := 380211, stop := 380218 ), rec( content := " is a du\ plicate-free list of\n vertices of ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "A", next := 380278, root := ~, start := 380264, stop := 380277 ), rec( content := ", then\n\ ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sIndependentSet(", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "C", next := 380313, root := ~, start := 380289, stop := 380312 ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "A", next := 380327, root := ~, start := 380313, stop := 380326 ), rec( attributes := rec( ), content := [ rec( content := ",\ ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "C", next := 380335, root := ~, start := 380327, stop := 380334 ), rec( attributes := rec( ), content := [ rec( content := "l\ ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "A", next := 380343, root := ~, start := 380335, stop := 380342 ), rec( attributes := rec( ), content := [ rec( content := ")\ ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "C", next := 380351, root := ~, start := 380343, stop := 380350 ), rec( content := " returns\ \n ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "K", next := 380375, root := ~, start := 380364, stop := 380374 ), rec( content := " if ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "A", next := 380387, root := ~, start := 380379, stop := 380386 ), rec( content := " is an " , count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ndependent set", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "E", next := 380416, root := ~, start := 380394, stop := 380415 ), rec( content := " of ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "A", next := 380434, root := ~, start := 380420, stop := 380433 ), rec( content := " and\n \ ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "K", next := 380455, root := ~, start := 380443, stop := 380454 ), rec( content := " if it i\ s not. Similarly,\n ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ sMaximalIndependentSet(", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "C", next := 380517, root := ~, start := 380486, stop := 380516 ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "A", next := 380531, root := ~, start := 380517, stop := 380530 ), rec( attributes := rec( ), content := [ rec( content := ",\ ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "C", next := 380539, root := ~, start := 380531, stop := 380538 ), rec( attributes := rec( ), content := [ rec( content := "l\ ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "A", next := 380547, root := ~, start := 380539, stop := 380546 ), rec( attributes := rec( ), content := [ rec( content := ")\ ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "C", next := 380555, root := ~, start := 380547, stop := 380554 ), rec( content := "\n re\ turns ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "t\ rue", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "K", next := 380579, root := ~, start := 380568, stop := 380578 ), rec( content := " if ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "A", next := 380591, root := ~, start := 380583, stop := 380590 ), rec( content := " is a ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ aximal independent set", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "E", next := 380627, root := ~, start := 380597, stop := 380626 ), rec( content := " of\n \ ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "A", next := 380649, root := ~, start := 380635, stop := 380648 ), rec( content := " and ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ alse", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "K", next := 380666, root := ~, start := 380654, stop := 380665 ), rec( content := " if it i\ s not. ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 2, 1, 6 ], mathmode := "Text", name := "P", next := 380686, root := ~, start := 380682, stop := 380685 ), rec( content := "\n\n \ An ", count := [ 8, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ ndependent set", count := [ 8, 2, 1, 6 ], mathmode := "Text", name := "PCDATA" , root := ~ ) ], count := [ 8, 2, 1, 6 ], mathmode := "Text", name := "E", next := 380717, root := ~, start := 380695, stop := 380716 ), rec( content := " of a di\ graph is a set of mutually non-adjacent\n vertices of the digraph. A ", count := [ 8, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ aximal independent set", count := [ 8, 2, 1, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 8, 2, 1, 6 ], mathmode := "Text", name := "E", next := 380826, root := ~, start := 380796, stop := 380825 ), rec( content := " is an i\ ndependent\n set that is not properly contained in another independent set.\ An\n independent set is permitted, but not required, to contain vertices a\ t\n which there is a loop.\n ", count := [ 8, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CycleDigraph(4);;\ngap> IsIndependentSet(D, [1]);\ntrue\ngap> IsMax\ imalIndependentSet(D, [1]);\nfalse\ngap> IsIndependentSet(D, [1, 4, 3]);\nfals\ e\ngap> IsIndependentSet(D, [2, 4]);\ntrue\ngap> IsMaximalIndependentSet(D, [2\ , 4]);\ntrue\ngap> D := CycleDigraph(IsMutableDigraph, 4);;\ngap> IsIndependen\ tSet(D, [1]);\ntrue", count := [ 8, 2, 1, 7 ], name := "PCDATA", root := ~ ) ] , count := [ 8, 2, 1, 7 ], mathmode := "Text", name := "Example", next := 381370, root := ~, start := 381021, stop := 381369 ), rec( content := "\n ", count := [ 8, 2, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "Description", next := 381387, root := ~, start := 380158, stop := 381386 ) ], count := [ 8, 2, 1, 1 ], mathmode := "Text", name := "ManSection", next := 381401, root := ~, start := 379984, stop := 381400 ), rec( content := "\n\n ", count := [ 8, 2, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph[, includ\ e[, exclude[, size]]]", Name := "DigraphIndependentSet" ), content := 0, count := [ 8, 2, 2, 2 ], mathmode := "Text", name := "Func", next := 381506, root := ~, start := 381422, stop := 381505 ), rec( attributes := rec( Arg := "digraph[, includ\ e[, exclude[,\n size]]]", Name := "DigraphMaximalIndependentSet" ), content := 0, count := [ 8, 2, 2, 4 ], mathmode := "Text", name := "Func", next := 381604, root := ~, start := 381509, stop := 381603 ), rec( attributes := rec( ), content := [ rec( content := "An immuta\ ble list of positive integers, or ", count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "K", next := 381670, root := ~, start := 381659, stop := 381669 ), rec( content := ".", count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "Returns", next := 381681, root := ~, start := 381607, stop := 381680 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "A", next := 381719, root := ~, start := 381705, stop := 381718 ), rec( content := " is a di\ graph, then these functions returns an independent\n set of ", count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "A", next := 381803, root := ~, start := 381789, stop := 381802 ), rec( content := " if one \ exists that satisfies the arguments, else it\n returns ", count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "K", next := 381879, root := ~, start := 381868, stop := 381878 ), rec( content := ". An in\ dependent set is defined by the set of vertices\n that it contains; see ", count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "IsIndep\ endentSet" ), content := 0, count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "Ref", next := 381991, root := ~, start := 381961, stop := 381990 ), rec( content := " and ", count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "IsMaxim\ alIndependentSet" ), content := 0, count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "Ref", next := 382039, root := ~, start := 381996, stop := 382038 ), rec( content := ".", count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "P", next := 382044, root := ~, start := 382040, stop := 382043 ), rec( content := "\n\n \ The optional arguments ", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nclude", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "A", next := 382087, root := ~, start := 382073, stop := 382086 ), rec( content := " and ", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ xclude", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "A", next := 382106, root := ~, start := 382092, stop := 382105 ), rec( content := " must ea\ ch be a\n (possibly empty) duplicate-free list of vertices of ", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "A", next := 382192, root := ~, start := 382178, stop := 382191 ), rec( content := ", and th\ e\n optional argument ", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ize", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "A", next := 382235, root := ~, start := 382224, stop := 382234 ), rec( content := " must be\ a positive integer. By default,\n ", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nclude", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "A", next := 382295, root := ~, start := 382281, stop := 382294 ), rec( content := " and ", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ xclude", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "A", next := 382314, root := ~, start := 382300, stop := 382313 ), rec( content := " are emp\ ty. These functions will search\n for an independent set of ", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "A", next := 382398, root := ~, start := 382384, stop := 382397 ), rec( content := " that in\ cludes the vertices of\n ", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nclude", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "A", next := 382447, root := ~, start := 382433, stop := 382446 ), rec( content := " but doe\ s not include any vertices in ", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ xclude", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "A", next := 382499, root := ~, start := 382485, stop := 382498 ), rec( content := ";\n i\ f the argument ", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ize", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "A", next := 382532, root := ~, start := 382521, stop := 382531 ), rec( content := " is supp\ lied, then additionally the independent\n set will be required to contain p\ recisely ", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ize", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "A", next := 382637, root := ~, start := 382626, stop := 382636 ), rec( content := " vertice\ s.", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 2, 2, 7 ], mathmode := "Text", name := "P", next := 382651, root := ~, start := 382647, stop := 382650 ), rec( content := "\n\n \ If ", count := [ 8, 2, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nclude", count := [ 8, 2, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 7 ], mathmode := "Text", name := "A", next := 382674, root := ~, start := 382660, stop := 382673 ), rec( content := " is not \ an independent set, then these functions return\n ", count := [ 8, 2, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ail", count := [ 8, 2, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 7 ], mathmode := "Text", name := "K", next := 382745, root := ~, start := 382734, stop := 382744 ), rec( content := ". Other\ wise, the functions behave in the following way,\n depending on the number \ of arguments:\n\n ", count := [ 8, 2, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "One or two arguments", count := [ 8, 2\ , 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 8 ], name := "Mar\ k", next := 382895, root := ~, start := 382862, stop := 382894 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n If one or two arguments are\ supplied, then ", count := [ 8, 2, 2, 9 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Dig\ raphIndependentSet", count := [ 8, 2, 2, 9 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 8, 2, 2, 9 ], mathmode := "Text", name := "C", next\ := 382988, root := ~, start := 382960, stop := 382987 ), rec( content := "\n \ and ", count := [ 8, 2, 2, 9 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "DigraphMaxi\ malIndependentSet", count := [ 8, 2, 2, 9 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 8, 2, 2, 9 ], mathmode := "Text", name := "C", next\ := 383036, root := ~, start := 383001, stop := 383035 ), rec( content := " gr\ eedily enlarge the\n independent set ", count := [ 8, 2, 2, 9 ], mathmo\ de := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), conte\ nt := [ rec( content := "include", count := [ 8, 2, 2, 9 ], mathmode := "Text"\ , name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 9 ], mathmode := "Text" , name\ := "A", next := 383096, root := ~, start := 383082, stop := 383095 ), rec( cont\ ent := " until it can not continue. The result\n is guaranteed to be a\ maximal independent set. This may or may not\n return an answer more q\ uickly than using ", count := [ 8, 2, 2, 9 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ), rec( attributes := rec( Func := "DigraphMaximalIndependentS\ ets" ), content := 0, count := [ 8, 2, 2, 9 ], mathmode := "Text", name := "Re\ f", next := 383313, root := ~, start := 383260, stop := 383312 ), rec( content\ := ". with a limit of 1.\n ", count := [ 8, 2, 2, 9 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 9 ], name := "Item", next := 3833\ 48, root := ~, start := 382902, stop := 383347 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "Three arguments", count := [ 8, 2, 2, 10 ], mathmode := "Text", name :\ = "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 10 ], name := "Mark", next := 3833\ 83, root := ~, start := 383355, stop := 383382 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "\n If three arguments are supplied, then ", count := [ 8, 2, 2,\ 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\ c( ), content := [ rec( content := "DigraphIndependentSet", count := [ 8, 2, \ 2, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2,\ 2, 11 ], mathmode := "Text", name := "C", next := 383471, root := ~, start :=\ 383443, stop := 383470 ), rec( content := "\n greedily enlarges the in\ dependent set ", count := [ 8, 2, 2, 11 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "incl\ ude", count := [ 8, 2, 2, 11 ], mathmode := "Text", name := "PCDATA", root := \ ~ ) ], count := [ 8, 2, 2, 11 ], mathmode := "Text", name := "A", next := 3835\ 32, root := ~, start := 383518, stop := 383531 ), rec( content := " until it c\ an not\n continue, although this independent set may not be maximal.", coun\ t := [ 8, 2, 2, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := 0, count := [ 8, 2, 2, 12 ], mathmode := "Text", name\ := "P", next := 383621, root := ~, start := 383617, stop := 383620 ), rec( cont\ ent := "\n\n Given three arguments, ", count := [ 8, 2, 2, 12 ], mathmo\ de := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), conte\ nt := [ rec( content := "DigraphMaximalIndependentSet", count := [ 8, 2, 2, 12\ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 1\ 2 ], mathmode := "Text", name := "C", next := 383689, root := ~, start := 3836\ 54, stop := 383688 ), rec( content := " returns the\n maximal independe\ nt set returned by\n ", count := [ 8, 2, 2, 12 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "DigraphMaximalIndependentSets(", count := [ 8, 2, 2, 12 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 12 ], mathmode :=\ "Text", name := "C", next := 383791, root := ~, start := 383754, stop := 3837\ 90 ), rec( attributes := rec( ), content := [ rec( content := "digraph", coun\ t := [ 8, 2, 2, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 8, 2, 2, 12 ], mathmode := "Text", name := "A", next := 383805, root :=\ ~, start := 383791, stop := 383804 ), rec( attributes := rec( ), content := [ \ rec( content := ",\n ", count := [ 8, 2, 2, 12 ], mathmode := "Text", n\ ame := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 12 ], mathmode := "Text", name\ := "C", next := 383822, root := ~, start := 383805, stop := 383821 ), rec( attr\ ibutes := rec( ), content := [ rec( content := "include", count := [ 8, 2, 2,\ 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2\ , 12 ], mathmode := "Text", name := "A", next := 383836, root := ~, start := 3\ 83822, stop := 383835 ), rec( attributes := rec( ), content := [ rec( content\ := ", ", count := [ 8, 2, 2, 12 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 8, 2, 2, 12 ], mathmode := "Text", name := "C", next := \ 383845, root := ~, start := 383836, stop := 383844 ), rec( attributes := rec( \ ), content := [ rec( content := "exclude", count := [ 8, 2, 2, 12 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 12 ], mathmod\ e := "Text", name := "A", next := 383859, root := ~, start := 383845, stop := \ 383858 ), rec( attributes := rec( ), content := [ rec( content := ", 1)", cou\ nt := [ 8, 2, 2, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 8, 2, 2, 12 ], mathmode := "Text", name := "C", next := 383870, root :=\ ~, start := 383859, stop := 383869 ), rec( content := " if one exists,\n \ else ", count := [ 8, 2, 2, 12 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "fail", coun\ t := [ 8, 2, 2, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 8, 2, 2, 12 ], mathmode := "Text", name := "K", next := 383910, root :=\ ~, start := 383899, stop := 383909 ), rec( content := ".\n ", count := [ \ 8, 2, 2, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 11 ], name := "Ite\ m", next := 383925, root := ~, start := 383390, stop := 383924 ), rec( attributes :\ = rec( ), content := [ rec( content := "Four arguments", count := [ 8, 2, 2, \ 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 13 ], name := "Mar\ k", next := 383959, root := ~, start := 383932, stop := 383958 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n If four arguments are suppl\ ied, then ", count := [ 8, 2, 2, 14 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "DigraphInde\ pendentSet", count := [ 8, 2, 2, 14 ], mathmode := "Text", name := "PCDATA", r\ oot := ~ ) ], count := [ 8, 2, 2, 14 ], mathmode := "Text", name := "C", next \ := 384046, root := ~, start := 384018, stop := 384045 ), rec( content := "\n \ returns the independent set returned by\n ", count := [ 8, 2, 2, \ 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\ c( ), content := [ rec( content := "DigraphIndependentSets(", count := [ 8, 2\ , 2, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, \ 2, 2, 14 ], mathmode := "Text", name := "C", next := 384133, root := ~, start \ := 384103, stop := 384132 ), rec( attributes := rec( ), content := [ rec( con\ tent := "digraph", count := [ 8, 2, 2, 14 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 8, 2, 2, 14 ], mathmode := "Text", name := "A", next\ := 384147, root := ~, start := 384133, stop := 384146 ), rec( attributes := re\ c( ), content := [ rec( content := ", ", count := [ 8, 2, 2, 14 ], mathmode :\ = "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 14 ], mathmode \ := "Text", name := "C", next := 384156, root := ~, start := 384147, stop := 38\ 4155 ), rec( attributes := rec( ), content := [ rec( content := "include", co\ unt := [ 8, 2, 2, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 8, 2, 2, 14 ], mathmode := "Text", name := "A", next := 384170, root :=\ ~, start := 384156, stop := 384169 ), rec( attributes := rec( ), content := [ \ rec( content := ",\n ", count := [ 8, 2, 2, 14 ], mathmode := "Text", n\ ame := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 14 ], mathmode := "Text", name\ := "C", next := 384187, root := ~, start := 384170, stop := 384186 ), rec( attr\ ibutes := rec( ), content := [ rec( content := "exclude", count := [ 8, 2, 2,\ 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2\ , 14 ], mathmode := "Text", name := "A", next := 384201, root := ~, start := 3\ 84187, stop := 384200 ), rec( attributes := rec( ), content := [ rec( content\ := ", 1, ", count := [ 8, 2, 2, 14 ], mathmode := "Text", name := "PCDATA", r\ oot := ~ ) ], count := [ 8, 2, 2, 14 ], mathmode := "Text", name := "C", next \ := 384213, root := ~, start := 384201, stop := 384212 ), rec( attributes := re\ c( ), content := [ rec( content := "size", count := [ 8, 2, 2, 14 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 14 ], mathmod\ e := "Text", name := "A", next := 384224, root := ~, start := 384213, stop := \ 384223 ), rec( attributes := rec( ), content := [ rec( content := ")", count \ := [ 8, 2, 2, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count\ := [ 8, 2, 2, 14 ], mathmode := "Text", name := "C", next := 384232, root := \ ~, start := 384224, stop := 384231 ), rec( content := " if one exists, else\n \ ", count := [ 8, 2, 2, 14 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "fail", coun\ t := [ 8, 2, 2, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 8, 2, 2, 14 ], mathmode := "Text", name := "K", next := 384272, root :=\ ~, start := 384261, stop := 384271 ), rec( content := ". This independent set\ may not be maximal.", count := [ 8, 2, 2, 14 ], mathmode := "Text", name := "\ PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, \ 2, 2, 15 ], mathmode := "Text", name := "P", next := 384318, root := ~, start \ := 384314, stop := 384317 ), rec( content := " Given four\n arguments, \ ", count := [ 8, 2, 2, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attr\ ibutes := rec( ), content := [ rec( content := "DigraphMaximalIndependentSet"\ , count := [ 8, 2, 2, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ] , coun\ t := [ 8, 2, 2, 15 ], mathmode := "Text", name := "C", next := 384384, root :=\ ~, start := 384349, stop := 384383 ), rec( content := " returns the maximal\n\ independent set returned by\n ", count := [ 8, 2, 2, 15 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "DigraphMaximalIndependentSets(", count := [ 8, 2, 2,\ 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2\ , 15 ], mathmode := "Text", name := "C", next := 384486, root := ~, start := 3\ 84449, stop := 384485 ), rec( attributes := rec( ), content := [ rec( content\ := "digraph", count := [ 8, 2, 2, 15 ], mathmode := "Text", name := "PCDATA",\ root := ~ ) ], count := [ 8, 2, 2, 15 ], mathmode := "Text", name := "A", next\ := 384500, root := ~, start := 384486, stop := 384499 ), rec( attributes := re\ c( ), content := [ rec( content := ",\n ", count := [ 8, 2, 2, 15 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 15 ] , math\ mode := "Text", name := "C", next := 384519, root := ~, start := 384500, stop \ := 384518 ), rec( attributes := rec( ), content := [ rec( content := "include\ ", count := [ 8, 2, 2, 15 ], mathmode := "Text", name := "PCDATA", root := ~ )\ ], count := [ 8, 2, 2, 15 ], mathmode := "Text", name := "A", next := 384533, root\ := ~, start := 384519, stop := 384532 ), rec( attributes := rec( ), content \ := [ rec( content := ", ", count := [ 8, 2, 2, 15 ], mathmode := "Text", name \ := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 15 ], mathmode := "Text", name\ := "C", next := 384542, root := ~, start := 384533, stop := 384541 ), rec( attr\ ibutes := rec( ), content := [ rec( content := "exclude", count := [ 8, 2, 2,\ 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2\ , 15 ], mathmode := "Text", name := "A", next := 384556, root := ~, start := 3\ 84542, stop := 384555 ), rec( attributes := rec( ), content := [ rec( content\ := ", 1,\n ", count := [ 8, 2, 2, 15 ], mathmode := "Text", name := "P\ CDATA", root := ~ ) ], count := [ 8, 2, 2, 15 ], mathmode := "Text", name := "\ C", next := 384576, root := ~, start := 384556, stop := 384575 ), rec( attribu\ tes := rec( ), content := [ rec( content := "size", count := [ 8, 2, 2, 15 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 15 ] , math\ mode := "Text", name := "A", next := 384587, root := ~, start := 384576, stop \ := 384586 ), rec( attributes := rec( ), content := [ rec( content := ")", cou\ nt := [ 8, 2, 2, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 8, 2, 2, 15 ], mathmode := "Text", name := "C", next := 384595, root :=\ ~, start := 384587, stop := 384594 ), rec( content := " if one exists, else " , coun\ t := [ 8, 2, 2, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "fail", count := [ 8, 2, 2, 15\ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 1\ 5 ], mathmode := "Text", name := "K", next := 384627, root := ~, start := 3846\ 16, stop := 384626 ), rec( content := ".\n ", count := [ 8, 2, 2, 15 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 14 ], name := "Ite\ m", next := 384642, root := ~, start := 383966, stop := 384641 ) ], count := [ 8, 2, 2, 8 ], mathmode := "Text", name := "List", next := 384654, root := ~, start := 382849, stop := 384653 ), rec( content := "\n ", count := [ 8, 2, 2, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := ChainDigraph(6);\n\ngap> D\ igraphIndependentSet(D);\n[ 6, 4, 2 ]\ngap> DigraphMaximalIndependentSet(D);\n\ [ 6, 4, 2 ]\ngap> DigraphIndependentSet(D, [2, 4]);\n[ 2, 4, 6 ]\ngap> Digraph\ MaximalIndependentSet(D, [1, 3]);\n[ 1, 3, 6 ]\ngap> DigraphIndependentSet(D, \ [2, 4], [6]);\n[ 2, 4 ]\ngap> DigraphMaximalIndependentSet(D, [2, 4], [6]);\nf\ ail\ngap> DigraphIndependentSet(D, [1], [], 2);\n[ 1, 3 ]\ngap> DigraphMaximal\ IndependentSet(D, [1], [], 2);\nfail\ngap> DigraphMaximalIndependentSet(D, [1]\ , [], 3);\n[ 1, 3, 5 ]\ngap> D := ChainDigraph(IsMutableDigraph, 6);\n\ngap> DigraphIndependentSet(D);\n[ 6, 4, 2 \ ]\ngap> DigraphMaximalIndependentSet(D);\n[ 6, 4, 2 ]\ngap> DigraphIndependent\ Set(D, [2, 4]);\n[ 2, 4, 6 ]\ngap> DigraphMaximalIndependentSet(D, [1, 3]);\n[\ 1, 3, 6 ]\ngap> DigraphIndependentSet(D, [2, 4], [6]);\n[ 2, 4 ]\ngap> Digrap\ hMaximalIndependentSet(D, [2, 4], [6]);\nfail\ngap> DigraphIndependentSet(D, [\ 1], [], 2);\n[ 1, 3 ]\ngap> DigraphMaximalIndependentSet(D, [1], [], 2);\nfail\ \ngap> DigraphMaximalIndependentSet(D, [1], [], 3);\n[ 1, 3, 5 ]", count := [ 8, 2, 2, 18 ], name := "PCD\ ATA", root := ~ ) ], count := [ 8, 2, 2, 18 ], mathmode := "Text", name := "Example", next := 385807, root := ~, start := 384659, stop := 385806 ), rec( content := "\n ", count := [ 8, 2, 2, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "Description", next := 385824, root := ~, start := 381684, stop := 385823 ) ], count := [ 8, 2, 2, 1 ], mathmode := "Text", name := "ManSection", next := 385838, root := ~, start := 381407, stop := 385837 ), rec( content := "\n\n ", count := [ 8, 2, 2, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph[, includ\ e[, exclude[,\n limit[, size]]]]", Name := "DigraphMaximalIndependentSets" ), content := 0, count := [ 8, 2, 3, 2 ], mathmode := "Text", name := "Func", next := 385960, root := ~, start := 385859, stop := 385959 ), rec( attributes := rec( Arg := "digraph[, includ\ e[,\n exclude[, limit[, size]]]]", Name := "DigraphMaximalIndependentSetsRe\ ps" ), content := 0, count := [ 8, 2, 3, 4 ], mathmode := "Text", name := "Func", next := 386068, root := ~, start := 385963, stop := 386067 ), rec( attributes := rec( Arg := "digraph[, includ\ e[,\n exclude[, limit[, size]]]]", Name := "DigraphIndependentSets" ), content := 0, count := [ 8, 2, 3, 6 ], mathmode := "Text", name := "Func", next := 386165, root := ~, start := 386071, stop := 386164 ), rec( attributes := rec( Arg := "digraph[, includ\ e[,\n exclude[, limit[, size]]]]", Name := "DigraphIndependentSetsReps" ), content := 0, count := [ 8, 2, 3, 8 ], mathmode := "Text", name := "Func", next := 386266, root := ~, start := 386168, stop := 386265 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphMaximalI\ ndependentSetsAttr" ), content := 0, count := [ 8, 2, 3, 10 ], mathmode := "Text", name := "Attr", next := 386331, root := ~, start := 386269, stop := 386330 ), rec( attributes := rec( Arg := "digraph", Name := "DigraphMaximalI\ ndependentSetsRepsAttr" ), content := 0, count := [ 8, 2, 3, 12 ], mathmode := "Text", name := "Attr", next := 386400, root := ~, start := 386334, stop := 386399 ), rec( attributes := rec( ), content := [ rec( content := "An immuta\ ble list of lists of positive integers.", count := [ 8, 2, 3, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 13 ], mathmode := "Text", name := "Returns", next := 386470, root := ~, start := 386403, stop := 386469 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 8, 2, 3, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 2, 3, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 13 ], mathmode := "Text", name := "A", next := 386508, root := ~, start := 386494, stop := 386507 ), rec( content := " is digr\ aph, then these functions and attributes use ", count := [ 8, 2, 3, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Cliques\ Finder" ), content := 0, count := [ 8, 2, 3, 13 ], mathmode := "Text", name := "Ref", next := 386594, root := ~, start := 386561, stop := 386593 ), rec( content := " to retu\ rn independent sets of ", count := [ 8, 2, 3, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 2, 3, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 13 ], mathmode := "Text", name := "A", next := 386639, root := ~, start := 386625, stop := 386638 ), rec( content := ". An\n \ independent set is defined by the set of vertices that it contains; see\n \ ", count := [ 8, 2, 3, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "IsMaxim\ alIndependentSet" ), content := 0, count := [ 8, 2, 3, 13 ], mathmode := "Text", name := "Ref", next := 386761, root := ~, start := 386724, stop := 386760 ), rec( content := " and ", count := [ 8, 2, 3, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "IsIndep\ endentSet" ), content := 0, count := [ 8, 2, 3, 13 ], mathmode := "Text", name := "Ref", next := 386802, root := ~, start := 386766, stop := 386801 ), rec( content := ".", count := [ 8, 2, 3, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "P", next := 386807, root := ~, start := 386803, stop := 386806 ), rec( content := "\n\n \ The optional arguments ", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nclude", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "A", next := 386850, root := ~, start := 386836, stop := 386849 ), rec( content := " and ", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ xclude", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "A", next := 386869, root := ~, start := 386855, stop := 386868 ), rec( content := " must ea\ ch be a\n (possibly empty) list of vertices of ", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "A", next := 386940, root := ~, start := 386926, stop := 386939 ), rec( content := ", the op\ tional argument\n ", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ imit", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "A", next := 386980, root := ~, start := 386968, stop := 386979 ), rec( content := " must be\ either a positive integer or ", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nfinity", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "C", next := 387033, root := ~, start := 387018, stop := 387032 ), rec( content := ", and th\ e\n optional argument ", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ize", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "A", next := 387076, root := ~, start := 387065, stop := 387075 ), rec( content := " must be\ a positive integer. If not\n specified, then ", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nclude", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "A", next := 387147, root := ~, start := 387133, stop := 387146 ), rec( content := " and ", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ xclude", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "A", next := 387166, root := ~, start := 387152, stop := 387165 ), rec( content := " are cho\ sen to be empty\n lists, and ", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ imit", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "A", next := 387217, root := ~, start := 387205, stop := 387216 ), rec( content := " is set \ to ", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nfinity", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "C", next := 387243, root := ~, start := 387228, stop := 387242 ), rec( content := ". ", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "P", next := 387249, root := ~, start := 387245, stop := 387248 ), rec( content := "\n\n \ The functions will return as many suitable independent sets as possible, up\n \ to the number ", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "l\ imit", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "A", next := 387361, root := ~, start := 387349, stop := 387360 ), rec( content := ". These\ functions will find independent sets\n that contain all of the vertices of\ ", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ nclude", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "A", next := 387461, root := ~, start := 387447, stop := 387460 ), rec( content := " but do \ not\n contain any of the vertices of ", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ xclude", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "A", next := 387522, root := ~, start := 387508, stop := 387521 ), rec( content := " The arg\ ument ", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ize", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "A", next := 387547, root := ~, start := 387536, stop := 387546 ), rec( content := "\n re\ stricts the search to those cliques that contain precisely ", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ ize", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "A", next := 387624, root := ~, start := 387613, stop := 387623 ), rec( content := "\n ve\ rtices. If the function or attribute has ", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "M\ aximal", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "C", next := 387687, root := ~, start := 387673, stop := 387686 ), rec( content := " in its \ name,\n then only maximal independent sets will be returned; otherwise non-\ maximal\n independent sets may be returned.\n ", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 2, 3, 16 ], mathmode := "Text", name := "P", next := 387826, root := ~, start := 387822, stop := 387825 ), rec( content := "\n\n \ Let ", count := [ 8, 2, 3, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ ", count := [ 8, 2, 3, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 16 ], mathmode := "Text", name := "C", next := 387844, root := ~, start := 387836, stop := 387843 ), rec( content := " denote \ the ", count := [ 8, 2, 3, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Automor\ phismGroup", Label := "for a digraph" ), content := 0, count := [ 8, 2, 3, 16 ], mathmode := "Text", name := "Ref", next := 387909, root := ~, start := 387856, stop := 387908 ), rec( content := "\n of\ the ", count := [ 8, 2, 3, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ SymmetricClosure" ), content := 0, count := [ 8, 2, 3, 16 ], mathmode := "Text", name := "Ref", next := 387958, root := ~, start := 387921, stop := 387957 ), rec( content := " of the \ digraph formed from\n ", count := [ 8, 2, 3, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 8, 2, 3, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 16 ], mathmode := "Text", name := "A", next := 388004, root := ~, start := 387990, stop := 388003 ), rec( content := " by remo\ ving loops and ignoring the multiplicity of edges.\n\n ", count := [ 8, 2, 3, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "Distinct independent sets", count := [ \ 8, 2, 3, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 17 ], name := "Mar\ k", next := 388119, root := ~, start := 388081, stop := 388118 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n ", count := [ 8, 2, 3, 18 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "DigraphMaximalIndependentSets", count := [ 8, 2, 3, \ 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3,\ 18 ], mathmode := "Text", name := "C", next := 388177, root := ~, start := 38\ 8141, stop := 388176 ), rec( content := " and ", count := [ 8, 2, 3, 18 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "DigraphIndependentSets", count := [ 8, 2, 3, 18 ], m\ athmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 18 ], math\ mode := "Text", name := "C", next := 388211, root := ~, start := 388182, stop \ := 388210 ), rec( content := "\n each return a duplicate-free list of a\ t most ", count := [ 8, 2, 3, 18 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "limit", cou\ nt := [ 8, 2, 3, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 8, 2, 3, 18 ], mathmode := "Text", name := "A", next := 388277, root :=\ ~, start := 388265, stop := 388276 ), rec( content := " independent\n \ sets of ", count := [ 8, 2, 3, 18 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "digraph", c\ ount := [ 8, 2, 3, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 8, 2, 3, 18 ], mathmode := "Text", name := "A", next := 388320, root :=\ ~, start := 388306, stop := 388319 ), rec( content := " that satisfy the argu\ ments.", count := [ 8, 2, 3, 18 ], mathmode := "Text", name := "PCDATA", root \ := ~ ), rec( attributes := rec( ), content := 0, count := [ 8, 2, 3, 19 ], math\ mode := "Text", name := "P", next := 388352, root := ~, start := 388348, stop \ := 388351 ), rec( content := "\n\n The computation may be significantly\ faster if ", count := [ 8, 2, 3, 19 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "include", c\ ount := [ 8, 2, 3, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 8, 2, 3, 19 ], mathmode := "Text", name := "A", next := 388423, root :=\ ~, start := 388409, stop := 388422 ), rec( content := " and\n ", count\ := [ 8, 2, 3, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "exclude", count := [ 8, 2, 3,\ 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3\ , 19 ], mathmode := "Text", name := "A", next := 388450, root := ~, start := 3\ 88436, stop := 388449 ), rec( content := " are invariant under the action of " , coun\ t := [ 8, 2, 3, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "G", count := [ 8, 2, 3, 19 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 19 ] , math\ mode := "Text", name := "C", next := 388493, root := ~, start := 388485, stop \ := 388492 ), rec( content := " on sets of\n vertices.\n ", count :\ = [ 8, 2, 3, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 18 ], name := "Ite\ m", next := 388536, root := ~, start := 388126, stop := 388535 ), rec( attributes :\ = rec( ), content := [ rec( content := "Representatives of distinct orbits of\ independent sets", count := [ 8, 2, 3, 20 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 8, 2, 3, 20 ], name := "Mark", next := 388611, root := ~, start := 388\ 544, stop := 388610 ), rec( attributes := rec( ), content := [ rec( content :\ = "\n To use ", count := [ 8, 2, 3, 21 ], mathmode := "Text", name := "\ PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content :=\ "DigraphMaximalIndependentSetsReps", count := [ 8, 2, 3, 21 ], mathmode := "T\ ext", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 21 ], mathmode := "\ Text", name := "C", next := 388680, root := ~, start := 388640, stop := 388679\ ), rec( content := " or\n ", count := [ 8, 2, 3, 21 ], mathmode := "Te\ xt", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ r\ ec( content := "DigraphIndependentSetsReps", count := [ 8, 2, 3, 21 ], mathmod\ e := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 21 ], mathmo\ de := "Text", name := "C", next := 388725, root := ~, start := 388692, stop :=\ 388724 ), rec( content := ", the arguments ", count := [ 8, 2, 3, 21 ], mathm\ ode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "include", count := [ 8, 2, 3, 21 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 21 ], mathmode := "Te\ xt", name := "A", next := 388755, root := ~, start := 388741, stop := 388754 ) , rec( cont\ ent := " and\n ", count := [ 8, 2, 3, 21 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content \ := "exclude", count := [ 8, 2, 3, 21 ], mathmode := "Text", name := "PCDATA", \ root := ~ ) ], count := [ 8, 2, 3, 21 ], mathmode := "Text", name := "A", next\ := 388782, root := ~, start := 388768, stop := 388781 ), rec( content := " mu\ st each be invariant under the action of ", count := [ 8, 2, 3, 21 ], mathmode\ := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content\ := [ rec( content := "G", count := [ 8, 2, 3, 21 ], mathmode := "Text", name \ := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 21 ], mathmode := "Text", name\ := "C", next := 388834, root := ~, start := 388826, stop := 388833 ), rec( cont\ ent := " on\n sets of vertices.", count := [ 8, 2, 3, 21 ], mathmode :=\ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content :=\ 0, count := [ 8, 2, 3, 22 ], mathmode := "Text", name := "P", next := 388867, root\ := ~, start := 388863, stop := 388866 ), rec( content := "\n\n If this\ is the case, then ", count := [ 8, 2, 3, 22 ], mathmode := "Text", name := "P\ CDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := \ "DigraphMaximalIndependentSetsReps", count := [ 8, 2, 3, 22 ], mathmode := "Te\ xt", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 22 ], mathmode := "T\ ext", name := "C", next := 388943, root := ~, start := 388903, stop := 388942 ), rec( cont\ ent := " and\n ", count := [ 8, 2, 3, 22 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content \ := "DigraphIndependentSetsReps", count := [ 8, 2, 3, 22 ], mathmode := "Text",\ name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 22 ], mathmode := "Text" , name\ := "C", next := 388989, root := ~, start := 388956, stop := 388988 ), rec( cont\ ent := " each return a list of\n at most ", count := [ 8, 2, 3, 22 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "limit", count := [ 8, 2, 3, 22 ], mathmode := "Text"\ , name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 22 ], mathmode := "Text\ ", name := "A", next := 389040, root := ~, start := 389028, stop := 389039 ), rec( cont\ ent := " orbits representatives (under the action of\n ", count := [ 8,\ 2, 3, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribute\ s := rec( ), content := [ rec( content := "G", count := [ 8, 2, 3, 22 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 22 ], math\ mode := "Text", name := "C", next := 389101, root := ~, start := 389093, stop \ := 389100 ), rec( content := " on sets of vertices) of independent sets of ", coun\ t := [ 8, 2, 3, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "digraph", count := [ 8, 2, 3,\ 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3\ , 22 ], mathmode := "Text", name := "A", next := 389160, root := ~, start := 3\ 89146, stop := 389159 ), rec( content := "\n that satisfy the arguments\ . ", count := [ 8, 2, 3, 22 ], mathmode := "Text", name := "PCDATA", root := ~\ ), rec( attributes := rec( ), content := 0, count := [ 8, 2, 3, 23 ], mathmo\ de := "Text", name := "P", next := 389201, root := ~, start := 389197, stop :=\ 389200 ), rec( content := "\n\n The representatives are not guaranteed\ to be in distinct orbits.\n However, if ", count := [ 8, 2, 3, 23 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "lim", count := [ 8, 2, 3, 23 ], mathmode := "Text", \ name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 23 ], mathmode := "Text", name\ := "A", next := 389306, root := ~, start := 389296, stop := 389305 ), rec( cont\ ent := " is not specified, or fewer than ", count := [ 8, 2, 3, 23 ], mathmode\ := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content\ := [ rec( content := "lim", count := [ 8, 2, 3, 23 ], mathmode := "Text", nam\ e := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 23 ], mathmode := "Text", name\ := "A", next := 389349, root := ~, start := 389339, stop := 389348 ), rec( cont\ ent := "\n results are returned, then there will be at least one repres\ entative\n from each orbit of maximal independent sets.\n ", count\ := [ 8, 2, 3, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 21 ], name := "Ite\ m", next := 389493, root := ~, start := 388618, stop := 389492 ) ], count := [ 8, 2, 3, 17 ], mathmode := "Text", name := "List", next := 389505, root := ~, start := 388068, stop := 389504 ), rec( content := "\n\n \ ", count := [ 8, 2, 3, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CycleDigraph(5);\n\ngap> D\ igraphMaximalIndependentSetsReps(D);\n[ [ 1, 3 ] ]\ngap> DigraphIndependentSet\ sReps(D);\n[ [ 1 ], [ 1, 3 ] ]\ngap> Set(DigraphMaximalIndependentSets(D));\n[\ [ 1, 3 ], [ 1, 4 ], [ 2, 4 ], [ 2, 5 ], [ 3, 5 ] ]\ngap> DigraphMaximalIndepe\ ndentSets(D, [1]);\n[ [ 1, 3 ], [ 1, 4 ] ]\ngap> DigraphIndependentSets(D, [],\ [4, 5]);\n[ [ 1 ], [ 2 ], [ 3 ], [ 1, 3 ] ]\ngap> DigraphIndependentSets(D, [\ ], [4, 5], 1, 2);\n[ [ 1, 3 ] ]\ngap> D := CycleDigraph(IsMutableDigraph, 5);\ \n\ngap> DigraphMaximalIndependentSe\ tsReps(D);\n[ [ 1, 3 ] ]\ngap> DigraphIndependentSetsReps(D);\n[ [ 1 ], [ 1, 3\ ] ]\ngap> Set(DigraphMaximalIndependentSets(D));\n[ [ 1, 3 ], [ 1, 4 ], [ 2, \ 4 ], [ 2, 5 ], [ 3, 5 ] ]\ngap> DigraphMaximalIndependentSets(D, [1]);\n[ [ 1,\ 3 ], [ 1, 4 ] ]\ngap> DigraphIndependentSets(D, [], [4, 5]);\n[ [ 1 ], [ 2 ],\ [ 3 ], [ 1, 3 ] ]\ngap> DigraphIndependentSets(D, [], [4, 5], 1, 2);\n[ [ 1, \ 3 ] ]", count := [ 8, 2, 3, 26 ], name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 26 ], mathmode := "Text", name := "Example", next := 390533, root := ~, start := 389511, stop := 390532 ), rec( content := "\n ", count := [ 8, 2, 3, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 13 ], mathmode := "Text", name := "Description", next := 390550, root := ~, start := 386473, stop := 390549 ) ], count := [ 8, 2, 3, 1 ], mathmode := "Text", name := "ManSection", next := 390564, root := ~, start := 385844, stop := 390563 ), rec( content := "\n\n ", count := [ 8, 2, 3, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 0, 1 ], mathmode := "Text", name := "Section", next := 390578, root := ~, start := 379927, stop := 390577 ) , rec( content := "\n", count := [ 8, 2, 3, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 0, 0, 1 ], mathmode := "Text", name := "Chapter", next := 390589, root := ~, start := 358650, stop := 390588 ), rec( content := "\n ", count := [ 8, 2, 3, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := " cliques ", count := [ 8, 2, 3, 27 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( content := "\n ", count := [ 8, 2, 3, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "Visualising and IO" ), content := [ rec( attributes := rec( ), content := [ rec( content := "Visualising and IO", count := [ 9, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 0, 0, 2 ], mathmode := "Text", name := "Heading", next := 390683, root := ~, start := 390646, stop := 390682 ) , rec( content := "\n\n ", count := [ 9, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Visualising a dig\ raph", count := [ 9, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 0, 2 ], mathmode := "Text", name := "Heading", next := 390736, root := ~, start := 390696, stop := 390735 ), rec( content := "\n ", count := [ 9, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "str, [opts]", Name := "Splash" ), content := 0, count := [ 9, 1, 1, 2 ], mathmode := "Text", name := "Func", next := 390799, root := ~, start := 390760, stop := 390798 ), rec( attributes := rec( ), content := [ rec( content := "Nothing." , count := [ 9, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 3 ], mathmode := "Text", name := "Returns", next := 390831, root := ~, start := 390804, stop := 390830 ), rec( attributes := rec( ), content := [ rec( content := "\n T\ his function attempts to convert the string ", count := [ 9, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ tr", count := [ 9, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 3 ], mathmode := "Text", name := "A", next := 390911, root := ~, start := 390901, stop := 390910 ), rec( content := " into a \ pdf\n document and open this document, i.e. to splash it all over your mo\ nitor.", count := [ 9, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "P", next := 391006, root := ~, start := 391002, stop := 391005 ), rec( content := "\n\n \ The string ", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ tr", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "A", next := 391035, root := ~, start := 391025, stop := 391034 ), rec( content := " must co\ rrespond to a valid ", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ ot", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "C", next := 391073, root := ~, start := 391063, stop := 391072 ), rec( content := " or\n \ ", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "L\ aTeX", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "C", next := 391095, root := ~, start := 391083, stop := 391094 ), rec( content := " text fi\ le and you must have have ", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ raphViz", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "C", next := 391144, root := ~, start := 391129, stop := 391143 ), rec( content := " and\n \ ", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "p\ dflatex", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "C", next := 391170, root := ~, start := 391155, stop := 391169 ), rec( content := " install\ ed on your computer. For details about these file\n formats, see ", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "h\ ttp://www.latex-project.org", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "URL", next := 391287, root := ~, start := 391248, stop := 391286 ), rec( content := " and\n \ ", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "h\ ttp://www.graphviz.org", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "URL", next := 391332, root := ~, start := 391298, stop := 391331 ), rec( content := ".", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 1, 5 ], mathmode := "Text", name := "P", next := 391337, root := ~, start := 391333, stop := 391336 ), rec( content := "\n\n \ This function is provided to allow convenient, immediate viewing of the\n \ pictures produced by the function ", count := [ 9, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "DotDigr\ aph" ), content := 0, count := [ 9, 1, 1, 5 ], mathmode := "Text", name := "Ref", next := 391481, root := ~, start := 391457, stop := 391480 ), rec( content := ".", count := [ 9, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 1, 6 ], mathmode := "Text", name := "P", next := 391486, root := ~, start := 391482, stop := 391485 ), rec( content := "\n\n \ The optional second argument ", count := [ 9, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ pts", count := [ 9, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 6 ], mathmode := "Text", name := "A", next := 391534, root := ~, start := 391523, stop := 391533 ), rec( content := " should \ be a record with\n components corresponding to various options, given bel\ ow.\n\n ", count := [ 9, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "path", count := [ 9, 1, 1, 7 ], mathmo\ de := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 7 ], name := "Mar\ k", next := 391662, root := ~, start := 391645, stop := 391661 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n this should be a string r\ epresenting the path to the directory where\n you want ", count := [ \ 9, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribut\ es := rec( ), content := [ rec( content := "Splash", count := [ 9, 1, 1, 8 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 8 ], math\ mode := "Text", name := "C", next := 391789, root := ~, start := 391776, stop \ := 391788 ), rec( content := " to do its work. The default value of this\n \ option is ", count := [ 9, 1, 1, 8 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\"~\ /\"", count := [ 9, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~\ ) ], count := [ 9, 1, 1, 8 ], mathmode := "Text", name := "C", next := 391863 , root\ := ~, start := 391852, stop := 391862 ), rec( content := ".\n ", count\ := [ 9, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 8 ], name := "Ite\ m", next := 391880, root := ~, start := 391671, stop := 391879 ), rec( attributes :\ = rec( ), content := [ rec( content := "directory", count := [ 9, 1, 1, 9 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 9 ], name := "Mar\ k", next := 391912, root := ~, start := 391890, stop := 391911 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n this should be a string r\ epresenting the name of the directory in\n ", count := [ 9, 1, 1, 10 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "path", count := [ 9, 1, 1, 10 ], mathmode := "Text",\ name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 10 ], mathmode := "Text" , name\ := "C", next := 392025, root := ~, start := 392014, stop := 392024 ), rec( cont\ ent := " where you want ", count := [ 9, 1, 1, 10 ], mathmode := "Text", name \ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conten\ t := "Splash", count := [ 9, 1, 1, 10 ], mathmode := "Text", name := "PCDATA",\ root := ~ ) ], count := [ 9, 1, 1, 10 ], mathmode := "Text", name := "C", next\ := 392054, root := ~, start := 392041, stop := 392053 ), rec( content := " to\ do its work. This function\n will create this directory if does not \ already exist. ", count := [ 9, 1, 1, 10 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 1,\ 11 ], mathmode := "Text", name := "P", next := 392153, root := ~, start := 39\ 2149, stop := 392152 ), rec( content := "\n\n The default value of th\ is option is ", count := [ 9, 1, 1, 11 ], mathmode := "Text", name := "PCDATA" , root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "\"tmp.viz\"\ ", count := [ 9, 1, 1, 11 ], mathmode := "Text", name := "PCDATA", root := ~ )\ ], count := [ 9, 1, 1, 11 ], mathmode := "Text", name := "C", next := 392217, root\ := ~, start := 392201, stop := 392216 ), rec( content := " if the option\n \ ", count := [ 9, 1, 1, 11 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "path", coun\ t := [ 9, 1, 1, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 9, 1, 1, 11 ], mathmode := "Text", name := "C", next := 392253, root :=\ ~, start := 392242, stop := 392252 ), rec( content := " is present, and the r\ esult of\n ", count := [ 9, 1, 1, 11 ], mathmode := "Text", name := "\ PCDATA", root := ~ ), rec( attributes := rec( BookName := "ref", Func := "Dire\ ctoryTemporary" ), content := 0, count := [ 9, 1, 1, 11 ], mathmode := "Text", name\ := "Ref", next := 392341, root := ~, start := 392294, stop := 392340 ), rec( cont\ ent := " is used otherwise.\n ", count := [ 9, 1, 1, 11 ], mathmode := \ "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 10 ], name := "Ite\ m", next := 392376, root := ~, start := 391921, stop := 392375 ), rec( attributes :\ = rec( ), content := [ rec( content := "filename", count := [ 9, 1, 1, 12 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 12 ], name := "Mar\ k", next := 392407, root := ~, start := 392386, stop := 392406 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n this should be a string r\ epresenting the name of the file where\n ", count := [ 9, 1, 1, 13 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "str", count := [ 9, 1, 1, 13 ], mathmode := "Text", \ name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 13 ], mathmode := "Text", name\ := "A", next := 392517, root := ~, start := 392507, stop := 392516 ), rec( cont\ ent := " will be written. The default value of this option is\n ", coun\ t := [ 9, 1, 1, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "\"vizpicture\"", count := [ 9\ , 1, 1, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ \ 9, 1, 1, 13 ], mathmode := "Text", name := "C", next := 392601, root := ~, star\ t := 392582, stop := 392600 ), rec( content := ".\n ", count := [ 9, 1,\ 1, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 13 ], name := "Ite\ m", next := 392618, root := ~, start := 392416, stop := 392617 ), rec( attributes :\ = rec( ), content := [ rec( content := "viewer", count := [ 9, 1, 1, 14 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 14 ], name := "Mar\ k", next := 392647, root := ~, start := 392628, stop := 392646 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n this should be a string r\ epresenting the name of the program which\n should open the files pro\ duced by ", count := [ 9, 1, 1, 15 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "GraphViz", \ count := [ 9, 1, 1, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 9, 1, 1, 15 ], mathmode := "Text", name := "C", next := 392799, root :=\ ~, start := 392784, stop := 392798 ), rec( content := " or ", count := [ 9, 1\ , 1, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes \ := rec( ), content := [ rec( content := "pdflatex", count := [ 9, 1, 1, 15 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 15 ] , math\ mode := "Text", name := "C", next := 392818, root := ~, start := 392803, stop \ := 392817 ), rec( content := ".\n ", count := [ 9, 1, 1, 15 ], mathmode\ := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 15 ], name := "Ite\ m", next := 392835, root := ~, start := 392656, stop := 392834 ), rec( attributes :\ = rec( ), content := [ rec( content := "type", count := [ 9, 1, 1, 16 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 16 ], name := "Mar\ k", next := 392862, root := ~, start := 392845, stop := 392861 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n this option can be used t\ o specify that the string ", count := [ 9, 1, 1, 17 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "str", count := [ 9, 1, 1, 17 ], mathmode := "Text", name := "PCDATA", r\ oot := ~ ) ], count := [ 9, 1, 1, 17 ], mathmode := "Text", name := "A", next \ := 392949, root := ~, start := 392939, stop := 392948 ), rec( content := " con\ tains\n a ", count := [ 9, 1, 1, 17 ], mathmode := "Text", name := "P\ CDATA", root := ~ ), rec( attributes := rec( Only := "LaTeX" ), content := [ r\ ec( content := "{\\LaTeX}", count := [ 9, 1, 1, 17 ], name := "PCDATA", root :\ = ~ ) ], count := [ 9, 1, 1, 17 ], mathmode := "Text", name := "Alt", next := \ 33, root := ~, start := 1, stop := 32 ), rec( attributes := rec( Not := "LaTeX\ " ), content := [ rec( content := "LaTeX", count := [ 9, 1, 1, 17 ], mathmode \ := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 17 ], name := \ "Alt", next := 61, root := ~, start := 33, stop := 60 ), rec( content := " or \ ", count := [ 9, 1, 1, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attr\ ibutes := rec( ), content := [ rec( content := "dot", count := [ 9, 1, 1, 17 \ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 17\ ], mathmode := "Text", name := "C", next := 392992, root := ~, start := 39298\ 2, stop := 392991 ), rec( content := " document. You can specify this option i\ n\n ", count := [ 9, 1, 1, 17 ], mathmode := "Text", name := "PCDATA" , root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "str", count\ := [ 9, 1, 1, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 9, 1, 1, 17 ], mathmode := "Text", name := "A", next := 393054, root :=\ ~, start := 393044, stop := 393053 ), rec( content := " directly by making th\ e first line ", count := [ 9, 1, 1, 17 ], mathmode := "Text", name := "PCDATA" , root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "\"%latex\""\ , count := [ 9, 1, 1, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ] , coun\ t := [ 9, 1, 1, 17 ], mathmode := "Text", name := "C", next := 393104, root :=\ ~, start := 393089, stop := 393103 ), rec( content := " or\n ", coun\ t := [ 9, 1, 1, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "\"//dot\"", count := [ 9, 1, \ 1, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1,\ 1, 17 ], mathmode := "Text", name := "C", next := 393132, root := ~, start :=\ 393118, stop := 393131 ), rec( content := ". There is no default value for t\ his option, this\n option must be specified in ", count := [ 9, 1, 1,\ 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\ c( ), content := [ rec( content := "str", count := [ 9, 1, 1, 17 ], mathmode \ := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 17 ], mathmode\ := "Text", name := "A", next := 393231, root := ~, start := 393221, stop := 3\ 93230 ), rec( content := " or in ", count := [ 9, 1, 1, 17 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ re\ c( content := "opt.type", count := [ 9, 1, 1, 17 ], mathmode := "Text", name :\ = "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 17 ], mathmode := "Text", name \ := "A", next := 393253, root := ~, start := 393238, stop := 393252 ), rec( cont\ ent := ".\n ", count := [ 9, 1, 1, 17 ], mathmode := "Text", name := "P\ CDATA", root := ~ ) ], count := [ 9, 1, 1, 17 ], name := "Item", next := 39327\ 0, root := ~, start := 392871, stop := 393269 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "engine", count := [ 9, 1, 1, 18 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 9, 1, 1, 18 ], name := "Mark", next := 393299, root := ~, start := 393\ 280, stop := 393298 ), rec( attributes := rec( ), content := [ rec( content :\ = "\n this option can be used to specify the GraphViz engine to use\n\ to render a ", count := [ 9, 1, 1, 19 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content \ := "dot", count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "C", next := \ 393419, root := ~, start := 393409, stop := 393418 ), rec( content := " docume\ nt. The valid choices are ", count := [ 9, 1, 1, 19 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "\"dot\"", count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "C", next\ := 393464, root := ~, start := 393452, stop := 393463 ), rec( content := ",\n\ ", count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "\"neato\"",\ count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ] , coun\ t := [ 9, 1, 1, 19 ], mathmode := "Text", name := "C", next := 393490, root :=\ ~, start := 393476, stop := 393489 ), rec( content := ", ", count := [ 9, 1, \ 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :=\ rec( ), content := [ rec( content := "\"circo\"", count := [ 9, 1, 1, 19 ], \ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 19 ], math\ mode := "Text", name := "C", next := 393506, root := ~, start := 393492, stop \ := 393505 ), rec( content := ", ", count := [ 9, 1, 1, 19 ], mathmode := "Text\ ", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec\ ( content := "\"twopi\"", count := [ 9, 1, 1, 19 ], mathmode := "Text", name :\ = "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 19 ], mathmode := "Text", name \ := "C", next := 393522, root := ~, start := 393508, stop := 393521 ), rec( cont\ ent := ", ", count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "\"fdp\"", c\ ount := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 9, 1, 1, 19 ], mathmode := "Text", name := "C", next := 393536, root :=\ ~, start := 393524, stop := 393535 ), rec( content := ",\n ", count \ := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "\"sfdp\"", count := [ 9, 1, 1\ , 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, \ 1, 19 ], mathmode := "Text", name := "C", next := 393561, root := ~, start := \ 393548, stop := 393560 ), rec( content := ", and ", count := [ 9, 1, 1, 19 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "\"patchwork\"", count := [ 9, 1, 1, 19 ], mathmode :\ = "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 19 ], mathmode \ := "Text", name := "C", next := 393585, root := ~, start := 393567, stop := 39\ 3584 ), rec( content := ". Please refer to the\n GraphViz documentati\ on for details on these engines.\n The default value for this option \ is ", count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA", root := \ ~ ), rec( attributes := rec( ), content := [ rec( content := "\"dot\"", count\ := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 9, 1, 1, 19 ], mathmode := "Text", name := "C", next := 393729, root :=\ ~, start := 393717, stop := 393728 ), rec( content := ", and it\n mu\ st be specified in ", count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "P\ CDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := \ "opt.engine", count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA", \ root := ~ ) ], count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "A", next\ := 393786, root := ~, start := 393769, stop := 393785 ), rec( content := ".\n\ ", count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 9, 1, 1, 19 ], name := "Item", next := 393803, root := ~, start := 393\ 308, stop := 393802 ), rec( attributes := rec( ), content := [ rec( content :\ = "filetype", count := [ 9, 1, 1, 20 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 9, 1, 1, 20 ], name := "Mark", next := 393834, root := ~, start := 393\ 813, stop := 393833 ), rec( attributes := rec( ), content := [ rec( content :\ = "\n this should be a string representing the type of file which\n \ ", count := [ 9, 1, 1, 21 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "Splash", co\ unt := [ 9, 1, 1, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\ t := [ 9, 1, 1, 21 ], mathmode := "Text", name := "C", next := 393943, root :=\ ~, start := 393930, stop := 393942 ), rec( content := " should produce. For " , coun\ t := [ 9, 1, 1, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( Only := "LaTeX" ), content := [ rec( content := "{\\LaTeX}", co\ unt := [ 9, 1, 1, 21 ], name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 2\ 1 ], mathmode := "Text", name := "Alt", next := 33, root := ~, start := 1, stop\ := 32 ), rec( attributes := rec( Not := "LaTeX" ), content := [ rec( content \ := "LaTeX", count := [ 9, 1, 1, 21 ], mathmode := "Text", name := "PCDATA", ro\ ot := ~ ) ], count := [ 9, 1, 1, 21 ], name := "Alt", next := 61, root := ~, star\ t := 33, stop := 60 ), rec( content := " files, this option is\n igno\ red and the default value ", count := [ 9, 1, 1, 21 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "\"pdf\"", count := [ 9, 1, 1, 21 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 9, 1, 1, 21 ], mathmode := "Text", name := "C", next\ := 394046, root := ~, start := 394034, stop := 394045 ), rec( content := " is\ used.\n ", count := [ 9, 1, 1, 21 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 9, 1, 1, 21 ], name := "Item", next := 394071, root := ~, start := 393\ 843, stop := 394070 ) ], count := [ 9, 1, 1, 7 ], mathmode := "Text", name := "List", next := 394085, root := ~, start := 391630, stop := 394084 ), rec( content := "\n\n \ This function was written by Attila Egri-Nagy and Manuel Delgado with some\n\ minor changes by J. D. Mitchell.", count := [ 9, 1, 1, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 1, 24 ], mathmode := "Text", name := "P", next := 394210, root := ~, start := 394206, stop := 394209 ), rec( content := "\n\n \ ", count := [ 9, 1, 1, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> Splash(DotDigraph(RandomDigraph(4)));\n", count := [ 9, 1, 1, 25 ], name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 1, 25 ], mathmode := "Text", name := "Log", next := 394285, root := ~, start := 394218, stop := 394284 ), rec( content := "\n ", count := [ 9, 1, 1, 26 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 3 ], mathmode := "Text", name := "Description", next := 394304, root := ~, start := 390836, stop := 394303 ) ], count := [ 9, 1, 1, 1 ], mathmode := "Text", name := "ManSection", next := 394320, root := ~, start := 390743, stop := 394319 ), rec( content := "\n\n ", count := [ 9, 1, 1, 26 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DotDigraph" ), content := 0, count := [ 9, 1, 2, 2 ], mathmode := "Text", name := "Attr", next := 394384, root := ~, start := 394345, stop := 394383 ), rec( attributes := rec( Arg := "digraph", Name := "DotVertexLabell\ edDigraph" ), content := 0, count := [ 9, 1, 2, 4 ], mathmode := "Text", name := "Oper", next := 394442, root := ~, start := 394389, stop := 394441 ), rec( attributes := rec( ), content := [ rec( content := "A string.\ ", count := [ 9, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 2, 5 ], mathmode := "Text", name := "Returns", next := 394475, root := ~, start := 394447, stop := 394474 ), rec( attributes := rec( ), content := [ rec( content := "\n " , count := [ 9, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ otDigraph", count := [ 9, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 2, 5 ], mathmode := "Text", name := "C", next := 394517, root := ~, start := 394500, stop := 394516 ), rec( content := " produce\ s a graphical representation of the digraph\n ", count := [ 9, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 2, 5 ], mathmode := "Text", name := "A", next := 394589, root := ~, start := 394575, stop := 394588 ), rec( content := ". Vertic\ es are displayed as circles, numbered consistently\n with ", count := [ 9, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 2, 5 ], mathmode := "Text", name := "A", next := 394673, root := ~, start := 394659, stop := 394672 ), rec( content := ". Edges \ are displayed as arrowed lines between\n vertices, with the arrowhead of \ each line pointing towards the range\n of the edge.", count := [ 9, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 2, 6 ], mathmode := "Text", name := "P", next := 394817, root := ~, start := 394813, stop := 394816 ), rec( content := "\n\n \ ", count := [ 9, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ otVertexLabelledDigraph", count := [ 9, 1, 2, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 2, 6 ], mathmode := "Text", name := "C", next := 394856, root := ~, start := 394825, stop := 394855 ), rec( content := " differs\ from ", count := [ 9, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ otDigraph", count := [ 9, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 2, 6 ], mathmode := "Text", name := "C", next := 394887, root := ~, start := 394870, stop := 394886 ), rec( content := " only in\ \n that the values in ", count := [ 9, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ VertexLabels" ), content := 0, count := [ 9, 1, 2, 6 ], mathmode := "Text", name := "Ref", next := 394954, root := ~, start := 394921, stop := 394953 ), rec( content := " are use\ d to label\n the vertices in the produced picture rather than the numbers\ ", count := [ 9, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "1\ ", count := [ 9, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 2, 6 ], mathmode := "Text", name := "C", next := 395048, root := ~, start := 395040, stop := 395047 ), rec( content := " to\n \ the number of vertices of the digraph. ", count := [ 9, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 2, 7 ], mathmode := "Text", name := "P", next := 395101, root := ~, start := 395097, stop := 395100 ), rec( content := "\n\n \ The output is in ", count := [ 9, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ ot", count := [ 9, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 2, 7 ], mathmode := "Text", name := "C", next := 395136, root := ~, start := 395126, stop := 395135 ), rec( content := " format \ (also known as ", count := [ 9, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ raphViz", count := [ 9, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 2, 7 ], mathmode := "Text", name := "C", next := 395174, root := ~, start := 395159, stop := 395173 ), rec( content := ")\n \ format. For details about this file format, and information about how to\n \ display or edit this format see ", count := [ 9, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "h\ ttp://www.graphviz.org", count := [ 9, 1, 2, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 2, 7 ], mathmode := "Text", name := "URL", next := 395327, root := ~, start := 395293, stop := 395326 ), rec( content := ". ", count := [ 9, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 2, 8 ], mathmode := "Text", name := "P", next := 395333, root := ~, start := 395329, stop := 395332 ), rec( content := "\n\n \ The string returned by ", count := [ 9, 1, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ otDigraph", count := [ 9, 1, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 2, 8 ], mathmode := "Text", name := "C", next := 395381, root := ~, start := 395364, stop := 395380 ), rec( content := " or\n \ ", count := [ 9, 1, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ otVertexLabelledDigraph", count := [ 9, 1, 2, 8 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 2, 8 ], mathmode := "Text", name := "C", next := 395422, root := ~, start := 395391, stop := 395421 ), rec( content := " can be \ written to a file using\n the command ", count := [ 9, 1, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "GAP\ Doc", Func := "FileString" ), content := 0, count := [ 9, 1, 2, 8 ], mathmode := "Text", name := "Ref", next := 395514, root := ~, start := 395472, stop := 395513 ), rec( content := ".", count := [ 9, 1, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 2, 9 ], mathmode := "Text", name := "P", next := 395519, root := ~, start := 395515, stop := 395518 ), rec( content := "\n\n \ ", count := [ 9, 1, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> adj := List([1 .. 4], x -> [1, 1, 1, 1]);\n[ [ 1, 1, 1, 1 ], [ 1, 1, 1, \ 1 ], [ 1, 1, 1, 1 ], [ 1, 1, 1, 1 ] ]\ngap> adj[1][3] := 0;\n0\ngap> gr := Dig\ raphByAdjacencyMatrix(adj);\n\nga\ p> FileString(\"dot/k4.dot\", DotDigraph(gr));\n154", count := [ 9, 1, 2, 10 ] , name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 2, 10 ], mathmode := "Text", name := "Log", next := 395826, root := ~, start := 395527, stop := 395825 ), rec( content := "\n ", count := [ 9, 1, 2, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 2, 5 ], mathmode := "Text", name := "Description", next := 395845, root := ~, start := 394480, stop := 395844 ) ], count := [ 9, 1, 2, 1 ], mathmode := "Text", name := "ManSection", next := 395861, root := ~, start := 394328, stop := 395860 ), rec( content := "\n\n ", count := [ 9, 1, 2, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DotSymmetricDig\ raph" ), content := 0, count := [ 9, 1, 3, 2 ], mathmode := "Text", name := "Attr", next := 395934, root := ~, start := 395886, stop := 395933 ), rec( attributes := rec( ), content := [ rec( content := "A string.\ ", count := [ 9, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 3, 3 ], mathmode := "Text", name := "Returns", next := 395967, root := ~, start := 395939, stop := 395966 ), rec( attributes := rec( ), content := [ rec( content := "\n T\ his function produces a graphical representation of the symmetric\n digra\ ph ", count := [ 9, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 3, 3 ], mathmode := "Text", name := "A", next := 396087, root := ~, start := 396073, stop := 396086 ), rec( content := ". ", count := [ 9, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ otSymmetricDigraph", count := [ 9, 1, 3, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 3, 3 ], mathmode := "Text", name := "C", next := 396115, root := ~, start := 396089, stop := 396114 ), rec( content := " will re\ turn an\n error if ", count := [ 9, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 3, 3 ], mathmode := "Text", name := "A", next := 396160, root := ~, start := 396146, stop := 396159 ), rec( content := " is not \ a symmetric digraph. See\n ", count := [ 9, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsSymme\ tricDigraph" ), content := 0, count := [ 9, 1, 3, 3 ], mathmode := "Text", name := "Ref", next := 396231, root := ~, start := 396199, stop := 396230 ), rec( content := ".", count := [ 9, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 3, 4 ], mathmode := "Text", name := "P", next := 396236, root := ~, start := 396232, stop := 396235 ), rec( content := "\n\n \ Vertices are displayed as circles, numbered consistently with\n ", count := [ 9, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 3, 4 ], mathmode := "Text", name := "A", next := 396326, root := ~, start := 396312, stop := 396325 ), rec( content := ". Since \ ", count := [ 9, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 3, 4 ], mathmode := "Text", name := "A", next := 396348, root := ~, start := 396334, stop := 396347 ), rec( content := " is symm\ etric, for every non-loop\n edge there is a complementary edge with oppos\ ite source and range.\n ", count := [ 9, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ otSymmetricDigraph", count := [ 9, 1, 3, 4 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 3, 4 ], mathmode := "Text", name := "C", next := 396487, root := ~, start := 396461, stop := 396486 ), rec( content := " display\ s each pair of complementary edges\n as a single line between the relevan\ t vertices, with no arrowhead.", count := [ 9, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 3, 5 ], mathmode := "Text", name := "P", next := 396606, root := ~, start := 396602, stop := 396605 ), rec( content := "\n\n \ The output is in ", count := [ 9, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ ot", count := [ 9, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 3, 5 ], mathmode := "Text", name := "C", next := 396641, root := ~, start := 396631, stop := 396640 ), rec( content := " format \ (also known as ", count := [ 9, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ raphViz", count := [ 9, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 3, 5 ], mathmode := "Text", name := "C", next := 396679, root := ~, start := 396664, stop := 396678 ), rec( content := ")\n \ format. For details about this file format, and information about how\n \ to display or edit this format see\n ", count := [ 9, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "h\ ttp://www.graphviz.org", count := [ 9, 1, 3, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 3, 5 ], mathmode := "Text", name := "URL", next := 396838, root := ~, start := 396804, stop := 396837 ), rec( content := ". ", count := [ 9, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 3, 6 ], mathmode := "Text", name := "P", next := 396844, root := ~, start := 396840, stop := 396843 ), rec( content := "\n\n \ The string returned by ", count := [ 9, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ otSymmetricDigraph", count := [ 9, 1, 3, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 3, 6 ], mathmode := "Text", name := "C", next := 396901, root := ~, start := 396875, stop := 396900 ), rec( content := " can be \ written to a\n file using the command ", count := [ 9, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "GAP\ Doc", Func := "FileString" ), content := 0, count := [ 9, 1, 3, 6 ], mathmode := "Text", name := "Ref", next := 396993, root := ~, start := 396951, stop := 396992 ), rec( content := ".", count := [ 9, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 3, 7 ], mathmode := "Text", name := "P", next := 396998, root := ~, start := 396994, stop := 396997 ), rec( content := "\n\n \ ", count := [ 9, 1, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> star := Digraph([[2, 2, 3, 4], [1, 1], [1], [1, 4]]);\n\ngap> IsSymmetricDigraph(star);\ntrue\ngap> F\ ileString(\"dot/star.dot\", DotSymmetricDigraph(gr));\n83", count := [ 9, 1, 3, 8 ], name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 3, 8 ], mathmode := "Text", name := "Log", next := 397235, root := ~, start := 397006, stop := 397234 ), rec( content := "\n ", count := [ 9, 1, 3, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 3, 3 ], mathmode := "Text", name := "Description", next := 397254, root := ~, start := 395972, stop := 397253 ) ], count := [ 9, 1, 3, 1 ], mathmode := "Text", name := "ManSection", next := 397270, root := ~, start := 395869, stop := 397269 ), rec( content := "\n\n ", count := [ 9, 1, 3, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DotPartialOrder\ Digraph" ), content := 0, count := [ 9, 1, 4, 2 ], mathmode := "Text", name := "Attr", next := 397346, root := ~, start := 397295, stop := 397345 ), rec( attributes := rec( ), content := [ rec( content := "A string.\ ", count := [ 9, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 4, 3 ], mathmode := "Text", name := "Returns", next := 397379, root := ~, start := 397351, stop := 397378 ), rec( attributes := rec( ), content := [ rec( content := "\n T\ his function produces a graphical representation of a partial order\n dig\ raph ", count := [ 9, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 4, 3 ], mathmode := "Text", name := "A", next := 397501, root := ~, start := 397487, stop := 397500 ), rec( content := ". ", count := [ 9, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ otPartialOrderDigraph", count := [ 9, 1, 4, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 4, 3 ], mathmode := "Text", name := "C", next := 397532, root := ~, start := 397503, stop := 397531 ), rec( content := " will re\ turn an error\n if ", count := [ 9, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 4, 3 ], mathmode := "Text", name := "A", next := 397577, root := ~, start := 397563, stop := 397576 ), rec( content := " is not \ a partial order digraph. See ", count := [ 9, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsParti\ alOrderDigraph" ), content := 0, count := [ 9, 1, 4, 3 ], mathmode := "Text", name := "Ref", next := 397657, root := ~, start := 397614, stop := 397656 ), rec( content := ".", count := [ 9, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 4, 4 ], mathmode := "Text", name := "P", next := 397662, root := ~, start := 397658, stop := 397661 ), rec( content := "\n\n \ Since ", count := [ 9, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 4, 4 ], mathmode := "Text", name := "A", next := 397690, root := ~, start := 397676, stop := 397689 ), rec( content := " is a pa\ rtial order, it is both reflexive and\n transitive. The output of ", count := [ 9, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ otPartialOrderDigraph", count := [ 9, 1, 4, 4 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 4, 4 ], mathmode := "Text", name := "C", next := 397797, root := ~, start := 397768, stop := 397796 ), rec( content := " is the\\ n ", count := [ 9, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "DotDigr\ aph" ), content := 0, count := [ 9, 1, 4, 4 ], mathmode := "Text", name := "Ref", next := 397835, root := ~, start := 397811, stop := 397834 ), rec( content := " of the\\ n ", count := [ 9, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ ReflexiveTransitiveReduction" ), content := 0, count := [ 9, 1, 4, 4 ], mathmode := "Text", name := "Ref", next := 397898, root := ~, start := 397849, stop := 397897 ), rec( content := " of ", count := [ 9, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 4, 4 ], mathmode := "Text", name := "A", next := 397916, root := ~, start := 397902, stop := 397915 ), rec( content := ".", count := [ 9, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 4, 5 ], mathmode := "Text", name := "P", next := 397921, root := ~, start := 397917, stop := 397920 ), rec( content := "\n\n \ The output is in ", count := [ 9, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ ot", count := [ 9, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 4, 5 ], mathmode := "Text", name := "C", next := 397956, root := ~, start := 397946, stop := 397955 ), rec( content := " format \ (also known as ", count := [ 9, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ raphViz", count := [ 9, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 4, 5 ], mathmode := "Text", name := "C", next := 397994, root := ~, start := 397979, stop := 397993 ), rec( content := ")\n \ format. For details about this file format, and information about how\n \ to display or edit this format see\n ", count := [ 9, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "h\ ttp://www.graphviz.org", count := [ 9, 1, 4, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 4, 5 ], mathmode := "Text", name := "URL", next := 398153, root := ~, start := 398119, stop := 398152 ), rec( content := ". ", count := [ 9, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 4, 6 ], mathmode := "Text", name := "P", next := 398159, root := ~, start := 398155, stop := 398158 ), rec( content := "\n\n \ The string returned by ", count := [ 9, 1, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ otPartialOrderDigraph", count := [ 9, 1, 4, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 4, 6 ], mathmode := "Text", name := "C", next := 398219, root := ~, start := 398190, stop := 398218 ), rec( content := " can be \ written to a\n file using the command ", count := [ 9, 1, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "GAP\ Doc", Func := "FileString" ), content := 0, count := [ 9, 1, 4, 6 ], mathmode := "Text", name := "Ref", next := 398311, root := ~, start := 398269, stop := 398310 ), rec( content := ".", count := [ 9, 1, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 4, 7 ], mathmode := "Text", name := "P", next := 398316, root := ~, start := 398312, stop := 398315 ), rec( content := "\n\n \ ", count := [ 9, 1, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> poset := Digraph([[1, 4], [2], [2, 3, 4], [4]);\ngap> IsPartialOrderDigr\ aph(gr);\ntrue\ngap> FileString(\"dot/poset.dot\", DotPartialOrderDigraph(gr))\ ;\n83", count := [ 9, 1, 4, 8 ], name := "PCDATA", root := ~ ) ], count := [ 9, 1, 4, 8 ], mathmode := "Text", name := "Log", next := 398502, root := ~, start := 398324, stop := 398501 ), rec( content := "\n ", count := [ 9, 1, 4, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 4, 3 ], mathmode := "Text", name := "Description", next := 398521, root := ~, start := 397384, stop := 398520 ) ], count := [ 9, 1, 4, 1 ], mathmode := "Text", name := "ManSection", next := 398537, root := ~, start := 397278, stop := 398536 ), rec( content := "\n\n ", count := [ 9, 1, 4, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "DotPreorderDigr\ aph" ), content := 0, count := [ 9, 1, 5, 2 ], mathmode := "Text", name := "Attr", next := 398609, root := ~, start := 398562, stop := 398608 ), rec( attributes := rec( Arg := "digraph", Name := "DotQuasiorderDi\ graph" ), content := 0, count := [ 9, 1, 5, 4 ], mathmode := "Text", name := "Attr", next := 398663, root := ~, start := 398614, stop := 398662 ), rec( attributes := rec( ), content := [ rec( content := "A string.\ ", count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "Returns", next := 398696, root := ~, start := 398668, stop := 398695 ), rec( attributes := rec( ), content := [ rec( content := "\n T\ his function produces a graphical representation of a preorder\n digraph \ ", count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "A", next := 398813, root := ~, start := 398799, stop := 398812 ), rec( content := ". ", count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ otPreorderDigraph", count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "C", next := 398840, root := ~, start := 398815, stop := 398839 ), rec( content := " will re\ turn an error\n if ", count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "A", next := 398885, root := ~, start := 398871, stop := 398884 ), rec( content := " is not \ a preorder digraph. See ", count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsPreor\ derDigraph" ), content := 0, count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "Ref", next := 398956, root := ~, start := 398917, stop := 398955 ), rec( content := ".", count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "P", next := 398961, root := ~, start := 398957, stop := 398960 ), rec( content := "\n\n \ A preorder digraph is reflexive and transitive but in general it is\n n\ ot anti-symmetric and may have strongly connected components\n containing\ more than one vertex. The ", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Quotien\ tDigraph" ), content := 0, count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "Ref", next := 399177, root := ~, start := 399148, stop := 399176 ), rec( content := "\n \ ", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Q\ ", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "A", next := 399192, root := ~, start := 399184, stop := 399191 ), rec( content := " obtaine\ d by forming the quotient of ", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "A", next := 399243, root := ~, start := 399229, stop := 399242 ), rec( content := " by the\\ n partition of its vertices into the strongly connected components\n \ satisfies ", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsParti\ alOrderDigraph" ), content := 0, count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "Ref", next := 399373, root := ~, start := 399338, stop := 399372 ), rec( content := ". Thus e\ very vertex of\n ", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Q\ ", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "A", next := 399410, root := ~, start := 399402, stop := 399409 ), rec( content := " corresp\ onds to a strongly connected component of ", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "A", next := 399474, root := ~, start := 399460, stop := 399473 ), rec( content := ".\n \ The output of ", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ otPreorderDigraph", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "C", next := 399521, root := ~, start := 399496, stop := 399520 ), rec( content := " display\ s the \n ", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ ReflexiveTransitiveReduction" ), content := 0, count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "Ref", next := 399591, root := ~, start := 399542, stop := 399590 ), rec( content := " of ", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Q\ ", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "A", next := 399603, root := ~, start := 399595, stop := 399602 ), rec( content := " with\n \ vertices displayed as rounded rectangles labelled by all of the vertices\ \n of ", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "A", next := 399711, root := ~, start := 399697, stop := 399710 ), rec( content := " in the \ corresponding strongly connected component. ", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 5, 7 ], mathmode := "Text", name := "P", next := 399767, root := ~, start := 399763, stop := 399766 ), rec( content := "\n\n \ The output is in ", count := [ 9, 1, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ ot", count := [ 9, 1, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 5, 7 ], mathmode := "Text", name := "C", next := 399802, root := ~, start := 399792, stop := 399801 ), rec( content := " format \ (also known as ", count := [ 9, 1, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "G\ raphViz", count := [ 9, 1, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 5, 7 ], mathmode := "Text", name := "C", next := 399840, root := ~, start := 399825, stop := 399839 ), rec( content := ")\n \ format. For details about this file format, and information about how\n \ to display or edit this format see\n ", count := [ 9, 1, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "h\ ttp://www.graphviz.org", count := [ 9, 1, 5, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 5, 7 ], mathmode := "Text", name := "URL", next := 399999, root := ~, start := 399965, stop := 399998 ), rec( content := ". ", count := [ 9, 1, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 5, 8 ], mathmode := "Text", name := "P", next := 400005, root := ~, start := 400001, stop := 400004 ), rec( content := "\n\n \ The string returned by ", count := [ 9, 1, 5, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ otPreorderDigraph", count := [ 9, 1, 5, 8 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 9, 1, 5, 8 ], mathmode := "Text", name := "C", next := 400061, root := ~, start := 400036, stop := 400060 ), rec( content := " can be \ written to a\n file using the command ", count := [ 9, 1, 5, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "GAP\ Doc", Func := "FileString" ), content := 0, count := [ 9, 1, 5, 8 ], mathmode := "Text", name := "Ref", next := 400153, root := ~, start := 400111, stop := 400152 ), rec( content := ".", count := [ 9, 1, 5, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 5, 9 ], mathmode := "Text", name := "P", next := 400158, root := ~, start := 400154, stop := 400157 ), rec( content := "\n\n \ ", count := [ 9, 1, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> preset := Digraph([[1, 2, 4, 5], [1, 2, 4, 5], [3, 4], [4], [1, 2, 4, 5]\ );\ngap> IsPreorderDigraph(gr);\ntrue\ngap> FileString(\"dot/preset.dot\", Dot\ ProrderDigraph(gr));\n83", count := [ 9, 1, 5, 10 ], name := "PCDATA", root := ~ ) ], count := [ 9, 1, 5, 10 ], mathmode := "Text", name := "Log", next := 400363, root := ~, start := 400166, stop := 400362 ), rec( content := "\n ", count := [ 9, 1, 5, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "Description", next := 400382, root := ~, start := 398701, stop := 400381 ) ], count := [ 9, 1, 5, 1 ], mathmode := "Text", name := "ManSection", next := 400398, root := ~, start := 398545, stop := 400397 ), rec( content := "\n\n ", count := [ 9, 1, 5, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph, verts [\ , colour1, colour2]", Name := "DotHighlightedDigraph" ), content := 0, count := [ 9, 1, 6, 2 ], mathmode := "Text", name := "Oper", next := 400501, root := ~, start := 400423, stop := 400500 ), rec( attributes := rec( ), content := [ rec( content := "A string.\ ", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "Returns", next := 400534, root := ~, start := 400506, stop := 400533 ), rec( attributes := rec( ), content := [ rec( content := "\n " , count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ otHighlightedDigraph", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "C", next := 400587, root := ~, start := 400559, stop := 400586 ), rec( content := " produce\ s a graphical represenation of the\n digraph ", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "A", next := 400658, root := ~, start := 400644, stop := 400657 ), rec( content := ", where \ the vertices in the list ", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ erts", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "A", next := 400703, root := ~, start := 400691, stop := 400702 ), rec( content := ", and\n \ edges between them, are drawn with colour ", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olour1", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "A", next := 400771, root := ~, start := 400757, stop := 400770 ), rec( content := " and all\ other\n vertices and edges in ", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "A", next := 400828, root := ~, start := 400814, stop := 400827 ), rec( content := " are dra\ wn with colour ", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olour2", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "A", next := 400865, root := ~, start := 400851, stop := 400864 ), rec( content := ".\n \ If ", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olour1", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "A", next := 400890, root := ~, start := 400876, stop := 400889 ), rec( content := " and ", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olour2", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "A", next := 400909, root := ~, start := 400895, stop := 400908 ), rec( content := " are not\ given then\n ", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ otHighlightedDigraph", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "C", next := 400963, root := ~, start := 400935, stop := 400962 ), rec( content := " uses bl\ ack and grey respectively. ", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 6, 4 ], mathmode := "Text", name := "P", next := 401002, root := ~, start := 400998, stop := 401001 ), rec( content := "\n\n \ Note that ", count := [ 9, 1, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ otHighlightedDigraph", count := [ 9, 1, 6, 4 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 6, 4 ], mathmode := "Text", name := "C", next := 401048, root := ~, start := 401020, stop := 401047 ), rec( content := " does no\ t validate the colours\n ", count := [ 9, 1, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olour1", count := [ 9, 1, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 6, 4 ], mathmode := "Text", name := "A", next := 401099, root := ~, start := 401085, stop := 401098 ), rec( content := " and ", count := [ 9, 1, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ olour2", count := [ 9, 1, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 6, 4 ], mathmode := "Text", name := "A", next := 401118, root := ~, start := 401104, stop := 401117 ), rec( content := " - consu\ lt the GraphViz documentation to\n see what is available.\n\n See ", count := [ 9, 1, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "DotDigr\ aph" ), content := 0, count := [ 9, 1, 6, 4 ], mathmode := "Text", name := "Ref", next := 401223, root := ~, start := 401199, stop := 401222 ), rec( content := " for mor\ e details on the output.", count := [ 9, 1, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 1, 6, 5 ], mathmode := "Text", name := "P", next := 401259, root := ~, start := 401255, stop := 401258 ), rec( content := "\n\n \ ", count := [ 9, 1, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> digraph := Digraph([[2, 3], [2], [1, 3]]);\n\ngap> FileString(\"dot/my_digraph.dot\",\n> DotHighlightedDigraph(digra\ ph, [1, 2], \"red\", \"black\"));\n264", count := [ 9, 1, 6, 6 ], name := "PCD\ ATA", root := ~ ) ], count := [ 9, 1, 6, 6 ], mathmode := "Text", name := "Log", next := 401474, root := ~, start := 401267, stop := 401473 ), rec( content := "\n ", count := [ 9, 1, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "Description", next := 401493, root := ~, start := 400539, stop := 401492 ) ], count := [ 9, 1, 6, 1 ], mathmode := "Text", name := "ManSection", next := 401509, root := ~, start := 400406, stop := 401508 ), rec( content := "\n\n ", count := [ 9, 1, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 0, 1 ], mathmode := "Text", name := "Section", next := 401523, root := ~, start := 390687, stop := 401522 ) , rec( content := "\n\n ", count := [ 9, 1, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Reading and writi\ ng digraphs to a file", count := [ 9, 2, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 2 ], mathmode := "Text", name := "Heading", next := 401593, root := ~, start := 401536, stop := 401592 ), rec( content := "\n This section descr\ ibes different ways to store and read graphs\n from a file in the ", count := [ 9, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Digraphs", count := [ 9, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 3 ], mathmode := "Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), rec( content := " package.\n ", count := [ 9, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := " Graph6 " , count := [ 9, 2, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 4 ], name := "Mark", next := 401742, root := ~, start := 401721, stop := 401741 ), rec( attributes := rec( ), content := [ rec( content := "\n\t", count := [ 9, 2, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := " \ Graph6 ", count := [ 9, 2, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 5 ], mathmode := "Text", name := "E", next := 401772, root := ~, start := 401757, stop := 401771 ), rec( content := " is a gr\ aph data format for storing undirected graphs\n\twith no multiple edges nor lo\ ops of size up to ", count := [ 9, 2, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := " \ 2^{36} - 1 ", count := [ 9, 2, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 5 ], mathmode := "Text", name := "M", next := 401893, root := ~, start := 401874, stop := 401892 ), rec( content := " in\n\tp\ rintable chracters. The format consists of two parts. The first part\n\tuses o\ ne to eight bytes to store the number of vertices. And the second\n\tpart is t\ he upper half of the adjacency matrix converted into ASCII\n\tcharacters. For \ a more detail description see ", count := [ 9, 2, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Text := "Graph6"\ ), content := [ rec( content := "\n\thttp://cs.anu.edu.au/~bdm/data/formats.t\ xt", count := [ 9, 2, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 5 ], mathmode := "Text", name := "URL", next := 402226, root := ~, start := 402157, stop := 402225 ), rec( content := ".\n \ ", count := [ 9, 2, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 5 ], name := "Item", next := 402241, root := ~, start := 401749, stop := 402240 ), rec( attributes := rec( ), content := [ rec( content := " Sparse6 \ ", count := [ 9, 2, 0, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 6 ], name := "Mark", next := 402271, root := ~, start := 402249, stop := 402270 ), rec( attributes := rec( ), content := [ rec( content := "\n\t", count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := " \ Sparse6 ", count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "E", next := 402302, root := ~, start := 402286, stop := 402301 ), rec( content := " is a gr\ aph data format for storing undirected graphs\n\twith possibly multiple edges \ or loops. The maximal number of vertices\n\tallowed is ", count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := " \ 2^{36} - 1 ", count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "M", next := 402458, root := ~, start := 402439, stop := 402457 ), rec( content := ". The fo\ rmat consists of two parts. The\n\tfirst part uses one to eight bytes to store\ the number of vertices.\n\tAnd the second part only stores information about \ the edges.\n\tTherefore, the ", count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := " \ Sparse6 ", count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "E", next := 402661, root := ~, start := 402645, stop := 402660 ), rec( content := " format \ return a more compact encoding\n\tthen ", count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := " \ Graph6 ", count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "E", next := 402721, root := ~, start := 402706, stop := 402720 ), rec( content := " for spa\ rse graph, i.e. graphs where the number\n\tof edges is much less than the num\ ber of vertices squared. For a more\n\tdetail description see ", count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Text := "Sparse6\ " ), content := [ rec( content := "\n http://cs.anu.edu.au/~bdm/data/fo\ rmats.txt", count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "URL", next := 402943, root := ~, start := 402866, stop := 402942 ), rec( content := ".\n \ ", count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 7 ], name := "Item", next := 402958, root := ~, start := 402278, stop := 402957 ), rec( attributes := rec( ), content := [ rec( content := " Digraph6\ ", count := [ 9, 2, 0, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 8 ], name := "Mark", next := 402989, root := ~, start := 402966, stop := 402988 ), rec( attributes := rec( ), content := [ rec( content := "\n\t", count := [ 9, 2, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraph6", count := [ 9, 2, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 9 ], mathmode := "Text", name := "E", next := 403019, root := ~, start := 403004, stop := 403018 ), rec( content := " is a ne\ w format based on ", count := [ 9, 2, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := " \ Graph6 ", count := [ 9, 2, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 9 ], mathmode := "Text", name := "E", next := 403060, root := ~, start := 403045, stop := 403059 ), rec( content := ", but de\ signed\n\tfor digraphs. The entire adjacency matrix is stored, and\n\ttherefor\ e there is support for directed edges and single-vertex loops.\n\tHowever, mul\ tiple edges are not supported.\n ", count := [ 9, 2, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 9 ], name := "Item", next := 403262, root := ~, start := 402996, stop := 403261 ), rec( attributes := rec( ), content := [ rec( content := " DiSparse\ 6 ", count := [ 9, 2, 0, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 10 ], name := "Mark", next := 403294, root := ~, start := 403270, stop := 403293 ), rec( attributes := rec( ), content := [ rec( content := "\n\t", count := [ 9, 2, 0, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ iSparse6", count := [ 9, 2, 0, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 11 ], mathmode := "Text", name := "E", next := 403325, root := ~, start := 403309, stop := 403324 ), rec( content := " is a ne\ w format based on ", count := [ 9, 2, 0, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := " \ Sparse6 ", count := [ 9, 2, 0, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 11 ], mathmode := "Text", name := "E", next := 403367, root := ~, start := 403351, stop := 403366 ), rec( content := ", but\n\\ tdesigned for digraphs. In this format the list of edges is\n\tpartitioned int\ o inceasing and decreasing edges, depending whether the\n\tedge has its source\ bigger than the range. Then both sets of edges are\n\twritten separetly in ", count := [ 9, 2, 0, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := " \ Sparse6 ", count := [ 9, 2, 0, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 11 ], mathmode := "Text", name := "E", next := 403615, root := ~, start := 403599, stop := 403614 ), rec( content := " format \ with a separation symbol\n\tin between.\n ", count := [ 9, 2, 0, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 0, 11 ], name := "Item", next := 403674, root := ~, start := 403301, stop := 403673 ) ], count := [ 9, 2, 0, 4 ], mathmode := "Text", name := "List", next := 403686, root := ~, start := 401708, stop := 403685 ), rec( content := "\n ", count := [ 9, 2, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "String" ), content := 0, count := [ 9, 2, 1, 2 ], mathmode := "Text", name := "Attr", next := 403741, root := ~, start := 403706, stop := 403740 ), rec( attributes := rec( Arg := "digraph", Name := "PrintString" ), content := 0, count := [ 9, 2, 1, 4 ], mathmode := "Text", name := "Oper", next := 403784, root := ~, start := 403744, stop := 403783 ), rec( attributes := rec( ), content := [ rec( content := "A string.\ ", count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "Returns", next := 403815, root := ~, start := 403787, stop := 403814 ), rec( attributes := rec( ), content := [ rec( content := "\n Ret\ urns a string ", count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ tring", count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "C", next := 403866, root := ~, start := 403853, stop := 403865 ), rec( content := " such th\ at ", count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "E\ valString(string)", count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "C", next := 403902, root := ~, start := 403877, stop := 403901 ), rec( content := "\n is\ equal to ", count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "A", next := 403933, root := ~, start := 403919, stop := 403932 ), rec( content := ", and ha\ s the same mutability.\n See ", count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "ref\ ", Func := "EvalString" ), content := 0, count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "Ref", next := 404012, root := ~, start := 403972, stop := 404011 ), rec( content := ".\n " , count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 1, 6 ], mathmode := "Text", name := "P", next := 404022, root := ~, start := 404018, stop := 404021 ), rec( content := "\n\n \ The methods installed for ", count := [ 9, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "S\ tring", count := [ 9, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 1, 6 ], mathmode := "Text", name := "C", next := 404067, root := ~, start := 404054, stop := 404066 ), rec( content := " make so\ me attempts to\n ensure that ", count := [ 9, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ tring", count := [ 9, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 1, 6 ], mathmode := "Text", name := "C", next := 404119, root := ~, start := 404106, stop := 404118 ), rec( content := " has as \ short a length as possible, but\n there may exist shorter strings that also\ evaluate to ", count := [ 9, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 1, 6 ], mathmode := "Text", name := "A", next := 404231, root := ~, start := 404217, stop := 404230 ), rec( content := ".\n " , count := [ 9, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "P", next := 404241, root := ~, start := 404237, stop := 404240 ), rec( content := "\n\n \ It is possible that ", count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ tring", count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "C", next := 404280, root := ~, start := 404267, stop := 404279 ), rec( content := " may con\ tain escaped special\n characters. To obtain a representation of ", count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "A", next := 404369, root := ~, start := 404355, stop := 404368 ), rec( content := " that\n \ can be entered as GAP input, please use\n ", count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "ref\ ", Func := "Print" ), content := 0, count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "Ref", next := 404458, root := ~, start := 404423, stop := 404457 ), rec( content := ".\n N\ ote that ", count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "P\ rint", count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "C", next := 404486, root := ~, start := 404474, stop := 404485 ), rec( content := " for a d\ igraph delegates to\n ", count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "P\ rintString", count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "C", next := 404537, root := ~, start := 404519, stop := 404536 ), rec( content := ", which \ delegates to ", count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "S\ tring", count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "C", next := 404571, root := ~, start := 404558, stop := 404570 ), rec( content := ".\n " , count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> D := CycleDigraph(3);\n\ngap> P\ rint(D);\nCycleDigraph(3);\ngap> G := PetersenGraph(IsMutableDigraph);\n\ngap> String(G);\n\"DigraphFromGraph6St\ ring(IsMutableDigraph, \\\"IheA@GUAo\\\");\"\ngap> Print(last);\nDigraphFromGr\ aph6String(IsMutableDigraph, \"IheA@GUAo\");\ngap> DigraphFromGraph6String(IsM\ utableDigraph, \"IheA@GUAo\");\n\n\ ", count := [ 9, 2, 1, 8 ], name := "PCDATA", root := ~ ) ], count := [ 9, 2, 1, 8 ], mathmode := "Text", name := "Log", next := 405046, root := ~, start := 404577, stop := 405045 ), rec( content := "\n ", count := [ 9, 2, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "Description", next := 405063, root := ~, start := 403818, stop := 405062 ) ], count := [ 9, 2, 1, 1 ], mathmode := "Text", name := "ManSection", next := 405077, root := ~, start := 403691, stop := 405076 ), rec( content := "\n\n ", count := [ 9, 2, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "[filt, ]str", Name := "DigraphFromGrap\ h6String" ), content := 0, count := [ 9, 2, 2, 2 ], mathmode := "Text", name := "Oper", next := 405157, root := ~, start := 405098, stop := 405156 ), rec( attributes := rec( Arg := "[filt, ]str", Name := "DigraphFromDigr\ aph6String" ), content := 0, count := [ 9, 2, 2, 4 ], mathmode := "Text", name := "Oper", next := 405219, root := ~, start := 405160, stop := 405218 ), rec( attributes := rec( Arg := "[filt, ]str", Name := "DigraphFromSpar\ se6String" ), content := 0, count := [ 9, 2, 2, 6 ], mathmode := "Text", name := "Oper", next := 405281, root := ~, start := 405222, stop := 405280 ), rec( attributes := rec( Arg := "[filt, ]str", Name := "DigraphFromDiSp\ arse6String" ), content := 0, count := [ 9, 2, 2, 8 ], mathmode := "Text", name := "Oper", next := 405343, root := ~, start := 405284, stop := 405342 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 9, 2, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 2, 9 ], mathmode := "Text", name := "Returns", next := 405375, root := ~, start := 405346, stop := 405374 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 9, 2, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ tr", count := [ 9, 2, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 2, 9 ], mathmode := "Text", name := "A", next := 405409, root := ~, start := 405399, stop := 405408 ), rec( content := " is a st\ ring encoding a graph in Graph6, Digraph6, Sparse6 or\n DiSparse6 format, t\ hen the corresponding function returns a digraph. In the\n case of either G\ raph6 or Sparse6, formats which do not support directed\n edges, this will \ be a digraph such that for every edge, the edge going in\n the opposite dir\ ection is also present.", count := [ 9, 2, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 2, 10 ], mathmode := "Text", name := "P", next := 405752, root := ~, start := 405748, stop := 405751 ), rec( content := "\n\n \ Each of these functions takes an optional first argument ", count := [ 9, 2, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilt", count := [ 9, 2, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 2, 10 ], mathmode := "Text", name := "A", next := 405826, root := ~, start := 405815, stop := 405825 ), rec( content := ",\n w\ hich should be either ", count := [ 9, 2, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 9, 2, 2, 10 ], mathmode := "Text", name := "Ref", next := 405885, root := ~, start := 405855, stop := 405884 ), rec( content := "\n or\ ", count := [ 9, 2, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 9, 2, 2, 10 ], mathmode := "Text", name := "Ref", next := 405925, root := ~, start := 405893, stop := 405924 ), rec( content := ",\n a\ nd which specifies whether the output digraph shall\n be mutable or immutab\ le.\n If no first argument is provided, then an immutable\n digraph is r\ eturned by default.\n ", count := [ 9, 2, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> DigraphFromGraph6String(\"?\");\n\ngap> DigraphFromGraph6String(\"C]\");\n\ngap> DigraphFromGraph6String(\"H?AAEM{\");\n\ngap> DigraphFromDigraph6String(\"&?\");\n\ngap> DigraphFromDigraph6String(IsMutableDigraph,\ \"&DOOOW?\");\n\ngap> DigraphFromDi\ graph6String(\"&CQFG\");\n\ngap> D\ igraphFromDigraph6String(\"&IM[SrKLc~lhesbU[F_\");\n\ngap> DigraphFromDiSparse6String(\".CaWBGA?b\");\n\n", count := [ 9, 2, 2, 11 ], name := "PCD\ ATA", root := ~ ) ], count := [ 9, 2, 2, 11 ], mathmode := "Text", name := "Example", next := 406854, root := ~, start := 406109, stop := 406853 ), rec( content := "\n ", count := [ 9, 2, 2, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 2, 9 ], mathmode := "Text", name := "Description", next := 406873, root := ~, start := 405378, stop := 406872 ) ], count := [ 9, 2, 2, 1 ], mathmode := "Text", name := "ManSection", next := 406887, root := ~, start := 405083, stop := 406886 ), rec( content := "\n\n ", count := [ 9, 2, 2, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "Graph6String" ) , content := 0, count := [ 9, 2, 3, 2 ], mathmode := "Text", name := "Oper", next := 406949, root := ~, start := 406908, stop := 406948 ), rec( attributes := rec( Arg := "digraph", Name := "Digraph6String"\ ), content := 0, count := [ 9, 2, 3, 4 ], mathmode := "Text", name := "Oper", next := 406995, root := ~, start := 406952, stop := 406994 ), rec( attributes := rec( Arg := "digraph", Name := "Sparse6String" ), content := 0, count := [ 9, 2, 3, 6 ], mathmode := "Text", name := "Oper", next := 407040, root := ~, start := 406998, stop := 407039 ), rec( attributes := rec( Arg := "digraph", Name := "DiSparse6String\ " ), content := 0, count := [ 9, 2, 3, 8 ], mathmode := "Text", name := "Oper", next := 407087, root := ~, start := 407043, stop := 407086 ), rec( attributes := rec( ), content := [ rec( content := "A string.\ ", count := [ 9, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 3, 9 ], mathmode := "Text", name := "Returns", next := 407118, root := ~, start := 407090, stop := 407117 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ se four functions return a highly compressed string fully describing the\n \ digraph ", count := [ 9, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 3, 9 ], mathmode := "Text", name := "A", next := 407241, root := ~, start := 407227, stop := 407240 ), rec( content := ". ", count := [ 9, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 3, 10 ], mathmode := "Text", name := "P", next := 407247, root := ~, start := 407243, stop := 407246 ), rec( content := "\n\n \ Graph6 and Digraph6 are formats best used on small, dense graphs, if\n appl\ icable. For larger, sparse graphs use ", count := [ 9, 2, 3, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "S\ parse6", count := [ 9, 2, 3, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 3, 10 ], mathmode := "Text", name := "E", next := 407382, root := ~, start := 407368, stop := 407381 ), rec( content := " and\n \ ", count := [ 9, 2, 3, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ isparse6", count := [ 9, 2, 3, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 3, 10 ], mathmode := "Text", name := "E", next := 407407, root := ~, start := 407391, stop := 407406 ), rec( content := " (this l\ atter also preserves multiple edges). ", count := [ 9, 2, 3, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 3, 11 ], mathmode := "Text", name := "P", next := 407457, root := ~, start := 407453, stop := 407456 ), rec( content := "\n\n \ See ", count := [ 9, 2, 3, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "WriteDi\ graphs" ), content := 0, count := [ 9, 2, 3, 11 ], mathmode := "Text", name := "Ref", next := 407494, root := ~, start := 407467, stop := 407493 ), rec( content := ".\n " , count := [ 9, 2, 3, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := Digraph([[2, 3], [1], [1]]);\n\ngap> Sparse6String(gr);\n\":Bc\"\ngap> DiSparse6String(gr);\n\".Bc{f\ \"\n", count := [ 9, 2, 3, 12 ], name := "PCDATA", root := ~ ) ], count := [ 9, 2, 3, 12 ], mathmode := "Text", name := "Example", next := 407681, root := ~, start := 407500, stop := 407680 ), rec( content := "\n ", count := [ 9, 2, 3, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 3, 9 ], mathmode := "Text", name := "Description", next := 407698, root := ~, start := 407121, stop := 407697 ) ], count := [ 9, 2, 3, 1 ], mathmode := "Text", name := "ManSection", next := 407712, root := ~, start := 406893, stop := 407711 ), rec( content := "\n\n ", count := [ 9, 2, 3, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "filename [, code\ r][, mode]", Name := "DigraphFile" ), content := 0, count := [ 9, 2, 4, 2 ], mathmode := "Text", name := "Func", next := 407792, root := ~, start := 407733, stop := 407791 ), rec( attributes := rec( ), content := [ rec( content := "An IO fil\ e object.", count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "Returns", next := 407832, root := ~, start := 407795, stop := 407831 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilename", count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "A", next := 407871, root := ~, start := 407856, stop := 407870 ), rec( content := " is a st\ ring representing the name of a file, then\n ", count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphFile", count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "C", next := 407944, root := ~, start := 407926, stop := 407943 ), rec( content := " returns\ an ", count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "IO" ), content := [ rec( content := "\n http://gap-packages\ .github.io/io/\n", count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "URL", next := 78, root := ~, start := 17, stop := 77 ) ], count := [ 9, 2, 4, 3 ], name := "Alt", next := 84, root := ~, start := 1, stop := 83 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "IO", count := [ 9, 2, 4, 3 ], name := \ "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 3 ], name := "Package", next := 122, root := ~, start := 101 , stop := 121 ) ], count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "Alt", next := 128, root := ~, start := 84, stop := 127 ), rec( content := " package\ file object for that file.\n ", count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "P", next := 408004, root := ~, start := 408000, stop := 408003 ), rec( content := "\n\n \ If the optional argument ", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ oder", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "A", next := 408047, root := ~, start := 408035, stop := 408046 ), rec( content := " is spec\ ified\n and is a function which either encodes a digraph as a string, or de\ codes a\n string into a digraph, then this function will be used when readi\ ng or\n writing to the returned file object. If the optional argument ", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "c\ oder", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "A", next := 408293, root := ~, start := 408281, stop := 408292 ), rec( content := "\n is\ not specified, then the encoding of the digraphs in the returned file\n ob\ ject must be specified in the the file extension. The file extension must\n \ be one of: ", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ g6", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "C", next := 408476, root := ~, start := 408466, stop := 408475 ), rec( content := ", ", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ s6", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "C", next := 408488, root := ~, start := 408478, stop := 408487 ), rec( content := ", ", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ d6", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "C", next := 408500, root := ~, start := 408490, stop := 408499 ), rec( content := ", ", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ ds6", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "C", next := 408513, root := ~, start := 408502, stop := 408512 ), rec( content := ", ", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ txt", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "C", next := 408526, root := ~, start := 408515, stop := 408525 ), rec( content := ",\n " , count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ p", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "C", next := 408541, root := ~, start := 408532, stop := 408540 ), rec( content := ", or ", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ pickle", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "C", next := 408560, root := ~, start := 408546, stop := 408559 ), rec( content := "; more d\ etails of these file formats is given\n below. ", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "P", next := 408621, root := ~, start := 408617, stop := 408620 ), rec( content := "\n\n \ If the optional argument ", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ode", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "A", next := 408663, root := ~, start := 408652, stop := 408662 ), rec( content := " is spec\ ified, then it must be one of:\n ", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ "w\"", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "C", next := 408716, root := ~, start := 408706, stop := 408715 ), rec( content := " (for wr\ ite), ", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ "a\"", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "C", next := 408740, root := ~, start := 408730, stop := 408739 ), rec( content := " (for ap\ pend), or ", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ "r\"", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "C", next := 408768, root := ~, start := 408758, stop := 408767 ), rec( content := " (for re\ ad).\n If ", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ode", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "A", next := 408799, root := ~, start := 408788, stop := 408798 ), rec( content := " is not \ specified, then ", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ "r\"", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "C", next := 408833, root := ~, start := 408823, stop := 408832 ), rec( content := " is used\ by default. ", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "P", next := 408858, root := ~, start := 408854, stop := 408857 ), rec( content := "\n\n \ If ", count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilename", count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "A", next := 408882, root := ~, start := 408867, stop := 408881 ), rec( content := " ends in\ one of: ", count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ gz", count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "C", next := 408909, root := ~, start := 408899, stop := 408908 ), rec( content := ", ", count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ bz2", count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "C", next := 408922, root := ~, start := 408911, stop := 408921 ), rec( content := ", or\n \ ", count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ xz", count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "C", next := 408941, root := ~, start := 408931, stop := 408940 ), rec( content := ", then t\ he digraphs which are read from, or written to, the\n returned file object \ are decompressed, or compressed, appropriately.\n ", count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 4, 7 ], mathmode := "Text", name := "P", next := 409082, root := ~, start := 409078, stop := 409081 ), rec( content := "\n\n \ The file object returned by ", count := [ 9, 2, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphFile", count := [ 9, 2, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 7 ], mathmode := "Text", name := "C", next := 409134, root := ~, start := 409116, stop := 409133 ), rec( content := " can be \ given as the first\n argument for either of the functions ", count := [ 9, 2, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "ReadDig\ raphs" ), content := 0, count := [ 9, 2, 4, 7 ], mathmode := "Text", name := "Ref", next := 409228, root := ~, start := 409202, stop := 409227 ), rec( content := " or ", count := [ 9, 2, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "WriteDi\ graphs" ), content := 0, count := [ 9, 2, 4, 7 ], mathmode := "Text", name := "Ref", next := 409265, root := ~, start := 409232, stop := 409264 ), rec( content := ". The pu\ rpose of this is to reduce the overhead of\n recreating the file object ins\ ide the functions ", count := [ 9, 2, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "ReadDig\ raphs" ), content := 0, count := [ 9, 2, 4, 7 ], mathmode := "Text", name := "Ref", next := 409394, root := ~, start := 409368, stop := 409393 ), rec( content := "\n or\ ", count := [ 9, 2, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( Func := "WriteDi\ graphs" ), content := 0, count := [ 9, 2, 4, 7 ], mathmode := "Text", name := "Ref", next := 409429, root := ~, start := 409402, stop := 409428 ), rec( content := " when, f\ or example, reading or writing many\n digraphs in a loop.\n ", count := [ 9, 2, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 4, 8 ], mathmode := "Text", name := "P", next := 409505, root := ~, start := 409501, stop := 409504 ), rec( content := "\n\n \ The currently supported file formats, and associated filename extensions,\n \ are:\n ", count := [ 9, 2, 4, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "graph6 (.g6)", count := [ 9, 2, 4, 9 ] , math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 9 ], name := "Mar\ k", next := 409636, root := ~, start := 409611, stop := 409635 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n\tA standard and widely-used format\ for undirected graphs, with no support\n\tfor loops or multiple edges. Only \ symmetric graphs are allowed -- each\n\tedge is combined with its converse edg\ e to produce a single undirected\n\tedge. This format is best used for \"dens\ e\" graphs -- those with many\n\tedges per vertex.\n ", count := [ 9, 2, \ 4, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 10 ], name := "Ite\ m", next := 409972, root := ~, start := 409643, stop := 409971 ), rec( attributes :\ = rec( ), content := [ rec( content := "sparse6 (.s6)", count := [ 9, 2, 4, 1\ 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 11 ], name := "Mar\ k", next := 410005, root := ~, start := 409979, stop := 410004 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n\tUnlike graph6, sparse6 has suppor\ t for loops and multiple edges.\n\tHowever, its use is still limited to symmet\ ric graphs. This format is\n\tbetter-suited to \"sparse\" graphs -- those wit\ h few edges per vertex.\n ", count := [ 9, 2, 4, 12 ], mathmode := "Text" , name\ := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 12 ], name := "Item", next := 4102\ 40, root := ~, start := 410012, stop := 410239 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "digraph6 (.d6)", count := [ 9, 2, 4, 13 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 13 ], name := "Mark", next := 4102\ 74, root := ~, start := 410247, stop := 410273 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "\n\tThis format is based on graph6, but stores direction information -\ \n\ttherefore is not limited to symmetric graphs. Loops are allowed, but\n\tm\ ultiple edges are not. Best compression with \"dense\" graphs.\n ", coun\ t := [ 9, 2, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 14 ], name := "Ite\ m", next := 410504, root := ~, start := 410281, stop := 410503 ), rec( attributes :\ = rec( ), content := [ rec( content := "disparse6 (.ds6)", count := [ 9, 2, 4\ , 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 15 ], name := "Mar\ k", next := 410540, root := ~, start := 410511, stop := 410539 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n\tAny type of digraph can be encode\ d in disparse6: directions, loops, and\n\tmultiple edges are all allowed. Sim\ ilar to sparse6, this has the best\n\tcompression rate with \"sparse\" graphs.\ \n ", count := [ 9, 2, 4, 16 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 9, 2, 4, 16 ], name := "Item", next := 410752, root := ~, start := 410\ 547, stop := 410751 ), rec( attributes := rec( ), content := [ rec( content :\ = "plain text (.txt)", count := [ 9, 2, 4, 17 ], mathmode := "Text", name := "\ PCDATA", root := ~ ) ], count := [ 9, 2, 4, 17 ], name := "Mark", next := 4107\ 89, root := ~, start := 410759, stop := 410788 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "\n\tThis is a human-readable format which stores graphs in the form\n \ ", count := [ 9, 2, 4, 18 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "0 7 0 8 1\ 7 2 8 3 8 4 8 5 8 6 8", count := [ 9, 2, 4, 18 ], mathmode := "Text", na\ me := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 18 ], mathmode := "Text", name\ := "C", next := 410921, root := ~, start := 410876, stop := 410920 ), rec( cont\ ent := " i.e. pairs of vertices\n describing edges in a graph. More spe\ cifically, the vertices making up\n one edge must be separated by a sin\ gle space, and pairs of vertices must\n be separated by two spaces. ", coun\ t := [ 9, 2, 4, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := 0, count := [ 9, 2, 4, 19 ], mathmode := "Text", name\ := "P", next := 411145, root := ~, start := 411141, stop := 411144 ), rec( cont\ ent := "\n\n See ", count := [ 9, 2, 4, 19 ], mathmode := "Text", name \ := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "ReadPlainTextDigrap\ h" ), content := 0, count := [ 9, 2, 4, 19 ], mathmode := "Text", name := "Ref\ ", next := 411193, root := ~, start := 411159, stop := 411192 ), rec( content \ := " for a more flexible way to store\n digraphs in a plain text file. \ ", count := [ 9, 2, 4, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attr\ ibutes := rec( ), content := 0, count := [ 9, 2, 4, 20 ], mathmode := "Text", name\ := "P", next := 411270, root := ~, start := 411266, stop := 411269 ), rec( cont\ ent := "\n ", count := [ 9, 2, 4, 20 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 9, 2, 4, 18 ], name := "Item", next := 411284, root := ~, start := 410\ 796, stop := 411283 ), rec( attributes := rec( ), content := [ rec( content :\ = "pickled (", count := [ 9, 2, 4, 21 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := ".p", count \ := [ 9, 2, 4, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count\ := [ 9, 2, 4, 21 ], mathmode := "Text", name := "F", next := 411316, root := \ ~, start := 411307, stop := 411315 ), rec( content := " or ", count := [ 9, 2,\ 4, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := ".pickle", count := [ 9, 2, 4, 21 ], m\ athmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 21 ], math\ mode := "Text", name := "F", next := 411334, root := ~, start := 411320, stop \ := 411333 ), rec( content := ")", count := [ 9, 2, 4, 21 ], mathmode := "Text" , name\ := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 21 ], name := "Mark", next := 4113\ 42, root := ~, start := 411292, stop := 411341 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "\n Digraphs are pickled using the ", count := [ 9, 2, 4, 22 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := \ "Text" ), content := [ rec( attributes := rec( Text := "IO" ), content := [ re\ c( content := "\n http://gap-packages.github.io/io/\n", count := [ 9, 2, 4\ , 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, \ 4, 22 ], mathmode := "Text", name := "URL", next := 78, root := ~, start := 17\ , stop := 77 ) ], count := [ 9, 2, 4, 22 ], name := "Alt", next := 84, root :=\ ~, start := 1, stop := 83 ), rec( attributes := rec( Only := "Text" ), conten\ t := [ rec( attributes := rec( ), content := [ rec( content := "IO", count :=\ [ 9, 2, 4, 22 ], name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 22 ], n\ ame := "Package", next := 122, root := ~, start := 101, stop := 121 ) ], count\ := [ 9, 2, 4, 22 ], mathmode := "Text", name := "Alt", next := 128, root := ~ , star\ t := 84, stop := 127 ), rec( content := " package. This is particularly good\n\ when the ", count := [ 9, 2, 4, 22 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ), rec( attributes := rec( Attr := "DigraphGroup" ), content :\ = 0, count := [ 9, 2, 4, 22 ], mathmode := "Text", name := "Ref", next := 4114\ 78, root := ~, start := 411452, stop := 411477 ), rec( content := " is non-tri\ vial.\n ", count := [ 9, 2, 4, 22 ], mathmode := "Text", name := "PCDATA" , root\ := ~ ) ], count := [ 9, 2, 4, 22 ], name := "Item", next := 411508, root := ~, start := 411\ 349, stop := 411507 ) ], count := [ 9, 2, 4, 9 ], mathmode := "Text", name := "List", next := 411520, root := ~, start := 409598, stop := 411519 ), rec( content := "\n\n \ ", count := [ 9, 2, 4, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> filename := Concatenation(DIGRAPHS_Dir(), \"/tst/out/man.d6.gz\");;\ngap\ > file := DigraphFile(filename, \"w\");;\ngap> for i in [1 .. 10] do\n> WriteD\ igraphs(file, Digraph([[1, 3], [2], [1, 2]]));\n> od;\ngap> IO_Close(file);;\n\ gap> file := DigraphFile(filename, \"r\");;\ngap> ReadDigraphs(file, 9);\n", count := [ 9, 2, 4, 25 ], name := "PCD\ ATA", root := ~ ) ], count := [ 9, 2, 4, 25 ], mathmode := "Text", name := "Example", next := 411895, root := ~, start := 411526, stop := 411894 ), rec( content := "\n ", count := [ 9, 2, 4, 26 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "Description", next := 411914, root := ~, start := 407835, stop := 411913 ) ], count := [ 9, 2, 4, 1 ], mathmode := "Text", name := "ManSection", next := 411928, root := ~, start := 407718, stop := 411927 ), rec( content := "\n\n ", count := [ 9, 2, 4, 26 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "filename[, decod\ er][, n]", Name := "ReadDigraphs" ), content := 0, count := [ 9, 2, 5, 2 ], mathmode := "Text", name := "Func", next := 412007, root := ~, start := 411949, stop := 412006 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ , or a list of digraphs.", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "Returns", next := 412062, root := ~, start := 412010, stop := 412061 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilename", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "A", next := 412101, root := ~, start := 412086, stop := 412100 ), rec( content := " is a st\ ring containing the name of a file containing\n encoded digraphs or an ", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "IO" ), content := [ rec( content := "\n http://gap-packages\ .github.io/io/\n", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "URL", next := 78, root := ~, start := 17, stop := 77 ) ], count := [ 9, 2, 5, 3 ], name := "Alt", next := 84, root := ~, start := 1, stop := 83 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "IO", count := [ 9, 2, 5, 3 ], name := \ "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 3 ], name := "Package", next := 122, root := ~, start := 101 , stop := 121 ) ], count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "Alt", next := 128, root := ~, start := 84, stop := 127 ), rec( content := " file ob\ ject created using ", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ File" ), content := 0, count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "Ref", next := 412244, root := ~, start := 412213, stop := 412243 ), rec( content := ", then " , count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "R\ eadDigraphs", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "C", next := 412270, root := ~, start := 412251, stop := 412269 ), rec( content := " returns\ the digraphs\n encoded in the file as a list. Note that if ", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilename", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "A", next := 412356, root := ~, start := 412341, stop := 412355 ), rec( content := " is a\n \ compressed file, which has been compressed appropriately to give a filename\ \n extension of ", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ gz", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "C", next := 412469, root := ~, start := 412459, stop := 412468 ), rec( content := ", ", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ bz2", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "C", next := 412482, root := ~, start := 412471, stop := 412481 ), rec( content := ", or ", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ xz", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "C", next := 412497, root := ~, start := 412487, stop := 412496 ), rec( content := ", then\n\ ", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "R\ eadDigraphs", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "C", next := 412527, root := ~, start := 412508, stop := 412526 ), rec( content := " can rea\ d ", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilename", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "A", next := 412552, root := ~, start := 412537, stop := 412551 ), rec( content := " without\ it first needing to be\n decompressed.\n ", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 5, 4 ], mathmode := "Text", name := "P", next := 412610, root := ~, start := 412606, stop := 412609 ), rec( content := "\n\n \ If the optional argument ", count := [ 9, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ ecoder", count := [ 9, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 4 ], mathmode := "Text", name := "A", next := 412655, root := ~, start := 412641, stop := 412654 ), rec( content := " is spec\ ified\n and is a function which decodes a string into a digraph,\n then \ ", count := [ 9, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "R\ eadDigraphs", count := [ 9, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 4 ], mathmode := "Text", name := "C", next := 412758, root := ~, start := 412739, stop := 412757 ), rec( content := " will us\ e ", count := [ 9, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ ecoder", count := [ 9, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 4 ], mathmode := "Text", name := "A", next := 412782, root := ~, start := 412768, stop := 412781 ), rec( content := " to deco\ de the digraphs\n contained in ", count := [ 9, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilename", count := [ 9, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 4 ], mathmode := "Text", name := "A", next := 412838, root := ~, start := 412823, stop := 412837 ), rec( content := ".", count := [ 9, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 5, 5 ], mathmode := "Text", name := "P", next := 412843, root := ~, start := 412839, stop := 412842 ), rec( content := "\n\n \ If the optional argument ", count := [ 9, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 9, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 5 ], mathmode := "Text", name := "A", next := 412882, root := ~, start := 412874, stop := 412881 ), rec( content := " is spec\ ified, then ", count := [ 9, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "R\ eadDigraphs", count := [ 9, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 5 ], mathmode := "Text", name := "C", next := 412921, root := ~, start := 412902, stop := 412920 ), rec( content := "\n re\ turns the ", count := [ 9, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 9, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 5 ], mathmode := "Text", name := "A", next := 412946, root := ~, start := 412938, stop := 412945 ), rec( content := "th digra\ ph encoded in the file ", count := [ 9, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilename", count := [ 9, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 5 ], mathmode := "Text", name := "A", next := 412992, root := ~, start := 412977, stop := 412991 ), rec( content := ".\n " , count := [ 9, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "P", next := 413002, root := ~, start := 412998, stop := 413001 ), rec( content := "\n\n \ If the optional argument ", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ ecoder", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "A", next := 413047, root := ~, start := 413033, stop := 413046 ), rec( content := " is not \ specified, then\n ", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "R\ eadDigraphs", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "C", next := 413094, root := ~, start := 413075, stop := 413093 ), rec( content := " will de\ duce which decoder to use based on the filename\n extension of ", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilename", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "A", next := 413182, root := ~, start := 413167, stop := 413181 ), rec( content := " (after \ removing the compression-related\n filename extensions ", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ gz", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "C", next := 413257, root := ~, start := 413247, stop := 413256 ), rec( content := ", ", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ bz2", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "C", next := 413270, root := ~, start := 413259, stop := 413269 ), rec( content := ", and ", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ xz", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "C", next := 413286, root := ~, start := 413276, stop := 413285 ), rec( content := "). For \ example,\n if the filename extension is ", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ g6", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "C", next := 413346, root := ~, start := 413336, stop := 413345 ), rec( content := ", then " , count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "R\ eadDigraphs", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "C", next := 413372, root := ~, start := 413353, stop := 413371 ), rec( content := " will us\ e\n the graph6 decoder ", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ FromGraph6String" ), content := 0, count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "Ref", next := 413442, root := ~, start := 413405, stop := 413441 ), rec( content := ".\n " , count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 5, 7 ], mathmode := "Text", name := "P", next := 413452, root := ~, start := 413448, stop := 413451 ), rec( content := "\n\n \ The currently supported file formats, and associated filename extensions,\n \ are:\n ", count := [ 9, 2, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "graph6 (.g6)", count := [ 9, 2, 5, 8 ] , math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 8 ], name := "Mar\ k", next := 413583, root := ~, start := 413558, stop := 413582 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n\tA standard and widely-used format\ for undirected graphs, with no support\n\tfor loops or multiple edges. Only \ symmetric graphs are allowed -- each\n\tedge is combined with its converse edg\ e to produce a single undirected\n\tedge. This format is best used for \"dens\ e\" graphs -- those with many\n\tedges per vertex.\n ", count := [ 9, 2, \ 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 9 ], name := "Ite\ m", next := 413919, root := ~, start := 413590, stop := 413918 ), rec( attributes :\ = rec( ), content := [ rec( content := "sparse6 (.s6)", count := [ 9, 2, 5, 1\ 0 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 10 ], name := "Mar\ k", next := 413952, root := ~, start := 413926, stop := 413951 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n\tUnlike graph6, sparse6 has suppor\ t for loops and multiple edges.\n\tHowever, its use is still limited to symmet\ ric graphs. This format is\n\tbetter-suited to \"sparse\" graphs -- those wit\ h few edges per vertex.\n ", count := [ 9, 2, 5, 11 ], mathmode := "Text" , name\ := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 11 ], name := "Item", next := 4141\ 87, root := ~, start := 413959, stop := 414186 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "digraph6 (.d6)", count := [ 9, 2, 5, 12 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 12 ], name := "Mark", next := 4142\ 21, root := ~, start := 414194, stop := 414220 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "\n\tThis format is based on graph6, but stores direction information -\ \n\ttherefore is not limited to symmetric graphs. Loops are allowed, but\n\tm\ ultiple edges are not. Best compression with \"dense\" graphs.\n ", coun\ t := [ 9, 2, 5, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 13 ], name := "Ite\ m", next := 414451, root := ~, start := 414228, stop := 414450 ), rec( attributes :\ = rec( ), content := [ rec( content := "disparse6 (.ds6)", count := [ 9, 2, 5\ , 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 14 ], name := "Mar\ k", next := 414487, root := ~, start := 414458, stop := 414486 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n\tAny type of digraph can be encode\ d in disparse6: directions, loops, and\n\tmultiple edges are all allowed. Sim\ ilar to sparse6, this has the best\n\tcompression rate with \"sparse\" graphs.\ \n ", count := [ 9, 2, 5, 15 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 9, 2, 5, 15 ], name := "Item", next := 414699, root := ~, start := 414\ 494, stop := 414698 ), rec( attributes := rec( ), content := [ rec( content :\ = "plain text (.txt)", count := [ 9, 2, 5, 16 ], mathmode := "Text", name := "\ PCDATA", root := ~ ) ], count := [ 9, 2, 5, 16 ], name := "Mark", next := 4147\ 36, root := ~, start := 414706, stop := 414735 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "\n\tThis is a human-readable format which stores graphs in the form\n \ ", count := [ 9, 2, 5, 17 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "0 7 0 8 1\ 7 2 8 3 8 4 8 5 8 6 8", count := [ 9, 2, 5, 17 ], mathmode := "Text", na\ me := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 17 ], mathmode := "Text", name\ := "C", next := 414868, root := ~, start := 414823, stop := 414867 ), rec( cont\ ent := " i.e. pairs of vertices\n describing edges in a graph. More spe\ cifically, the vertices making up\n one edge must be separated by a sin\ gle space, and pairs of vertices must\n be separated by two spaces. ", coun\ t := [ 9, 2, 5, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := 0, count := [ 9, 2, 5, 18 ], mathmode := "Text", name\ := "P", next := 415092, root := ~, start := 415088, stop := 415091 ), rec( cont\ ent := "\n\n See ", count := [ 9, 2, 5, 18 ], mathmode := "Text", name \ := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "ReadPlainTextDigrap\ h" ), content := 0, count := [ 9, 2, 5, 18 ], mathmode := "Text", name := "Ref\ ", next := 415140, root := ~, start := 415106, stop := 415139 ), rec( content \ := " for a more flexible way to store\n digraphs in a plain text file. \ ", count := [ 9, 2, 5, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attr\ ibutes := rec( ), content := 0, count := [ 9, 2, 5, 19 ], mathmode := "Text", name\ := "P", next := 415217, root := ~, start := 415213, stop := 415216 ), rec( cont\ ent := "\n", count := [ 9, 2, 5, 19 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( content := "\n Just so I remember:\n ReadPlainT\ extDigraph(\"data-local/soc-Epinions1.txt.gz\", \"\\t\", 1,\n '#');\ \n", count := [ 9, 2, 5, 19 ], mathmode := "Text", name := "XMLCOMMENT", root \ := ~ ), rec( content := "\n ", count := [ 9, 2, 5, 19 ], mathmode := "Tex\ t", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 17 ], name := "Item", next := 4153\ 62, root := ~, start := 414743, stop := 415361 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "pickled (", count := [ 9, 2, 5, 20 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ p", count := [ 9, 2, 5, 20 ], mathmode := "Text", name := "PCDATA", root := ~ \ ) ], count := [ 9, 2, 5, 20 ], mathmode := "Text", name := "F", next := 415394 , root\ := ~, start := 415385, stop := 415393 ), rec( content := " or ", count := [ 9\ , 2, 5, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribut\ es := rec( ), content := [ rec( content := ".pickle", count := [ 9, 2, 5, 20 \ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 20\ ], mathmode := "Text", name := "F", next := 415412, root := ~, start := 41539\ 8, stop := 415411 ), rec( content := ")", count := [ 9, 2, 5, 20 ], mathmode :\ = "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 20 ], name := "Mar\ k", next := 415420, root := ~, start := 415370, stop := 415419 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n Digraphs are pickled using \ the ", count := [ 9, 2, 5, 21 ], mathmode := "Text", name := "PCDATA", root :=\ ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "IO" ), content := [ rec( content := "\n http://gap-packages\ .github.io/io/\n", count := [ 9, 2, 5, 21 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 9, 2, 5, 21 ], mathmode := "Text", name := "URL\ ", next := 78, root := ~, start := 17, stop := 77 ) ], count := [ 9, 2, 5, 21 ] , name\ := "Alt", next := 84, root := ~, start := 1, stop := 83 ), rec( attributes :=\ rec( Only := "Text" ), content := [ rec( attributes := rec( ), content := [ \ rec( content := "IO", count := [ 9, 2, 5, 21 ], name := "PCDATA", root := ~ ) \ ], count := [ 9, 2, 5, 21 ], name := "Package", next := 122, root := ~, start \ := 101, stop := 121 ) ], count := [ 9, 2, 5, 21 ], mathmode := "Text", name :=\ "Alt", next := 128, root := ~, start := 84, stop := 127 ), rec( content := " \ package. This is particularly good\n when the ", count := [ 9, 2, 5, 21\ ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(\ Attr := "DigraphGroup" ), content := 0, count := [ 9, 2, 5, 21 ], mathmode :=\ "Text", name := "Ref", next := 415556, root := ~, start := 415530, stop := 41\ 5555 ), rec( content := " is non-trivial.\n ", count := [ 9, 2, 5, 21 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 21 ], name := "Ite\ m", next := 415586, root := ~, start := 415427, stop := 415585 ) ], count := [ 9, 2, 5, 8 ], mathmode := "Text", name := "List", next := 415598, root := ~, start := 413545, stop := 415597 ), rec( content := "\n\n \ ", count := [ 9, 2, 5, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> ReadDigraphs(\n> Concatenation(DIGRAPHS_Dir(), \"/data/graph5.g6.gz\"), \ 10);\n\ngap> ReadDigraphs(\n> Conc\ atenation(DIGRAPHS_Dir(), \"/data/graph5.g6.gz\"), 17);\n\ngap> ReadDigraphs(\n> Concatenation(DIGRAPHS_Dir(), \ \"/data/tree9.4.txt\"));\n[ , \n \ , \n , \n , \n , \n , \n , \n , \n , \n , \n , \n , \ \n , \n ]", count := [ 9, 2, 5, 24 ], name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 24 ], mathmode := "Text", name := "Example", next := 416644, root := ~, start := 415604, stop := 416643 ), rec( content := "\n ", count := [ 9, 2, 5, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "Description", next := 416663, root := ~, start := 412065, stop := 416662 ) ], count := [ 9, 2, 5, 1 ], mathmode := "Text", name := "ManSection", next := 416677, root := ~, start := 411934, stop := 416676 ), rec( content := "\n\n ", count := [ 9, 2, 5, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "filename, digrap\ hs[, encoder] [, mode]", Name := "WriteDigraphs" ), content := 0, count := [ 9, 2, 6, 2 ], mathmode := "Text", name := "Func", next := 416771, root := ~, start := 416698, stop := 416770 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraphs", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "A", next := 416810, root := ~, start := 416795, stop := 416809 ), rec( content := " is a li\ st of digraphs or a digraph and ", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilename", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "A", next := 416865, root := ~, start := 416850, stop := 416864 ), rec( content := "\n is\ a string or an ", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\ rec( Text := "IO" ), content := [ rec( content := "\n http://gap-packages\ .github.io/io/\n", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "URL", next := 78, root := ~, start := 17, stop := 77 ) ], count := [ 9, 2, 6, 3 ], name := "Alt", next := 84, root := ~, start := 1, stop := 83 ), rec( attributes := rec( Only := "Text" ) , content := [ rec( attributes :=\ rec( ), content := [ rec( content := "IO", count := [ 9, 2, 6, 3 ], name := \ "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 3 ], name := "Package", next := 122, root := ~, start := 101 , stop := 121 ) ], count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "Alt", next := 128, root := ~, start := 84, stop := 127 ), rec( content := " file ob\ ject created using ", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digraph\ File" ), content := 0, count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "Ref", next := 416944, root := ~, start := 416919, stop := 416943 ), rec( content := ",\n t\ hen ", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "W\ riteDigraphs", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "C", next := 416975, root := ~, start := 416955, stop := 416974 ), rec( content := " writes \ the digraphs to the file represented by\n ", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilename", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "A", next := 417042, root := ~, start := 417027, stop := 417041 ), rec( content := ". If th\ e supplied filename ends in one of the extensions\n ", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ gz", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "C", next := 417114, root := ~, start := 417104, stop := 417113 ), rec( content := ", ", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ bz2", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "C", next := 417127, root := ~, start := 417116, stop := 417126 ), rec( content := ", or ", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ xz", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "C", next := 417142, root := ~, start := 417132, stop := 417141 ), rec( content := ", then t\ he file will be compressed\n appropriately. Excluding these extensions, if\ the file ends with an\n extension in the list below, the corresponding gra\ ph format will be used to\n encode it. If such an extension is not include\ d, an appropriate format\n will be chosen intelligently, and an extension a\ ppended, to minimise file\n size.\n ", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 6, 4 ], mathmode := "Text", name := "P", next := 417502, root := ~, start := 417498, stop := 417501 ), rec( content := "\n\n \ ", count := [ 9, 2, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( content := " TODO: e\ ncode and mode. ", count := [ 9, 2, 6, 4 ], mathmode := "Text", name := "XMLCOMMENT" , root := ~ ), rec( content := "\n\n \ For more verbose information on the progress of the function, set the info\n \ level of ", count := [ 9, 2, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ nfoDigraphs", count := [ 9, 2, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 4 ], mathmode := "Text", name := "A", next := 417652, root := ~, start := 417633, stop := 417651 ), rec( content := " to 1 or\ higher, using ", count := [ 9, 2, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "S\ etInfoLevel", count := [ 9, 2, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 4 ], mathmode := "Text", name := "C", next := 417694, root := ~, start := 417675, stop := 417693 ), rec( content := ".", count := [ 9, 2, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 6, 5 ], mathmode := "Text", name := "P", next := 417699, root := ~, start := 417695, stop := 417698 ), rec( content := "\n\n \ The currently supported file formats are:\n ", count := [ 9, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "graph6 (.g6)", count := [ 9, 2, 6, 6 ] , math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 6 ], name := "Mar\ k", next := 417789, root := ~, start := 417764, stop := 417788 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n\tA standard and widely-used format\ for undirected graphs, with no support\n\tfor loops or multiple edges. Only \ symmetric graphs are allowed -- each\n\tedge is combined with its converse edg\ e to produce a single undirected\n\tedge. This format is best used for \"dens\ e\" graphs -- those with many\n\tedges per vertex.\n ", count := [ 9, 2, \ 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 7 ], name := "Ite\ m", next := 418125, root := ~, start := 417796, stop := 418124 ), rec( attributes :\ = rec( ), content := [ rec( content := "sparse6 (.s6)", count := [ 9, 2, 6, 8\ ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 8 ], name := "Mar\ k", next := 418158, root := ~, start := 418132, stop := 418157 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n\tUnlike graph6, sparse6 has suppor\ t for loops and multiple edges.\n\tHowever, its use is still limited to symmet\ ric graphs. This format is\n\tbetter-suited to \"sparse\" graphs -- those wit\ h few edges per vertex.\n ", count := [ 9, 2, 6, 9 ], mathmode := "Text", name\ := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 9 ], name := "Item", next := 4183\ 93, root := ~, start := 418165, stop := 418392 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "digraph6 (.d6)", count := [ 9, 2, 6, 10 ], mathmode := "Text", name :=\ "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 10 ], name := "Mark", next := 4184\ 27, root := ~, start := 418400, stop := 418426 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "\n\tThis format is based on graph6, but stores direction information -\ \n\ttherefore is not limited to symmetric graphs. Loops are allowed, but\n\tm\ ultiple edges are not. Best compression with \"dense\" graphs.\n ", coun\ t := [ 9, 2, 6, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 11 ], name := "Ite\ m", next := 418657, root := ~, start := 418434, stop := 418656 ), rec( attributes :\ = rec( ), content := [ rec( content := "disparse6 (.ds6)", count := [ 9, 2, 6\ , 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 12 ], name := "Mar\ k", next := 418693, root := ~, start := 418664, stop := 418692 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n\tAny type of digraph can be encode\ d in disparse6: directions, loops, and\n\tmultiple edges are all allowed. Sim\ ilar to sparse6, this has the best\n\tcompression rate with \"sparse\" graphs.\ \n ", count := [ 9, 2, 6, 13 ], mathmode := "Text", name := "PCDATA", root\ := ~ ) ], count := [ 9, 2, 6, 13 ], name := "Item", next := 418905, root := ~, start := 418\ 700, stop := 418904 ), rec( attributes := rec( ), content := [ rec( content :\ = "plain text (.txt)", count := [ 9, 2, 6, 14 ], mathmode := "Text", name := "\ PCDATA", root := ~ ) ], count := [ 9, 2, 6, 14 ], name := "Mark", next := 4189\ 43, root := ~, start := 418913, stop := 418942 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "\n\tThis is a human-readable format which stores graphs in the form\n \ ", count := [ 9, 2, 6, 15 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := "0 7 0 8 1\ 7 2 8 3 8 4 8 5 8 6 8", count := [ 9, 2, 6, 15 ], mathmode := "Text", na\ me := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 15 ], mathmode := "Text", name\ := "C", next := 419075, root := ~, start := 419030, stop := 419074 ), rec( cont\ ent := " i.e. pairs of vertices\n describing edges in a graph. More spe\ cifically, the vertices making up\n one edge must be separated by a sin\ gle space, and pairs of vertices must\n be separated by two spaces. ", coun\ t := [ 9, 2, 6, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := 0, count := [ 9, 2, 6, 16 ], mathmode := "Text", name\ := "P", next := 419299, root := ~, start := 419295, stop := 419298 ), rec( cont\ ent := "\n\n See ", count := [ 9, 2, 6, 16 ], mathmode := "Text", name \ := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "ReadPlainTextDigrap\ h" ), content := 0, count := [ 9, 2, 6, 16 ], mathmode := "Text", name := "Ref\ ", next := 419347, root := ~, start := 419313, stop := 419346 ), rec( content \ := " for a more flexible way to store\n digraphs in a plain text file. \ ", count := [ 9, 2, 6, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attr\ ibutes := rec( ), content := 0, count := [ 9, 2, 6, 17 ], mathmode := "Text", name\ := "P", next := 419424, root := ~, start := 419420, stop := 419423 ), rec( cont\ ent := "\n", count := [ 9, 2, 6, 17 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( content := "\n Just so I remember:\n ReadPlainT\ extDigraph(\"data-local/soc-Epinions1.txt.gz\", \"\\t\", 1, '#');\n", coun\ t := [ 9, 2, 6, 17 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), rec( cont\ ent := "\n ", count := [ 9, 2, 6, 17 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 9, 2, 6, 15 ], name := "Item", next := 419561, root := ~, start := 418\ 950, stop := 419560 ), rec( attributes := rec( ), content := [ rec( content :\ = "pickled (", count := [ 9, 2, 6, 18 ], mathmode := "Text", name := "PCDATA", root\ := ~ ), rec( attributes := rec( ), content := [ rec( content := ".p", count \ := [ 9, 2, 6, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count\ := [ 9, 2, 6, 18 ], mathmode := "Text", name := "F", next := 419592, root := \ ~, start := 419583, stop := 419591 ), rec( content := " or ", count := [ 9, 2,\ 6, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\ = rec( ), content := [ rec( content := ".pickle", count := [ 9, 2, 6, 18 ], m\ athmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 18 ], math\ mode := "Text", name := "F", next := 419610, root := ~, start := 419596, stop \ := 419609 ), rec( content := ")", count := [ 9, 2, 6, 18 ], mathmode := "Text" , name\ := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 18 ], name := "Mark", next := 4196\ 18, root := ~, start := 419568, stop := 419617 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "\n Digraphs are pickled using the ", count := [ 9, 2, 6, 19 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := \ "Text" ), content := [ rec( attributes := rec( Text := "IO" ), content := [ re\ c( content := "\n http://gap-packages.github.io/io/\n", count := [ 9, 2, 6\ , 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, \ 6, 19 ], mathmode := "Text", name := "URL", next := 78, root := ~, start := 17\ , stop := 77 ) ], count := [ 9, 2, 6, 19 ], name := "Alt", next := 84, root :=\ ~, start := 1, stop := 83 ), rec( attributes := rec( Only := "Text" ), conten\ t := [ rec( attributes := rec( ), content := [ rec( content := "IO", count :=\ [ 9, 2, 6, 19 ], name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 19 ], n\ ame := "Package", next := 122, root := ~, start := 101, stop := 121 ) ], count\ := [ 9, 2, 6, 19 ], mathmode := "Text", name := "Alt", next := 128, root := ~ , star\ t := 84, stop := 127 ), rec( content := " package. This is particularly good\n\ when the ", count := [ 9, 2, 6, 19 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ), rec( attributes := rec( Attr := "DigraphGroup" ), content :\ = 0, count := [ 9, 2, 6, 19 ], mathmode := "Text", name := "Ref", next := 4197\ 54, root := ~, start := 419728, stop := 419753 ), rec( content := " is non-tri\ vial.\n ", count := [ 9, 2, 6, 19 ], mathmode := "Text", name := "PCDATA" , root\ := ~ ) ], count := [ 9, 2, 6, 19 ], name := "Item", next := 419784, root := ~, start := 419\ 625, stop := 419783 ) ], count := [ 9, 2, 6, 6 ], mathmode := "Text", name := "List", next := 419796, root := ~, start := 417751, stop := 419795 ), rec( content := "\n\n \ ", count := [ 9, 2, 6, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> grs := [];;\ngap> grs[1] := Digraph([]);\n\ngap> grs[2] := Digraph([[1, 3], [2], [1, 2]]);\n\ngap> grs[3] := Digraph([\n> [6, 7], [6, 9], [1, 3\ , 4, 5, 8, 9],\n> [1, 2, 3, 4, 5, 6, 7, 10], [1, 5, 6, 7, 10], [2, 4, 5, 9, 10\ ],\n> [3, 4, 5, 6, 7, 8, 9, 10], [1, 3, 5, 7, 8, 9], [1, 2, 5],\n> [1, 2, 4, 6\ , 7, 8]]);\n\ngap> filename := C\ oncatenation(DIGRAPHS_Dir(), \"/tst/out/man.d6.gz\");;\ngap> WriteDigraphs(fil\ ename, grs, \"w\");\nIO_OK\ngap> ReadDigraphs(filename);\n[ , \n , \n \ ]", count := [ 9, 2, 6, 22 ], name := "PCD\ ATA", root := ~ ) ], count := [ 9, 2, 6, 22 ], mathmode := "Text", name := "Example", next := 420563, root := ~, start := 419802, stop := 420562 ), rec( content := "\n ", count := [ 9, 2, 6, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "Description", next := 420582, root := ~, start := 416774, stop := 420581 ) ], count := [ 9, 2, 6, 1 ], mathmode := "Text", name := "ManSection", next := 420596, root := ~, start := 416683, stop := 420595 ), rec( content := "\n\n ", count := [ 9, 2, 6, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "filename [, deco\ der]", Name := "IteratorFromDigraphFile" ), content := 0, count := [ 9, 2, 7, 2 ], mathmode := "Text", name := "Func", next := 420682, root := ~, start := 420617, stop := 420681 ), rec( attributes := rec( ), content := [ rec( content := "An iterat\ or.", count := [ 9, 2, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 7, 3 ], mathmode := "Text", name := "Returns", next := 420716, root := ~, start := 420685, stop := 420715 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 9, 2, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilename", count := [ 9, 2, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 7, 3 ], mathmode := "Text", name := "A", next := 420755, root := ~, start := 420740, stop := 420754 ), rec( content := " is a st\ ring representing the name of a file containing\n encoded digraphs, then ", count := [ 9, 2, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ teratorFromDigraphFile", count := [ 9, 2, 7, 3 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 2, 7, 3 ], mathmode := "Text", name := "C", next := 420868, root := ~, start := 420838, stop := 420867 ), rec( content := " returns\ an iterator\n for which the value of ", count := [ 9, 2, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( BookName := "ref\ ", Oper := "NextIterator" ), content := 0, count := [ 9, 2, 7, 3 ], mathmode := "Text", name := "Ref", next := 420957, root := ~, start := 420916, stop := 420956 ), rec( content := " is the\\ n next digraph encoded in the file.\n ", count := [ 9, 2, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 7, 4 ], mathmode := "Text", name := "P", next := 421011, root := ~, start := 421007, stop := 421010 ), rec( content := "\n\n \ If the optional argument ", count := [ 9, 2, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ ecoder", count := [ 9, 2, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 7, 4 ], mathmode := "Text", name := "A", next := 421056, root := ~, start := 421042, stop := 421055 ), rec( content := " is spec\ ified and is a function\n which decodes a string into a digraph, then ", count := [ 9, 2, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "I\ teratorFromDigraphFile", count := [ 9, 2, 7, 4 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 2, 7, 4 ], mathmode := "Text", name := "C", next := 421166, root := ~, start := 421136, stop := 421165 ), rec( content := "\n wi\ ll use ", count := [ 9, 2, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ ecoder", count := [ 9, 2, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 7, 4 ], mathmode := "Text", name := "A", next := 421194, root := ~, start := 421180, stop := 421193 ), rec( content := " to deco\ de the digraphs contained in ", count := [ 9, 2, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilename", count := [ 9, 2, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 7, 4 ], mathmode := "Text", name := "A", next := 421246, root := ~, start := 421231, stop := 421245 ), rec( content := ".\n " , count := [ 9, 2, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 7, 5 ], mathmode := "Text", name := "P", next := 421256, root := ~, start := 421252, stop := 421255 ), rec( content := "\n\n \ The purpose of this function is to easily allow looping over digraphs\n enc\ oded in a file when loading all of the encoded digraphs would require\n too\ much memory. ", count := [ 9, 2, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 7, 6 ], mathmode := "Text", name := "P", next := 421434, root := ~, start := 421430, stop := 421433 ), rec( content := "\n\n \ To see what file types are available, see ", count := [ 9, 2, 7, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "WriteDi\ graphs" ), content := 0, count := [ 9, 2, 7, 6 ], mathmode := "Text", name := "Ref", next := 421509, root := ~, start := 421482, stop := 421508 ), rec( content := ".\n\n \ ", count := [ 9, 2, 7, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "\\ ngap> filename := Concatenation(DIGRAPHS_Dir(), \"/tst/out/man.d6.gz\");;\ngap\ > file := DigraphFile(filename, \"w\");;\ngap> for i in [1 .. 10] do\n> Writ\ eDigraphs(file, Digraph([[1, 3], [2], [1, 2]]));\n> od;\ngap> IO_Close(file);;\ \ngap> iter := IteratorFromDigraphFile(filename);\n\ngap> for x in i\ ter do od;\n", count := [ 9, 2, 7, 7 ], name := "PCDATA", root := ~ ) ], count := [ 9, 2, 7, 7 ], mathmode := "Text", name := "Example", next := 421858, root := ~, start := 421516, stop := 421857 ), rec( content := "\n ", count := [ 9, 2, 7, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 7, 3 ], mathmode := "Text", name := "Description", next := 421875, root := ~, start := 420719, stop := 421874 ) ], count := [ 9, 2, 7, 1 ], mathmode := "Text", name := "ManSection", next := 421889, root := ~, start := 420602, stop := 421888 ), rec( content := "\n\n ", count := [ 9, 2, 7, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "delimiter1, [del\ imiter2,] offset", Name := "DigraphPlainTextLineEncoder" ), content := 0, count := [ 9, 2, 8, 2 ], mathmode := "Text", name := "Func", next := 421991, root := ~, start := 421910, stop := 421990 ), rec( attributes := rec( Arg := "delimiter1, [del\ imiter2,] offset", Name := "DigraphPlainTextLineDecoder" ), content := 0, count := [ 9, 2, 8, 4 ], mathmode := "Text", name := "Oper", next := 422075, root := ~, start := 421994, stop := 422074 ), rec( attributes := rec( ), content := [ rec( content := "A string.\ ", count := [ 9, 2, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 8, 5 ], mathmode := "Text", name := "Returns", next := 422106, root := ~, start := 422078, stop := 422105 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ se two functions return a function which encodes or decodes a digraph in\n \ a plain text format.", count := [ 9, 2, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 8, 6 ], mathmode := "Text", name := "P", next := 422231, root := ~, start := 422227, stop := 422230 ), rec( content := "\n\n \ ", count := [ 9, 2, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphPlainTextLineEncoder", count := [ 9, 2, 8, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 2, 8, 6 ], mathmode := "Text", name := "A", next := 422271, root := ~, start := 422237, stop := 422270 ), rec( content := " returns\ a function which takes a single\n digraph as an argument. The function re\ turns a string describing the edges\n of that digraph; each edge is written\ as a pair of integers separated by the\n string ", count := [ 9, 2, 8, 6 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ elimiter2", count := [ 9, 2, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 8, 6 ], mathmode := "Text", name := "A", next := 422501, root := ~, start := 422484, stop := 422500 ), rec( content := ", and th\ e edges themselves are separated by the\n string ", count := [ 9, 2, 8, 6 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ elimiter1", count := [ 9, 2, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 8, 6 ], mathmode := "Text", name := "A", next := 422577, root := ~, start := 422560, stop := 422576 ), rec( content := ". ", count := [ 9, 2, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphPlainTextLineDecoder", count := [ 9, 2, 8, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 2, 8, 6 ], mathmode := "Text", name := "A", next := 422614, root := ~, start := 422580, stop := 422613 ), rec( content := " returns\ the\n corresponding decoder function, which takes a string argument in thi\ s format\n and returns a digraph.", count := [ 9, 2, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 8, 7 ], mathmode := "Text", name := "P", next := 422738, root := ~, start := 422734, stop := 422737 ), rec( content := "\n\n \ If only one delimiter is passed as an argument to\n ", count := [ 9, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphPlainTextLineDecoder", count := [ 9, 2, 8, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 2, 8, 7 ], mathmode := "Text", name := "A", next := 422832, root := ~, start := 422798, stop := 422831 ), rec( content := ", it wil\ l return a function which decodes\n a single edge, returning its contents a\ s a list of integers.", count := [ 9, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 8, 8 ], mathmode := "Text", name := "P", next := 422942, root := ~, start := 422938, stop := 422941 ), rec( content := "\n\n \ The argument ", count := [ 9, 2, 8, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ ffset", count := [ 9, 2, 8, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 8, 8 ], mathmode := "Text", name := "A", next := 422974, root := ~, start := 422961, stop := 422973 ), rec( content := " should \ be an integer, which will describe a\n number to be added to each vertex be\ fore it is encoded, or after it is\n decoded. This may be used, for exampl\ e, to label vertices starting at 0\n instead of 1.", count := [ 9, 2, 8, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 8, 9 ], mathmode := "Text", name := "P", next := 423192, root := ~, start := 423188, stop := 423191 ), rec( content := "\n\n \ Note that the number of vertices of a digraph is not stored, and so vertices\n\ which are not connected to any edge may be lost.\n\n ", count := [ 9, 2, 8, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := Digraph([[2, 3], [1], [1]]);\n\ngap> enc := DigraphPlainTextLineEncoder(\" \", \" \", -1);;\ngap> d\ ec := DigraphPlainTextLineDecoder(\" \", \" \", 1);;\ngap> enc(gr);\n\"0 1 0\ 2 1 0 2 0\"\ngap> dec(last);\n\ \n", count := [ 9, 2, 8, 10 ], name := "PCDATA", root := ~ ) ], count := [ 9, 2, 8, 10 ], mathmode := "Text", name := "Example", next := 423659, root := ~, start := 423333, stop := 423658 ), rec( content := "\n ", count := [ 9, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 8, 5 ], mathmode := "Text", name := "Description", next := 423676, root := ~, start := 422109, stop := 423675 ) ], count := [ 9, 2, 8, 1 ], mathmode := "Text", name := "ManSection", next := 423690, root := ~, start := 421895, stop := 423689 ), rec( content := "\n\n ", count := [ 9, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "str", Name := "TournamentLineD\ ecoder" ), content := 0, count := [ 9, 2, 9, 2 ], mathmode := "Text", name := "Oper", next := 423757, root := ~, start := 423711, stop := 423756 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 9, 2, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 9, 3 ], mathmode := "Text", name := "Returns", next := 423789, root := ~, start := 423760, stop := 423788 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function takes a string ", count := [ 9, 2, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ tr", count := [ 9, 2, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 9, 3 ], mathmode := "Text", name := "A", next := 423849, root := ~, start := 423839, stop := 423848 ), rec( content := ", decode\ s it, and then returns the\n tournament [see ", count := [ 9, 2, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsTourn\ ament" ), content := 0, count := [ 9, 2, 9, 3 ], mathmode := "Text", name := "Ref", next := 423930, root := ~, start := 423904, stop := 423929 ), rec( content := "] which \ it defines, according to\n the following rules. ", count := [ 9, 2, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 9, 4 ], mathmode := "Text", name := "P", next := 423992, root := ~, start := 423988, stop := 423991 ), rec( content := "\n\n \ The characters of the string ", count := [ 9, 2, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ tr", count := [ 9, 2, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 9, 4 ], mathmode := "Text", name := "A", next := 424037, root := ~, start := 424027, stop := 424036 ), rec( content := " represe\ nt the entries in the upper\n triangle of a tournament's adjacency matrix. \ The number of vertices\n ", count := [ 9, 2, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 9, 2, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 9, 4 ], mathmode := "Text", name := "C", next := 424157, root := ~, start := 424149, stop := 424156 ), rec( content := " will be\ detected from the length of the string and will be as\n large as possible.\ ", count := [ 9, 2, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "P", next := 424248, root := ~, start := 424244, stop := 424247 ), rec( content := "\n\n \ The first character represents the possible edge ", count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "1\ -> 2", count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "C", next := 424316, root := ~, start := 424303, stop := 424315 ), rec( content := ", the se\ cond\n represents ", count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "1\ -> 3", count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "C", next := 424357, root := ~, start := 424344, stop := 424356 ), rec( content := " and so \ on until ", count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "1\ -> n", count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "C", next := 424387, root := ~, start := 424374, stop := 424386 ), rec( content := "; then t\ he following\n character represents ", count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "2\ -> 3", count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "C", next := 424446, root := ~, start := 424433, stop := 424445 ), rec( content := ", and so\ on up to the character which\n represents the edge ", count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ -1 -> n", count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "C", next := 424523, root := ~, start := 424508, stop := 424522 ), rec( content := ". ", count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "P", next := 424529, root := ~, start := 424525, stop := 424528 ), rec( content := "\n\n \ If a character of the string with corresponding edge ", count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ -> j", count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "C", next := 424601, root := ~, start := 424588, stop := 424600 ), rec( content := " is equa\ l\n to ", count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "1\ ", count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "C", next := 424626, root := ~, start := 424618, stop := 424625 ), rec( content := ", then t\ he edge ", count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ -> j", count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "C", next := 424655, root := ~, start := 424642, stop := 424654 ), rec( content := " is pres\ ent in the tournament.\n Otherwise, the edge ", count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ -> j", count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "C", next := 424723, root := ~, start := 424710, stop := 424722 ), rec( content := " is pres\ ent instead. In this way, all the\n possible edges are encoded one-by-one.\ \n\n ", count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := TournamentLineDecoder(\"100001\");\n\ngap> OutNeighbours(gr);\n[ [ 2 ], [ ], [ 1, 2, 4 ], [ 1, 2 ] \ ]\n", count := [ 9, 2, 9, 7 ], name := "PCDATA", root := ~ ) ], count := [ 9, 2, 9, 7 ], mathmode := "Text", name := "Example", next := 424998, root := ~, start := 424814, stop := 424997 ), rec( content := "\n ", count := [ 9, 2, 9, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 9, 3 ], mathmode := "Text", name := "Description", next := 425015, root := ~, start := 423792, stop := 425014 ) ], count := [ 9, 2, 9, 1 ], mathmode := "Text", name := "ManSection", next := 425029, root := ~, start := 423696, stop := 425028 ), rec( content := "\n\n ", count := [ 9, 2, 9, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "str", Name := "AdjacencyMatrix\ UpperTriangleLineDecoder" ), content := 0, count := [ 9, 2, 10, 2 ], mathmode := "Text", name := "Oper", next := 425114, root := ~, start := 425050, stop := 425113 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 9, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 10, 3 ], mathmode := "Text", name := "Returns", next := 425146, root := ~, start := 425117, stop := 425145 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function takes a string ", count := [ 9, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ tr", count := [ 9, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 10, 3 ], mathmode := "Text", name := "A", next := 425206, root := ~, start := 425196, stop := 425205 ), rec( content := ", decode\ s it, and then returns the\n topologically sorted digraph [see ", count := [ 9, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digraph\ TopologicalSort" ), content := 0, count := [ 9, 2, 10, 3 ], mathmode := "Text", name := "Ref", next := 425315, root := ~, start := 425279, stop := 425314 ), rec( content := "]\n w\ hich it defines, according to the following rules. ", count := [ 9, 2, 10, 3 ] , mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 10, 4 ], mathmode := "Text", name := "P", next := 425377, root := ~, start := 425373, stop := 425376 ), rec( content := "\n\n \ The characters of the string ", count := [ 9, 2, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ tr", count := [ 9, 2, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 10, 4 ], mathmode := "Text", name := "A", next := 425422, root := ~, start := 425412, stop := 425421 ), rec( content := " represe\ nt the entries in the upper\n triangle of a digraph's adjacency matrix. The\ number of vertices ", count := [ 9, 2, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ ", count := [ 9, 2, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 10, 4 ], mathmode := "Text", name := "C", next := 425535, root := ~, start := 425527, stop := 425534 ), rec( content := "\n wi\ ll be detected from the length of the string and will be as large as\n poss\ ible. ", count := [ 9, 2, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "P", next := 425630, root := ~, start := 425626, stop := 425629 ), rec( content := "\n\n \ The first character represents the possible edge ", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "1\ -> 2", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "C", next := 425698, root := ~, start := 425685, stop := 425697 ), rec( content := ", the se\ cond\n represents ", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "1\ -> 3", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "C", next := 425739, root := ~, start := 425726, stop := 425738 ), rec( content := " and so \ on until ", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "1\ -> n", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "C", next := 425769, root := ~, start := 425756, stop := 425768 ), rec( content := "; then t\ he following\n character represents ", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "2\ -> 3", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "C", next := 425828, root := ~, start := 425815, stop := 425827 ), rec( content := ", and so\ on up to the character which\n represents the edge ", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "n\ -1 -> n", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "C", next := 425905, root := ~, start := 425890, stop := 425904 ), rec( content := ". If a \ character of the string with\n corresponding edge ", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "i\ -> j", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "C", next := 425978, root := ~, start := 425965, stop := 425977 ), rec( content := " is equa\ l to ", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "1\ ", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "C", next := 425999, root := ~, start := 425991, stop := 425998 ), rec( content := ", then t\ his edge is\n present in the digraph. Otherwise, it is not present. In thi\ s way, all the\n possible edges are encoded one-by-one. ", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 10, 6 ], mathmode := "Text", name := "P", next := 426146, root := ~, start := 426142, stop := 426145 ), rec( content := "\n\n \ In particular, note that there exists no edge ", count := [ 9, 2, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ i, j]", count := [ 9, 2, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 10, 6 ], mathmode := "Text", name := "C", next := 426211, root := ~, start := 426198, stop := 426210 ), rec( content := " if ", count := [ 9, 2, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "j\ \\leq\n i", count := [ 9, 2, 10, 6 ], mathmode := "Text", name := "PCDAT\ A", root := ~ ) ], count := [ 9, 2, 10, 6 ], mathmode := "Text", name := "M", next := 426236, root := ~, start := 426215, stop := 426235 ), rec( content := ". In or\ der words, the digraph will be topologically sorted.\n\n ", count := [ 9, 2, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := AdjacencyMatrixUpperTriangleLineDecoder(\"100001\");\n\ngap> OutNeighbours(gr);\n[ [ 2 ], [ ], [ 4 \ ], [ ] ]\ngap> gr := AdjacencyMatrixUpperTriangleLineDecoder(\"111111x111\");\ \n\ngap> OutNeighbours(gr);\n[ [ 2\ , 3, 4, 5 ], [ 3, 4 ], [ 4, 5 ], [ 5 ], [ ] ]\n", count := [ 9, 2, 10, 7 ], name := "PCD\ ATA", root := ~ ) ], count := [ 9, 2, 10, 7 ], mathmode := "Text", name := "Example", next := 426681, root := ~, start := 426302, stop := 426680 ), rec( content := "\n ", count := [ 9, 2, 10, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 10, 3 ], mathmode := "Text", name := "Description", next := 426698, root := ~, start := 425149, stop := 426697 ) ], count := [ 9, 2, 10, 1 ], mathmode := "Text", name := "ManSection", next := 426712, root := ~, start := 425035, stop := 426711 ), rec( content := "\n\n ", count := [ 9, 2, 10, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "str", Name := "TCodeDecoder" ) , content := 0, count := [ 9, 2, 11, 2 ], mathmode := "Text", name := "Oper", next := 426770, root := ~, start := 426733, stop := 426769 ), rec( attributes := rec( ), content := [ rec( content := "A digraph\ .", count := [ 9, 2, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 11, 3 ], mathmode := "Text", name := "Returns", next := 426802, root := ~, start := 426773, stop := 426801 ), rec( attributes := rec( ), content := [ rec( content := "\n If \ ", count := [ 9, 2, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "s\ tr", count := [ 9, 2, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 11, 3 ], mathmode := "Text", name := "A", next := 426836, root := ~, start := 426826, stop := 426835 ), rec( content := " is a st\ ring consisting of at least two non-negative integers\n separated by spaces\ , then this function will attempt to return the digraph\n which it defines \ as a TCode string. ", count := [ 9, 2, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "P", next := 427021, root := ~, start := 427017, stop := 427020 ), rec( content := "\n\n \ The first integer of the string defines the number of vertices ", count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "C", next := 427098, root := ~, start := 427090, stop := 427097 ), rec( content := " in\n \ the digraph, and the second defines the number of edges ", count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "e\ ", count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "C", next := 427170, root := ~, start := 427162, stop := 427169 ), rec( content := ". The\n\ following ", count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "2\ e", count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "C", next := 427200, root := ~, start := 427191, stop := 427199 ), rec( content := " integer\ s should be vertex numbers in the range ", count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ 0 ..\n v-1]", count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "PCDA\ TA", root := ~ ) ], count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "C", next := 427271, root := ~, start := 427248, stop := 427270 ), rec( content := ". These \ integers are read in pairs and define the digraph's\n edges. This function\ will return an error if ", count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "s\ tr", count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "A", next := 427391, root := ~, start := 427381, stop := 427390 ), rec( content := " has few\ er than\n ", count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "2\ e+2", count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "C", next := 427422, root := ~, start := 427411, stop := 427421 ), rec( content := " entries\ . ", count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 11, 5 ], mathmode := "Text", name := "P", next := 427436, root := ~, start := 427432, stop := 427435 ), rec( content := "\n\n \ Note that the vertex numbers will be incremented by 1 in the digraph\n retu\ rned. Hence the string fragment ", count := [ 9, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "0\ 6", count := [ 9, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 11, 5 ], mathmode := "Text", name := "C", next := 427562, root := ~, start := 427552, stop := 427561 ), rec( content := " will de\ scribe the edge\n ", count := [ 9, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "[\ 1,7]", count := [ 9, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 11, 5 ], mathmode := "Text", name := "C", next := 427602, root := ~, start := 427590, stop := 427601 ), rec( content := ".\n " , count := [ 9, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := TCodeDecoder(\"3 2 0 2 2 1\");\n\ngap> OutNeighbours(gr);\n[ [ 3 ], [ ], [ 2 ] ]\ngap> gr := TCodeD\ ecoder(\"12 3 0 10 5 2 8 8\");\n\ \ngap> OutNeighbours(gr);\n[ [ 11 ], [ ], [ ], [ ], [ ], [ 3 ], [ ], [ ]\ , [ 9 ], [ ], \n [ ], [ ] ]\n", count := [ 9, 2, 11, 6 ], name := "PCDATA" , root := ~ ) ], count := [ 9, 2, 11, 6 ], mathmode := "Text", name := "Example", next := 427970, root := ~, start := 427608, stop := 427969 ), rec( content := "\n ", count := [ 9, 2, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 11, 3 ], mathmode := "Text", name := "Description", next := 427987, root := ~, start := 426805, stop := 427986 ) ], count := [ 9, 2, 11, 1 ], mathmode := "Text", name := "ManSection", next := 428001, root := ~, start := 426718, stop := 428000 ), rec( content := "\n\n ", count := [ 9, 2, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "digraph", Name := "PlainTextString\ " ), content := 0, count := [ 9, 2, 12, 2 ], mathmode := "Text", name := "Oper", next := 428066, root := ~, start := 428022, stop := 428065 ), rec( attributes := rec( Arg := "s", Name := "DigraphFromPlai\ nTextString" ), content := 0, count := [ 9, 2, 12, 4 ], mathmode := "Text", name := "Oper", next := 428118, root := ~, start := 428069, stop := 428117 ), rec( attributes := rec( ), content := [ rec( content := "A string.\ ", count := [ 9, 2, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 12, 5 ], mathmode := "Text", name := "Returns", next := 428149, root := ~, start := 428121, stop := 428148 ), rec( attributes := rec( ), content := [ rec( content := "\n ", count := [ 9, 2, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "P\ lainTextString", count := [ 9, 2, 12, 5 ], mathmode := "Text", name := "PCDATA\ ", root := ~ ) ], count := [ 9, 2, 12, 5 ], mathmode := "Text", name := "A", next := 428192, root := ~, start := 428170, stop := 428191 ), rec( content := " takes a\ single digraph, and returns a string\n describing the edges of that digrap\ h. ", count := [ 9, 2, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphFromPlainTextString", count := [ 9, 2, 12, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 2, 12, 5 ], mathmode := "Text", name := "A", next := 428314, root := ~, start := 428281, stop := 428313 ), rec( content := "\n ta\ kes such a string and returns the digraph which it describes. Each edge\n \ is written as a pair of integers separated by a single space. The edges\n \ themselves are separated by a double space. Vertex numbers are reduced by\n \ 1 when they are encoded, so that vertices in the string are labelled\n st\ arting at 0.", count := [ 9, 2, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 12, 6 ], mathmode := "Text", name := "P", next := 428645, root := ~, start := 428641, stop := 428644 ), rec( content := "\n\n \ Note that the number of vertices of a digraph is not stored, and so vertices\n\ which are not connected to any edge may be lost.", count := [ 9, 2, 12, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 12, 7 ], mathmode := "Text", name := "P", next := 428784, root := ~, start := 428780, stop := 428783 ), rec( content := "\n\n \ \n The operation ", count := [ 9, 2, 12, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "D\ igraphFromPlainTextString", count := [ 9, 2, 12, 7 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 2, 12, 7 ], mathmode := "Text", name := "C", next := 428842, root := ~, start := 428809, stop := 428841 ), rec( content := "\n ta\ kes an optional first argument ", count := [ 9, 2, 12, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsMutab\ leDigraph" ), content := 0, count := [ 9, 2, 12, 7 ], mathmode := "Text", name := "Ref", next := 428910, root := ~, start := 428880, stop := 428909 ), rec( content := "\n or\ ", count := [ 9, 2, 12, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Filt := "IsImmut\ ableDigraph" ), content := 0, count := [ 9, 2, 12, 7 ], mathmode := "Text", name := "Ref", next := 428950, root := ~, start := 428918, stop := 428949 ), rec( content := ", which \ specifies whether the output digraph shall\n be mutable or immutable. If no\ first argument is provided, then an immutable\n digraph is returned by def\ ault.\n\n ", count := [ 9, 2, 12, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := Digraph([[2, 3], [1], [1]]);\n\ngap> PlainTextString(gr);\n\"0 1 0 2 1 0 2 0\"\ngap> DigraphFromP\ lainTextString(last);\n\n", count := [ 9, 2, 12, 8 ], name := "PCD\ ATA", root := ~ ) ], count := [ 9, 2, 12, 8 ], mathmode := "Text", name := "Example", next := 429371, root := ~, start := 429123, stop := 429370 ), rec( content := "\n ", count := [ 9, 2, 12, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 12, 5 ], mathmode := "Text", name := "Description", next := 429388, root := ~, start := 428152, stop := 429387 ) ], count := [ 9, 2, 12, 1 ], mathmode := "Text", name := "ManSection", next := 429402, root := ~, start := 428007, stop := 429401 ), rec( content := "\n\n ", count := [ 9, 2, 12, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "filename, digrap\ h, delimiter, offset", Name := "WritePlainTextDigraph" ), content := 0, count := [ 9, 2, 13, 2 ], mathmode := "Text", name := "Func", next := 429502, root := ~, start := 429423, stop := 429501 ), rec( attributes := rec( Arg := "filename, delimi\ ter, offset, ignore", Name := "ReadPlainTextDigraph" ), content := 0, count := [ 9, 2, 13, 4 ], mathmode := "Text", name := "Oper", next := 429582, root := ~, start := 429505, stop := 429581 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ se functions write and read a single digraph in a human-readable plain\n te\ xt format as follows: each line contains a single edge, and each edge is\n \ written as a pair of integers separated by the string ", count := [ 9, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ elimiter", count := [ 9, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 13, 5 ], mathmode := "Text", name := "A", next := 429830, root := ~, start := 429814, stop := 429829 ), rec( content := ".", count := [ 9, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "P", next := 429835, root := ~, start := 429831, stop := 429834 ), rec( content := "\n\n \ ", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "f\ ilename", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "A", next := 429856, root := ~, start := 429841, stop := 429855 ), rec( content := " should \ be the name of a file which will be written to or\n read from, and ", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ ffset", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "A", next := 429946, root := ~, start := 429933, stop := 429945 ), rec( content := " should \ be an integer which is added to each\n vertex number as it is written or re\ ad. For example, if\n ", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "W\ ritePlainTextDigraph", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "C", next := 430084, root := ~, start := 430056, stop := 430083 ), rec( content := " is call\ ed with ", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ ffset", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "A", next := 430113, root := ~, start := 430100, stop := 430112 ), rec( content := " ", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "-\ 1", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "C", next := 430123, root := ~, start := 430114, stop := 430122 ), rec( content := ", then\n\ the vertices will be numbered in the file starting from 0 instead of 1 -\n\ ", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "R\ eadPlainTextDigraph", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "C", next := 430238, root := ~, start := 430211, stop := 430237 ), rec( content := " would t\ hen need to be called with ", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "o\ ffset", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "A", next := 430286, root := ~, start := 430273, stop := 430285 ), rec( content := "\n ", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "1\ ", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "C", next := 430299, root := ~, start := 430291, stop := 430298 ), rec( content := " to conv\ ert back to the original graph.", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 13, 7 ], mathmode := "Text", name := "P", next := 430342, root := ~, start := 430338, stop := 430341 ), rec( content := "\n\n \ ", count := [ 9, 2, 13, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := [ rec( content := "i\ gnore", count := [ 9, 2, 13, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 13, 7 ], mathmode := "Text", name := "A", next := 430361, root := ~, start := 430348, stop := 430360 ), rec( content := " should \ be a list of characters which will be ignored when\n reading the graph.\n \ ", count := [ 9, 2, 13, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> gr := Digraph([[1, 2, 3], [1, 1], [2]]);\n\ngap> filename := Concatenation(DIGRAPHS_Dir(), \"/tst/out\ /plain.txt\");;\ngap> WritePlainTextDigraph(filename, gr, \",\", -1);\ngap> Re\ adPlainTextDigraph(filename, \",\", 1, ['/', '%']);\n\n", count := [ 9, 2, 13, 8 ], name := "PCDATA", root := ~ ) ], count := [ 9, 2, 13, 8 ], mathmode := "Text", name := "Example", next := 430804, root := ~, start := 430447, stop := 430803 ), rec( content := "\n ", count := [ 9, 2, 13, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 13, 5 ], mathmode := "Text", name := "Description", next := 430821, root := ~, start := 429585, stop := 430820 ) ], count := [ 9, 2, 13, 1 ], mathmode := "Text", name := "ManSection", next := 430835, root := ~, start := 429408, stop := 430834 ), rec( content := "\n\n ", count := [ 9, 2, 13, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "filename, digrap\ h", Name := "WriteDIMACSDigraph" ), content := 0, count := [ 9, 2, 14, 2 ], mathmode := "Text", name := "Oper", next := 430913, root := ~, start := 430856, stop := 430912 ), rec( attributes := rec( Arg := "filename", Name := "ReadDIMACSDigra\ ph" ), content := 0, count := [ 9, 2, 14, 4 ], mathmode := "Text", name := "Oper", next := 430963, root := ~, start := 430916, stop := 430962 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ se operations write or read the single symmetric digraph ", count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "A", next := 431058, root := ~, start := 431044, stop := 431057 ), rec( content := "\n to\ or from a file in DIMACS format, as appropriate. The operation\n ", count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "W\ riteDIMACSDigraph", count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "C", next := 431158, root := ~, start := 431133, stop := 431157 ), rec( content := " records\ the vertices and edges of ", count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "A", next := 431207, root := ~, start := 431193, stop := 431206 ), rec( content := ".\n T\ he vertex labels of ", count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "d\ igraph", count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "A", next := 431248, root := ~, start := 431234, stop := 431247 ), rec( content := " will be\ recorded only if they are\n integers. See ", count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsSymme\ tricDigraph" ), content := 0, count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "Ref", next := 431333, root := ~, start := 431301, stop := 431332 ), rec( content := " and ", count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digraph\ VertexLabels" ), content := 0, count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "Ref", next := 431377, root := ~, start := 431338, stop := 431376 ), rec( content := ".", count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "P", next := 431382, root := ~, start := 431378, stop := 431381 ), rec( content := "\n\n \ The first argument ", count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilename", count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "A", next := 431422, root := ~, start := 431407, stop := 431421 ), rec( content := " should \ be the name of the file which will\n be written to or read from. A file ca\ n contain one symmetric digraph in\n DIMACS format. If ", count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ ilename", count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "A", next := 431579, root := ~, start := 431564, stop := 431578 ), rec( content := " ends in\ one of ", count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ gz", count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "C", next := 431605, root := ~, start := 431595, stop := 431604 ), rec( content := ", ", count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ bz2", count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "C", next := 431618, root := ~, start := 431607, stop := 431617 ), rec( content := ",\n o\ r ", count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := ".\ xz", count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "C", next := 431637, root := ~, start := 431627, stop := 431636 ), rec( content := ", then t\ he file is compressed, or decompressed, appropriately.\n ", count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 9, 2, 14, 7 ], mathmode := "Text", name := "P", next := 431708, root := ~, start := 431704, stop := 431707 ), rec( content := "\n\n \ The DIMACS format is described as follows. Each line in the DIMACS file has\n\ one of four types:\n ", count := [ 9, 2, 14, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes :=\ rec( ), content := [ rec( content := "\n A line beginning with ", coun\ t := [ 9, 2, 14, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "c", count := [ 9, 2, 14, 9 ],\ mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 9 ] , math\ mode := "Text", name := "C", next := 431876, root := ~, start := 431868, stop \ := 431875 ), rec( content := " and followed by any number of characters\n \ is a comment line, and is ignored.\n ", count := [ 9, 2, 14, 9 ], math\ mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 9 ], name := "Ite\ m", next := 431974, root := ~, start := 431831, stop := 431973 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n A line beginning with ", coun\ t := [ 9, 2, 14, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "p", count := [ 9, 2, 14, 11 ]\ , mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 11\ ], mathmode := "Text", name := "C", next := 432026, root := ~, start := 43201\ 8, stop := 432025 ), rec( content := " defines the numbers of vertices and edg\ es\n the digraph. This line has the format ", count := [ 9, 2, 14, 11 ] , math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "p edge \n ", count :\ = [ 9, 2, 14, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count\ := [ 9, 2, 14, 11 ], mathmode := "Text", name := "C", next := 432176, root :=\ ~, start := 432116, stop := 432175 ), rec( content := ", where ", count := [ \ 9, 2, 14, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attrib\ utes := rec( ), content := [ rec( content := "", count := [ 9, 2\ , 14, 11 ], mathmode := "Text", name := "PCDATA", next := 6, root := ~ ) ], coun\ t := [ 9, 2, 14, 11 ], mathmode := "Text", name := "C", next := 432210, root :\ = ~, start := 432184, stop := 432209 ), rec( content := " and\n ", coun\ t := [ 9, 2, 14, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "", count := [ 9, 2,\ 14, 11 ], mathmode := "Text", name := "PCDATA", next := 6, root := ~ ) ], coun\ t := [ 9, 2, 14, 11 ], mathmode := "Text", name := "C", next := 432246, root :\ = ~, start := 432223, stop := 432245 ), rec( content := " are replaced by the \ relevant integers. There\n must be exactly one such line in the file, a\ nd it must occur before any\n of the following kinds of line.", count :\ = [ 9, 2, 14, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := 0, count := [ 9, 2, 14, 12 ], mathmode := "Text" , name\ := "P", next := 432415, root := ~, start := 432411, stop := 432414 ), rec( cont\ ent := "\n\n Although it is required to be present, the value of\n \ ", count := [ 9, 2, 14, 12 ], mathmode := "Text", name := "PCDATA", root :=\ ~ ), rec( attributes := rec( ), content := [ rec( content := "", c\ ount := [ 9, 2, 14, 12 ], mathmode := "Text", name := "PCDATA", next := 6, roo\ t := ~ ) ], count := [ 9, 2, 14, 12 ], mathmode := "Text", name := "C", next :\ = 432508, root := ~, start := 432485, stop := 432507 ), rec( content := " will\ be ignored. The correct number of edges\n will be deduced from the res\ t of the information in the file.\n ", count := [ 9, 2, 14, 12 ], mathmod\ e := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 11 ], name := "Ite\ m", next := 432637, root := ~, start := 431981, stop := 432636 ), rec( attributes :\ = rec( ), content := [ rec( content := "\n A line of the form ", count\ := [ 9, 2, 14, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "e ", count := [ 9, 2, \ 14, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2\ , 14, 14 ], mathmode := "Text", name := "C", next := 432706, root := ~, start \ := 432678, stop := 432705 ), rec( content := ", where ", count := [ 9, 2, 14, \ 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\ c( ), content := [ rec( content := "", count := [ 9, 2, 14, 14 ], mathmode\ := "Text", name := "PCDATA", next := 6, root := ~ ) ], count := [ 9, 2, 14, 1\ 4 ], mathmode := "Text", name := "C", next := 432730, root := ~, start := 4327\ 14, stop := 432729 ), rec( content := "\n and ", count := [ 9, 2, 14, 1\ 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec\ ( ), content := [ rec( content := "", count := [ 9, 2, 14, 14 ], mathmode \ := "Text", name := "PCDATA", next := 6, root := ~ ) ], count := [ 9, 2, 14, 14\ ], mathmode := "Text", name := "C", next := 432759, root := ~, start := 43274\ 3, stop := 432758 ), rec( content := " are integers in the range ", count := [ \ 9, 2, 14, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attrib\ utes := rec( ), content := [ rec( content := "[1 ..\n ]\ ", count := [ 9, 2, 14, 14 ], mathmode := "Text", name := "PCDATA", root := ~ \ ) ], count := [ 9, 2, 14, 14 ], mathmode := "Text", name := "C", next := 43282\ 9, root := ~, start := 432786, stop := 432828 ), rec( content := ", specifies \ that there is a (symmetric) edge\n in the digraph between the vertices \ ", count := [ 9, 2, 14, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\ ibutes := rec( ), content := [ rec( content := "", count := [ 9, 2, 14, 14\ ], mathmode := "Text", name := "PCDATA", next := 6, root := ~ ) ], count := [ \ 9, 2, 14, 14 ], mathmode := "Text", name := "C", next := 432934, root := ~, star\ t := 432918, stop := 432933 ), rec( content := " and\n ", count := [ 9,\ 2, 14, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribut\ es := rec( ), content := [ rec( content := "", count := [ 9, 2, 14, 14 ], \ mathmode := "Text", name := "PCDATA", next := 6, root := ~ ) ], count := [ 9, \ 2, 14, 14 ], mathmode := "Text", name := "C", next := 432963, root := ~, start\ := 432947, stop := 432962 ), rec( content := ". A symmetric edge only needs t\ o be defined once; an\n additional line ", count := [ 9, 2, 14, 14 ], math\ mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), cont\ ent := [ rec( content := "e ", count := [ 9, 2, 14, 14 ], mathmode := "\ Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 14 ], mathmode :=\ "Text", name := "C", next := 433068, root := ~, start := 433040, stop := 4330\ 67 ), rec( content := ", or ", count := [ 9, 2, 14, 14 ], mathmode := "Text", name\ := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( conte\ nt := "e \n ", count := [ 9, 2, 14, 14 ], mathmode := "Text", n\ ame := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 14 ], mathmode := "Text", name\ := "C", next := 433111, root := ~, start := 433073, stop := 433110 ), rec( cont\ ent := ", will be interpreted as an additional, multiple, edge.\n Loops\ are permitted.\n ", count := [ 9, 2, 14, 14 ], mathmode := "Text", name \ := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 14 ], name := "Item", next := 4332\ 09, root := ~, start := 432644, stop := 433208 ), rec( attributes := rec( ), content := [ rec( cont\ ent := "\n A line of the form ", count := [ 9, 2, 14, 16 ], mathmode :=\ "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content :=\ [ rec( content := "n
\n
3 Cr\ eating digraphs\n\n
 3.2 Changing representations\n\n
\n
  
3.2-1 AsBinaryRelation\n
  3.2\ -2 AsDigraph
\n
&n\ bsp; 3.2-3 Graph\n
  <\ a href=\"chap3_mj.html#X7C4F13E080EC16B0\">3.2-4 AsGraph
\n
  3.2-5 AsTransformation
\n
\n 3.3 New\ digraphs from old\n\n
\n\n\n
\n\n
5 Attributes and operations\n\n\n\n
 5.4 Cayley g\ raphs of groups\n\n
\ \n\n\n
\n
6 Properties of digraphs\n\n\n\n 6.4 Plana\ rity\n\n
\n\n
\n
7 Homomorphisms\n
 7.\ 1 Acting on digraphs\n\n\n\n\n
\n\n\n\n\n\n\n\n\n
 3.3 New digraphs from old\n\n
\n
<\ span class=\"nocss\">  
3.3-1 DigraphImmutableCopy\n
  
3.3-2 DigraphImmutableCopyIfImmutable\n  3.3-3 InducedSubdigraph\n
  
3.3-4 ReducedDigraph\n
  3.3-\ 5 MaximalSymmetricSubdigraph
\n
  3\ .3-6 MaximalAntiSymmetricSubdigraph
\n
<\ span class=\"nocss\">  
3.3-7 UndirectedSpanningForest\n
\   3.3-8 QuotientDigraph
\n
  3\ .3-9 DigraphReverse
\n
  3.3-10 Dig\ raphDual
\n
 \  3.3-11 DigraphSymmetr\ icClosure
\n
 \ ; 3.3-12 DigraphTransi\ tiveClosure
\n
&nb\ sp; 3.3-13 DigraphTran\ sitiveReduction
\n
  3.3-14 Digraph\ AddVertex
\n
 \ ; 3.3-15 DigraphAddVer\ tices
\n
 &nb\ sp;3.3-16 DigraphAddEdge
\n
  
3.3-17 DigraphAddEdgeOrbit\n
  <\ a href=\"chap3_mj.html#X8693A61B7F752C76\">3.3-18 DigraphAddEdges
\n\
  3.3-19 DigraphRemoveVertex
\n
  3.3-20 DigraphRemoveVertices\n
  3.3-21 DigraphRemoveEdge\n
  3.3-22 DigraphRemoveEdgeOrbit
\n
  3.3-23 DigraphRemoveEdges
\n
  3.3-24 DigraphRemoveLoops
\n
  3.3-25 DigraphRemoveAllMultipleEdges
\n
  3.3-26 DigraphReverseEdges
\n
  3.3-27 DigraphDisjointUnion
\n
  3.3-28 DigraphEdgeUnion
\n
  3.3-29 DigraphJoin
\n
  
3.3-30 DigraphCartesianProduct\n
<\ span class=\"nocss\">  
3.3-31 DigraphDirectProduct\n
  
3.3-32 DigraphCartesianProductProjections\n
  3.3-33 DigraphDirectProductProjections
\n
  3.3-34 LineDigraph
\n
  3.3-35 LineUndirectedDigraph
\n\
  3.3-36 DoubleDigraph
\n
  
3.3-37 BipartiteDoubleDigraph\n
  
3.3-38 DigraphAddAllLoops\n
  \ 3.3-39 DistanceDigraph
\n
  3.3-40 \ DigraphClosure
\n
\   3.3-41 DigraphM\ ycielskian
\n
\n\n\n
5 \ Attributes and operations\n\n\n\n\n\n
\n
\n\n\n\n
\ \n\n
9 Visualising and IO\ \n\n\n\n\n\n" ) gap> gap> #I Digraphs package is not available. To see further details, enter #I SetInfoLevel(InfoPackageLoading,4); and try to load the package again. #I File: /builddir/build/BUILD/digraphs-1.2.1/../pkg/digraphs-1.2.1/doc/manual.lab written. gap> gap> + rm -fr ../pkg + RPM_EC=0 ++ jobs -p + exit 0 Executing(%install): /bin/sh -e /var/tmp/rpm-tmp.zDSTyK + umask 022 + cd /builddir/build/BUILD + '[' /builddir/build/BUILDROOT/gap-pkg-digraphs-1.2.1-1.fc33.riscv64 '!=' / ']' + rm -rf /builddir/build/BUILDROOT/gap-pkg-digraphs-1.2.1-1.fc33.riscv64 ++ dirname /builddir/build/BUILDROOT/gap-pkg-digraphs-1.2.1-1.fc33.riscv64 + mkdir -p /builddir/build/BUILDROOT + mkdir /builddir/build/BUILDROOT/gap-pkg-digraphs-1.2.1-1.fc33.riscv64 + cd digraphs-1.2.1 + mkdir -p /builddir/build/BUILDROOT/gap-pkg-digraphs-1.2.1-1.fc33.riscv64/usr/lib/gap/pkg/digraphs-1.2.1/doc + cp -a bin data gap tst VERSIONS PackageInfo.g init.g makedoc.g read.g /builddir/build/BUILDROOT/gap-pkg-digraphs-1.2.1-1.fc33.riscv64/usr/lib/gap/pkg/digraphs-1.2.1 + cp -p doc/digraphs.bib doc/lefttoc.css doc/manual.css doc/nocolorprompt.css doc/ragged.css doc/times.css doc/toggless.css doc/chap0.html doc/chap0_mj.html doc/chap1.html doc/chap1_mj.html doc/chap2.html doc/chap2_mj.html doc/chap3.html doc/chap3_mj.html doc/chap4.html doc/chap4_mj.html doc/chap5.html doc/chap5_mj.html doc/chap6.html doc/chap6_mj.html doc/chap7.html doc/chap7_mj.html doc/chap8.html doc/chap8_mj.html doc/chap9.html doc/chap9_mj.html doc/chapA.html doc/chapA_mj.html doc/chapBib.html doc/chapBib_mj.html doc/chapInd.html doc/chapInd_mj.html doc/chooser.html doc/manual.js doc/rainbow.js doc/toggless.js doc/manual.lab doc/manual.pdf doc/manual.six doc/chap0.txt doc/chap1.txt doc/chap2.txt doc/chap3.txt doc/chap4.txt doc/chap5.txt doc/chap6.txt doc/chap7.txt doc/chap8.txt doc/chap9.txt doc/chapA.txt doc/chapBib.txt doc/chapInd.txt doc/attr.xml doc/cliques.xml doc/constructors.xml doc/digraph.xml doc/display.xml doc/examples.xml doc/grahom.xml doc/grape.xml doc/io.xml doc/isomorph.xml doc/labels.xml doc/main.xml doc/oper.xml doc/orbits.xml doc/planar.xml doc/prop.xml doc/utils.xml doc/z-appA.xml doc/z-chap0.xml doc/z-chap1.xml doc/z-chap2.xml doc/z-chap3.xml doc/z-chap4.xml doc/z-chap5.xml doc/z-chap6.xml doc/z-chap8.xml doc/z-chap9.xml doc/z-title.xml /builddir/build/BUILDROOT/gap-pkg-digraphs-1.2.1-1.fc33.riscv64/usr/lib/gap/pkg/digraphs-1.2.1/doc + /usr/lib/rpm/find-debuginfo.sh -j8 --strict-build-id -m -i --build-id-seed 1.2.1-1.fc33 --unique-debug-suffix -1.2.1-1.fc33.riscv64 --unique-debug-src-base gap-pkg-digraphs-1.2.1-1.fc33.riscv64 --run-dwz --dwz-low-mem-die-limit 10000000 --dwz-max-die-limit 50000000 -S debugsourcefiles.list /builddir/build/BUILD/digraphs-1.2.1 explicitly decompress any DWARF compressed ELF sections in /builddir/build/BUILDROOT/gap-pkg-digraphs-1.2.1-1.fc33.riscv64/usr/lib/gap/pkg/digraphs-1.2.1/bin/riscv64-redhat-linux-gnu-default64-kv7/digraphs.so extracting debug info from /builddir/build/BUILDROOT/gap-pkg-digraphs-1.2.1-1.fc33.riscv64/usr/lib/gap/pkg/digraphs-1.2.1/bin/riscv64-redhat-linux-gnu-default64-kv7/digraphs.so original debug info size: 2840kB, size after compression: 2676kB /usr/lib/rpm/sepdebugcrcfix: Updated 1 CRC32s, 0 CRC32s did match. 980 blocks + /usr/lib/rpm/check-buildroot + /usr/lib/rpm/redhat/brp-ldconfig + /usr/lib/rpm/brp-compress + /usr/lib/rpm/redhat/brp-strip-lto /usr/bin/strip + /usr/lib/rpm/brp-strip-static-archive /usr/bin/strip + /usr/lib/rpm/redhat/brp-python-bytecompile /usr/bin/python 1 0 + /usr/lib/rpm/brp-python-hardlink + /usr/lib/rpm/redhat/brp-mangle-shebangs *** WARNING: ./usr/src/debug/gap-pkg-digraphs-1.2.1-1.fc33.riscv64/extern/bliss-0.73/graph.cc is executable but has no shebang, removing executable bit Executing(%check): /bin/sh -e /var/tmp/rpm-tmp.saif8L + umask 022 + cd /builddir/build/BUILD + cd digraphs-1.2.1 + export LC_ALL=C.UTF-8 + LC_ALL=C.UTF-8 + cd tst + gap -l '/builddir/build/BUILDROOT/gap-pkg-digraphs-1.2.1-1.fc33.riscv64/usr/lib/gap;/usr/lib/gap' ┌───────┐ GAP 4.11.0 of 29-Feb-2020 │ GAP │ https://www.gap-system.org └───────┘ Architecture: riscv64-redhat-linux-gnu-default64-kv7 Configuration: gmp 6.2.0, GASMAN, readline Loading the library and packages ... #I autpgrp package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I alnuth package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I crisp package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I ctbllib package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I factint package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I fga package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I irredsol package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I laguna package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I polenta package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I polycyclic package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I resclasses package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I sophus package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') #I tomlib package is not available. Check that the name is correct #I and it is present in one of the GAP root directories (see '??RootPaths') Packages: GAPDoc 1.6.3, PrimGrp 3.4.1, SmallGrp 1.4.1, TransGrp 2.0.5 Try '??help' for help. See also '?copyright', '?cite' and '?authors' gap> #I Digraphs package is not available. To see further details, enter #I SetInfoLevel(InfoPackageLoading,4); and try to load the package again. fail gap> ########> Diff in testinstall.tst:14 # Input is: DIGRAPHS_StartTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StartTest' must have a value ######## ########> Diff in testinstall.tst:17 # Input is: gr := Digraph( [[8], [4, 5, 6, 8, 9], [2, 4, 5, 7, 10], [9], [1, 4, 6, 7, 9], [2, 3, 6, 7, 10], [3, 4, 5, 8, 9], [3, 4, 9, 10], [1, 2, 3, 5, 6, 9, 10], [2, 4, 5, 6, 9]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:22 # Input is: OutNeighbours(gr); # Expected output: [ [ 8 ], [ 4, 5, 6, 8, 9 ], [ 2, 4, 5, 7, 10 ], [ 9 ], [ 1, 4, 6, 7, 9 ], [ 2, 3, 6, 7, 10 ], [ 3, 4, 5, 8, 9 ], [ 3, 4, 9, 10 ], [ 1, 2, 3, 5, 6, 9, 10 ], [ 2, 4, 5, 6, 9 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in testinstall.tst:26 # Input is: not DIGRAPHS_IsGrapeLoaded or (DIGRAPHS_IsGrapeLoaded and Digraph(Graph(gr)) = gr); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_IsGrapeLoaded' must have a value ######## ########> Diff in testinstall.tst:29 # Input is: not DIGRAPHS_IsGrapeLoaded or (DIGRAPHS_IsGrapeLoaded and Graph(Digraph(Graph(gr))).adjacencies = Graph(gr).adjacencies); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_IsGrapeLoaded' must have a value ######## ########> Diff in testinstall.tst:41 # Input is: not DIGRAPHS_IsGrapeLoaded or (DIGRAPHS_IsGrapeLoaded and Digraph(Graph(Group(()), [1 .. 20], OnPoints, func, true)) = Digraph(adj)); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_IsGrapeLoaded' must have a value ######## ########> Diff in testinstall.tst:47 # Input is: gr := Digraph([ [1, 2, 4, 10], [3, 15], [3, 15], [1, 3, 7, 8, 9, 11, 12, 13], [4, 8], [1, 2, 4, 5, 6, 7, 8, 10, 14, 15], [3, 4, 6, 11, 13, 15], [3, 5, 6, 7, 8, 9, 10, 15], [2, 5, 6, 7, 8, 9, 10, 11, 12], [2, 3, 10, 11, 14], [3, 5, 14, 15], [7, 9, 10, 14, 15], [1, 4, 7, 8, 10, 14, 15], [1, 2, 4, 7, 13, 14, 15], [1, 2, 3, 9, 10, 11, 12, 13, 14, 15]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:55 # Input is: IsMultiDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsMultiDigraph' must have a value ######## ########> Diff in testinstall.tst:57 # Input is: IsAcyclicDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in testinstall.tst:67 # Input is: gr := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:69 # Input is: IsAcyclicDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in testinstall.tst:71 # Input is: gr := DigraphRemoveEdge(gr, 10000, 1); # Expected output: # But found: Error, Variable: 'DigraphRemoveEdge' must have a value ######## ########> Diff in testinstall.tst:73 # Input is: IsAcyclicDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in testinstall.tst:75 # Input is: gr := Digraph([[2, 3], [4, 5], [5, 6], [], [], [], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:77 # Input is: IsDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsDigraph' must have a value ######## ########> Diff in testinstall.tst:82 # Input is: gr := Digraph(rec(DigraphNrVertices := 1000, DigraphSource := [1 .. 1000], DigraphRange := Concatenation([2 .. 1000], [1])));; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:85 # Input is: OutNeighbours(gr);; # Expected output: # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in testinstall.tst:88 # Input is: d := Digraph(rec(DigraphVertices := [1 .. 5], DigraphRange := [], DigraphSource := [])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:92 # Input is: IsMultiDigraph(d); # Expected output: false # But found: Error, Variable: 'IsMultiDigraph' must have a value ######## ########> Diff in testinstall.tst:96 # Input is: DigraphFromSparse6String(":Fa@x^"); # Expected output: # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in testinstall.tst:100 # Input is: gr := Digraph([[4], [2, 2], [2, 3, 1, 4], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:102 # Input is: InDegreeOfVertex(gr, 2); # Expected output: 3 # But found: Error, Variable: 'InDegreeOfVertex' must have a value ######## ########> Diff in testinstall.tst:104 # Input is: InNeighboursOfVertex(gr, 2); # Expected output: [ 2, 2, 3 ] # But found: Error, Variable: 'InNeighboursOfVertex' must have a value ######## ########> Diff in testinstall.tst:106 # Input is: InNeighbours(gr); # Expected output: [ [ 3, 4 ], [ 2, 2, 3 ], [ 3 ], [ 1, 3 ] ] # But found: Error, Variable: 'InNeighbours' must have a value ######## ########> Diff in testinstall.tst:108 # Input is: gr := Digraph(rec(DigraphNrVertices := 10, DigraphSource := [1, 1, 2, 3, 3, 3], DigraphRange := [3, 1, 1, 4, 4, 1])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:112 # Input is: InNeighboursOfVertex(gr, 5); # Expected output: [ ] # But found: Error, Variable: 'InNeighboursOfVertex' must have a value ######## ########> Diff in testinstall.tst:114 # Input is: InDegreeOfVertex(gr, 5); # Expected output: 0 # But found: Error, Variable: 'InDegreeOfVertex' must have a value ######## ########> Diff in testinstall.tst:116 # Input is: InNeighbours(gr); # Expected output: [ [ 1, 2, 3 ], [ ], [ 1 ], [ 3, 3 ], [ ], [ ], [ ], [ ], [ ], [ ] ] # But found: Error, Variable: 'InNeighbours' must have a value ######## ########> Diff in testinstall.tst:118 # Input is: InDegreeOfVertex(gr, 1); # Expected output: 3 # But found: Error, Variable: 'InDegreeOfVertex' must have a value ######## ########> Diff in testinstall.tst:120 # Input is: OutDegreeOfVertex(gr, 3); # Expected output: 3 # But found: Error, Variable: 'OutDegreeOfVertex' must have a value ######## ########> Diff in testinstall.tst:122 # Input is: OutNeighboursOfVertex(gr, 3); # Expected output: [ 4, 4, 1 ] # But found: Error, Variable: 'OutNeighboursOfVertex' must have a value ######## ########> Diff in testinstall.tst:124 # Input is: OutNeighbours(gr); # Expected output: [ [ 3, 1 ], [ 1 ], [ 4, 4, 1 ], [ ], [ ], [ ], [ ], [ ], [ ], [ ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in testinstall.tst:128 # Input is: gr := Digraph([[5, 5, 1, 5], [], [], [2, 3, 1], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:130 # Input is: DigraphInEdges(gr, 5); # Expected output: [ [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ] # But found: Error, Variable: 'DigraphInEdges' must have a value ######## ########> Diff in testinstall.tst:132 # Input is: DigraphOutEdges(gr, 2); # Expected output: [ ] # But found: Error, Variable: 'DigraphOutEdges' must have a value ######## ########> Diff in testinstall.tst:134 # Input is: DigraphOutEdges(gr, 4); # Expected output: [ [ 4, 2 ], [ 4, 3 ], [ 4, 1 ] ] # But found: Error, Variable: 'DigraphOutEdges' must have a value ######## ########> Diff in testinstall.tst:138 # Input is: gr := Digraph([[2], [3], [4], [5], [1], [7], [6]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:140 # Input is: DigraphPeriod(gr); # Expected output: 1 # But found: Error, Variable: 'DigraphPeriod' must have a value ######## ########> Diff in testinstall.tst:142 # Input is: IsAperiodicDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsAperiodicDigraph' must have a value ######## ########> Diff in testinstall.tst:144 # Input is: gr := Digraph([[2], [3], [4], [5], [6], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:146 # Input is: DigraphPeriod(gr); # Expected output: 6 # But found: Error, Variable: 'DigraphPeriod' must have a value ######## ########> Diff in testinstall.tst:148 # Input is: IsAperiodicDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsAperiodicDigraph' must have a value ######## ########> Diff in testinstall.tst:152 # Input is: gr := Digraph(rec(DigraphNrVertices := 5, DigraphSource := [1, 2, 3, 4, 5], DigraphRange := [2, 3, 4, 5, 1])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:156 # Input is: IsDigraphEdge(gr, [1, 2]); # Expected output: true # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in testinstall.tst:158 # Input is: IsDigraphEdge(gr, [2, 2]); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in testinstall.tst:164 # Input is: gr := Digraph([[2], [3, 5], [4], [5], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:166 # Input is: DigraphEdges(gr); # Expected output: [ [ 1, 2 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 2 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in testinstall.tst:168 # Input is: gr2 := DigraphReverseEdge(gr, [2, 3]); # Expected output: # But found: Error, Variable: 'DigraphReverseEdge' must have a value ######## ########> Diff in testinstall.tst:170 # Input is: DigraphEdges(gr2); # Expected output: [ [ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 3, 2 ], [ 4, 5 ], [ 5, 1 ], [ 5, 2 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in testinstall.tst:174 # Input is: gr := Digraph([[1, 2, 3], [3, 5], [4], [5], [1, 2], [5, 7], [6]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:176 # Input is: gr2 := DigraphReverseEdge(gr, [1, 1]); # Expected output: # But found: Error, Variable: 'DigraphReverseEdge' must have a value ######## ########> Diff in testinstall.tst:178 # Input is: gr = gr2; # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in testinstall.tst:180 # Input is: gr2 := DigraphReverseEdge(gr, 1, 2); # Expected output: # But found: Error, Variable: 'DigraphReverseEdge' must have a value ######## ########> Diff in testinstall.tst:184 # Input is: gr := Digraph([[2, 3], [3], [], [5, 6], [6], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:186 # Input is: topo := DigraphTopologicalSort(gr); # Expected output: [ 3, 2, 1, 6, 5, 4 ] # But found: Error, Variable: 'DigraphTopologicalSort' must have a value ######## ########> Diff in testinstall.tst:188 # Input is: p := Permutation(Transformation(topo), topo); # Expected output: (1,3)(4,6) # But found: Error, Variable: 'topo' must have a value ######## ########> Diff in testinstall.tst:190 # Input is: gr1 := OnDigraphs(gr, p);; # Expected output: # But found: Error, Variable: 'OnDigraphs' must have a value ######## ########> Diff in testinstall.tst:191 # Input is: DigraphTopologicalSort(gr1) = DigraphVertices(gr1); # Expected output: true # But found: Error, Variable: 'DigraphTopologicalSort' must have a value ######## ########> Diff in testinstall.tst:193 # Input is: gr := Digraph([[], [3], [], [5], [], [2, 3, 7, 1], [1], [2, 3, 4, 5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:195 # Input is: topo := DigraphTopologicalSort(gr); # Expected output: [ 1, 3, 2, 5, 4, 7, 6, 8 ] # But found: Error, Variable: 'DigraphTopologicalSort' must have a value ######## ########> Diff in testinstall.tst:197 # Input is: p := Permutation(Transformation(topo), topo); # Expected output: (2,3)(4,5)(6,7) # But found: Error, Variable: 'topo' must have a value ######## ########> Diff in testinstall.tst:199 # Input is: gr1 := OnDigraphs(gr, p ^ -1);; # Expected output: # But found: Error, Variable: 'OnDigraphs' must have a value ######## ########> Diff in testinstall.tst:200 # Input is: DigraphTopologicalSort(gr1) = DigraphVertices(gr1); # Expected output: true # But found: Error, Variable: 'DigraphTopologicalSort' must have a value ######## ########> Diff in testinstall.tst:206 # Input is: gr := Digraph(List([1 .. 5], x -> [1 .. 5]));; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:207 # Input is: out := OutNeighbours(gr); # Expected output: [ [ 1 .. 5 ], [ 1 .. 5 ], [ 1 .. 5 ], [ 1 .. 5 ], [ 1 .. 5 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in testinstall.tst:209 # Input is: IsMultiDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsMultiDigraph' must have a value ######## ########> Diff in testinstall.tst:211 # Input is: out; # Expected output: [ [ 1, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ] ] # But found: Error, Variable: 'out' must have a value ######## ########> Diff in testinstall.tst:214 # Input is: InNeighbours(gr) = out; # Expected output: true # But found: Error, Variable: 'InNeighbours' must have a value ######## ########> Diff in testinstall.tst:218 # Input is: gr := Digraph([[3], [4], [5], [1, 5], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:220 # Input is: DigraphAllSimpleCircuits(gr); # Expected output: [ [ 1, 3, 5 ], [ 1, 3, 5, 2, 4 ], [ 5, 2, 4 ] ] # But found: Error, Variable: 'DigraphAllSimpleCircuits' must have a value ######## ########> Diff in testinstall.tst:226 # Input is: gr := DigraphFromGraph6String("L~~~ySrJ[N{NT^"); # Expected output: # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in testinstall.tst:228 # Input is: gr = MaximalSymmetricSubdigraphWithoutLoops(gr); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in testinstall.tst:230 # Input is: DigraphMaximalCliquesReps(gr); # Expected output: [ [ 1, 2, 3, 4, 5, 6, 7 ], [ 1, 2, 3, 12 ], [ 2, 8, 12, 13 ], [ 4, 9, 13 ], [ 8, 9, 10, 11, 12, 13 ] ] # But found: Error, Variable: 'DigraphMaximalCliquesReps' must have a value ######## ########> Diff in testinstall.tst:233 # Input is: gr := DigraphFromGraph6String("I~~wzfJhw"); # Expected output: # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in testinstall.tst:235 # Input is: gr = MaximalSymmetricSubdigraphWithoutLoops(gr); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in testinstall.tst:237 # Input is: DigraphMaximalCliquesReps(gr); # Expected output: [ [ 1, 2, 3, 4, 5, 6 ], [ 1, 2, 5, 9 ], [ 1, 9, 10 ], [ 7, 8, 9, 10 ] ] # But found: Error, Variable: 'DigraphMaximalCliquesReps' must have a value ######## ########> Diff in testinstall.tst:241 # Input is: gr := CompleteDigraph(7);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in testinstall.tst:242 # Input is: gr2 := DigraphClosure(gr, 7);; # Expected output: # But found: Error, Variable: 'DigraphClosure' must have a value ######## ########> Diff in testinstall.tst:243 # Input is: gr = gr2; # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in testinstall.tst:245 # Input is: gr := DigraphRemoveEdge(gr, [1, 2]);; # Expected output: # But found: Error, Variable: 'DigraphRemoveEdge' must have a value ######## ########> Diff in testinstall.tst:246 # Input is: gr := DigraphRemoveEdges(gr, [[1, 2], [2, 1]]);; # Expected output: # But found: Error, Variable: 'DigraphRemoveEdges' must have a value ######## ########> Diff in testinstall.tst:247 # Input is: DigraphNrEdges(gr); # Expected output: 40 # But found: Error, Variable: 'DigraphNrEdges' must have a value ######## ########> Diff in testinstall.tst:249 # Input is: gr2 := DigraphClosure(gr, 7);; # Expected output: # But found: Error, Variable: 'DigraphClosure' must have a value ######## ########> Diff in testinstall.tst:250 # Input is: DigraphNrEdges(gr2); # Expected output: 42 # But found: Error, Variable: 'DigraphNrEdges' must have a value ######## ########> Diff in testinstall.tst:255 # Input is: gr := Digraph([[]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:257 # Input is: DigraphSource(gr); # Expected output: [ ] # But found: Error, Variable: 'DigraphSource' must have a value ######## ########> Diff in testinstall.tst:259 # Input is: DigraphRange(gr); # Expected output: [ ] # But found: Error, Variable: 'DigraphRange' must have a value ######## ########> Diff in testinstall.tst:263 # Input is: d := Digraph([[2], [3], [1, 1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:265 # Input is: OutNeighbours(OnDigraphs(d, PermList([2, 3, 1]))); # Expected output: [ [ 2, 2 ], [ 3 ], [ 1 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in testinstall.tst:267 # Input is: OutNeighbours(OnDigraphs(d, Transformation([2, 3, 1]))); # Expected output: [ [ 2, 2 ], [ 3 ], [ 1 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in testinstall.tst:273 # Input is: AsDigraph(f); # Expected output: # But found: Error, Variable: 'AsDigraph' must have a value ######## ########> Diff in testinstall.tst:275 # Input is: AsDigraph(f, 4); # Expected output: fail # But found: Error, Variable: 'AsDigraph' must have a value ######## ########> Diff in testinstall.tst:279 # Input is: gr := Digraph([[1], [2], [1 .. 3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:280 # Input is: IsAntisymmetricDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsAntisymmetricDigraph' must have a value ######## ########> Diff in testinstall.tst:284 # Input is: gr := Digraph([[1 .. 4], [2, 4], [3, 4], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:286 # Input is: DigraphTopologicalSort(gr); # Expected output: [ 4, 2, 3, 1 ] # But found: Error, Variable: 'DigraphTopologicalSort' must have a value ######## ########> Diff in testinstall.tst:290 # Input is: gr := Digraph([[1],, [2]]); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphCons' on 2 arguments # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:293 # Input is: gr := Digraph([[1], 2, [2]]); # Expected output: Error, the argument must be a list of lists of positive integers not ex\ \ ceeding the length of the argument, # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:298 # Input is: gr := EmptyDigraph(0);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in testinstall.tst:299 # Input is: DigraphSymmetricClosure(gr); # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in testinstall.tst:303 # Input is: not DIGRAPHS_NautyAvailable or NautyAutomorphismGroup(NullDigraph(0)) = Group(()); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in testinstall.tst:306 # Input is: not DIGRAPHS_NautyAvailable or NautyAutomorphismGroup(NullDigraph(0), []) = Group(()); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in testinstall.tst:309 # Input is: not DIGRAPHS_NautyAvailable or NautyCanonicalLabelling(NullDigraph(0)) = (); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in testinstall.tst:312 # Input is: not DIGRAPHS_NautyAvailable or NautyCanonicalLabelling(NullDigraph(0), []) = (); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in testinstall.tst:317 # Input is: SortedList(DigraphEdges(DigraphFromDigraph6String("&DI?AO?")) - 1); # Expected output: [ [ 0, 2 ], [ 0, 4 ], [ 3, 1 ], [ 3, 4 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in testinstall.tst:320 # Input is: gr := DigraphFromDigraph6String(str); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in testinstall.tst:322 # Input is: str = Digraph6String(gr); # Expected output: true # But found: Error, Variable: 'Digraph6String' must have a value ######## ########> Diff in testinstall.tst:326 # Input is: D := NullDigraph(IsMutableDigraph, 10); # Expected output: # But found: Error, Variable: 'NullDigraph' must have a value ######## ########> Diff in testinstall.tst:328 # Input is: MakeImmutable(D); # Expected output: # But found: Error, Variable: 'D' must have a value ######## ########> Diff in testinstall.tst:332 # Input is: D := Digraph([[2], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in testinstall.tst:333 # Input is: IsCompleteDigraph(D); # Expected output: false # But found: Error, Variable: 'IsCompleteDigraph' must have a value ######## ########> Diff in testinstall.tst:335 # Input is: D; # Expected output: # But found: Error, Variable: 'D' must have a value ######## ########> Diff in testinstall.tst:339 # Input is: D := EmptyDigraph(IsMutableDigraph, 3); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in testinstall.tst:341 # Input is: IsAcyclicDigraph(D); # Expected output: true # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in testinstall.tst:343 # Input is: DigraphDisjointUnion(D, CycleDigraph(IsMutableDigraph, 3)); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in testinstall.tst:345 # Input is: IsAcyclicDigraph(D); # Expected output: false # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in testinstall.tst:347 # Input is: D := EmptyDigraph(IsMutableDigraph, 3); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in testinstall.tst:349 # Input is: IsAcyclicDigraph(D); # Expected output: true # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in testinstall.tst:351 # Input is: DigraphDisjointUnion(D, CycleDigraph(IsImmutableDigraph, 3)); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in testinstall.tst:353 # Input is: IsAcyclicDigraph(D); # Expected output: false # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in testinstall.tst:357 # Input is: D := EmptyDigraph(IsMutableDigraph, 3); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in testinstall.tst:359 # Input is: DigraphDisjointUnion(D, CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in testinstall.tst:361 # Input is: IsMutable(D!.OutNeighbours); # Expected output: true # But found: Error, Variable: 'D' must have a value ######## ########> Diff in testinstall.tst:363 # Input is: ForAll(D!.OutNeighbours, IsMutable); # Expected output: true # But found: Error, Variable: 'D' must have a value ######## ########> Diff in testinstall.tst:367 # Input is: HomomorphismDigraphsFinder(NullDigraph(1), NullDigraph(100), fail, [], infinit\ y, fail, 2, [1 .. 100], [], fail, fail); # Expected output: [ IdentityTransformation ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in testinstall.tst:370 # Input is: HomomorphismDigraphsFinder(NullDigraph(1), NullDigraph(100), fail, [], infinit\ y, fail, 2, [1 .. 100], [], fail, fail); # Expected output: [ IdentityTransformation ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in testinstall.tst:373 # Input is: HomomorphismDigraphsFinder(NullDigraph(2), NullDigraph(2), fail, [], infinity,\ fail, 2, [1, 2], [], fail, fail); # Expected output: [ IdentityTransformation ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in testinstall.tst:376 # Input is: HomomorphismDigraphsFinder(NullDigraph(1), NullDigraph(100), fail, [], infinit\ y, fail, 2, [1 .. 100], [], fail, fail); # Expected output: [ IdentityTransformation ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in testinstall.tst:396 # Input is: DIGRAPHS_StopTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StopTest' must have a value ######## Digraphs package: testinstall.tst msecs: 245 false gap> ########> Diff in standard/attr.tst:15 # Input is: DIGRAPHS_StartTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StartTest' must have a value ######## ########> Diff in standard/attr.tst:26 # Input is: gr := Digraph(nbs); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:28 # Input is: HasDigraphSource(gr); # Expected output: false # But found: Error, Variable: 'HasDigraphSource' must have a value ######## ########> Diff in standard/attr.tst:30 # Input is: HasDigraphRange(gr); # Expected output: false # But found: Error, Variable: 'HasDigraphRange' must have a value ######## ########> Diff in standard/attr.tst:32 # Input is: DigraphNrVertices(gr); # Expected output: 25 # But found: Error, Variable: 'DigraphNrVertices' must have a value ######## ########> Diff in standard/attr.tst:34 # Input is: DigraphSource(gr); # Expected output: [ 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 16, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 20, 20, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 24, 24, 24, 25, 25, 25 ] # But found: Error, Variable: 'DigraphSource' must have a value ######## ########> Diff in standard/attr.tst:40 # Input is: HasDigraphSource(gr); # Expected output: true # But found: Error, Variable: 'HasDigraphSource' must have a value ######## ########> Diff in standard/attr.tst:42 # Input is: HasDigraphRange(gr); # Expected output: true # But found: Error, Variable: 'HasDigraphRange' must have a value ######## ########> Diff in standard/attr.tst:44 # Input is: DigraphRange(gr); # Expected output: [ 12, 22, 17, 1, 10, 11, 23, 21, 21, 16, 15, 5, 22, 11, 12, 8, 10, 1, 21, 15, 23, 5, 23, 8, 24, 20, 17, 25, 25, 5, 24, 22, 5, 2, 11, 8, 19, 18, 20, 13, 3, 11, 15, 18, 12, 10, 8, 23, 15, 25, 8, 19, 17, 19, 2, 17, 21, 18, 9, 4, 7, 3, 14, 10, 2, 11, 24, 14, 2, 21, 12, 9, 2, 11, 9, 21, 24, 16, 8, 8, 3, 5, 6, 14, 2, 24, 24, 20, 19, 8, 20, 7, 1, 2, 15, 13, 9, 16, 12, 19 ] # But found: Error, Variable: 'DigraphRange' must have a value ######## ########> Diff in standard/attr.tst:50 # Input is: gr := Digraph(nbs); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:52 # Input is: HasDigraphSource(gr); # Expected output: false # But found: Error, Variable: 'HasDigraphSource' must have a value ######## ########> Diff in standard/attr.tst:54 # Input is: HasDigraphRange(gr); # Expected output: false # But found: Error, Variable: 'HasDigraphRange' must have a value ######## ########> Diff in standard/attr.tst:56 # Input is: DigraphRange(gr); # Expected output: [ 12, 22, 17, 1, 10, 11, 23, 21, 21, 16, 15, 5, 22, 11, 12, 8, 10, 1, 21, 15, 23, 5, 23, 8, 24, 20, 17, 25, 25, 5, 24, 22, 5, 2, 11, 8, 19, 18, 20, 13, 3, 11, 15, 18, 12, 10, 8, 23, 15, 25, 8, 19, 17, 19, 2, 17, 21, 18, 9, 4, 7, 3, 14, 10, 2, 11, 24, 14, 2, 21, 12, 9, 2, 11, 9, 21, 24, 16, 8, 8, 3, 5, 6, 14, 2, 24, 24, 20, 19, 8, 20, 7, 1, 2, 15, 13, 9, 16, 12, 19 ] # But found: Error, Variable: 'DigraphRange' must have a value ######## ########> Diff in standard/attr.tst:62 # Input is: HasDigraphSource(gr); # Expected output: true # But found: Error, Variable: 'HasDigraphSource' must have a value ######## ########> Diff in standard/attr.tst:64 # Input is: HasDigraphRange(gr); # Expected output: true # But found: Error, Variable: 'HasDigraphRange' must have a value ######## ########> Diff in standard/attr.tst:66 # Input is: DigraphSource(gr); # Expected output: [ 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 16, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 20, 20, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 24, 24, 24, 25, 25, 25 ] # But found: Error, Variable: 'DigraphSource' must have a value ######## ########> Diff in standard/attr.tst:74 # Input is: gr := Digraph([[6, 7], [6, 9], [1, 3, 4, 5, 8, 9], [1, 2, 3, 4, 5, 6, 7, 10], [1, 5, 6, 7, 10], [2, 4, 5, 9, 10], [3, 4, 5, 6, 7, 8, 9, 10], [1, 3, 5, 7, 8, 9], [1, 2, 5], [1, 2, 4, 6, 7, 8]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:78 # Input is: OutNeighbours(DigraphDual(gr)); # Expected output: [ [ 1, 2, 3, 4, 5, 8, 9, 10 ], [ 1, 2, 3, 4, 5, 7, 8, 10 ], [ 2, 6, 7, 10 ], [ 8, 9 ], [ 2, 3, 4, 8, 9 ], [ 1, 3, 6, 7, 8 ], [ 1, 2 ], [ 2, 4, 6, 10 ], [ 3, 4, 6, 7, 8, 9, 10 ], [ 3, 5, 9, 10 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/attr.tst:82 # Input is: gr := Digraph(rec(DigraphVertices := ["a", "b"], DigraphSource := ["b", "b"], DigraphRange := ["a", "a"])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:85 # Input is: DigraphDual(gr); # Expected output: Error, the argument must be a digraph with no multiple edges, # But found: Error, Variable: 'DigraphDual' must have a value ######## ########> Diff in standard/attr.tst:87 # Input is: DigraphDual(DigraphMutableCopy(gr)); # Expected output: Error, the argument must be a digraph with no multiple edges, # But found: Error, Variable: 'DigraphDual' must have a value ######## ########> Diff in standard/attr.tst:89 # Input is: gr := Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:91 # Input is: DigraphDual(gr); # Expected output: # But found: Error, Variable: 'DigraphDual' must have a value ######## ########> Diff in standard/attr.tst:93 # Input is: DigraphDual(gr); # Expected output: # But found: Error, Variable: 'DigraphDual' must have a value ######## ########> Diff in standard/attr.tst:95 # Input is: gr := Digraph([[], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:97 # Input is: DigraphDual(gr); # Expected output: # But found: Error, Variable: 'DigraphDual' must have a value ######## ########> Diff in standard/attr.tst:99 # Input is: gr := Digraph(rec(DigraphNrVertices := 2, DigraphSource := [], DigraphRange :=\ [])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:101 # Input is: DigraphDual(gr); # Expected output: # But found: Error, Variable: 'DigraphDual' must have a value ######## ########> Diff in standard/attr.tst:103 # Input is: gr := Digraph([[2, 2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:105 # Input is: DigraphDual(gr); # Expected output: Error, the argument must be a digraph with no multiple edges, # But found: Error, Variable: 'DigraphDual' must have a value ######## ########> Diff in standard/attr.tst:110 # Input is: gr := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:112 # Input is: DigraphDual(gr); # Expected output: # But found: Error, Variable: 'DigraphDual' must have a value ######## ########> Diff in standard/attr.tst:115 # Input is: gr := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:117 # Input is: DigraphDual(gr); # Expected output: # But found: Error, Variable: 'DigraphDual' must have a value ######## ########> Diff in standard/attr.tst:119 # Input is: gr := Digraph(r);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:120 # Input is: SetDigraphVertexLabels(gr, [4, 3, 2, 1]); # Expected output: # But found: Error, Variable: 'SetDigraphVertexLabels' must have a value ######## ########> Diff in standard/attr.tst:121 # Input is: gr2 := DigraphDual(gr);; # Expected output: # But found: Error, Variable: 'DigraphDual' must have a value ######## ########> Diff in standard/attr.tst:122 # Input is: DigraphVertexLabels(gr2); # Expected output: [ 4, 3, 2, 1 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/attr.tst:124 # Input is: DigraphNrVertices(gr2); # Expected output: 4 # But found: Error, Variable: 'DigraphNrVertices' must have a value ######## ########> Diff in standard/attr.tst:126 # Input is: gr := Digraph([[1], [1, 3], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:128 # Input is: DigraphGroup(gr) = Group((2, 3)); # Expected output: true # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/attr.tst:130 # Input is: gr2 := DigraphDual(gr); # Expected output: # But found: Error, Variable: 'DigraphDual' must have a value ######## ########> Diff in standard/attr.tst:132 # Input is: OutNeighbours(gr2); # Expected output: [ [ 2, 3 ], [ 2 ], [ 3 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/attr.tst:134 # Input is: HasDigraphGroup(gr2); # Expected output: true # But found: Error, Variable: 'HasDigraphGroup' must have a value ######## ########> Diff in standard/attr.tst:136 # Input is: DigraphGroup(gr2) = Group((2, 3)); # Expected output: true # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/attr.tst:138 # Input is: DigraphGroup(gr2) = DigraphGroup(gr); # Expected output: true # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/attr.tst:142 # Input is: gr := Digraph(rec(DigraphNrVertices := 10, DigraphSource := [1, 1, 1, 1, 1, 1, 1, 1], DigraphRange := [2, 2, 3, 3, 4, 4, 5, 5])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:146 # Input is: AdjacencyMatrix(gr); # Expected output: [ [ 0, 2, 2, 2, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ] # But found: Error, Variable: 'AdjacencyMatrix' must have a value ######## ########> Diff in standard/attr.tst:152 # Input is: AdjacencyMatrix(Digraph([[]])); # Expected output: [ [ 0 ] ] # But found: Error, Variable: 'AdjacencyMatrix' must have a value ######## ########> Diff in standard/attr.tst:154 # Input is: AdjacencyMatrix(Digraph([])); # Expected output: [ ] # But found: Error, Variable: 'AdjacencyMatrix' must have a value ######## ########> Diff in standard/attr.tst:159 # Input is: gr := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:161 # Input is: adj1 := AdjacencyMatrix(gr); # Expected output: [ [ 0, 0, 1, 1, 0, 0, 0 ], [ 0, 1, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 2, 0, 0 ] ] # But found: Error, Variable: 'AdjacencyMatrix' must have a value ######## ########> Diff in standard/attr.tst:165 # Input is: gr := Digraph(OutNeighbours(gr)); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:167 # Input is: adj2 := AdjacencyMatrix(gr); # Expected output: [ [ 0, 0, 1, 1, 0, 0, 0 ], [ 0, 1, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 2, 0, 0 ] ] # But found: Error, Variable: 'AdjacencyMatrix' must have a value ######## ########> Diff in standard/attr.tst:171 # Input is: adj1 = adj2; # Expected output: true # But found: Error, Variable: 'adj1' must have a value ######## ########> Diff in standard/attr.tst:174 # Input is: gr := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:176 # Input is: adj1 := AdjacencyMatrix(gr); # Expected output: [ [ 2 ] ] # But found: Error, Variable: 'AdjacencyMatrix' must have a value ######## ########> Diff in standard/attr.tst:178 # Input is: gr := Digraph(OutNeighbours(gr)); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:180 # Input is: adj2 := AdjacencyMatrix(gr); # Expected output: [ [ 2 ] ] # But found: Error, Variable: 'AdjacencyMatrix' must have a value ######## ########> Diff in standard/attr.tst:182 # Input is: adj1 = adj2; # Expected output: true # But found: Error, Variable: 'adj1' must have a value ######## ########> Diff in standard/attr.tst:184 # Input is: AdjacencyMatrix(Digraph([])); # Expected output: [ ] # But found: Error, Variable: 'AdjacencyMatrix' must have a value ######## ########> Diff in standard/attr.tst:186 # Input is: AdjacencyMatrix( Digraph(rec(DigraphNrVertices := 0, DigraphSource := [], DigraphRange := [])))\ ; # Expected output: [ ] # But found: Error, Variable: 'AdjacencyMatrix' must have a value ######## ########> Diff in standard/attr.tst:202 # Input is: circuit := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:204 # Input is: topo := DigraphTopologicalSort(circuit);; # Expected output: # But found: Error, Variable: 'DigraphTopologicalSort' must have a value ######## ########> Diff in standard/attr.tst:205 # Input is: Length(topo); # Expected output: 20000 # But found: Error, Variable: 'topo' must have a value ######## ########> Diff in standard/attr.tst:207 # Input is: topo[1] = 20000; # Expected output: true # But found: Error, Variable: 'topo' must have a value ######## ########> Diff in standard/attr.tst:209 # Input is: topo[20000] = 10001; # Expected output: true # But found: Error, Variable: 'topo' must have a value ######## ########> Diff in standard/attr.tst:211 # Input is: topo[12345]; # Expected output: 17656 # But found: Error, Variable: 'topo' must have a value ######## ########> Diff in standard/attr.tst:213 # Input is: gr := Digraph([[2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:215 # Input is: DigraphTopologicalSort(gr); # Expected output: fail # But found: Error, Variable: 'DigraphTopologicalSort' must have a value ######## ########> Diff in standard/attr.tst:218 # Input is: multiple := Digraph(r);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:219 # Input is: DigraphTopologicalSort(multiple); # Expected output: [ 2, 1 ] # But found: Error, Variable: 'DigraphTopologicalSort' must have a value ######## ########> Diff in standard/attr.tst:221 # Input is: gr := Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:223 # Input is: DigraphTopologicalSort(gr); # Expected output: [ ] # But found: Error, Variable: 'DigraphTopologicalSort' must have a value ######## ########> Diff in standard/attr.tst:225 # Input is: gr := Digraph([[]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:227 # Input is: DigraphTopologicalSort(gr); # Expected output: [ 1 ] # But found: Error, Variable: 'DigraphTopologicalSort' must have a value ######## ########> Diff in standard/attr.tst:229 # Input is: gr := Digraph([[1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:231 # Input is: DigraphTopologicalSort(gr); # Expected output: [ 1 ] # But found: Error, Variable: 'DigraphTopologicalSort' must have a value ######## ########> Diff in standard/attr.tst:233 # Input is: gr := Digraph([[2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:235 # Input is: DigraphTopologicalSort(gr); # Expected output: fail # But found: Error, Variable: 'DigraphTopologicalSort' must have a value ######## ########> Diff in standard/attr.tst:240 # Input is: grid := Digraph(r);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:241 # Input is: DigraphTopologicalSort(grid); # Expected output: [ 8, 2, 6, 4, 3, 1, 7, 5 ] # But found: Error, Variable: 'DigraphTopologicalSort' must have a value ######## ########> Diff in standard/attr.tst:244 # Input is: gr := Digraph(adj); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:246 # Input is: IsAcyclicDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/attr.tst:248 # Input is: DigraphTopologicalSort(gr); # Expected output: [ 2, 4, 3, 1 ] # But found: Error, Variable: 'DigraphTopologicalSort' must have a value ######## ########> Diff in standard/attr.tst:250 # Input is: gr := Digraph([ [7], [], [], [6], [], [3], [], [], [5, 15], [], [], [6], [19], [], [11], [13], [], [17], [], [17]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:254 # Input is: DigraphTopologicalSort(gr); # Expected output: [ 7, 1, 2, 3, 6, 4, 5, 8, 11, 15, 9, 10, 12, 19, 13, 14, 16, 17, 18, 20 ] # But found: Error, Variable: 'DigraphTopologicalSort' must have a value ######## ########> Diff in standard/attr.tst:256 # Input is: gr := Digraph([[2], [], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:258 # Input is: DigraphTopologicalSort(gr); # Expected output: [ 2, 1, 3 ] # But found: Error, Variable: 'DigraphTopologicalSort' must have a value ######## ########> Diff in standard/attr.tst:271 # Input is: gr := Digraph(adj); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:273 # Input is: DigraphStronglyConnectedComponents(gr); # Expected output: rec( comps := [ [ 1, 11, 15 ], [ 2, 3, 10, 14 ], [ 4, 6, 9, 13 ], [ 5, 7, 8, 12 ] ], id := [ 1, 2, 2, 3, 4, 3, 4, 4, 3, 2, 1, 4, 3, 2, 1 ] ) # But found: Error, Variable: 'DigraphStronglyConnectedComponents' must have a value ######## ########> Diff in standard/attr.tst:281 # Input is: gr := Digraph(adj); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:283 # Input is: scc := DigraphStronglyConnectedComponents(gr); # Expected output: rec( comps := [ [ 1, 3, 2, 4, 9, 8, 5, 6, 7, 10, 11 ] ], id := [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ) # But found: Error, Variable: 'DigraphStronglyConnectedComponents' must have a value ######## ########> Diff in standard/attr.tst:286 # Input is: gr := Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:288 # Input is: DigraphStronglyConnectedComponents(gr); # Expected output: rec( comps := [ ], id := [ ] ) # But found: Error, Variable: 'DigraphStronglyConnectedComponents' must have a value ######## ########> Diff in standard/attr.tst:293 # Input is: gr := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:295 # Input is: scc := DigraphStronglyConnectedComponents(gr); # Expected output: rec( comps := [ [ 3 ], [ 1, 7, 9 ], [ 8, 4 ], [ 2, 6, 5 ] ], id := [ 2, 4, 1, 3, 4, 4, 2, 3, 2 ] ) # But found: Error, Variable: 'DigraphStronglyConnectedComponents' must have a value ######## ########> Diff in standard/attr.tst:298 # Input is: wcc := DigraphConnectedComponents(gr); # Expected output: rec( comps := [ [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ] ], id := [ 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ) # But found: Error, Variable: 'DigraphConnectedComponents' must have a value ######## ########> Diff in standard/attr.tst:301 # Input is: scc := DigraphStronglyConnectedComponents(circuit);; # Expected output: # But found: Error, Variable: 'DigraphStronglyConnectedComponents' must have a value ######## ########> Diff in standard/attr.tst:302 # Input is: Length(scc.comps); # Expected output: 20000 # But found: Error, Variable: 'scc' must have a value ######## ########> Diff in standard/attr.tst:304 # Input is: Length(scc.comps) = DigraphNrVertices(circuit); # Expected output: true # But found: Error, Variable: 'scc' must have a value ######## ########> Diff in standard/attr.tst:306 # Input is: gr := CycleDigraph(10); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/attr.tst:308 # Input is: gr2 := DigraphRemoveEdge(gr, 10, 1); # Expected output: # But found: Error, Variable: 'DigraphRemoveEdge' must have a value ######## ########> Diff in standard/attr.tst:310 # Input is: IsStronglyConnectedDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsStronglyConnectedDigraph' must have a value ######## ########> Diff in standard/attr.tst:312 # Input is: DigraphStronglyConnectedComponents(gr); # Expected output: rec( comps := [ [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ] ], id := [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ) # But found: Error, Variable: 'DigraphStronglyConnectedComponents' must have a value ######## ########> Diff in standard/attr.tst:315 # Input is: IsAcyclicDigraph(gr2); # Expected output: true # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/attr.tst:317 # Input is: DigraphStronglyConnectedComponents(gr2); # Expected output: rec( comps := [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8 ], [ 9 ], [ 10 ] ], id := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ] ) # But found: Error, Variable: 'DigraphStronglyConnectedComponents' must have a value ######## ########> Diff in standard/attr.tst:322 # Input is: D := CycleDigraph(10);; # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/attr.tst:323 # Input is: for i in [1 .. 50] do D := DigraphDisjointUnion(D, CycleDigraph(10)); od; # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have an assigned value ######## ########> Diff in standard/attr.tst:326 # Input is: DigraphNrStronglyConnectedComponents(D); # Expected output: 51 # But found: Error, Variable: 'DigraphNrStronglyConnectedComponents' must have a value ######## ########> Diff in standard/attr.tst:328 # Input is: D := CayleyDigraph(SymmetricGroup(6));; # Expected output: # But found: Error, Variable: 'CayleyDigraph' must have a value ######## ########> Diff in standard/attr.tst:329 # Input is: DigraphNrStronglyConnectedComponents(D); # Expected output: 1 # But found: Error, Variable: 'DigraphNrStronglyConnectedComponents' must have a value ######## ########> Diff in standard/attr.tst:331 # Input is: D := Digraph([[2, 3], [1, 4, 5], [3], [2, 5], [6], [3, 5]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:332 # Input is: DigraphNrStronglyConnectedComponents(D); # Expected output: 3 # But found: Error, Variable: 'DigraphNrStronglyConnectedComponents' must have a value ######## ########> Diff in standard/attr.tst:334 # Input is: D := Digraph([[]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:335 # Input is: DigraphNrStronglyConnectedComponents(D); # Expected output: 1 # But found: Error, Variable: 'DigraphNrStronglyConnectedComponents' must have a value ######## ########> Diff in standard/attr.tst:337 # Input is: D := EmptyDigraph(0);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/attr.tst:338 # Input is: DigraphNrStronglyConnectedComponents(D); # Expected output: 0 # But found: Error, Variable: 'DigraphNrStronglyConnectedComponents' must have a value ######## ########> Diff in standard/attr.tst:342 # Input is: gr := Digraph([[1, 2], [1], [2], [5], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:344 # Input is: wcc := DigraphConnectedComponents(gr); # Expected output: rec( comps := [ [ 1, 2, 3 ], [ 4, 5 ] ], id := [ 1, 1, 1, 2, 2 ] ) # But found: Error, Variable: 'DigraphConnectedComponents' must have a value ######## ########> Diff in standard/attr.tst:346 # Input is: gr := Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:348 # Input is: DigraphConnectedComponents(gr); # Expected output: rec( comps := [ ], id := [ ] ) # But found: Error, Variable: 'DigraphConnectedComponents' must have a value ######## ########> Diff in standard/attr.tst:350 # Input is: gr := Digraph([[]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:352 # Input is: DigraphConnectedComponents(gr); # Expected output: rec( comps := [ [ 1 ] ], id := [ 1 ] ) # But found: Error, Variable: 'DigraphConnectedComponents' must have a value ######## ########> Diff in standard/attr.tst:354 # Input is: gr := Digraph([[1], [2], [3], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:356 # Input is: DigraphConnectedComponents(gr); # Expected output: rec( comps := [ [ 1 ], [ 2 ], [ 3 ], [ 4 ] ], id := [ 1, 2, 3, 4 ] ) # But found: Error, Variable: 'DigraphConnectedComponents' must have a value ######## ########> Diff in standard/attr.tst:358 # Input is: gr := Digraph([[3, 4, 5, 7, 8, 9], [1, 4, 5, 8, 9, 5, 10], [2, 4, 5, 6, 7, 10], [6], [1, 1, 1, 7, 8, 9], [2, 2, 6, 8], [1, 5, 6, 9, 10], [3, 4, 6, 7], [1, 2, 3, 5], [5, 7]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:362 # Input is: DigraphConnectedComponents(gr); # Expected output: rec( comps := [ [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ] ], id := [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ) # But found: Error, Variable: 'DigraphConnectedComponents' must have a value ######## ########> Diff in standard/attr.tst:365 # Input is: gr := Digraph(rec( DigraphNrVertices := 100, DigraphSource := [8, 9, 11, 11, 12, 13, 14, 14, 18, 19, 22, 27, 31, 32, 32, 34\ , 37, 40, 45, 48, 50, 52, 58, 58, 58, 59, 60, 60, 65, 66, 73, 75, 79, 81, 81, 83, 84, 86, 86, 89, 96, 100, 100, 100], DigraphRange := [54, 62, 28, 55, 70, 37, 20, 32, 53, 16, 42, 66, 63, 13, 73, 8\ 9, 36, 5, 4, 58, 26, 48, 36, 56, 65, 78, 95, 96, 97, 60, 11, 66, 66, 19, 79, 21, 13, 29, 78, 98, 100, 44, 53, 69])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:374 # Input is: OutNeighbours(gr); # Expected output: [ [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ 54 ], [ 62 ], [ ], [ 28, 55 ], [ 70 ], [ 37 ], [ 20, 32 ], [ ], [ ], [ ], [ 53 ], [ 16 ], [ ], [ ], [ 42 ], [ ], [ ], [ ], [ ], [ 66 ], [ ], [ ], [ ], [ 63 ], [ 13, 73 ], [ ], [ 89 ], [ ], [ ], [ 36 ], [ ], [ ], [ 5 ], [ ], [ ], [ ], [ ], [ 4 ], [ ], [ ], [ 58 ], [ ], [ 26 ], [ ], [ 48 ], [ ], [ ], [ ], [ ], [ ], [ 36, 56, 65 ], [ 78 ], [ 95, 96 ], [ ], [ ], [ ], [ ], [ 97 ], [ 60 ], [ ], [ ], [ ], [ ], [ ], [ ], [ 11 ], [ ], [ 66 ], [ ], [ ], [ ], [ 66 ], [ ], [ 19, 79 ], [ ], [ 21 ], [ 13 ], [ ], [ 29, 78 ], [ ], [ ], [ 98 ], [ ], [ ], [ ], [ ], [ ], [ ], [ 100 ], [ ], [ ], [ ], [ 44, 53, 69 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/attr.tst:385 # Input is: DigraphConnectedComponents(gr); # Expected output: rec( comps := [ [ 1 ], [ 2 ], [ 3 ], [ 4, 45 ], [ 5, 40 ], [ 6 ], [ 7 ], [ 8, 54 ], [ 9, 62 ], [ 10 ], [ 11, 13, 14, 20, 28, 32, 36, 37, 48, 52, 55, 56, 58, 65, 73, 84, 97 ], [ 12, 70 ], [ 15 ], [ 16, 18, 19, 27, 44, 53, 60, 66, 69, 75, 79, 81, 95, 96, 100 ], [ 17 ], [ 21, 83 ], [ 22, 42 ], [ 23 ], [ 24 ], [ 25 ], [ 26, 50 ], [ 29, 59, 78, 86 ], [ 30 ], [ 31, 63 ], [ 33 ], [ 34, 89, 98 ], [ 35 ], [ 38 ], [ 39 ], [ 41 ], [ 43 ], [ 46 ], [ 47 ], [ 49 ], [ 51 ], [ 57 ], [ 61 ], [ 64 ], [ 67 ], [ 68 ], [ 71 ], [ 72 ], [ 74 ], [ 76 ], [ 77 ], [ 80 ], [ 82 ], [ 85 ], [ 87 ], [ 88 ], [ 90 ], [ 91 ], [ 92 ], [ 93 ], [ 94 ], [ 99 ] ], id := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 11, 11, 13, 14, 15, 14, 14, 11, 16, 17, 18, 19, 20, 21, 14, 11, 22, 23, 24, 11, 25, 26, 27, 11, 11, 28, 29, 5, 30, 17, 31, 14, 4, 32, 33, 11, 34, 21, 35, 11, 14, 8, 11, 11, 36, 11, 22, 14, 37, 9, 24, 38, 11, 14, 39, 40, 14, 12, 41, 42, 11, 43, 14, 44, 45, 22, 14, 46, 14, 47, 16, 11, 48, 22, 49, 50, 26, 51, 52, 53, 54, 55, 14, 14, 11, 26, 56, 14 ] ) # But found: Error, Variable: 'DigraphConnectedComponents' must have a value ######## ########> Diff in standard/attr.tst:406 # Input is: cycle12 := Digraph(adj); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:408 # Input is: mat := DigraphShortestDistances(cycle12);; # Expected output: # But found: Error, Variable: 'DigraphShortestDistances' must have a value ######## ########> Diff in standard/attr.tst:409 # Input is: Display(mat); # Expected output: [ [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ], [ 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ], [ 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ], [ 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8 ], [ 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7 ], [ 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6 ], [ 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5 ], [ 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4 ], [ 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3 ], [ 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2 ], [ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0 ] ] # But found: Error, Variable: 'mat' must have a value ######## ########> Diff in standard/attr.tst:422 # Input is: DigraphShortestDistances(Digraph([])); # Expected output: [ ] # But found: Error, Variable: 'DigraphShortestDistances' must have a value ######## ########> Diff in standard/attr.tst:424 # Input is: mat := DigraphShortestDistances(Digraph([[], []])); # Expected output: [ [ 0, fail ], [ fail, 0 ] ] # But found: Error, Variable: 'DigraphShortestDistances' must have a value ######## ########> Diff in standard/attr.tst:433 # Input is: complete15 := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:435 # Input is: Display(DigraphShortestDistances(complete15)); # Expected output: [ [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0 ] ] # But found: Error, Variable: 'DigraphShortestDistances' must have a value ######## ########> Diff in standard/attr.tst:453 # Input is: gr := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:455 # Input is: Display(DigraphShortestDistances(gr)); # Expected output: [ [ 0, 2, 1, 3, 1, 3, 2 ], [ fail, 0, 2, 1, 3, 1, 4 ], [ fail, 1, 0, 2, 1, 2, 2 ], [ fail, 2, 1, 0, 2, 3, 3 ], [ fail, 2, 1, 3, 0, 3, 1 ], [ fail, fail, fail, fail, fail, 0, fail ], [ fail, 1, 3, 2, 4, 2, 0 ] ] # But found: Error, Variable: 'DigraphShortestDistances' must have a value ######## ########> Diff in standard/attr.tst:465 # Input is: gr := CycleDigraph(3);; # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/attr.tst:466 # Input is: DIGRAPHS_ConnectivityData(gr); # Expected output: [ ] # But found: Error, Variable: 'DIGRAPHS_ConnectivityData' must have a value ######## ########> Diff in standard/attr.tst:468 # Input is: DigraphShortestDistances(gr); # Expected output: [ [ 0, 1, 2 ], [ 2, 0, 1 ], [ 1, 2, 0 ] ] # But found: Error, Variable: 'DigraphShortestDistances' must have a value ######## ########> Diff in standard/attr.tst:470 # Input is: gr := CompleteDigraph(3);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/attr.tst:471 # Input is: DIGRAPH_ConnectivityDataForVertex(gr, 2);; # Expected output: # But found: Error, Variable: 'DIGRAPH_ConnectivityDataForVertex' must have a value ######## ########> Diff in standard/attr.tst:472 # Input is: DigraphShortestDistances(gr); # Expected output: [ [ 0, 1, 1 ], [ 1, 0, 1 ], [ 1, 1, 0 ] ] # But found: Error, Variable: 'DigraphShortestDistances' must have a value ######## ########> Diff in standard/attr.tst:476 # Input is: gr := Digraph(rec(DigraphNrVertices := 10, DigraphSource := [1, 1, 5, 5, 7, 10\ ], DigraphRange := [3, 3, 1, 10, 7, 1])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:479 # Input is: InNeighbours(gr); # Expected output: [ [ 5, 10 ], [ ], [ 1, 1 ], [ ], [ ], [ ], [ 7 ], [ ], [ ], [ 5 ] ] # But found: Error, Variable: 'InNeighbours' must have a value ######## ########> Diff in standard/attr.tst:481 # Input is: OutNeighbours(gr); # Expected output: [ [ 3, 3 ], [ ], [ ], [ ], [ 1, 10 ], [ ], [ 7 ], [ ], [ ], [ 1 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/attr.tst:483 # Input is: gr := Digraph([[1, 1, 4], [2, 3, 4], [2, 4, 4, 4], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:485 # Input is: InNeighbours(gr); # Expected output: [ [ 1, 1 ], [ 2, 3, 4 ], [ 2 ], [ 1, 2, 3, 3, 3 ] ] # But found: Error, Variable: 'InNeighbours' must have a value ######## ########> Diff in standard/attr.tst:487 # Input is: OutNeighbours(gr); # Expected output: [ [ 1, 1, 4 ], [ 2, 3, 4 ], [ 2, 4, 4, 4 ], [ 2 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/attr.tst:492 # Input is: gr1 := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:494 # Input is: OutDegrees(gr1); # Expected output: [ ] # But found: Error, Variable: 'OutDegrees' must have a value ######## ########> Diff in standard/attr.tst:496 # Input is: OutDegreeSequence(gr1); # Expected output: [ ] # But found: Error, Variable: 'OutDegreeSequence' must have a value ######## ########> Diff in standard/attr.tst:498 # Input is: InDegrees(gr1); # Expected output: [ ] # But found: Error, Variable: 'InDegrees' must have a value ######## ########> Diff in standard/attr.tst:500 # Input is: InDegreeSequence(gr1); # Expected output: [ ] # But found: Error, Variable: 'InDegreeSequence' must have a value ######## ########> Diff in standard/attr.tst:502 # Input is: gr2 := Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:504 # Input is: OutDegrees(gr2); # Expected output: [ ] # But found: Error, Variable: 'OutDegrees' must have a value ######## ########> Diff in standard/attr.tst:506 # Input is: OutDegreeSequence(gr2); # Expected output: [ ] # But found: Error, Variable: 'OutDegreeSequence' must have a value ######## ########> Diff in standard/attr.tst:508 # Input is: InDegrees(gr2); # Expected output: [ ] # But found: Error, Variable: 'InDegrees' must have a value ######## ########> Diff in standard/attr.tst:510 # Input is: InDegreeSequence(gr2); # Expected output: [ ] # But found: Error, Variable: 'InDegreeSequence' must have a value ######## ########> Diff in standard/attr.tst:512 # Input is: gr3 := Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:514 # Input is: InNeighbours(gr3); # Expected output: [ ] # But found: Error, Variable: 'InNeighbours' must have a value ######## ########> Diff in standard/attr.tst:516 # Input is: OutDegrees(gr3); # Expected output: [ ] # But found: Error, Variable: 'OutDegrees' must have a value ######## ########> Diff in standard/attr.tst:518 # Input is: OutDegreeSequence(gr3); # Expected output: [ ] # But found: Error, Variable: 'OutDegreeSequence' must have a value ######## ########> Diff in standard/attr.tst:520 # Input is: InDegrees(gr3); # Expected output: [ ] # But found: Error, Variable: 'InDegrees' must have a value ######## ########> Diff in standard/attr.tst:522 # Input is: InDegreeSequence(gr3); # Expected output: [ ] # But found: Error, Variable: 'InDegreeSequence' must have a value ######## ########> Diff in standard/attr.tst:527 # Input is: gr1 := Digraph(adj); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:529 # Input is: OutDegrees(gr1); # Expected output: [ 3, 4, 1, 5, 5, 2, 6, 2 ] # But found: Error, Variable: 'OutDegrees' must have a value ######## ########> Diff in standard/attr.tst:531 # Input is: OutDegreeSequence(gr1); # Expected output: [ 6, 5, 5, 4, 3, 2, 2, 1 ] # But found: Error, Variable: 'OutDegreeSequence' must have a value ######## ########> Diff in standard/attr.tst:533 # Input is: InDegrees(gr1); # Expected output: [ 5, 0, 3, 5, 4, 5, 5, 1 ] # But found: Error, Variable: 'InDegrees' must have a value ######## ########> Diff in standard/attr.tst:535 # Input is: InDegreeSequence(gr1); # Expected output: [ 5, 5, 5, 5, 4, 3, 1, 0 ] # But found: Error, Variable: 'InDegreeSequence' must have a value ######## ########> Diff in standard/attr.tst:537 # Input is: gr2 := Digraph(adj); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:539 # Input is: InNeighbours(gr2);; # Expected output: # But found: Error, Variable: 'InNeighbours' must have a value ######## ########> Diff in standard/attr.tst:540 # Input is: InDegrees(gr2); # Expected output: [ 5, 0, 3, 5, 4, 5, 5, 1 ] # But found: Error, Variable: 'InDegrees' must have a value ######## ########> Diff in standard/attr.tst:542 # Input is: InDegreeSequence(gr2); # Expected output: [ 5, 5, 5, 5, 4, 3, 1, 0 ] # But found: Error, Variable: 'InDegreeSequence' must have a value ######## ########> Diff in standard/attr.tst:549 # Input is: gr3 := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:551 # Input is: OutDegrees(gr3); # Expected output: [ 3, 4, 1, 5, 5, 2, 6, 2 ] # But found: Error, Variable: 'OutDegrees' must have a value ######## ########> Diff in standard/attr.tst:553 # Input is: OutDegreeSequence(gr3); # Expected output: [ 6, 5, 5, 4, 3, 2, 2, 1 ] # But found: Error, Variable: 'OutDegreeSequence' must have a value ######## ########> Diff in standard/attr.tst:555 # Input is: InDegrees(gr3); # Expected output: [ 5, 0, 3, 5, 4, 5, 5, 1 ] # But found: Error, Variable: 'InDegrees' must have a value ######## ########> Diff in standard/attr.tst:557 # Input is: InDegreeSequence(gr3); # Expected output: [ 5, 5, 5, 5, 4, 3, 1, 0 ] # But found: Error, Variable: 'InDegreeSequence' must have a value ######## ########> Diff in standard/attr.tst:559 # Input is: OutDegrees(EmptyDigraph(5)); # Expected output: [ 0, 0, 0, 0, 0 ] # But found: Error, Variable: 'OutDegrees' must have a value ######## ########> Diff in standard/attr.tst:561 # Input is: InDegrees(EmptyDigraph(5)); # Expected output: [ 0, 0, 0, 0, 0 ] # But found: Error, Variable: 'InDegrees' must have a value ######## ########> Diff in standard/attr.tst:563 # Input is: gr := EmptyDigraph(5);; OutNeighbours(gr);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/attr.tst:564 # Input is: OutDegrees(gr); # Expected output: [ 0, 0, 0, 0, 0 ] # But found: Error, Variable: 'OutDegrees' must have a value ######## ########> Diff in standard/attr.tst:566 # Input is: gr := EmptyDigraph(5);; OutNeighbours(gr);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/attr.tst:567 # Input is: InDegrees(gr); # Expected output: [ 0, 0, 0, 0, 0 ] # But found: Error, Variable: 'InDegrees' must have a value ######## ########> Diff in standard/attr.tst:577 # Input is: gr := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:579 # Input is: DigraphEdges(gr); # Expected output: [ [ 1, 1 ], [ 1, 4 ], [ 2, 3 ], [ 3, 5 ], [ 5, 2 ], [ 5, 2 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/attr.tst:581 # Input is: gr := Digraph([[4], [2, 3, 1, 3], [3, 3], [], [1, 4, 5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:583 # Input is: DigraphEdges(gr); # Expected output: [ [ 1, 4 ], [ 2, 2 ], [ 2, 3 ], [ 2, 1 ], [ 2, 3 ], [ 3, 3 ], [ 3, 3 ], [ 5, 1 ], [ 5, 4 ], [ 5, 5 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/attr.tst:586 # Input is: gr := Digraph([[1, 2, 3, 5, 6, 8], [6, 6, 7, 8], [1, 2, 3, 4, 6, 7], [2, 3, 5, 6, 2, 7], [5, 6, 5, 5], [3, 2, 8], [1, 5, 7], [6, 7]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:589 # Input is: DigraphEdges(gr); # Expected output: [ [ 1, 1 ], [ 1, 2 ], [ 1, 3 ], [ 1, 5 ], [ 1, 6 ], [ 1, 8 ], [ 2, 6 ], [ 2, 6 ], [ 2, 7 ], [ 2, 8 ], [ 3, 1 ], [ 3, 2 ], [ 3, 3 ], [ 3, 4 ], [ 3, 6 ], [ 3, 7 ], [ 4, 2 ], [ 4, 3 ], [ 4, 5 ], [ 4, 6 ], [ 4, 2 ], [ 4, 7 ], [ 5, 5 ], [ 5, 6 ], [ 5, 5 ], [ 5, 5 ], [ 6, 3 ], [ 6, 2 ], [ 6, 8 ], [ 7, 1 ], [ 7, 5 ], [ 7, 7 ], [ 8, 6 ], [ 8, 7 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/attr.tst:600 # Input is: gr := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:602 # Input is: DigraphSinks(gr); # Expected output: [ 1, 4, 6, 8, 10 ] # But found: Error, Variable: 'DigraphSinks' must have a value ######## ########> Diff in standard/attr.tst:604 # Input is: DigraphSources(gr); # Expected output: [ 1, 3, 7, 9, 10 ] # But found: Error, Variable: 'DigraphSources' must have a value ######## ########> Diff in standard/attr.tst:606 # Input is: gr := Digraph(OutNeighbours(gr));; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:607 # Input is: DigraphSinks(gr); # Expected output: [ 1, 4, 6, 8, 10 ] # But found: Error, Variable: 'DigraphSinks' must have a value ######## ########> Diff in standard/attr.tst:609 # Input is: DigraphSources(gr); # Expected output: [ 1, 3, 7, 9, 10 ] # But found: Error, Variable: 'DigraphSources' must have a value ######## ########> Diff in standard/attr.tst:611 # Input is: gr := Digraph(r);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:612 # Input is: InNeighbours(gr); # Expected output: [ [ ], [ 2, 2, 3, 7, 9 ], [ ], [ 5, 9 ], [ 9 ], [ 3, 7, 7 ], [ ], [ 3, 7, 9, 9 ], [ ], [ ] ] # But found: Error, Variable: 'InNeighbours' must have a value ######## ########> Diff in standard/attr.tst:615 # Input is: DigraphSinks(gr); # Expected output: [ 1, 4, 6, 8, 10 ] # But found: Error, Variable: 'DigraphSinks' must have a value ######## ########> Diff in standard/attr.tst:617 # Input is: DigraphSources(gr); # Expected output: [ 1, 3, 7, 9, 10 ] # But found: Error, Variable: 'DigraphSources' must have a value ######## ########> Diff in standard/attr.tst:619 # Input is: gr := Digraph(r);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:620 # Input is: OutDegrees(gr); # Expected output: [ 0, 2, 3, 0, 1, 0, 4, 0, 5, 0 ] # But found: Error, Variable: 'OutDegrees' must have a value ######## ########> Diff in standard/attr.tst:622 # Input is: InDegrees(gr); # Expected output: [ 0, 5, 0, 2, 1, 3, 0, 4, 0, 0 ] # But found: Error, Variable: 'InDegrees' must have a value ######## ########> Diff in standard/attr.tst:624 # Input is: DigraphSinks(gr); # Expected output: [ 1, 4, 6, 8, 10 ] # But found: Error, Variable: 'DigraphSinks' must have a value ######## ########> Diff in standard/attr.tst:626 # Input is: DigraphSources(gr); # Expected output: [ 1, 3, 7, 9, 10 ] # But found: Error, Variable: 'DigraphSources' must have a value ######## ########> Diff in standard/attr.tst:630 # Input is: gr := EmptyDigraph(100); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/attr.tst:632 # Input is: DigraphPeriod(gr); # Expected output: 0 # But found: Error, Variable: 'DigraphPeriod' must have a value ######## ########> Diff in standard/attr.tst:634 # Input is: gr := CompleteDigraph(100); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/attr.tst:636 # Input is: DigraphPeriod(gr); # Expected output: 1 # But found: Error, Variable: 'DigraphPeriod' must have a value ######## ########> Diff in standard/attr.tst:638 # Input is: gr := Digraph([[2, 2], [3], [4], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:640 # Input is: DigraphPeriod(gr); # Expected output: 4 # But found: Error, Variable: 'DigraphPeriod' must have a value ######## ########> Diff in standard/attr.tst:642 # Input is: gr := Digraph([[2], [3], [4], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:644 # Input is: HasIsAcyclicDigraph(gr); # Expected output: false # But found: Error, Variable: 'HasIsAcyclicDigraph' must have a value ######## ########> Diff in standard/attr.tst:646 # Input is: DigraphPeriod(gr); # Expected output: 0 # But found: Error, Variable: 'DigraphPeriod' must have a value ######## ########> Diff in standard/attr.tst:648 # Input is: HasIsAcyclicDigraph(gr); # Expected output: true # But found: Error, Variable: 'HasIsAcyclicDigraph' must have a value ######## ########> Diff in standard/attr.tst:650 # Input is: IsAcyclicDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/attr.tst:652 # Input is: gr := Digraph([[2], [3], [4], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:654 # Input is: IsAcyclicDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/attr.tst:656 # Input is: DigraphPeriod(gr); # Expected output: 0 # But found: Error, Variable: 'DigraphPeriod' must have a value ######## ########> Diff in standard/attr.tst:660 # Input is: gr := Digraph([[2], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:661 # Input is: DigraphDiameter(gr); # Expected output: fail # But found: Error, Variable: 'DigraphDiameter' must have a value ######## ########> Diff in standard/attr.tst:663 # Input is: gr := Digraph([[2], [3], [4, 5], [5], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:664 # Input is: DigraphDiameter(gr); # Expected output: 4 # But found: Error, Variable: 'DigraphDiameter' must have a value ######## ########> Diff in standard/attr.tst:666 # Input is: gr := Digraph([[1, 2], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:667 # Input is: DigraphDiameter(gr); # Expected output: 1 # But found: Error, Variable: 'DigraphDiameter' must have a value ######## ########> Diff in standard/attr.tst:669 # Input is: gr := Digraph([[2], [3], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:670 # Input is: IsStronglyConnectedDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsStronglyConnectedDigraph' must have a value ######## ########> Diff in standard/attr.tst:672 # Input is: DigraphDiameter(gr); # Expected output: fail # But found: Error, Variable: 'DigraphDiameter' must have a value ######## ########> Diff in standard/attr.tst:674 # Input is: gr := Digraph([[1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:675 # Input is: DigraphDiameter(gr); # Expected output: 0 # But found: Error, Variable: 'DigraphDiameter' must have a value ######## ########> Diff in standard/attr.tst:677 # Input is: gr := EmptyDigraph(0);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/attr.tst:678 # Input is: DigraphDiameter(gr); # Expected output: fail # But found: Error, Variable: 'DigraphDiameter' must have a value ######## ########> Diff in standard/attr.tst:680 # Input is: gr := EmptyDigraph(1);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/attr.tst:681 # Input is: DigraphDiameter(gr); # Expected output: 0 # But found: Error, Variable: 'DigraphDiameter' must have a value ######## ########> Diff in standard/attr.tst:725 # Input is: gr := DigraphFromDiSparse6String(str); # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/attr.tst:727 # Input is: DigraphDiameter(gr); # Expected output: fail # But found: Error, Variable: 'DigraphDiameter' must have a value ######## ########> Diff in standard/attr.tst:731 # Input is: gr1 := Digraph([[2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:733 # Input is: IsSymmetricDigraph(gr1); # Expected output: true # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:735 # Input is: gr2 := DigraphSymmetricClosure(gr1); # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/attr.tst:737 # Input is: IsIdenticalObj(gr1, gr2); # Expected output: true # But found: Error, Variable: 'gr1' must have a value ######## ########> Diff in standard/attr.tst:739 # Input is: gr1 = gr2; # Expected output: true # But found: Error, Variable: 'gr1' must have a value ######## ########> Diff in standard/attr.tst:741 # Input is: gr1 := Digraph([[1, 1, 1, 1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:743 # Input is: gr2 := DigraphSymmetricClosure(gr1); # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/attr.tst:745 # Input is: IsIdenticalObj(gr1, gr2); # Expected output: true # But found: Error, Variable: 'gr1' must have a value ######## ########> Diff in standard/attr.tst:747 # Input is: gr1 = gr2; # Expected output: true # But found: Error, Variable: 'gr1' must have a value ######## ########> Diff in standard/attr.tst:749 # Input is: gr1 := Digraph( [[], [4, 5], [12], [3], [2, 10, 11, 12], [2, 8, 10, 12], [5], [11, 12], [12], [12], [2, 6, 7, 8], [3, 8, 10]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:753 # Input is: IsSymmetricDigraph(gr1); # Expected output: false # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:755 # Input is: gr2 := DigraphSymmetricClosure(gr1); # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/attr.tst:757 # Input is: HasIsSymmetricDigraph(gr2); # Expected output: true # But found: Error, Variable: 'HasIsSymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:759 # Input is: IsSymmetricDigraph(gr2); # Expected output: true # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:761 # Input is: gr3 := Digraph( [[], [4, 5, 11, 6], [4, 12], [2, 3], [2, 10, 11, 12, 7], [8, 10, 12, 2, 11], [5, 11], [11, 12, 6], [12], [5, 6, 12], [7, 6, 2, 5, 8], [10, 5, 3, 8, 6, 9]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:765 # Input is: gr2 = gr3; # Expected output: true # But found: Error, Variable: 'gr2' must have a value ######## ########> Diff in standard/attr.tst:767 # Input is: gr := DigraphSymmetricClosure(ChainDigraph(10000)); # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/attr.tst:769 # Input is: IsSymmetricDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:771 # Input is: gr := DigraphCopy(gr); # Expected output: # But found: Error, Variable: 'DigraphCopy' must have a value ######## ########> Diff in standard/attr.tst:773 # Input is: IsSymmetricDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:777 # Input is: gr := Digraph(rec(DigraphNrVertices := 2, DigraphSource := [1, 1], DigraphRange := [2, 2])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:781 # Input is: DigraphReflexiveTransitiveClosure(gr); # Expected output: Error, the argument must be a digraph with no multiple edges, # But found: Error, Variable: 'DigraphReflexiveTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:783 # Input is: DigraphTransitiveClosure(gr); # Expected output: Error, the argument must be a digraph with no multiple edges, # But found: Error, Variable: 'DigraphTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:787 # Input is: gr := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:789 # Input is: IsAcyclicDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/attr.tst:791 # Input is: DigraphTopologicalSort(gr); # Expected output: fail # But found: Error, Variable: 'DigraphTopologicalSort' must have a value ######## ########> Diff in standard/attr.tst:793 # Input is: gr1 := DigraphTransitiveClosure(gr); # Expected output: # But found: Error, Variable: 'DigraphTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:795 # Input is: gr2 := DigraphReflexiveTransitiveClosure(gr); # Expected output: # But found: Error, Variable: 'DigraphReflexiveTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:797 # Input is: gr1 = gr2; # Expected output: true # But found: Error, Variable: 'gr1' must have a value ######## ########> Diff in standard/attr.tst:799 # Input is: gr1 = DigraphReflexiveTransitiveClosure(DigraphMutableCopy(gr)); # Expected output: true # But found: Error, Variable: 'gr1' must have a value ######## ########> Diff in standard/attr.tst:802 # Input is: gr := Digraph(adj); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:804 # Input is: IsAcyclicDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/attr.tst:806 # Input is: gr1 := DigraphTransitiveClosure(gr); # Expected output: # But found: Error, Variable: 'DigraphTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:808 # Input is: gr2 := DigraphReflexiveTransitiveClosure(DigraphImmutableCopy(gr)); # Expected output: # But found: Error, Variable: 'DigraphReflexiveTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:810 # Input is: gr := Digraph([[2], [3], [4], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:812 # Input is: gr1 := DigraphTransitiveClosure(gr); # Expected output: # But found: Error, Variable: 'DigraphTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:814 # Input is: gr2 := DigraphReflexiveTransitiveClosure(gr); # Expected output: # But found: Error, Variable: 'DigraphReflexiveTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:816 # Input is: gr := Digraph([[2], [3], [4, 5], [], [5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:818 # Input is: gr1 := DigraphTransitiveClosure(gr); # Expected output: # But found: Error, Variable: 'DigraphTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:820 # Input is: gr2 := DigraphReflexiveTransitiveClosure(gr); # Expected output: # But found: Error, Variable: 'DigraphReflexiveTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:822 # Input is: gr := Digraph( [[1, 4, 5, 6, 7, 8], [5, 7, 8, 9, 10, 13], [2, 4, 6, 10], [7, 9, 10, 11], [7, 9, 10, 12, 13, 15], [7, 8, 10, 13], [10, 11], [7, 10, 12, 13, 14, 15, 16], [7, 10, 11, 14, 16], [11], [11], [7, 13, 14], [10, 11], [7, 10, 11], [7, 13, 16], [7, 10, 11]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:828 # Input is: trans1 := DigraphTransitiveClosure(gr); # Expected output: # But found: Error, Variable: 'DigraphTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:830 # Input is: trans2 := DigraphByAdjacencyMatrix(DIGRAPH_TRANS_CLOSURE(gr)); # Expected output: # But found: Error, Variable: 'DigraphByAdjacencyMatrix' must have a value ######## ########> Diff in standard/attr.tst:832 # Input is: trans1 = trans2; # Expected output: true # But found: Error, Variable: 'trans1' must have a value ######## ########> Diff in standard/attr.tst:834 # Input is: trans := Digraph(OutNeighbours(trans1)); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:836 # Input is: IsReflexiveDigraph(trans); # Expected output: false # But found: Error, Variable: 'IsReflexiveDigraph' must have a value ######## ########> Diff in standard/attr.tst:838 # Input is: IsTransitiveDigraph(trans); # Expected output: true # But found: Error, Variable: 'IsTransitiveDigraph' must have a value ######## ########> Diff in standard/attr.tst:840 # Input is: IS_TRANSITIVE_DIGRAPH(trans); # Expected output: true # But found: Error, Variable: 'IS_TRANSITIVE_DIGRAPH' must have a value ######## ########> Diff in standard/attr.tst:842 # Input is: reflextrans1 := DigraphReflexiveTransitiveClosure(gr); # Expected output: # But found: Error, Variable: 'DigraphReflexiveTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:844 # Input is: reflextrans2 := DigraphByAdjacencyMatrix(DIGRAPH_REFLEX_TRANS_CLOSURE(gr)); # Expected output: # But found: Error, Variable: 'DigraphByAdjacencyMatrix' must have a value ######## ########> Diff in standard/attr.tst:847 # Input is: reflextrans1 = reflextrans2; # Expected output: true # But found: Error, Variable: 'reflextrans1' must have a value ######## ########> Diff in standard/attr.tst:849 # Input is: reflextrans := Digraph(OutNeighbours(reflextrans1)); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:851 # Input is: IsReflexiveDigraph(reflextrans); # Expected output: true # But found: Error, Variable: 'IsReflexiveDigraph' must have a value ######## ########> Diff in standard/attr.tst:853 # Input is: IsTransitiveDigraph(reflextrans); # Expected output: true # But found: Error, Variable: 'IsTransitiveDigraph' must have a value ######## ########> Diff in standard/attr.tst:855 # Input is: IS_TRANSITIVE_DIGRAPH(reflextrans); # Expected output: true # But found: Error, Variable: 'IS_TRANSITIVE_DIGRAPH' must have a value ######## ########> Diff in standard/attr.tst:859 # Input is: gr := EmptyDigraph(0);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/attr.tst:860 # Input is: ReducedDigraph(gr) = gr; # Expected output: true # But found: Error, Variable: 'ReducedDigraph' must have a value ######## ########> Diff in standard/attr.tst:862 # Input is: DigraphEdges(ReducedDigraph(Digraph(IsMutableDigraph, [[2], []]))); # Expected output: [ [ 1, 2 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/attr.tst:864 # Input is: gr := Digraph([[2, 4, 2, 6, 1], [], [], [2, 1, 4], [], [1, 7, 7, 7], [4, 6]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:867 # Input is: rd := ReducedDigraph(gr); # Expected output: # But found: Error, Variable: 'ReducedDigraph' must have a value ######## ########> Diff in standard/attr.tst:869 # Input is: DigraphVertexLabels(rd); # Expected output: [ 1, 2, 4, 6, 7 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/attr.tst:871 # Input is: gr := CompleteDigraph(10); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/attr.tst:873 # Input is: rd := ReducedDigraph(gr); # Expected output: # But found: Error, Variable: 'ReducedDigraph' must have a value ######## ########> Diff in standard/attr.tst:875 # Input is: rd = gr; # Expected output: true # But found: Error, Variable: 'rd' must have a value ######## ########> Diff in standard/attr.tst:877 # Input is: DigraphVertexLabels(gr) = DigraphVertexLabels(rd); # Expected output: true # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/attr.tst:879 # Input is: gr := Digraph([[], [4, 2], [], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:881 # Input is: SetDigraphVertexLabels(gr, ["one", "two", "three", "four"]); # Expected output: # But found: Error, Variable: 'SetDigraphVertexLabels' must have a value ######## ########> Diff in standard/attr.tst:882 # Input is: rd := ReducedDigraph(gr); # Expected output: # But found: Error, Variable: 'ReducedDigraph' must have a value ######## ########> Diff in standard/attr.tst:884 # Input is: DigraphVertexLabels(gr); # Expected output: [ "one", "two", "three", "four" ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/attr.tst:886 # Input is: DigraphVertexLabels(rd); # Expected output: [ "two", "three", "four" ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/attr.tst:888 # Input is: gr := Digraph([[], [4, 2], [], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:890 # Input is: SetDigraphEdgeLabels(gr, [[], ["a", "b"], [], ["c"]]); # Expected output: # But found: Error, Variable: 'SetDigraphEdgeLabels' must have a value ######## ########> Diff in standard/attr.tst:891 # Input is: rd := ReducedDigraph(gr); # Expected output: # But found: Error, Variable: 'ReducedDigraph' must have a value ######## ########> Diff in standard/attr.tst:893 # Input is: DigraphEdgeLabels(gr); # Expected output: [ [ ], [ "a", "b" ], [ ], [ "c" ] ] # But found: Error, Variable: 'DigraphEdgeLabels' must have a value ######## ########> Diff in standard/attr.tst:895 # Input is: DigraphEdgeLabels(rd); # Expected output: [ [ "a", "b" ], [ ], [ "c" ] ] # But found: Error, Variable: 'DigraphEdgeLabels' must have a value ######## ########> Diff in standard/attr.tst:899 # Input is: gr := Digraph([]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:900 # Input is: DigraphAllSimpleCircuits(gr); # Expected output: [ ] # But found: Error, Variable: 'DigraphAllSimpleCircuits' must have a value ######## ########> Diff in standard/attr.tst:902 # Input is: gr := ChainDigraph(4);; # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/attr.tst:903 # Input is: DigraphAllSimpleCircuits(gr); # Expected output: [ ] # But found: Error, Variable: 'DigraphAllSimpleCircuits' must have a value ######## ########> Diff in standard/attr.tst:905 # Input is: gr := CompleteDigraph(2);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/attr.tst:906 # Input is: DigraphAllSimpleCircuits(gr); # Expected output: [ [ 1, 2 ] ] # But found: Error, Variable: 'DigraphAllSimpleCircuits' must have a value ######## ########> Diff in standard/attr.tst:908 # Input is: gr := CompleteDigraph(3);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/attr.tst:909 # Input is: DigraphAllSimpleCircuits(gr); # Expected output: [ [ 1, 2 ], [ 1, 2, 3 ], [ 1, 3 ], [ 1, 3, 2 ], [ 2, 3 ] ] # But found: Error, Variable: 'DigraphAllSimpleCircuits' must have a value ######## ########> Diff in standard/attr.tst:911 # Input is: gr := Digraph(["a", "b"], ["a", "b"], ["b", "a"]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:913 # Input is: DigraphAllSimpleCircuits(gr); # Expected output: [ [ 1, 2 ] ] # But found: Error, Variable: 'DigraphAllSimpleCircuits' must have a value ######## ########> Diff in standard/attr.tst:915 # Input is: gr := Digraph([[], [3], [2, 4], [5, 4], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:917 # Input is: DigraphAllSimpleCircuits(gr); # Expected output: [ [ 4 ], [ 4, 5 ], [ 2, 3 ] ] # But found: Error, Variable: 'DigraphAllSimpleCircuits' must have a value ######## ########> Diff in standard/attr.tst:919 # Input is: gr := Digraph([[], [], [], [4], [], [], [8], [7]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:921 # Input is: DigraphAllSimpleCircuits(gr); # Expected output: [ [ 4 ], [ 7, 8 ] ] # But found: Error, Variable: 'DigraphAllSimpleCircuits' must have a value ######## ########> Diff in standard/attr.tst:923 # Input is: gr := Digraph([[1, 2], [2, 1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:925 # Input is: DigraphAllSimpleCircuits(gr); # Expected output: [ [ 1 ], [ 2 ], [ 1, 2 ] ] # But found: Error, Variable: 'DigraphAllSimpleCircuits' must have a value ######## ########> Diff in standard/attr.tst:927 # Input is: gr := Digraph([[4], [1, 3], [1, 2], [2, 3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:928 # Input is: DigraphAllSimpleCircuits(gr); # Expected output: [ [ 1, 4, 2 ], [ 1, 4, 2, 3 ], [ 1, 4, 3 ], [ 1, 4, 3, 2 ], [ 2, 3 ] ] # But found: Error, Variable: 'DigraphAllSimpleCircuits' must have a value ######## ########> Diff in standard/attr.tst:930 # Input is: gr := Digraph([[3, 6, 7], [3, 6, 8], [1, 2, 3, 6, 7, 8], [2, 3, 4, 8], [2, 3, 4, 5, 6, 7], [1, 3, 4, 5, 7], [2, 3, 6, 8], [1, 2, 3, 8]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:933 # Input is: Length(DigraphAllSimpleCircuits(gr)); # Expected output: 259 # But found: Error, Variable: 'DigraphAllSimpleCircuits' must have a value ######## ########> Diff in standard/attr.tst:937 # Input is: gr := Digraph([]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:938 # Input is: DigraphLongestSimpleCircuit(gr); # Expected output: fail # But found: Error, Variable: 'DigraphLongestSimpleCircuit' must have a value ######## ########> Diff in standard/attr.tst:940 # Input is: gr := Digraph([[], [2]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:941 # Input is: DigraphLongestSimpleCircuit(gr); # Expected output: [ 2 ] # But found: Error, Variable: 'DigraphLongestSimpleCircuit' must have a value ######## ########> Diff in standard/attr.tst:943 # Input is: gr := Digraph([[], [3], [2, 4], [5, 4], [4]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:944 # Input is: DigraphLongestSimpleCircuit(gr); # Expected output: [ 4, 5 ] # But found: Error, Variable: 'DigraphLongestSimpleCircuit' must have a value ######## ########> Diff in standard/attr.tst:946 # Input is: gr := ChainDigraph(10);; # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/attr.tst:947 # Input is: DigraphLongestSimpleCircuit(gr); # Expected output: fail # But found: Error, Variable: 'DigraphLongestSimpleCircuit' must have a value ######## ########> Diff in standard/attr.tst:949 # Input is: gr := Digraph([[3], [1], [1, 4], [1, 1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:950 # Input is: DigraphLongestSimpleCircuit(gr); # Expected output: [ 1, 3, 4 ] # But found: Error, Variable: 'DigraphLongestSimpleCircuit' must have a value ######## ########> Diff in standard/attr.tst:952 # Input is: gr := Digraph([[2, 6, 10], [3], [4], [5], [1], [7], [8], [9], [1], [11], [12], [13], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:954 # Input is: DigraphLongestSimpleCircuit(gr); # Expected output: [ 1, 2, 3, 4, 5 ] # But found: Error, Variable: 'DigraphLongestSimpleCircuit' must have a value ######## ########> Diff in standard/attr.tst:956 # Input is: gr := Digraph([[2, 6, 10], [3], [4], [5], [1], [7], [8], [9], [1], [11], [12], [1, 13], [14], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:958 # Input is: DigraphLongestSimpleCircuit(gr); # Expected output: [ 1, 10, 11, 12, 13, 14 ] # But found: Error, Variable: 'DigraphLongestSimpleCircuit' must have a value ######## ########> Diff in standard/attr.tst:962 # Input is: gr := Digraph([[2], [1, 3], [4], [3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:963 # Input is: AsTransformation(gr); # Expected output: fail # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/attr.tst:965 # Input is: gr := AsDigraph(Transformation([1, 1, 1]), 5); # Expected output: # But found: Error, Variable: 'AsDigraph' must have a value ######## ########> Diff in standard/attr.tst:967 # Input is: DigraphEdges(gr); # Expected output: [ [ 1, 1 ], [ 2, 1 ], [ 3, 1 ], [ 4, 4 ], [ 5, 5 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/attr.tst:969 # Input is: AsTransformation(gr); # Expected output: Transformation( [ 1, 1, 1 ] ) # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/attr.tst:973 # Input is: DigraphBicomponents(EmptyDigraph(0)); # Expected output: fail # But found: Error, Variable: 'DigraphBicomponents' must have a value ######## ########> Diff in standard/attr.tst:975 # Input is: DigraphBicomponents(EmptyDigraph(1)); # Expected output: fail # But found: Error, Variable: 'DigraphBicomponents' must have a value ######## ########> Diff in standard/attr.tst:977 # Input is: DigraphBicomponents(EmptyDigraph(2)); # Expected output: [ [ 1 ], [ 2 ] ] # But found: Error, Variable: 'DigraphBicomponents' must have a value ######## ########> Diff in standard/attr.tst:979 # Input is: DigraphBicomponents(EmptyDigraph(3)); # Expected output: [ [ 1, 2 ], [ 3 ] ] # But found: Error, Variable: 'DigraphBicomponents' must have a value ######## ########> Diff in standard/attr.tst:981 # Input is: DigraphBicomponents(EmptyDigraph(4)); # Expected output: [ [ 1, 2, 3 ], [ 4 ] ] # But found: Error, Variable: 'DigraphBicomponents' must have a value ######## ########> Diff in standard/attr.tst:983 # Input is: DigraphBicomponents(CompleteBipartiteDigraph(3, 5)); # Expected output: [ [ 1, 2, 3 ], [ 4, 5, 6, 7, 8 ] ] # But found: Error, Variable: 'DigraphBicomponents' must have a value ######## ########> Diff in standard/attr.tst:985 # Input is: DigraphBicomponents(Digraph([[2], [], [], [3]])); # Expected output: [ [ 1, 3 ], [ 2, 4 ] ] # But found: Error, Variable: 'DigraphBicomponents' must have a value ######## ########> Diff in standard/attr.tst:987 # Input is: DigraphBicomponents(CycleDigraph(3)); # Expected output: fail # But found: Error, Variable: 'DigraphBicomponents' must have a value ######## ########> Diff in standard/attr.tst:991 # Input is: gr := ChainDigraph(4);; # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/attr.tst:992 # Input is: DigraphHasLoops(gr); # Expected output: false # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/attr.tst:994 # Input is: DigraphLoops(gr); # Expected output: [ ] # But found: Error, Variable: 'DigraphLoops' must have a value ######## ########> Diff in standard/attr.tst:996 # Input is: gr := Digraph([[2], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:997 # Input is: DigraphLoops(gr); # Expected output: [ ] # But found: Error, Variable: 'DigraphLoops' must have a value ######## ########> Diff in standard/attr.tst:999 # Input is: gr := Digraph([[1, 5, 6], [1, 3, 4, 5, 6], [1, 3, 4], [2, 4, 6], [2], [1, 4, 5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1002 # Input is: DigraphLoops(gr); # Expected output: [ 1, 3, 4 ] # But found: Error, Variable: 'DigraphLoops' must have a value ######## ########> Diff in standard/attr.tst:1006 # Input is: gr := Digraph([[2, 3, 4, 5], [], [], [], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1007 # Input is: OutDegrees(gr); # Expected output: [ 4, 0, 0, 0, 0 ] # But found: Error, Variable: 'OutDegrees' must have a value ######## ########> Diff in standard/attr.tst:1009 # Input is: InDegrees(gr); # Expected output: [ 0, 1, 1, 1, 1 ] # But found: Error, Variable: 'InDegrees' must have a value ######## ########> Diff in standard/attr.tst:1011 # Input is: InDegreeSet(gr); # Expected output: [ 0, 1 ] # But found: Error, Variable: 'InDegreeSet' must have a value ######## ########> Diff in standard/attr.tst:1013 # Input is: OutDegrees(gr); # Expected output: [ 4, 0, 0, 0, 0 ] # But found: Error, Variable: 'OutDegrees' must have a value ######## ########> Diff in standard/attr.tst:1015 # Input is: OutDegreeSet(gr); # Expected output: [ 0, 4 ] # But found: Error, Variable: 'OutDegreeSet' must have a value ######## ########> Diff in standard/attr.tst:1017 # Input is: gr := Digraph([[2, 3, 4, 5], [], [], [], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1018 # Input is: InNeighbours(gr);; # Expected output: # But found: Error, Variable: 'InNeighbours' must have a value ######## ########> Diff in standard/attr.tst:1019 # Input is: DigraphGroup(gr); # Expected output: Group([ (4,5), (3,4), (2,3) ]) # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/attr.tst:1021 # Input is: InDegreeSequence(gr); # Expected output: [ 1, 1, 1, 1, 0 ] # But found: Error, Variable: 'InDegreeSequence' must have a value ######## ########> Diff in standard/attr.tst:1023 # Input is: gr := DigraphSymmetricClosure(ChainDigraph(4));; # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/attr.tst:1024 # Input is: DigraphGroup(gr); # Expected output: Group([ (1,4)(2,3) ]) # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/attr.tst:1026 # Input is: HasDigraphGroup(gr); # Expected output: true # But found: Error, Variable: 'HasDigraphGroup' must have a value ######## ########> Diff in standard/attr.tst:1028 # Input is: OutDegreeSequence(gr); # Expected output: [ 2, 2, 1, 1 ] # But found: Error, Variable: 'OutDegreeSequence' must have a value ######## ########> Diff in standard/attr.tst:1032 # Input is: gr := Digraph([[2, 3, 4, 5], [], [], [], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1033 # Input is: DigraphGroup(gr); # Expected output: Group([ (4,5), (3,4), (2,3) ]) # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/attr.tst:1035 # Input is: DigraphDiameter(gr); # Expected output: fail # But found: Error, Variable: 'DigraphDiameter' must have a value ######## ########> Diff in standard/attr.tst:1037 # Input is: gr := Digraph([[2, 3, 4, 5], [6], [6], [6], [6], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1038 # Input is: DigraphGroup(gr); # Expected output: Group([ (4,5), (3,4), (2,3) ]) # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/attr.tst:1040 # Input is: DigraphDiameter(gr); # Expected output: 3 # But found: Error, Variable: 'DigraphDiameter' must have a value ######## ########> Diff in standard/attr.tst:1042 # Input is: gr := DigraphSymmetricClosure(CycleDigraph(7));; # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/attr.tst:1043 # Input is: DigraphUndirectedGirth(gr); # Expected output: 7 # But found: Error, Variable: 'DigraphUndirectedGirth' must have a value ######## ########> Diff in standard/attr.tst:1045 # Input is: DigraphDiameter(gr); # Expected output: 3 # But found: Error, Variable: 'DigraphDiameter' must have a value ######## ########> Diff in standard/attr.tst:1047 # Input is: DigraphGroup(gr) = DihedralGroup(IsPermGroup, 14); # Expected output: true # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/attr.tst:1049 # Input is: gr := DigraphSymmetricClosure(CycleDigraph(7));; # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/attr.tst:1050 # Input is: DigraphDiameter(gr); # Expected output: 3 # But found: Error, Variable: 'DigraphDiameter' must have a value ######## ########> Diff in standard/attr.tst:1052 # Input is: DigraphUndirectedGirth(gr); # Expected output: 7 # But found: Error, Variable: 'DigraphUndirectedGirth' must have a value ######## ########> Diff in standard/attr.tst:1054 # Input is: DigraphGroup(gr) = DihedralGroup(IsPermGroup, 14); # Expected output: true # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/attr.tst:1056 # Input is: gr := Digraph([[], [3], [2]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1057 # Input is: DigraphUndirectedGirth(gr); # Expected output: infinity # But found: Error, Variable: 'DigraphUndirectedGirth' must have a value ######## ########> Diff in standard/attr.tst:1059 # Input is: DigraphDiameter(gr); # Expected output: fail # But found: Error, Variable: 'DigraphDiameter' must have a value ######## ########> Diff in standard/attr.tst:1061 # Input is: gr := Digraph([[2, 4], [1, 3], [2, 3], [1, 5], [4, 5]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1062 # Input is: DigraphGroup(gr); # Expected output: Group([ (2,4)(3,5) ]) # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/attr.tst:1064 # Input is: DigraphDiameter(gr); # Expected output: 4 # But found: Error, Variable: 'DigraphDiameter' must have a value ######## ########> Diff in standard/attr.tst:1066 # Input is: DigraphUndirectedGirth(gr); # Expected output: 1 # But found: Error, Variable: 'DigraphUndirectedGirth' must have a value ######## ########> Diff in standard/attr.tst:1068 # Input is: gr := Digraph([[2, 2, 4, 4], [1, 1, 3], [2], [1, 1, 5], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1070 # Input is: DigraphDiameter(gr); # Expected output: 4 # But found: Error, Variable: 'DigraphDiameter' must have a value ######## ########> Diff in standard/attr.tst:1072 # Input is: DigraphUndirectedGirth(gr); # Expected output: 2 # But found: Error, Variable: 'DigraphUndirectedGirth' must have a value ######## ########> Diff in standard/attr.tst:1074 # Input is: gr := EmptyDigraph(0);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/attr.tst:1075 # Input is: DigraphUndirectedGirth(gr); # Expected output: infinity # But found: Error, Variable: 'DigraphUndirectedGirth' must have a value ######## ########> Diff in standard/attr.tst:1077 # Input is: DigraphDiameter(gr); # Expected output: fail # But found: Error, Variable: 'DigraphDiameter' must have a value ######## ########> Diff in standard/attr.tst:1081 # Input is: gr := CompleteDigraph(4);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/attr.tst:1082 # Input is: mat := BooleanAdjacencyMatrix(gr); # Expected output: [ [ false, true, true, true ], [ true, false, true, true ], [ true, true, false, true ], [ true, true, true, false ] ] # But found: Error, Variable: 'BooleanAdjacencyMatrix' must have a value ######## ########> Diff in standard/attr.tst:1085 # Input is: IsSymmetricDigraph(gr) and mat = TransposedMat(mat); # Expected output: true # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:1087 # Input is: gr := EmptyDigraph(5);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/attr.tst:1088 # Input is: mat := BooleanAdjacencyMatrix(gr); # Expected output: [ [ false, false, false, false, false ], [ false, false, false, false, false ] , [ false, false, false, false, false ], [ false, false, false, false, false ], [ false, false, false, false, false ] ] # But found: Error, Variable: 'BooleanAdjacencyMatrix' must have a value ######## ########> Diff in standard/attr.tst:1093 # Input is: IsSymmetricDigraph(gr) and mat = TransposedMat(mat); # Expected output: true # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:1095 # Input is: gr := CycleDigraph(4);; # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/attr.tst:1096 # Input is: mat := BooleanAdjacencyMatrix(gr); # Expected output: [ [ false, true, false, false ], [ false, false, true, false ], [ false, false, false, true ], [ true, false, false, false ] ] # But found: Error, Variable: 'BooleanAdjacencyMatrix' must have a value ######## ########> Diff in standard/attr.tst:1099 # Input is: not (IsSymmetricDigraph(gr) or mat = TransposedMat(mat)); # Expected output: true # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:1101 # Input is: gr := ChainDigraph(4);; # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/attr.tst:1102 # Input is: mat := BooleanAdjacencyMatrix(gr); # Expected output: [ [ false, true, false, false ], [ false, false, true, false ], [ false, false, false, true ], [ false, false, false, false ] ] # But found: Error, Variable: 'BooleanAdjacencyMatrix' must have a value ######## ########> Diff in standard/attr.tst:1105 # Input is: not (IsSymmetricDigraph(gr) or mat = TransposedMat(mat)); # Expected output: true # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:1107 # Input is: gr := Digraph([ [1, 4, 6, 8], [2, 8, 10], [4], [1, 6], [6, 7], [1, 2, 4, 10], [3], [3], [1, 8], [2, 5]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1110 # Input is: mat := BooleanAdjacencyMatrix(gr); # Expected output: [ [ true, false, false, true, false, true, false, true, false, false ], [ false, true, false, false, false, false, false, true, false, true ], [ false, false, false, true, false, false, false, false, false, false ], [ true, false, false, false, false, true, false, false, false, false ], [ false, false, false, false, false, true, true, false, false, false ], [ true, true, false, true, false, false, false, false, false, true ], [ false, false, true, false, false, false, false, false, false, false ], [ false, false, true, false, false, false, false, false, false, false ], [ true, false, false, false, false, false, false, true, false, false ], [ false, true, false, false, true, false, false, false, false, false ] ] # But found: Error, Variable: 'BooleanAdjacencyMatrix' must have a value ######## ########> Diff in standard/attr.tst:1121 # Input is: gr = DigraphByAdjacencyMatrix(mat); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/attr.tst:1125 # Input is: gr := Digraph([[2], [3], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1126 # Input is: DigraphUndirectedGirth(gr); # Expected output: Error, the argument must be a symmetric digraph, # But found: Error, Variable: 'DigraphUndirectedGirth' must have a value ######## ########> Diff in standard/attr.tst:1128 # Input is: gr := Digraph([[2], [1, 3], [2, 3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1129 # Input is: DigraphUndirectedGirth(gr); # Expected output: 1 # But found: Error, Variable: 'DigraphUndirectedGirth' must have a value ######## ########> Diff in standard/attr.tst:1131 # Input is: gr := Digraph([[2, 2], [1, 1, 3], [2]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1132 # Input is: DigraphUndirectedGirth(gr); # Expected output: 2 # But found: Error, Variable: 'DigraphUndirectedGirth' must have a value ######## ########> Diff in standard/attr.tst:1136 # Input is: gr := Digraph([[1], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1138 # Input is: DigraphGirth(gr); # Expected output: 1 # But found: Error, Variable: 'DigraphGirth' must have a value ######## ########> Diff in standard/attr.tst:1140 # Input is: gr := Digraph([[2, 3], [3], [4], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1142 # Input is: DigraphGirth(gr); # Expected output: infinity # But found: Error, Variable: 'DigraphGirth' must have a value ######## ########> Diff in standard/attr.tst:1144 # Input is: gr := Digraph([[2, 3], [3], [4], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1146 # Input is: DigraphGirth(gr); # Expected output: 3 # But found: Error, Variable: 'DigraphGirth' must have a value ######## ########> Diff in standard/attr.tst:1148 # Input is: gr := EmptyDigraph(42);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/attr.tst:1149 # Input is: DigraphGirth(gr); # Expected output: infinity # But found: Error, Variable: 'DigraphGirth' must have a value ######## ########> Diff in standard/attr.tst:1151 # Input is: gr := EmptyDigraph(0);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/attr.tst:1152 # Input is: DigraphGirth(gr); # Expected output: infinity # But found: Error, Variable: 'DigraphGirth' must have a value ######## ########> Diff in standard/attr.tst:1154 # Input is: gr := Digraph([[2], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1155 # Input is: DigraphGirth(gr); # Expected output: 2 # But found: Error, Variable: 'DigraphGirth' must have a value ######## ########> Diff in standard/attr.tst:1157 # Input is: DigraphUndirectedGirth(gr); # Expected output: infinity # But found: Error, Variable: 'DigraphUndirectedGirth' must have a value ######## ########> Diff in standard/attr.tst:1159 # Input is: gr := Digraph([[2], [1], [4], [5, 6], [], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1160 # Input is: DigraphGirth(gr); # Expected output: 2 # But found: Error, Variable: 'DigraphGirth' must have a value ######## ########> Diff in standard/attr.tst:1162 # Input is: DigraphUndirectedGirth(gr); # Expected output: Error, the argument must be a symmetric digraph, # But found: Error, Variable: 'DigraphUndirectedGirth' must have a value ######## ########> Diff in standard/attr.tst:1166 # Input is: gr := Digraph([[2, 3], [3], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1168 # Input is: DigraphOddGirth(gr); # Expected output: 3 # But found: Error, Variable: 'DigraphOddGirth' must have a value ######## ########> Diff in standard/attr.tst:1170 # Input is: gr := Digraph([[2], [3], [], [3], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1172 # Input is: DigraphOddGirth(gr); # Expected output: infinity # But found: Error, Variable: 'DigraphOddGirth' must have a value ######## ########> Diff in standard/attr.tst:1174 # Input is: gr := Digraph([[1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1176 # Input is: DigraphOddGirth(gr); # Expected output: 1 # But found: Error, Variable: 'DigraphOddGirth' must have a value ######## ########> Diff in standard/attr.tst:1178 # Input is: gr := Digraph([[2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1180 # Input is: DigraphOddGirth(gr); # Expected output: infinity # But found: Error, Variable: 'DigraphOddGirth' must have a value ######## ########> Diff in standard/attr.tst:1182 # Input is: gr := CycleDigraph(4); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/attr.tst:1184 # Input is: DigraphOddGirth(gr); # Expected output: infinity # But found: Error, Variable: 'DigraphOddGirth' must have a value ######## ########> Diff in standard/attr.tst:1186 # Input is: gr := DigraphDisjointUnion(CycleDigraph(2), CycleDigraph(3));; # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/attr.tst:1187 # Input is: for i in [1 .. 50] do gr := DigraphDisjointUnion(gr, CycleDigraph(3)); od; # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have an assigned value ######## ########> Diff in standard/attr.tst:1190 # Input is: DigraphOddGirth(gr); # Expected output: 3 # But found: Error, Variable: 'DigraphOddGirth' must have a value ######## ########> Diff in standard/attr.tst:1192 # Input is: G := Digraph(IsMutableDigraph, [[]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1194 # Input is: for i in [2 .. 200] do DigraphAddVertex(G, i); DigraphAddEdges(G, [[1, i], [i, 1]]); od; # Expected output: # But found: Error, Variable: 'DigraphAddVertex' must have an assigned value ######## ########> Diff in standard/attr.tst:1198 # Input is: D := CycleDigraph(IsMutableDigraph, 7); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/attr.tst:1200 # Input is: for i in [1 .. 20] do DigraphDisjointUnion(D, G); od; # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have an assigned value ######## ########> Diff in standard/attr.tst:1203 # Input is: DigraphOddGirth(D); # Expected output: 7 # But found: Error, Variable: 'DigraphOddGirth' must have a value ######## ########> Diff in standard/attr.tst:1207 # Input is: D1 := DigraphSymmetricClosure(CycleDigraph(2)); # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/attr.tst:1209 # Input is: D2 := DigraphSymmetricClosure(CycleDigraph(5)); # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/attr.tst:1211 # Input is: IsIsomorphicDigraph(DigraphMycielskian(D1), D2); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/attr.tst:1213 # Input is: D := DigraphSymmetricClosure(CayleyDigraph(DihedralGroup(8))); # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/attr.tst:1215 # Input is: ChromaticNumber(D); # Expected output: 4 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1217 # Input is: D := DigraphMycielskian(D); # Expected output: # But found: Error, Variable: 'DigraphMycielskian' must have a value ######## ########> Diff in standard/attr.tst:1219 # Input is: ChromaticNumber(D); # Expected output: 5 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1221 # Input is: D1 := Digraph([[], [3], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1223 # Input is: D2 := Digraph([[], [3, 4], [2, 5], [2, 6], [3, 6], [4, 5, 7], [6]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1225 # Input is: IsIsomorphicDigraph(DigraphMycielskian(D1), D2); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/attr.tst:1227 # Input is: D := DigraphSymmetricClosure(CycleDigraph(5)); # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/attr.tst:1229 # Input is: D := DigraphMutableCopy(D); # Expected output: # But found: Error, Variable: 'DigraphMutableCopy' must have a value ######## ########> Diff in standard/attr.tst:1231 # Input is: DigraphMycielskian(D); # Expected output: # But found: Error, Variable: 'DigraphMycielskian' must have a value ######## ########> Diff in standard/attr.tst:1233 # Input is: D := DigraphSymmetricClosure(Digraph([[1, 2], [1]])); # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/attr.tst:1235 # Input is: D := DigraphMutableCopy(D); # Expected output: # But found: Error, Variable: 'DigraphMutableCopy' must have a value ######## ########> Diff in standard/attr.tst:1237 # Input is: DigraphMycielskian(D); # Expected output: # But found: Error, Variable: 'DigraphMycielskian' must have a value ######## ########> Diff in standard/attr.tst:1239 # Input is: D := DigraphEdgeUnion(CycleDigraph(3), CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/attr.tst:1241 # Input is: DigraphMycielskian(D); # Expected output: Error, the argument must be a symmetric digraph with no multiple edges, # But found: Error, Variable: 'DigraphMycielskian' must have a value ######## ########> Diff in standard/attr.tst:1243 # Input is: DigraphMycielskian(DigraphMutableCopy(D)); # Expected output: Error, the argument must be a symmetric digraph with no multiple edges, # But found: Error, Variable: 'DigraphMycielskian' must have a value ######## ########> Diff in standard/attr.tst:1245 # Input is: D := DigraphEdgeUnion(CompleteDigraph(3), CompleteDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/attr.tst:1247 # Input is: DigraphMycielskian(D); # Expected output: Error, the argument must be a symmetric digraph with no multiple edges, # But found: Error, Variable: 'DigraphMycielskian' must have a value ######## ########> Diff in standard/attr.tst:1249 # Input is: DigraphMycielskian(DigraphMutableCopy(D)); # Expected output: Error, the argument must be a symmetric digraph with no multiple edges, # But found: Error, Variable: 'DigraphMycielskian' must have a value ######## ########> Diff in standard/attr.tst:1253 # Input is: gr := Digraph([[2, 2], [1, 1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1254 # Input is: IsMultiDigraph(gr) and IsSymmetricDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsMultiDigraph' must have a value ######## ########> Diff in standard/attr.tst:1256 # Input is: DigraphDegeneracy(gr); # Expected output: Error, the argument must be a symmetric digraph with no multiple edges, # But found: Error, Variable: 'DigraphDegeneracy' must have a value ######## ########> Diff in standard/attr.tst:1258 # Input is: DigraphDegeneracyOrdering(gr); # Expected output: Error, the argument must be a symmetric digraph with no multiple edges, # But found: Error, Variable: 'DigraphDegeneracyOrdering' must have a value ######## ########> Diff in standard/attr.tst:1260 # Input is: gr := Digraph([[2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1262 # Input is: not IsMultiDigraph(gr) and not IsSymmetricDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsMultiDigraph' must have a value ######## ########> Diff in standard/attr.tst:1264 # Input is: DigraphDegeneracy(gr); # Expected output: Error, the argument must be a symmetric digraph with no multiple edges, # But found: Error, Variable: 'DigraphDegeneracy' must have a value ######## ########> Diff in standard/attr.tst:1266 # Input is: DigraphDegeneracyOrdering(gr); # Expected output: Error, the argument must be a symmetric digraph with no multiple edges, # But found: Error, Variable: 'DigraphDegeneracyOrdering' must have a value ######## ########> Diff in standard/attr.tst:1268 # Input is: gr := CompleteDigraph(5);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/attr.tst:1269 # Input is: DigraphDegeneracy(gr); # Expected output: 4 # But found: Error, Variable: 'DigraphDegeneracy' must have a value ######## ########> Diff in standard/attr.tst:1271 # Input is: DigraphDegeneracyOrdering(gr); # Expected output: [ 5, 4, 3, 2, 1 ] # But found: Error, Variable: 'DigraphDegeneracyOrdering' must have a value ######## ########> Diff in standard/attr.tst:1273 # Input is: gr := DigraphSymmetricClosure(ChainDigraph(4)); # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/attr.tst:1275 # Input is: DigraphDegeneracy(gr); # Expected output: 1 # But found: Error, Variable: 'DigraphDegeneracy' must have a value ######## ########> Diff in standard/attr.tst:1277 # Input is: DigraphDegeneracyOrdering(gr); # Expected output: [ 4, 3, 2, 1 ] # But found: Error, Variable: 'DigraphDegeneracyOrdering' must have a value ######## ########> Diff in standard/attr.tst:1279 # Input is: gr := Digraph([[3], [], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1281 # Input is: DigraphDegeneracy(gr); # Expected output: 1 # But found: Error, Variable: 'DigraphDegeneracy' must have a value ######## ########> Diff in standard/attr.tst:1283 # Input is: gr := DigraphSymmetricClosure(Digraph( [[2, 5], [3, 5], [4], [5, 6], [], []])); # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/attr.tst:1286 # Input is: DigraphDegeneracy(gr); # Expected output: 2 # But found: Error, Variable: 'DigraphDegeneracy' must have a value ######## ########> Diff in standard/attr.tst:1288 # Input is: DigraphDegeneracyOrdering(gr); # Expected output: [ 6, 4, 3, 2, 5, 1 ] # But found: Error, Variable: 'DigraphDegeneracyOrdering' must have a value ######## ########> Diff in standard/attr.tst:1292 # Input is: gr := Digraph([[2, 3, 4, 5], [6, 3], [6, 2], [6], [6], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1293 # Input is: DigraphGirth(gr); # Expected output: 2 # But found: Error, Variable: 'DigraphGirth' must have a value ######## ########> Diff in standard/attr.tst:1295 # Input is: gr := Digraph([[2, 3, 4, 5], [6, 3], [6, 2], [6], [6], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1296 # Input is: DigraphGroup(gr) = Group([(4, 5), (2, 3)]); # Expected output: true # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/attr.tst:1298 # Input is: DigraphGirth(gr); # Expected output: 2 # But found: Error, Variable: 'DigraphGirth' must have a value ######## ########> Diff in standard/attr.tst:1300 # Input is: gr := Digraph([[2, 6, 10], [3], [4], [5], [1], [7], [8], [9], [1], [11], [12], [13], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1302 # Input is: DigraphGirth(gr); # Expected output: 5 # But found: Error, Variable: 'DigraphGirth' must have a value ######## ########> Diff in standard/attr.tst:1304 # Input is: gr := Digraph([[2, 6, 10], [3], [4], [5], [1], [7], [8], [9], [1], [11], [12], [13], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1306 # Input is: DigraphGroup(gr); # Expected output: Group([ (6,10)(7,11)(8,12)(9,13), (2,6)(3,7)(4,8)(5,9) ]) # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/attr.tst:1308 # Input is: DigraphGirth(gr); # Expected output: 5 # But found: Error, Variable: 'DigraphGirth' must have a value ######## ########> Diff in standard/attr.tst:1312 # Input is: gr := Digraph([[2], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1313 # Input is: IsSymmetricDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:1315 # Input is: MaximalSymmetricSubdigraph(gr) = gr; # Expected output: true # But found: Error, Variable: 'MaximalSymmetricSubdigraph' must have a value ######## ########> Diff in standard/attr.tst:1317 # Input is: gr2 := Digraph([[2, 2], [1, 1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1318 # Input is: IsSymmetricDigraph(gr2) and IsMultiDigraph(gr2); # Expected output: true # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:1320 # Input is: MaximalSymmetricSubdigraph(gr2) = gr; # Expected output: true # But found: Error, Variable: 'MaximalSymmetricSubdigraph' must have a value ######## ########> Diff in standard/attr.tst:1322 # Input is: gr := Digraph([[2, 3], [1, 3], [4], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1324 # Input is: IsSymmetricDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:1326 # Input is: gr2 := MaximalSymmetricSubdigraph(gr); # Expected output: # But found: Error, Variable: 'MaximalSymmetricSubdigraph' must have a value ######## ########> Diff in standard/attr.tst:1328 # Input is: OutNeighbours(gr2); # Expected output: [ [ 2 ], [ 1 ], [ ], [ 4 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/attr.tst:1330 # Input is: gr2 := MaximalSymmetricSubdigraphWithoutLoops(gr); # Expected output: # But found: Error, Variable: 'MaximalSymmetricSubdigraphWithoutLoops' must have a value ######## ########> Diff in standard/attr.tst:1332 # Input is: OutNeighbours(gr2); # Expected output: [ [ 2 ], [ 1 ], [ ], [ ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/attr.tst:1334 # Input is: gr := Digraph([[2, 2], [1, 1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1336 # Input is: gr2 := MaximalSymmetricSubdigraphWithoutLoops(gr); # Expected output: # But found: Error, Variable: 'MaximalSymmetricSubdigraphWithoutLoops' must have a value ######## ########> Diff in standard/attr.tst:1338 # Input is: OutNeighbours(gr2); # Expected output: [ [ 2 ], [ 1 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/attr.tst:1340 # Input is: gr := Digraph([[1, 2, 2], [1, 1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1342 # Input is: IsSymmetricDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:1344 # Input is: gr3 := MaximalSymmetricSubdigraphWithoutLoops(gr); # Expected output: # But found: Error, Variable: 'MaximalSymmetricSubdigraphWithoutLoops' must have a value ######## ########> Diff in standard/attr.tst:1346 # Input is: gr2 = gr3; # Expected output: true # But found: Error, Variable: 'gr2' must have a value ######## ########> Diff in standard/attr.tst:1348 # Input is: gr := Digraph([[2, 3], [1], [1, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1350 # Input is: IsSymmetricDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:1352 # Input is: gr := MaximalSymmetricSubdigraphWithoutLoops(gr); # Expected output: # But found: Error, Variable: 'MaximalSymmetricSubdigraphWithoutLoops' must have a value ######## ########> Diff in standard/attr.tst:1354 # Input is: OutNeighbours(gr); # Expected output: [ [ 2, 3 ], [ 1 ], [ 1 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/attr.tst:1358 # Input is: gr := CycleDigraph(5); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/attr.tst:1360 # Input is: RepresentativeOutNeighbours(gr); # Expected output: [ [ 2 ] ] # But found: Error, Variable: 'RepresentativeOutNeighbours' must have a value ######## ########> Diff in standard/attr.tst:1362 # Input is: DigraphOrbitReps(gr); # Expected output: [ 1 ] # But found: Error, Variable: 'DigraphOrbitReps' must have a value ######## ########> Diff in standard/attr.tst:1364 # Input is: gr := Digraph([[2], [3], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1366 # Input is: RepresentativeOutNeighbours(gr); # Expected output: [ [ 2 ], [ 3 ], [ ] ] # But found: Error, Variable: 'RepresentativeOutNeighbours' must have a value ######## ########> Diff in standard/attr.tst:1370 # Input is: gr := Digraph([[1, 3], [2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1372 # Input is: adj := DigraphAdjacencyFunction(gr); # Expected output: function( u, v ) ... end # But found: Error, Variable: 'DigraphAdjacencyFunction' must have a value ######## ########> Diff in standard/attr.tst:1374 # Input is: adj(1, 1); # Expected output: true # But found: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `CallFuncList' on 2 arguments ######## ########> Diff in standard/attr.tst:1376 # Input is: adj(3, 1); # Expected output: false # But found: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `CallFuncList' on 2 arguments ######## ########> Diff in standard/attr.tst:1378 # Input is: adj(2, 7); # Expected output: false # But found: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `CallFuncList' on 2 arguments ######## ########> Diff in standard/attr.tst:1382 # Input is: ChromaticNumber(Digraph([[1]])); # Expected output: Error, the argument must be a digraph with no loops, # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1384 # Input is: ChromaticNumber(NullDigraph(10)); # Expected output: 1 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1386 # Input is: ChromaticNumber(CompleteDigraph(10)); # Expected output: 10 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1388 # Input is: ChromaticNumber(CompleteBipartiteDigraph(5, 5)); # Expected output: 2 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1390 # Input is: ChromaticNumber(DigraphRemoveEdge(CompleteDigraph(10), [1, 2])); # Expected output: 10 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1392 # Input is: ChromaticNumber(DigraphDisjointUnion(CompleteDigraph(10), CompleteBipartiteDigraph(50, 50))); # Expected output: 10 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1395 # Input is: ChromaticNumber(Digraph([[4, 8], [6, 10], [9], [2, 3, 9], [], [3], [4], [6], [], [5, 7]])); # Expected output: 3 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1398 # Input is: DigraphColouring(Digraph([[4, 8], [6, 10], [9], [2, 3, 9], [], [3], [4], [6], [], [5, 7]]), 2); # Expected output: fail # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/attr.tst:1401 # Input is: DigraphColouring(Digraph([[4, 8], [6, 10], [9], [2, 3, 9], [], [3], [4], [6], [], [5, 7]]), 3); # Expected output: Transformation( [ 2, 2, 3, 1, 2, 1, 2, 3, 2, 1 ] ) # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/attr.tst:1404 # Input is: ChromaticNumber(DigraphDisjointUnion(CompleteDigraph(1), Digraph([[2], [4], [1, 2], [3]]))); # Expected output: 3 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1407 # Input is: ChromaticNumber(DigraphDisjointUnion(CompleteDigraph(1), Digraph([[2], [4], [1, 2], [3], [1, 2, 3]]))); # Expected output: 4 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1410 # Input is: gr := DigraphFromDigraph6String(Concatenation( "&l??O?C?A_@???CE????GAAG?C??M?????@_?OO??G??@?IC???_C?G?o??C?AO???c_??A?", "A?S???OAA???OG???G_A??C?@?cC????_@G???S??C_?C???[??A?A?OA?O?@?A?@A???GGO", "??`?_O??G?@?A??G?@AH????AA?O@??_??b???Cg??C???_??W?G????d?G?C@A?C???GC?W", "?????K???__O[??????O?W???O@??_G?@?CG??G?@G?C??@G???_Q?O?O?c???OAO?C??C?G", "?O??A@??D??G?C_?A??O?_GA??@@?_?G???E?IW??????_@G?C??")); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/attr.tst:1417 # Input is: ChromaticNumber(gr); # Expected output: 3 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1419 # Input is: DigraphColouring(gr, 3); # Expected output: Transformation( [ 1, 2, 1, 2, 3, 2, 1, 1, 1, 2, 2, 1, 2, 3, 3, 1, 1, 1, 2, 1, 2, 2, 3, 3, 3, 1, 1, 2, 3, 3, 3, 2, 3, 2, 3, 2, 3, 1, 2, 1, 3, 1, 2, 3, 3 ] ) # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/attr.tst:1423 # Input is: DigraphColouring(gr, 2); # Expected output: fail # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/attr.tst:1425 # Input is: DigraphGreedyColouring(gr); # Expected output: Transformation( [ 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 3, 3, 2, 3, 3, 3, 2, 1, 4, 4, 2, 3, 3, 3, 3, 3, 1, 3, 4, 4, 3, 2, 1, 4, 3, 1 ] ) # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/attr.tst:1429 # Input is: gr := Digraph([[2, 3, 4], [3], [], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1431 # Input is: ChromaticNumber(gr); # Expected output: 3 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1433 # Input is: ChromaticNumber(EmptyDigraph(0)); # Expected output: 0 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1435 # Input is: gr := CompleteDigraph(4);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/attr.tst:1436 # Input is: gr := DigraphAddVertex(gr);; # Expected output: # But found: Error, Variable: 'DigraphAddVertex' must have a value ######## ########> Diff in standard/attr.tst:1437 # Input is: ChromaticNumber(gr); # Expected output: 4 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1439 # Input is: gr := DigraphFromDiSparse6String(Concatenation( ".~?C?_O?WF?MD?L`[DgX?}@oX`o?W^?}Fgb@mHOTa_?Od`ODOd`}EGnA?HW]`?IGfaULOLak", "LGA?sBoYAiMOt`[Lw_AGJWP`WHGs_gNWSBIMGF@oKhCASIWxc[BWUAgLGY@uFhKAY?OBBuRp", "EdGH_i_cDOaDEHGf_{COdcQNw|DEV?MCuPG`ASUhH`[I@ADqKOqEAHOiCiTgT`gNPSaWSgNB", "iSGTAeLpIcwS@SD[YGeE]L@UbGVGNBwSGE@_M@^`SHotBi[oBBOXH^_SEou_oG?sB[UGeA{\\", "Gq_CBo`AgK@WDeHPNE_[wXeq@oXDuGP\\aSIo{bK^hC`WJp`fMC_bEW\\G`AOK`[E_^iFF}IOy", "CMapZ_?BoWAw[@vGeN?~CKZGNBcPPwaOH_rD{ax?DKXAD_[P`u_CLISCsUgaAkbwKAKMGTAK", "O`BCgZQO_oT@T_oB_kB?[YTHaCoYA?OPkF?dGKEk\\ACHmAodAcL`RHiJPYDmW`jFYFpba_Pq", "MH[gGE@CJovE[aH}HUXa^e?ZWFA_I`jb?PpOF}?OODwXqRa?MGQCSRq___CoiCoVgOAcKOvE", "qQGBA{UQh`gG@YEkZh|akU@XGofaeIaYpsF{fwB?wCPKC{^q]_I@piJAMphEk_aB_KF`[D{X", "PngMJaCjkL`FHcgAw`{MPMDWkghB_W@sIAH`oH{jAzc{TPwHOjA|_WD_yC?TQ^ew[AQHwhap", "bKda`JUDo_G[hw[@{_aMc?P@JGOewPECXq[IGobB_cNbBa[XQBICjqs_gO`NDWhqoJMC_SAM", "CoYAWKpUIYFqj_?BpXEG[q?JCoycdygw|FGgqpaKK_vCC]A@Gskr@ao^AP_sG@EEwZqZISjw", "CIU?_iDOXP}JCogsKKpBEdKdxWE]V`gJksbS_?@_JGGaaxLiGOcBWTAt_KJ_tBoeXzG{oI?H", "[iRTL]GwK@STqLIoqG\\AwKp`ESfwaCOVPyGK`BK_GHowFoabPc[YPuGkmbR`?ZrIm_BOOFIA", "_\\HGjgKBGP`QEGWqjJ_nBSdwYrXMeK@mGweg?CCPG?FobrDMaEPUFo`bl`sQ`qHMU@^EC[aT", "HsrWFCCQ@IDSbROLWugPKOsW?Akhr[akL`\\FK`aFKmGQq`wS`dF_]apKeCp`Fg`qRL_yRl`S", "|goGG`h@JOlrnaSXq_LWwrs_oJ`?CKSqMIu^ry_WOqGHWtk?_G?GF?EB?B_{AgB_MD?A`MDo", "U`kAgG@KEwK?sCOR`]AOQaW?gU_kBGiAaDOX_CH_gawD_hb???SbGEGWbMCgG@cE__AaM?v_", "oE_paSHwV_SDw}?sHgF@]OOW@cLgCcOCOdAaC?kc_JhJByBgec{F_i_cD_l_ARwI?kDpPawK", "@J`?TG??SEomd_NxY?C@h[A?KgcASI`Yce?OF?cFOgbWSGi_gIPPDYQGdacI_yEINpWcGPPK", "__AO^BsRwL?{MwmB?QPR`yR`QEiRxH`SE?^`CC_l`oPgMA?Uhs?}A`j`KD?bCOXW`Ck[@ueA", "B?vDMJ_vEeM@kEyNp@fwCpi`OD`beYKPlFeK@WEk^IC?gBoRBoWHiFaKqBfmMpCDOVg`CORg", "KB?Xa@_SYP{fC`x`EW]GbaeYiQAaHhVEq[AOh[M@PF[]QF_WBogB?NpoFUA?pBOYgMD_VaP_", "WGpFE?`HGEmV``aCKpLDmPpjGmgPDDGUPz_oD`CHY?PK`cF@CaC`GRCOS@~bcW@xF}B?mGKa", "WK@oNO~CWU`wdKV@kGAB_VASKpgFoeWC?sD@gEkaAa_sEO~EW]`}IUK?{H{hH?D_^qHGkbQf", "_oJ@kGCdQdf[_wpBwRpRE?Z`x`GGpXDg^gL?wL@FGOiWRAOXAUJEIPgFQI@rGiN`OFcex|HW", "eqv`WE?_AsU`}fi@oZAOSa@__]QQJ]C@LGocWbA[RPMDO^qBa[O@NDUVQBGWhGZF?`aHIsjw", "HCGdXkFKaQwa?L@hGWjwqC?Yq[KUAPyGK`aqe[cyw_oH@GD{\\xjF}C`]EkbaPJAI?tC?YQ@_", "KO@bKm??RE_^Q}_WRAAHULpCC_\\AGKm?PeFS\\qyKmBoOIopBEKqAQCHSsi^LEMgF@olQuLQC", "@OHotwUEEuoPA{^A_K?pw`CG[@tHYH`a_sO`BCo`a__SCp]IspxGI?nrSdCdbILiCOsJStiZ", "JeDOqC?PaPHYC?jDSXR^hOpwTA_UQOHggG?@yK@@C_\\rEbwRQHKYG?aA[N`HK}A?gCKVwSAQ", "??mFEIpLFoiHZGWgqiLaK`wFsrILLmSQ[KC{XhGyVPnHoubdaoS`]D{lrl`WG?nB?QPPEwyg", "JD?Ta@Io|GX@wG@lHkkbYaCHOoJgrWqGkmRCL_wWIBo[AFIgpbZ_kQ`~IKlrD`GD_sGoewiB", "?QaKJr")); # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/attr.tst:1475 # Input is: gr := DigraphDisjointUnion(gr, CompleteDigraph(5)); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/attr.tst:1477 # Input is: ChromaticNumber(gr); # Expected output: 5 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1479 # Input is: gr := Digraph([[2, 4, 7, 3], [3, 5, 8, 1], [1, 6, 9, 2], [5, 7, 1, 6], [6, 8, 2, 4], [4, 9, 3, 5], [8, 1, 4, 9], [9, 2, 5, 7], [7, 3, 6, 8]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1482 # Input is: ChromaticNumber(gr); # Expected output: 3 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1484 # Input is: gr := DigraphSymmetricClosure(ChainDigraph(5)); # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/attr.tst:1486 # Input is: DigraphGreedyColouring(gr);; # Expected output: # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/attr.tst:1487 # Input is: ChromaticNumber(gr); # Expected output: 2 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1489 # Input is: gr := DigraphFromGraph6String("KmKk~K??G@_@"); # Expected output: # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/attr.tst:1491 # Input is: ChromaticNumber(gr); # Expected output: 4 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1493 # Input is: gr := CycleDigraph(7); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/attr.tst:1495 # Input is: ChromaticNumber(gr); # Expected output: 3 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1497 # Input is: gr := CycleDigraph(71); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/attr.tst:1499 # Input is: ChromaticNumber(gr); # Expected output: 3 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1501 # Input is: gr := CycleDigraph(1001); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/attr.tst:1503 # Input is: ChromaticNumber(gr); # Expected output: 3 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1505 # Input is: a := DigraphRemoveEdges(CompleteDigraph(50), [[1, 2], [2, 1]]);; # Expected output: # But found: Error, Variable: 'DigraphRemoveEdges' must have a value ######## ########> Diff in standard/attr.tst:1506 # Input is: b := DigraphAddVertex(a);; # Expected output: # But found: Error, Variable: 'DigraphAddVertex' must have a value ######## ########> Diff in standard/attr.tst:1507 # Input is: ChromaticNumber(a); # Expected output: 49 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1509 # Input is: ChromaticNumber(b); # Expected output: 49 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/attr.tst:1513 # Input is: gr := Digraph([[2, 3, 4], [2, 5], [1, 5, 4], [1], [1, 1, 2, 4]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1514 # Input is: DegreeMatrix(gr); # Expected output: [ [ 3, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 3, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 4 ] ] # But found: Error, Variable: 'DegreeMatrix' must have a value ######## ########> Diff in standard/attr.tst:1517 # Input is: DegreeMatrix(Digraph([])); # Expected output: [ ] # But found: Error, Variable: 'DegreeMatrix' must have a value ######## ########> Diff in standard/attr.tst:1519 # Input is: DegreeMatrix(Digraph([[]])); # Expected output: [ [ 0 ] ] # But found: Error, Variable: 'DegreeMatrix' must have a value ######## ########> Diff in standard/attr.tst:1521 # Input is: DegreeMatrix(Digraph([[1]])); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DegreeMatrix' must have a value ######## ########> Diff in standard/attr.tst:1525 # Input is: gr := Digraph([[2, 3, 4], [2, 5], [1, 5, 4], [1], [1, 1, 2, 4]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1526 # Input is: LaplacianMatrix(gr); # Expected output: [ [ 3, -1, -1, -1, 0 ], [ 0, 1, 0, 0, -1 ], [ -1, 0, 3, -1, -1 ], [ -1, 0, 0, 1, 0 ], [ -2, -1, 0, -1, 4 ] ] # But found: Error, Variable: 'LaplacianMatrix' must have a value ######## ########> Diff in standard/attr.tst:1529 # Input is: LaplacianMatrix(Digraph([])); # Expected output: [ ] # But found: Error, Variable: 'LaplacianMatrix' must have a value ######## ########> Diff in standard/attr.tst:1531 # Input is: LaplacianMatrix(Digraph([[1]])); # Expected output: [ [ 0 ] ] # But found: Error, Variable: 'LaplacianMatrix' must have a value ######## ########> Diff in standard/attr.tst:1533 # Input is: LaplacianMatrix(CycleDigraph(5)); # Expected output: [ [ 1, -1, 0, 0, 0 ], [ 0, 1, -1, 0, 0 ], [ 0, 0, 1, -1, 0 ], [ 0, 0, 0, 1, -1 ], [ -1, 0, 0, 0, 1 ] ] # But found: Error, Variable: 'LaplacianMatrix' must have a value ######## ########> Diff in standard/attr.tst:1536 # Input is: LaplacianMatrix(CompleteDigraph(5)); # Expected output: [ [ 4, -1, -1, -1, -1 ], [ -1, 4, -1, -1, -1 ], [ -1, -1, 4, -1, -1 ], [ -1, -1, -1, 4, -1 ], [ -1, -1, -1, -1, 4 ] ] # But found: Error, Variable: 'LaplacianMatrix' must have a value ######## ########> Diff in standard/attr.tst:1541 # Input is: NrSpanningTrees(CompleteDigraph(5)); # Expected output: 125 # But found: Error, Variable: 'NrSpanningTrees' must have a value ######## ########> Diff in standard/attr.tst:1543 # Input is: NrSpanningTrees(CycleDigraph(5)); # Expected output: Error, the argument must be a symmetric digraph, # But found: Error, Variable: 'NrSpanningTrees' must have a value ######## ########> Diff in standard/attr.tst:1545 # Input is: NrSpanningTrees(DigraphSymmetricClosure(CycleDigraph(5))); # Expected output: 5 # But found: Error, Variable: 'NrSpanningTrees' must have a value ######## ########> Diff in standard/attr.tst:1547 # Input is: NrSpanningTrees(Digraph([])); # Expected output: 0 # But found: Error, Variable: 'NrSpanningTrees' must have a value ######## ########> Diff in standard/attr.tst:1549 # Input is: NrSpanningTrees(Digraph([[1]])); # Expected output: 1 # But found: Error, Variable: 'NrSpanningTrees' must have a value ######## ########> Diff in standard/attr.tst:1551 # Input is: NrSpanningTrees(Digraph([[2, 3, 4], [1, 5], [1, 5], [1, 5], [2, 3, 4]])); # Expected output: 12 # But found: Error, Variable: 'NrSpanningTrees' must have a value ######## ########> Diff in standard/attr.tst:1555 # Input is: gr := EmptyDigraph(0); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/attr.tst:1557 # Input is: tree := UndirectedSpanningTree(gr); # Expected output: fail # But found: Error, Variable: 'UndirectedSpanningTree' must have a value ######## ########> Diff in standard/attr.tst:1559 # Input is: forest := UndirectedSpanningForest(gr); # Expected output: fail # But found: Error, Variable: 'UndirectedSpanningForest' must have a value ######## ########> Diff in standard/attr.tst:1561 # Input is: UndirectedSpanningForest(EmptyDigraph(IsMutableDigraph, 0)); # Expected output: fail # But found: Error, Variable: 'UndirectedSpanningForest' must have a value ######## ########> Diff in standard/attr.tst:1563 # Input is: gr := EmptyDigraph(1); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/attr.tst:1565 # Input is: tree := UndirectedSpanningTree(gr); # Expected output: # But found: Error, Variable: 'UndirectedSpanningTree' must have a value ######## ########> Diff in standard/attr.tst:1567 # Input is: forest := UndirectedSpanningForest(gr); # Expected output: # But found: Error, Variable: 'UndirectedSpanningForest' must have a value ######## ########> Diff in standard/attr.tst:1569 # Input is: IsUndirectedSpanningTree(gr, gr); # Expected output: true # But found: Error, Variable: 'IsUndirectedSpanningTree' must have a value ######## ########> Diff in standard/attr.tst:1571 # Input is: IsUndirectedSpanningTree(gr, forest); # Expected output: true # But found: Error, Variable: 'IsUndirectedSpanningTree' must have a value ######## ########> Diff in standard/attr.tst:1573 # Input is: gr = forest; # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/attr.tst:1575 # Input is: gr := EmptyDigraph(2); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/attr.tst:1577 # Input is: tree := UndirectedSpanningTree(gr); # Expected output: fail # But found: Error, Variable: 'UndirectedSpanningTree' must have a value ######## ########> Diff in standard/attr.tst:1579 # Input is: forest := UndirectedSpanningForest(gr); # Expected output: # But found: Error, Variable: 'UndirectedSpanningForest' must have a value ######## ########> Diff in standard/attr.tst:1581 # Input is: IsUndirectedTree(forest); # Expected output: false # But found: Error, Variable: 'IsUndirectedTree' must have a value ######## ########> Diff in standard/attr.tst:1583 # Input is: IsUndirectedSpanningForest(gr, forest); # Expected output: true # But found: Error, Variable: 'IsUndirectedSpanningForest' must have a value ######## ########> Diff in standard/attr.tst:1585 # Input is: gr = forest; # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/attr.tst:1587 # Input is: gr := DigraphFromDigraph6String("&IG@qqW?HO?BSQGA?CG"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/attr.tst:1589 # Input is: IsStronglyConnectedDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsStronglyConnectedDigraph' must have a value ######## ########> Diff in standard/attr.tst:1591 # Input is: UndirectedSpanningTree(gr); # Expected output: fail # But found: Error, Variable: 'UndirectedSpanningTree' must have a value ######## ########> Diff in standard/attr.tst:1593 # Input is: UndirectedSpanningTree(gr); # Expected output: fail # But found: Error, Variable: 'UndirectedSpanningTree' must have a value ######## ########> Diff in standard/attr.tst:1595 # Input is: DigraphEdges(UndirectedSpanningForest(gr)); # Expected output: [ [ 2, 7 ], [ 7, 2 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/attr.tst:1597 # Input is: DigraphEdges(UndirectedSpanningForest(gr)); # Expected output: [ [ 2, 7 ], [ 7, 2 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/attr.tst:1599 # Input is: IsUndirectedSpanningForest(gr, UndirectedSpanningForest(gr)); # Expected output: true # But found: Error, Variable: 'IsUndirectedSpanningForest' must have a value ######## ########> Diff in standard/attr.tst:1601 # Input is: D := DigraphFromDigraph6String("&I~~~~^Znn~|~~x^|v{"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/attr.tst:1603 # Input is: tree := UndirectedSpanningTree(D); # Expected output: # But found: Error, Variable: 'UndirectedSpanningTree' must have a value ######## ########> Diff in standard/attr.tst:1605 # Input is: IsUndirectedSpanningTree(D, tree); # Expected output: true # But found: Error, Variable: 'IsUndirectedSpanningTree' must have a value ######## ########> Diff in standard/attr.tst:1607 # Input is: tree := UndirectedSpanningTree(DigraphMutableCopy(D)); # Expected output: # But found: Error, Variable: 'UndirectedSpanningTree' must have a value ######## ########> Diff in standard/attr.tst:1609 # Input is: IsUndirectedSpanningTree(D, tree); # Expected output: true # But found: Error, Variable: 'IsUndirectedSpanningTree' must have a value ######## ########> Diff in standard/attr.tst:1613 # Input is: ArticulationPoints(CycleDigraph(5)); # Expected output: [ ] # But found: Error, Variable: 'ArticulationPoints' must have a value ######## ########> Diff in standard/attr.tst:1615 # Input is: ArticulationPoints(Digraph([[2, 7], [3, 5], [4], [2], [6], [1], []])); # Expected output: [ 2, 1 ] # But found: Error, Variable: 'ArticulationPoints' must have a value ######## ########> Diff in standard/attr.tst:1617 # Input is: ArticulationPoints(ChainDigraph(5)); # Expected output: [ 4, 3, 2 ] # But found: Error, Variable: 'ArticulationPoints' must have a value ######## ########> Diff in standard/attr.tst:1619 # Input is: ArticulationPoints(NullDigraph(5)); # Expected output: [ ] # But found: Error, Variable: 'ArticulationPoints' must have a value ######## ########> Diff in standard/attr.tst:1621 # Input is: gr := Digraph([[35, 55, 87], [38], [6, 53], [], [66], [56], [36], [] , [], [19], [23], [], [40, 76], [72, 79], [46, 48], [22, 68], [ 26], [17, 60], [17], [42], [34, 91], [68, 87], [14, 46], [23, 80 ], [6, 8], [], [], [], [], [], [28, 35], [], [18, 40, 94], [], [ 27, 44, 78], [], [25], [71], [72], [2, 33], [87], [], [42], [ ], [43], [63], [], [58, 89], [68, 97], [24, 40], [13], [9], [ 44], [80], [], [40], [78], [9], [], [35, 44, 57], [], [], [67, 74, 81], [], [86], [], [54, 93], [66, 79], [], [], [], [], [100 ], [19], [62, 68], [87], [4, 15, 89], [61, 86], [], [41], [21, 41], [59, 64], [], [53], [59], [14, 33], [], [], [37, 71, 92], [ 3, 20], [56], [56], [], [89], [], [1, 14, 38, 85], [], [19], [ 30], [56, 98]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1635 # Input is: IsConnectedDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsConnectedDigraph' must have a value ######## ########> Diff in standard/attr.tst:1637 # Input is: ArticulationPoints(gr); # Expected output: [ ] # But found: Error, Variable: 'ArticulationPoints' must have a value ######## ########> Diff in standard/attr.tst:1639 # Input is: gr := DigraphCopy(gr); # Expected output: # But found: Error, Variable: 'DigraphCopy' must have a value ######## ########> Diff in standard/attr.tst:1641 # Input is: ArticulationPoints(gr); # Expected output: [ ] # But found: Error, Variable: 'ArticulationPoints' must have a value ######## ########> Diff in standard/attr.tst:1643 # Input is: IsConnectedDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsConnectedDigraph' must have a value ######## ########> Diff in standard/attr.tst:1645 # Input is: ArticulationPoints(Digraph([[1, 2], [2]])); # Expected output: [ ] # But found: Error, Variable: 'ArticulationPoints' must have a value ######## ########> Diff in standard/attr.tst:1647 # Input is: gr := Digraph([[1, 1, 2, 2, 2, 2, 2], [2, 2, 3, 3], []]); # path # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1649 # Input is: ArticulationPoints(gr); # Expected output: [ 2 ] # But found: Error, Variable: 'ArticulationPoints' must have a value ######## ########> Diff in standard/attr.tst:1651 # Input is: gr := Digraph([[1, 1, 2, 2, 2, 2, 2], [2, 2, 3, 3], [1, 1, 1]]); # cycle # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1653 # Input is: ArticulationPoints(gr); # Expected output: [ ] # But found: Error, Variable: 'ArticulationPoints' must have a value ######## ########> Diff in standard/attr.tst:1655 # Input is: gr := Digraph([[2], [3], [], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1657 # Input is: ArticulationPoints(gr); # Expected output: [ 3, 2 ] # But found: Error, Variable: 'ArticulationPoints' must have a value ######## ########> Diff in standard/attr.tst:1659 # Input is: IsConnectedDigraph(DigraphRemoveVertex(gr, 3)); # Expected output: false # But found: Error, Variable: 'IsConnectedDigraph' must have a value ######## ########> Diff in standard/attr.tst:1661 # Input is: IsConnectedDigraph(DigraphRemoveVertex(gr, 2)); # Expected output: false # But found: Error, Variable: 'IsConnectedDigraph' must have a value ######## ########> Diff in standard/attr.tst:1663 # Input is: IsConnectedDigraph(DigraphRemoveVertex(gr, 1)); # Expected output: true # But found: Error, Variable: 'IsConnectedDigraph' must have a value ######## ########> Diff in standard/attr.tst:1665 # Input is: IsConnectedDigraph(DigraphRemoveVertex(gr, 4)); # Expected output: true # But found: Error, Variable: 'IsConnectedDigraph' must have a value ######## ########> Diff in standard/attr.tst:1667 # Input is: ArticulationPoints(Digraph([])); # Expected output: [ ] # But found: Error, Variable: 'ArticulationPoints' must have a value ######## ########> Diff in standard/attr.tst:1669 # Input is: ArticulationPoints(Digraph([[]])); # Expected output: [ ] # But found: Error, Variable: 'ArticulationPoints' must have a value ######## ########> Diff in standard/attr.tst:1671 # Input is: ArticulationPoints(Digraph([[1]])); # Expected output: [ ] # But found: Error, Variable: 'ArticulationPoints' must have a value ######## ########> Diff in standard/attr.tst:1673 # Input is: ArticulationPoints(Digraph([[1, 1]])); # Expected output: [ ] # But found: Error, Variable: 'ArticulationPoints' must have a value ######## ########> Diff in standard/attr.tst:1675 # Input is: ArticulationPoints(Digraph([[1], [2]])); # Expected output: [ ] # But found: Error, Variable: 'ArticulationPoints' must have a value ######## ########> Diff in standard/attr.tst:1677 # Input is: ArticulationPoints(Digraph([[2], [1]])); # Expected output: [ ] # But found: Error, Variable: 'ArticulationPoints' must have a value ######## ########> Diff in standard/attr.tst:1679 # Input is: ArticulationPoints(DigraphFromGraph6String("FlCX?")); # Expected output: [ 3, 4 ] # But found: Error, Variable: 'ArticulationPoints' must have a value ######## ########> Diff in standard/attr.tst:1681 # Input is: ArticulationPoints(Digraph([[2, 4, 5], [1, 4], [4, 7], [1, 2, 3, 5, 6, 7], [1, 4], [4, 7], [3, 4, 6]])); # Expected output: [ 4 ] # But found: Error, Variable: 'ArticulationPoints' must have a value ######## ########> Diff in standard/attr.tst:1684 # Input is: gr := DigraphFromSparse6String( ":~?@V`OINBg_McouHAxQD@gyYEW}Q_@_YdgE`?OgZgpEbfYQKDGqiDQEI`wGdjoADGZG\ FIJONFQSplq]y@IwvbPKhMh}JGK?OLzW{agKKfRCtarqTGayQGb]rMIurapkxPG?RGcI]\ IBtB_`EQKJ@LmxlL_?k^QieOkB|T"); # Expected output: # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/attr.tst:1689 # Input is: Set(ArticulationPoints(gr)); # Expected output: [ 1, 3, 8, 11, 12, 15, 17, 18, 19, 21, 23, 27, 30, 36, 37, 41, 42, 46, 51, 52, 59, 60, 61, 63, 66, 68, 69, 73, 75, 76, 79, 84, 87 ] # But found: Error, Variable: 'ArticulationPoints' must have a value ######## ########> Diff in standard/attr.tst:1692 # Input is: IsDuplicateFree(last); # Expected output: true # But found: false ######## ########> Diff in standard/attr.tst:1694 # Input is: ForAll(ArticulationPoints(gr), x -> not IsConnectedDigraph(DigraphRemoveVertex(gr, x))); # Expected output: true # But found: Error, Variable: 'ArticulationPoints' must have a value Syntax warning: Unbound global variable in stream:2 x -> not IsConnectedDigraph(DigraphRemoveVertex(gr, x))); ^^^^^^^^^^^^^^^^^^ Syntax warning: Unbound global variable in stream:2 x -> not IsConnectedDigraph(DigraphRemoveVertex(gr, x))); ^^^^^^^^^^^^^^^^^^^ Syntax warning: Unbound global variable in stream:2 x -> not IsConnectedDigraph(DigraphRemoveVertex(gr, x))); ^^ ######## ########> Diff in standard/attr.tst:1697 # Input is: Set(ArticulationPoints(gr)) = Filtered(DigraphVertices(gr), x -> not IsConnectedDigraph(DigraphRemoveVertex(gr, x))); # Expected output: true # But found: Error, Variable: 'ArticulationPoints' must have a value Syntax warning: Unbound global variable in stream:3 x -> not IsConnectedDigraph(DigraphRemoveVertex(gr, x))); ^^^^^^^^^^^^^^^^^^ Syntax warning: Unbound global variable in stream:3 x -> not IsConnectedDigraph(DigraphRemoveVertex(gr, x))); ^^^^^^^^^^^^^^^^^^^ Syntax warning: Unbound global variable in stream:3 x -> not IsConnectedDigraph(DigraphRemoveVertex(gr, x))); ^^ ######## ########> Diff in standard/attr.tst:1703 # Input is: g := Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1705 # Input is: HamiltonianPath(g); # Expected output: [ ] # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1707 # Input is: g := Digraph([[]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1709 # Input is: HamiltonianPath(g); # Expected output: [ 1 ] # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1711 # Input is: g := Digraph([[], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1713 # Input is: HamiltonianPath(g); # Expected output: fail # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1715 # Input is: g := Digraph([[1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1717 # Input is: HamiltonianPath(g); # Expected output: [ 1 ] # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1719 # Input is: g := Digraph([[2, 2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1721 # Input is: HamiltonianPath(g); # Expected output: fail # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1723 # Input is: g := Digraph([[2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1725 # Input is: HamiltonianPath(g); # Expected output: [ 1, 2 ] # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1727 # Input is: g := Digraph([[3], [3], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1729 # Input is: HamiltonianPath(g); # Expected output: fail # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1731 # Input is: g := Digraph([[3], [3], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1733 # Input is: HamiltonianPath(g); # Expected output: fail # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1735 # Input is: g := Digraph([[3], [], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1737 # Input is: HamiltonianPath(g); # Expected output: fail # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1739 # Input is: g := Digraph([[2], [3], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1741 # Input is: HamiltonianPath(g); # Expected output: [ 1, 2, 3 ] # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1743 # Input is: g := Digraph([[2], [3], [1], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1745 # Input is: HamiltonianPath(g); # Expected output: fail # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1747 # Input is: g := Digraph([[2], [3], [1, 4], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1749 # Input is: HamiltonianPath(g); # Expected output: fail # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1751 # Input is: g := Digraph([[3, 6], [4], [2, 1], [5, 1], [3], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1753 # Input is: HamiltonianPath(g); # Expected output: fail # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1755 # Input is: g := Digraph([[3, 6], [4, 1], [2, 1], [5, 1], [3], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1757 # Input is: HamiltonianPath(g); # Expected output: [ 1, 6, 4, 5, 3, 2 ] # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1759 # Input is: g := Digraph([[3, 6], [4], [2, 1], [5, 1], [3], [4, 7], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1761 # Input is: HamiltonianPath(g); # Expected output: fail # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1763 # Input is: g := Digraph([[3, 6, 7], [4, 1], [2, 1], [5, 1], [3], [4, 7], [6]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1765 # Input is: HamiltonianPath(g); # Expected output: [ 1, 7, 6, 4, 5, 3, 2 ] # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1767 # Input is: g := Digraph([[3, 6], [4], [2, 1], [5, 1], [3], [4, 7], [6]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1769 # Input is: HamiltonianPath(g); # Expected output: fail # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1771 # Input is: g := Digraph([[5, 6, 10], [2, 9], [3, 7], [2, 3], [9, 10], [2, 9], [1], [2, 3, 4, 7, 9], [3, 10], [4, 5, 6, 8]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1774 # Input is: HamiltonianPath(g); # Expected output: fail # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1776 # Input is: g := Digraph([[2, 4, 6, 10], [1, 3, 4, 5, 6, 7, 9, 10], [1, 5, 7, 8], [6, 10], [1, 7], [3, 4, 6, 7, 9], [2, 3, 4, 7], [2, 4, 5, 6], [2, 3, 5, 6, 7, 9, 10], [2, 3, 5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1780 # Input is: HamiltonianPath(g); # Expected output: [ 1, 4, 6, 9, 10, 3, 8, 5, 7, 2 ] # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1782 # Input is: IsDigraphMonomorphism(CycleDigraph(10), g, Transformation(HamiltonianPath(g))); # Expected output: true # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/attr.tst:1786 # Input is: g := CompleteMultipartiteDigraph([1, 30]); # Expected output: # But found: Error, Variable: 'CompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/attr.tst:1788 # Input is: HamiltonianPath(g); # Expected output: fail # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1790 # Input is: g := Digraph([[2, 5, 6], [3, 1, 7], [4, 2, 8], [5, 3, 9], [1, 4, 10], [1, 8, 9], [2, 9, 10], [3, 10, 6], [4, 6, 7], [5, 7, 8]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1793 # Input is: HamiltonianPath(g); # Expected output: fail # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1795 # Input is: g := CompleteMultipartiteDigraph([16, 15]); # Expected output: # But found: Error, Variable: 'CompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/attr.tst:1797 # Input is: HamiltonianPath(g); # Expected output: fail # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1799 # Input is: g := CompleteMultipartiteDigraph([1, 15, 1, 1, 1, 1, 1, 1]); # Expected output: # But found: Error, Variable: 'CompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/attr.tst:1801 # Input is: HamiltonianPath(g); # Expected output: fail # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1803 # Input is: g := CycleDigraph(100); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/attr.tst:1805 # Input is: HamiltonianPath(g); # Expected output: [ 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76 ] # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1812 # Input is: g := CycleDigraph(513); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/attr.tst:1814 # Input is: g := DigraphAddEdges(g, [[6, 8], [8, 7], [7, 9]]); # Expected output: # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/attr.tst:1816 # Input is: g := DigraphRemoveEdge(g, [6, 7]); # Expected output: # But found: Error, Variable: 'DigraphRemoveEdge' must have a value ######## ########> Diff in standard/attr.tst:1818 # Input is: HamiltonianPath(g); # Expected output: [ 1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 1 ] # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1852 # Input is: gr := DigraphAddEdges(DigraphAddVertex(CycleDigraph(600)), [[600, 601], [601, 600]]); # Expected output: # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/attr.tst:1855 # Input is: HamiltonianPath(gr); # Expected output: fail # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/attr.tst:1859 # Input is: D := Digraph([[3, 6], [1], [4], [5, 7], [1], [2, 7], [4, 1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1861 # Input is: DigraphCore(D); # Expected output: [ 1, 3, 4, 6, 7 ] # But found: Error, Variable: 'DigraphCore' must have a value ######## ########> Diff in standard/attr.tst:1863 # Input is: D := Digraph([[2, 3], [1, 3], [1, 2, 4], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1865 # Input is: DigraphCore(D); # Expected output: [ 1, 2, 3 ] # But found: Error, Variable: 'DigraphCore' must have a value ######## ########> Diff in standard/attr.tst:1867 # Input is: DigraphHomomorphism(D, InducedSubdigraph(D, DigraphCore(D))); # Expected output: Transformation( [ 1, 3, 2, 3 ] ) # But found: Error, Variable: 'DigraphHomomorphism' must have a value ######## ########> Diff in standard/attr.tst:1869 # Input is: D := CompleteDigraph(10); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/attr.tst:1871 # Input is: DigraphCore(D); # Expected output: [ 1 .. 10 ] # But found: Error, Variable: 'DigraphCore' must have a value ######## ########> Diff in standard/attr.tst:1873 # Input is: D := Digraph([[2], [3], [4], [5], [6], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1875 # Input is: DigraphCore(D); # Expected output: [ 2, 3, 4, 5, 6 ] # But found: Error, Variable: 'DigraphCore' must have a value ######## ########> Diff in standard/attr.tst:1877 # Input is: D := Digraph([[2], [1], [4, 5], [5], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1879 # Input is: DigraphCore(D); # Expected output: [ 3, 4, 5 ] # But found: Error, Variable: 'DigraphCore' must have a value ######## ########> Diff in standard/attr.tst:1881 # Input is: D := EmptyDigraph(0); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/attr.tst:1883 # Input is: DigraphCore(D); # Expected output: [ ] # But found: Error, Variable: 'DigraphCore' must have a value ######## ########> Diff in standard/attr.tst:1885 # Input is: D := EmptyDigraph(1000); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/attr.tst:1887 # Input is: DigraphCore(D); # Expected output: [ 1 ] # But found: Error, Variable: 'DigraphCore' must have a value ######## ########> Diff in standard/attr.tst:1889 # Input is: D := EmptyDigraph(IsMutableDigraph, 0); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/attr.tst:1891 # Input is: for i in [2 .. 15] do DigraphDisjointUnion(D, CycleDigraph(i)); od; # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have an assigned value ######## ########> Diff in standard/attr.tst:1894 # Input is: DigraphCore(D); # Expected output: [ 1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 21, 22, 23, 24, 25, 26, 27, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90 ] # But found: Error, Variable: 'DigraphCore' must have a value ######## ########> Diff in standard/attr.tst:1898 # Input is: D1 := DigraphFromDigraph6String("&FJBWqNbXV?"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/attr.tst:1900 # Input is: IsDigraphCore(D1); # Expected output: true # But found: Error, Variable: 'IsDigraphCore' must have a value ######## ########> Diff in standard/attr.tst:1902 # Input is: D2 := DigraphFromDigraph6String("&FJbWqNbWu?"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/attr.tst:1904 # Input is: IsDigraphCore(D2); # Expected output: true # But found: Error, Variable: 'IsDigraphCore' must have a value ######## ########> Diff in standard/attr.tst:1906 # Input is: M1 := DigraphMycielskian(D1); # Expected output: # But found: Error, Variable: 'DigraphMycielskian' must have a value ######## ########> Diff in standard/attr.tst:1908 # Input is: IsDigraphCore(M1); # Expected output: true # But found: Error, Variable: 'IsDigraphCore' must have a value ######## ########> Diff in standard/attr.tst:1910 # Input is: D := DigraphDisjointUnion(D1, D2, M1); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/attr.tst:1912 # Input is: DigraphCore(D); # Expected output: [ 8 .. 29 ] # But found: Error, Variable: 'DigraphCore' must have a value ######## ########> Diff in standard/attr.tst:1914 # Input is: IsDigraphCore(InducedSubdigraph(D, DigraphCore(D))); # Expected output: true # But found: Error, Variable: 'IsDigraphCore' must have a value ######## ########> Diff in standard/attr.tst:1918 # Input is: D := DigraphFromDiSparse6String(str); # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/attr.tst:1920 # Input is: DigraphCore(D); # Expected output: [ 1, 2, 4, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 29, 30, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50 ] # But found: Error, Variable: 'DigraphCore' must have a value ######## ########> Diff in standard/attr.tst:1923 # Input is: D := Digraph([[2, 8], [3], [1], [5], [6], [7], [4], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1925 # Input is: DigraphCore(D); # Expected output: [ 1 .. 7 ] # But found: Error, Variable: 'DigraphCore' must have a value ######## ########> Diff in standard/attr.tst:1927 # Input is: D := Digraph([[], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1929 # Input is: DigraphCore(D); # Expected output: [ 2 ] # But found: Error, Variable: 'DigraphCore' must have a value ######## ########> Diff in standard/attr.tst:1931 # Input is: D := DigraphDisjointUnion(EmptyDigraph(1), CompleteBipartiteDigraph(3, 3)); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/attr.tst:1933 # Input is: DigraphCore(D); # Expected output: [ 2, 5 ] # But found: Error, Variable: 'DigraphCore' must have a value ######## ########> Diff in standard/attr.tst:1935 # Input is: D := DigraphFromDigraph6String("&IO?_@?A?CG??O?_G??"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/attr.tst:1937 # Input is: DigraphCore(D); # Expected output: [ 7, 8, 9 ] # But found: Error, Variable: 'DigraphCore' must have a value ######## ########> Diff in standard/attr.tst:1939 # Input is: D := CycleDigraph(IsMutableDigraph, 2); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/attr.tst:1941 # Input is: for i in [1 .. 9] do DigraphDisjointUnion(D, D); od; # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have an assigned value ######## ########> Diff in standard/attr.tst:1944 # Input is: DigraphCore(D); # Expected output: [ 1, 2 ] # But found: Error, Variable: 'DigraphCore' must have a value ######## ########> Diff in standard/attr.tst:1948 # Input is: MaximalAntiSymmetricSubdigraph(Digraph([[2, 2], [1]])); # Expected output: # But found: Error, Variable: 'MaximalAntiSymmetricSubdigraph' must have a value ######## ########> Diff in standard/attr.tst:1950 # Input is: MaximalAntiSymmetricSubdigraph(Digraph(IsMutableDigraph, [[2, 2], [1]])); # Expected output: # But found: Error, Variable: 'MaximalAntiSymmetricSubdigraph' must have a value ######## ########> Diff in standard/attr.tst:1952 # Input is: D := Digraph(IsMutableDigraph, [[1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1954 # Input is: MaximalAntiSymmetricSubdigraph(D) = D; # Expected output: true # But found: Error, Variable: 'MaximalAntiSymmetricSubdigraph' must have a value ######## ########> Diff in standard/attr.tst:1956 # Input is: MaximalAntiSymmetricSubdigraph(NullDigraph(0)); # Expected output: # But found: Error, Variable: 'MaximalAntiSymmetricSubdigraph' must have a value ######## ########> Diff in standard/attr.tst:1958 # Input is: IsAntisymmetricDigraph(DigraphCopy(last)); # Expected output: true # But found: Error, Variable: 'IsAntisymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:1960 # Input is: MaximalAntiSymmetricSubdigraph(NullDigraph(1)); # Expected output: # But found: Error, Variable: 'MaximalAntiSymmetricSubdigraph' must have a value ######## ########> Diff in standard/attr.tst:1962 # Input is: IsAntisymmetricDigraph(DigraphCopy(last)); # Expected output: true # But found: Error, Variable: 'IsAntisymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:1964 # Input is: MaximalAntiSymmetricSubdigraph(CompleteDigraph(1)); # Expected output: # But found: Error, Variable: 'MaximalAntiSymmetricSubdigraph' must have a value ######## ########> Diff in standard/attr.tst:1966 # Input is: IsAntisymmetricDigraph(DigraphCopy(last)); # Expected output: true # But found: Error, Variable: 'IsAntisymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:1968 # Input is: MaximalAntiSymmetricSubdigraph(CompleteBipartiteDigraph(2, 30000)); # Expected output: # But found: Error, Variable: 'MaximalAntiSymmetricSubdigraph' must have a value ######## ########> Diff in standard/attr.tst:1970 # Input is: IsAntisymmetricDigraph(DigraphCopy(last)); # Expected output: true # But found: Error, Variable: 'IsAntisymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:1972 # Input is: MaximalAntiSymmetricSubdigraph(Digraph([[1, 1, 2, 2], []])); # Expected output: # But found: Error, Variable: 'MaximalAntiSymmetricSubdigraph' must have a value ######## ########> Diff in standard/attr.tst:1974 # Input is: OutNeighbours(last); # Expected output: [ [ 1, 2 ], [ ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/attr.tst:1976 # Input is: MaximalAntiSymmetricSubdigraph(CompleteDigraph(10)); # Expected output: # But found: Error, Variable: 'MaximalAntiSymmetricSubdigraph' must have a value ######## ########> Diff in standard/attr.tst:1978 # Input is: D := CompleteDigraph(10); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/attr.tst:1980 # Input is: MaximalAntiSymmetricSubdigraph(D); # Expected output: # But found: Error, Variable: 'MaximalAntiSymmetricSubdigraph' must have a value ######## ########> Diff in standard/attr.tst:1982 # Input is: MaximalAntiSymmetricSubdigraph(D); # Expected output: # But found: Error, Variable: 'MaximalAntiSymmetricSubdigraph' must have a value ######## ########> Diff in standard/attr.tst:1986 # Input is: gr := Digraph([ [2, 2, 2], [1, 3, 6, 8, 9, 10], [4, 6, 8], [1, 2, 3, 9], [3, 3], [3, 5, 6, 10], [1, 2, 7], [1, 2, 3, 10, 5, 6, 10], [1, 3, 4, 5, 8, 10], [2, 3, 4, 6, 7, 10]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:1992 # Input is: CharacteristicPolynomial(gr); # Expected output: x_1^10-3*x_1^9-7*x_1^8-x_1^7+14*x_1^6+x_1^5-26*x_1^4+51*x_1^3-10*x_1^2+18*x_1-\ \ 30 # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/attr.tst:1995 # Input is: gr := CompleteDigraph(5); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/attr.tst:1997 # Input is: CharacteristicPolynomial(gr); # Expected output: x_1^5-10*x_1^3-20*x_1^2-15*x_1-4 # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/attr.tst:2001 # Input is: IsVertexTransitive(Digraph([])); # Expected output: true # But found: Error, Variable: 'IsVertexTransitive' must have a value ######## ########> Diff in standard/attr.tst:2003 # Input is: IsVertexTransitive(Digraph([[1], [2]])); # Expected output: true # But found: Error, Variable: 'IsVertexTransitive' must have a value ######## ########> Diff in standard/attr.tst:2005 # Input is: IsVertexTransitive(Digraph([[2], [3], []])); # Expected output: false # But found: Error, Variable: 'IsVertexTransitive' must have a value ######## ########> Diff in standard/attr.tst:2007 # Input is: IsVertexTransitive(CompleteDigraph(20)); # Expected output: true # But found: Error, Variable: 'IsVertexTransitive' must have a value ######## ########> Diff in standard/attr.tst:2011 # Input is: IsEdgeTransitive(Digraph([])); # Expected output: true # But found: Error, Variable: 'IsEdgeTransitive' must have a value ######## ########> Diff in standard/attr.tst:2013 # Input is: IsEdgeTransitive(Digraph([[1], [2]])); # Expected output: true # But found: Error, Variable: 'IsEdgeTransitive' must have a value ######## ########> Diff in standard/attr.tst:2015 # Input is: IsEdgeTransitive(Digraph([[2], [3], []])); # Expected output: false # But found: Error, Variable: 'IsEdgeTransitive' must have a value ######## ########> Diff in standard/attr.tst:2017 # Input is: IsEdgeTransitive(CompleteDigraph(20)); # Expected output: true # But found: Error, Variable: 'IsEdgeTransitive' must have a value ######## ########> Diff in standard/attr.tst:2019 # Input is: IsEdgeTransitive(Digraph([[2], [3, 3, 3], []])); # Expected output: Error, the argument must be a digraph with no multiple edges, # But found: Error, Variable: 'IsEdgeTransitive' must have a value ######## ########> Diff in standard/attr.tst:2023 # Input is: D := NullDigraph(IsMutableDigraph, 3); # Expected output: # But found: Error, Variable: 'NullDigraph' must have a value ######## ########> Diff in standard/attr.tst:2025 # Input is: AsGraph(D); # Expected output: rec( adjacencies := [ [ ], [ ], [ ] ], group := Group(()), isGraph := true, names := [ 1 .. 3 ], order := 3, representatives := [ 1, 2, 3 ], schreierVector := [ -1, -2, -3 ] ) # But found: Error, Variable: 'AsGraph' must have a value ######## ########> Diff in standard/attr.tst:2031 # Input is: D := NullDigraph(IsMutableDigraph, 3); # Expected output: # But found: Error, Variable: 'NullDigraph' must have a value ######## ########> Diff in standard/attr.tst:2033 # Input is: DigraphSource(D); # Expected output: [ ] # But found: Error, Variable: 'DigraphSource' must have a value ######## ########> Diff in standard/attr.tst:2035 # Input is: DigraphRange(D); # Expected output: [ ] # But found: Error, Variable: 'DigraphRange' must have a value ######## ########> Diff in standard/attr.tst:2037 # Input is: DigraphSymmetricClosure(NullDigraph(IsMutableDigraph, 1)); # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/attr.tst:2039 # Input is: D := Digraph([[2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:2041 # Input is: DigraphSymmetricClosure(D); # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/attr.tst:2043 # Input is: DigraphSymmetricClosure(D); # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/attr.tst:2045 # Input is: D := Digraph(IsMutableDigraph, [[2, 2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:2047 # Input is: DigraphTransitiveClosure(D); # Expected output: Error, the argument must be a digraph with no multiple edges, # But found: Error, Variable: 'DigraphTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:2049 # Input is: DigraphReflexiveTransitiveClosure(D); # Expected output: Error, the argument must be a digraph with no multiple edges, # But found: Error, Variable: 'DigraphReflexiveTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:2051 # Input is: MakeImmutable(D); # Expected output: # But found: Error, Variable: 'D' must have a value ######## ########> Diff in standard/attr.tst:2053 # Input is: DigraphTransitiveClosure(D); # Expected output: Error, the argument must be a digraph with no multiple edges, # But found: Error, Variable: 'DigraphTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:2055 # Input is: D := Digraph([[2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:2057 # Input is: DigraphTransitiveClosure(D); # Expected output: # But found: Error, Variable: 'DigraphTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:2059 # Input is: DigraphTransitiveClosure(D); # Expected output: # But found: Error, Variable: 'DigraphTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:2061 # Input is: DigraphReflexiveTransitiveClosure(D); # Expected output: # But found: Error, Variable: 'DigraphReflexiveTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:2063 # Input is: DigraphReflexiveTransitiveClosure(D); # Expected output: # But found: Error, Variable: 'DigraphReflexiveTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:2065 # Input is: D := DigraphMutableCopy(DigraphSymmetricClosure(D)); # Expected output: # But found: Error, Variable: 'DigraphMutableCopy' must have a value ######## ########> Diff in standard/attr.tst:2067 # Input is: MaximalSymmetricSubdigraphWithoutLoops(D); # Expected output: # But found: Error, Variable: 'MaximalSymmetricSubdigraphWithoutLoops' must have a value ######## ########> Diff in standard/attr.tst:2069 # Input is: MaximalSymmetricSubdigraphWithoutLoops(MakeImmutable(D)); # Expected output: # But found: Error, Variable: 'MaximalSymmetricSubdigraphWithoutLoops' must have a value ######## ########> Diff in standard/attr.tst:2071 # Input is: MaximalSymmetricSubdigraphWithoutLoops(D); # Expected output: # But found: Error, Variable: 'MaximalSymmetricSubdigraphWithoutLoops' must have a value ######## ########> Diff in standard/attr.tst:2073 # Input is: D := CycleDigraph(IsMutableDigraph, 10); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/attr.tst:2075 # Input is: UndirectedSpanningForest(D); # Expected output: # But found: Error, Variable: 'UndirectedSpanningForest' must have a value ######## ########> Diff in standard/attr.tst:2081 # Input is: gr := Digraph([[2, 2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:2083 # Input is: DigraphTransitiveReduction(gr); # Expected output: Error, the argument must be a digraph with no multiple edges, # But found: Error, Variable: 'DigraphTransitiveReduction' must have a value ######## ########> Diff in standard/attr.tst:2085 # Input is: DigraphReflexiveTransitiveReduction(gr); # Expected output: Error, the argument must be a digraph with no multiple edges, # But found: Error, Variable: 'DigraphReflexiveTransitiveReduction' must have a value ######## ########> Diff in standard/attr.tst:2087 # Input is: gr := Digraph([[2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:2089 # Input is: DigraphTransitiveReduction(gr); # Expected output: Error, not yet implemented for non-topologically sortable digraphs, # But found: Error, Variable: 'DigraphTransitiveReduction' must have a value ######## ########> Diff in standard/attr.tst:2091 # Input is: DigraphReflexiveTransitiveReduction(gr); # Expected output: Error, not yet implemented for non-topologically sortable digraphs, # But found: Error, Variable: 'DigraphReflexiveTransitiveReduction' must have a value ######## ########> Diff in standard/attr.tst:2095 # Input is: gr1 := ChainDigraph(6); # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/attr.tst:2097 # Input is: gr2 := DigraphReflexiveTransitiveClosure(gr1); # Expected output: # But found: Error, Variable: 'DigraphReflexiveTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:2099 # Input is: DigraphTransitiveReduction(gr2) = gr1; # trans reduction contains loops # Expected output: false # But found: Error, Variable: 'DigraphTransitiveReduction' must have a value ######## ########> Diff in standard/attr.tst:2101 # Input is: DigraphReflexiveTransitiveReduction(gr2) = gr1; # ref trans reduct doesnt # Expected output: true # But found: Error, Variable: 'DigraphReflexiveTransitiveReduction' must have a value ######## ########> Diff in standard/attr.tst:2103 # Input is: gr3 := DigraphAddEdge(gr1, [3, 3]); # Expected output: # But found: Error, Variable: 'DigraphAddEdge' must have a value ######## ########> Diff in standard/attr.tst:2105 # Input is: DigraphHasLoops(gr3); # Expected output: true # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/attr.tst:2107 # Input is: gr4 := DigraphTransitiveClosure(gr3); # Expected output: # But found: Error, Variable: 'DigraphTransitiveClosure' must have a value ######## ########> Diff in standard/attr.tst:2109 # Input is: gr2 = gr4; # Expected output: false # But found: Error, Variable: 'gr2' must have a value ######## ########> Diff in standard/attr.tst:2111 # Input is: DigraphReflexiveTransitiveReduction(gr4) = gr1; # Expected output: true # But found: Error, Variable: 'DigraphReflexiveTransitiveReduction' must have a value ######## ########> Diff in standard/attr.tst:2113 # Input is: DigraphReflexiveTransitiveReduction(gr4) = gr3; # Expected output: false # But found: Error, Variable: 'DigraphReflexiveTransitiveReduction' must have a value ######## ########> Diff in standard/attr.tst:2115 # Input is: DigraphTransitiveReduction(gr4) = gr3; # Expected output: true # But found: Error, Variable: 'DigraphTransitiveReduction' must have a value ######## ########> Diff in standard/attr.tst:2119 # Input is: DigraphTransitiveReduction(EmptyDigraph(0)) = EmptyDigraph(0); # Expected output: true # But found: Error, Variable: 'DigraphTransitiveReduction' must have a value ######## ########> Diff in standard/attr.tst:2121 # Input is: DigraphReflexiveTransitiveReduction(EmptyDigraph(0)) = EmptyDigraph(0); # Expected output: true # But found: Error, Variable: 'DigraphReflexiveTransitiveReduction' must have a value ######## ########> Diff in standard/attr.tst:2125 # Input is: gr := DigraphFromDigraph6String("&DHUEe_"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/attr.tst:2127 # Input is: rgr := DigraphReverse(gr); # Expected output: # But found: Error, Variable: 'DigraphReverse' must have a value ######## ########> Diff in standard/attr.tst:2129 # Input is: OutNeighbours(rgr); # Expected output: [ [ 2, 3, 4 ], [ 4, 5 ], [ 1, 2, 5 ], [ 4 ], [ 2, 5 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/attr.tst:2131 # Input is: gr = DigraphReverse(rgr); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/attr.tst:2133 # Input is: gr := Digraph(rec(DigraphNrVertices := 5, DigraphSource := [1, 1, 2, 2, 2, 2, 2, 3, 4, 4, 4, 5, 5, 5], DigraphRange := [1, 3, 1, 2, 2, 4, 5, 4, 1, 3, 5, 1, 1, 3])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:2137 # Input is: e := DigraphEdges(gr); # Expected output: [ [ 1, 1 ], [ 1, 3 ], [ 2, 1 ], [ 2, 2 ], [ 2, 2 ], [ 2, 4 ], [ 2, 5 ], [ 3, 4 ], [ 4, 1 ], [ 4, 3 ], [ 4, 5 ], [ 5, 1 ], [ 5, 1 ], [ 5, 3 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/attr.tst:2140 # Input is: rev := DigraphReverse(gr); # Expected output: # But found: Error, Variable: 'DigraphReverse' must have a value ######## ########> Diff in standard/attr.tst:2142 # Input is: erev := DigraphEdges(rev);; # Expected output: # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/attr.tst:2143 # Input is: temp := List(erev, x -> [x[2], x[1]]);; # Expected output: # But found: Error, Variable: 'erev' must have a value ######## ########> Diff in standard/attr.tst:2144 # Input is: Sort(temp); # Expected output: # But found: Error, Variable: 'temp' must have a value ######## ########> Diff in standard/attr.tst:2145 # Input is: e = temp; # Expected output: true # But found: Error, Variable: 'e' must have a value ######## ########> Diff in standard/attr.tst:2147 # Input is: gr := Digraph([[2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:2149 # Input is: IsSymmetricDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:2151 # Input is: DigraphReverse(gr) = gr; # Expected output: true # But found: Error, Variable: 'DigraphReverse' must have a value ######## ########> Diff in standard/attr.tst:2153 # Input is: gr := Digraph([[2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:2155 # Input is: SetIsSymmetricDigraph(gr, true); # Expected output: # But found: Error, Variable: 'SetIsSymmetricDigraph' must have a value ######## ########> Diff in standard/attr.tst:2156 # Input is: gr = DigraphReverse(gr); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/attr.tst:2158 # Input is: DigraphReverse(Digraph(IsMutableDigraph, [[2], [1]])) = CompleteDigraph(2); # Expected output: true # But found: Error, Variable: 'DigraphReverse' must have a value ######## ########> Diff in standard/attr.tst:2162 # Input is: D := DigraphCartesianProduct(ChainDigraph(3), CycleDigraph(4), Digraph([[2], [2]]));; # Expected output: # But found: Error, Variable: 'DigraphCartesianProduct' must have a value ######## ########> Diff in standard/attr.tst:2164 # Input is: HasDigraphCartesianProductProjections(D); # Expected output: true # But found: Error, Variable: 'HasDigraphCartesianProductProjections' must have a value ######## ########> Diff in standard/attr.tst:2166 # Input is: proj := DigraphCartesianProductProjections(D);; Length(proj); # Expected output: 3 # But found: Error, Variable: 'DigraphCartesianProductProjections' must have a value Error, Variable: 'proj' must have a value ######## ########> Diff in standard/attr.tst:2168 # Input is: IsIdempotent(proj[2]); # Expected output: true # But found: Error, Variable: 'proj' must have a value ######## ########> Diff in standard/attr.tst:2170 # Input is: RankOfTransformation(proj[3]); # Expected output: 2 # But found: Error, Variable: 'proj' must have a value ######## ########> Diff in standard/attr.tst:2172 # Input is: S := ImageSetOfTransformation(proj[2]);; # Expected output: # But found: Error, Variable: 'proj' must have a value ######## ########> Diff in standard/attr.tst:2173 # Input is: IsIsomorphicDigraph(CycleDigraph(4), InducedSubdigraph(D, S)); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/attr.tst:2175 # Input is: G := DigraphRemoveLoops(RandomDigraph(12));; # Expected output: # But found: Error, Variable: 'DigraphRemoveLoops' must have a value ######## ########> Diff in standard/attr.tst:2176 # Input is: H := DigraphRemoveLoops(RandomDigraph(50));; # Expected output: # But found: Error, Variable: 'DigraphRemoveLoops' must have a value ######## ########> Diff in standard/attr.tst:2177 # Input is: D := DigraphCartesianProduct(G, H);; # Expected output: # But found: Error, Variable: 'DigraphCartesianProduct' must have a value ######## ########> Diff in standard/attr.tst:2178 # Input is: proj := DigraphCartesianProductProjections(D);; # Expected output: # But found: Error, Variable: 'DigraphCartesianProductProjections' must have a value ######## ########> Diff in standard/attr.tst:2179 # Input is: IsIdempotent(proj[1]); # Expected output: true # But found: Error, Variable: 'proj' must have a value ######## ########> Diff in standard/attr.tst:2181 # Input is: RankOfTransformation(proj[2]); # Expected output: 50 # But found: Error, Variable: 'proj' must have a value ######## ########> Diff in standard/attr.tst:2183 # Input is: S := ImageSetOfTransformation(proj[2]);; # Expected output: # But found: Error, Variable: 'proj' must have a value ######## ########> Diff in standard/attr.tst:2184 # Input is: IsIsomorphicDigraph(H, InducedSubdigraph(D, S)); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/attr.tst:2188 # Input is: D := DigraphDirectProduct(ChainDigraph(3), CycleDigraph(4), Digraph([[2], [2]]));; # Expected output: # But found: Error, Variable: 'DigraphDirectProduct' must have a value ######## ########> Diff in standard/attr.tst:2190 # Input is: HasDigraphDirectProductProjections(D); # Expected output: true # But found: Error, Variable: 'HasDigraphDirectProductProjections' must have a value ######## ########> Diff in standard/attr.tst:2192 # Input is: proj := DigraphDirectProductProjections(D);; Length(proj); # Expected output: 3 # But found: Error, Variable: 'DigraphDirectProductProjections' must have a value Error, Variable: 'proj' must have a value ######## ########> Diff in standard/attr.tst:2194 # Input is: IsIdempotent(proj[2]); # Expected output: true # But found: Error, Variable: 'proj' must have a value ######## ########> Diff in standard/attr.tst:2196 # Input is: RankOfTransformation(proj[3]); # Expected output: 2 # But found: Error, Variable: 'proj' must have a value ######## ########> Diff in standard/attr.tst:2198 # Input is: P := DigraphRemoveAllMultipleEdges(ReducedDigraph(OnDigraphs(D, proj[2])));; # Expected output: # But found: Error, Variable: 'DigraphRemoveAllMultipleEdges' must have a value ######## ########> Diff in standard/attr.tst:2199 # Input is: IsIsomorphicDigraph(CycleDigraph(4), P); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/attr.tst:2201 # Input is: G := RandomDigraph(12);; # Expected output: # But found: Error, Variable: 'RandomDigraph' must have a value ######## ########> Diff in standard/attr.tst:2202 # Input is: H := RandomDigraph(50);; # Expected output: # But found: Error, Variable: 'RandomDigraph' must have a value ######## ########> Diff in standard/attr.tst:2203 # Input is: D := DigraphDirectProduct(G, H);; # Expected output: # But found: Error, Variable: 'DigraphDirectProduct' must have a value ######## ########> Diff in standard/attr.tst:2204 # Input is: proj := DigraphDirectProductProjections(D);; # Expected output: # But found: Error, Variable: 'DigraphDirectProductProjections' must have a value ######## ########> Diff in standard/attr.tst:2205 # Input is: IsIdempotent(proj[1]); # Expected output: true # But found: Error, Variable: 'proj' must have a value ######## ########> Diff in standard/attr.tst:2207 # Input is: RankOfTransformation(proj[2]); # Expected output: 50 # But found: Error, Variable: 'proj' must have a value ######## ########> Diff in standard/attr.tst:2209 # Input is: P := DigraphRemoveAllMultipleEdges(ReducedDigraph(OnDigraphs(D, proj[2])));; # Expected output: # But found: Error, Variable: 'DigraphRemoveAllMultipleEdges' must have a value ######## ########> Diff in standard/attr.tst:2210 # Input is: IsIsomorphicDigraph(H, P); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/attr.tst:2214 # Input is: D := DigraphFromDigraph6String("&Sq_MN|bDCLy~Xj}u}GxOLlGfqJtnSQ|l\ Q?lYvjbqN~XNNAQYDJE[UHOhyGOqtsjCWJy["); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/attr.tst:2217 # Input is: M := DigraphMaximalMatching(D);; IsMaximalMatching(D, M); # Expected output: true # But found: Error, Variable: 'DigraphMaximalMatching' must have a value Error, Variable: 'IsMaximalMatching' must have a value ######## ########> Diff in standard/attr.tst:2219 # Input is: D := DigraphFromDigraph6String(IsMutable, "&Sq_MN|bDCLy~Xj}u}GxOLlGfqJtnSQ|l\ Q?lYvjbqN~XNNAQYDJE[UHOhyGOqtsjCWJy["); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/attr.tst:2222 # Input is: M := DigraphMaximalMatching(D);; IsMaximalMatching(D, M); # Expected output: true # But found: Error, Variable: 'DigraphMaximalMatching' must have a value Error, Variable: 'IsMaximalMatching' must have a value ######## ########> Diff in standard/attr.tst:2224 # Input is: D := Digraph(IsMutable, [[2], [3], [4], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:2226 # Input is: M := DigraphMaximalMatching(D);; # Expected output: # But found: Error, Variable: 'DigraphMaximalMatching' must have a value ######## ########> Diff in standard/attr.tst:2227 # Input is: M = [[1, 2], [3, 4]] or M = [[2, 3], [4, 1]]; # Expected output: true # But found: Error, Variable: 'M' must have a value ######## ########> Diff in standard/attr.tst:2229 # Input is: D; # Expected output: # But found: Error, Variable: 'D' must have a value ######## ########> Diff in standard/attr.tst:2233 # Input is: D := DigraphFromDiSparse6String(".]cBn@kqAlt?EpclQp|M}bAgFjHkoDsIuACyCM_Hj"); # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/attr.tst:2235 # Input is: M := DigraphMaximumMatching(D);; IsMaximalMatching(D, M); # Expected output: true # But found: Error, Variable: 'DigraphMaximumMatching' must have a value Error, Variable: 'IsMaximalMatching' must have a value ######## ########> Diff in standard/attr.tst:2237 # Input is: Length(M); # Expected output: 14 # But found: Error, Variable: 'M' must have a value ######## ########> Diff in standard/attr.tst:2239 # Input is: D := Digraph([[5, 6, 7, 8], [6, 7, 8], [7, 8], [8], [], [], [], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:2241 # Input is: DigraphMaximumMatching(D); # Expected output: [ [ 1, 5 ], [ 2, 6 ], [ 3, 7 ], [ 4, 8 ] ] # But found: Error, Variable: 'DigraphMaximumMatching' must have a value ######## ########> Diff in standard/attr.tst:2243 # Input is: D := Digraph(IsMutable, [[2, 3], [1, 4], [2, 4], [5], [3, 5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/attr.tst:2245 # Input is: M := DigraphMaximumMatching(D);; IsMaximalMatching(D, M); # Expected output: true # But found: Error, Variable: 'DigraphMaximumMatching' must have a value Error, Variable: 'IsMaximalMatching' must have a value ######## ########> Diff in standard/attr.tst:2247 # Input is: Length(M); # Expected output: 3 # But found: Error, Variable: 'M' must have a value ######## ########> Diff in standard/attr.tst:2249 # Input is: D := DigraphFromDiSparse6String("\ .~?B]zsE?cB?kH?cK?{M?{O?SIaWHaoQ_{X??@?wJ@gT`{[BKF@s^BG[_OOAca?{@@gXB_^bK?A\ gXbGc_gF@o\\dGG`gXC[X`K__OC?oG@GI@wOAGQAWSAoWBOZBo_CGgDGkDk?BGd_wMBgfdsFC{Q\ Ao]CGmdsJBGbC_ebGdD{ZDsXCgnEsC?oHAWkDsFbK@BGb`?PDsD?wfcGmE[Fb?ZD?mEWsE{LBGb\ DSmEW~aOmE[XB_^C[XbKmEW~G[gDp@_x?dop_wfdosGKWDp@dsJBGt`wYDopFHJH{FA{F_waG@I\ I[OC?mbGtdsUDor`?IAG_DGmFhVbWgDovGHH_GXBwbFcFCwqdpVJKXG{XGx]_wVISC?omFKXF[X\ CkFCP?IXSaOmEXCbGtIsXGs?BGddpP_xS_wKAwfIP_dpVJH\\_?TBGdDWnEowFXEGx]JxaKXfLC\ mEHJIKUDorJCFL[XDXfLkWDosGHLHpY`GkDox`WXEhOIsmEW~dorFxtbGjLhpcGmEW~MkA?_E@?\ H@ONA?PAWSBO_DGkDgmEGxFhJHxPIhVJH\\KHhL`mM[A@?IA?PA__DGlDo|IhVJH\\L`x_WF`wY\ DpPNKQAo]DorFxCJ@dL{IAGmJHkNHydopHxPNKUDorNkgDp@JS?BGdL@lbGeEk@@WLBG[BwbC_e\ DOtF`AGhOIpZKplMaBcGmEW~c?lDpxNSFdorFxBHCFL[mIHhNKmFHx_wfEP[aOUB?ZBo`D?mEWs\ Ew~GHBG`GHHLHpWJPdLxqMhuN@xNi?OIDPCSC?mNHybGbDPDOcFNYFbGbOaN_waIcF_wyQ[FLYH\ do|JHxNSFHPSLSmEW~OiLbOmIHhLpxPSF@`jaWmFHx__E@GNAWYD_mEGxHXNIH`LHmMXxNP{NyI\ PYXR[XChbLkXCgnKXlRkmGHMMQLdo|JHxNQUaWmFHxPY[dp@JQLbWmEx@HHYPkmFHxPY[SKFAxj\ PITdp@HhqPi^a?_DpTNHydp@JQLSSXEhUKqC_WFFQS_yFQCB?waFP?HPRI`cLPzOyOQQRQaVTQj\ dp@JQLSQbTCD?wK@oVBgfE?qFpKIP[K@jMAHPaTRQdTcFCxKJam_xSLQVTc_DgmNHyOsmGHMMQL\ dorNi?PkXCotOYCbHEKPfLk]DorNi?PkgDp@HHYPkFCw}HamT{FQYkdorFyDPiWdosGHLMQL_WF\ NYkdp@JQ@PkRDoxNIZRcAC?lDpxNSmGHqPi^SsWDp@MQLbGzJpaLkXC_tKqCagXChl_?TBGdLjC\ cGmEW~NALbGcEiCW[FIXSKak_WFFPSNYFQARQaiTYkVI{_gFCwoFqmb?mGHqPj@dp@JQ@Pi|a__\ DpTNHyPsmHxPNH~RcmEW~GXtMqLbGdDWzGpFJp^KPfLhpMytWSXCYCPyP_waIaQTcFLXoQimdor\ Ni?Pir_yRTaxXKF@`jRQm_x?HPSTc??GB?gF@WK@gMAgVBG[Bg^CObC_dCofDOjDonE?qEguF?y\ FW{Fp?GPDGpFHPKI@QIXSIpZJ`]Jx_KPbK`eKxgLPjLhoMHsMxzOQBOaFPIKPyOQIQQYSQiVRQ\\ \RqdTIiTYkTqnUAsUiwVI{WRBWbDWzGXJIYBPYRRYjUY{GDGmJHxNSAC?mNHyV{mGHMMQLUS]Do\ rNiLUsFLXoTrRYrW");; # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/attr.tst:2273 # Input is: M := DigraphMaximumMatching(D);; IsMaximalMatching(D, M); # Expected output: true # But found: Error, Variable: 'DigraphMaximumMatching' must have a value Error, Variable: 'IsMaximalMatching' must have a value ######## ########> Diff in standard/attr.tst:2275 # Input is: Length(M); # Expected output: 111 # But found: Error, Variable: 'M' must have a value ######## ########> Diff in standard/attr.tst:2295 # Input is: M = M1; # Expected output: true # But found: Error, Variable: 'M' must have a value ######## ########> Diff in standard/attr.tst:2297 # Input is: D := DigraphFromDiSparse6String("\ .~?@}~ggEb?eM@X?@_?CC@OWIAowO_PEPdOOPcX_HBHaPDgWICW[GAOoLE@e?@`ESbp]PfG_[cP\ M?@_gMCPk\\_OOJC@CQDPWYd@yHB@_[`pqPD`gdcQA[IH_XFHCUEaShapCd_?SEA_wPCpk\\GAK\ cHQiPJwMPHQeGFAE^frQPCqKn_OOJCPSUEaShJQwq__MA?o[GAOoLBpCSDp_XF@w^GQGeHq_jJB\ CrLBSwfrOtMWSMCQ}@CPGdfBePDaShKb]PCq{u_?SEA_wPEpscJrm]MW{^MXCdIRGvNgCPCaS{`\ os[IAkxNXCiJrAFFA_xPXCRGAgnKCYPGAgnQGOJCPSdIQwv_@C\\HA|?_PCdNCQA?pwpMBe@C@C\ db`CnOGCPHWCPHSPK_rCxRWs[IBc|PX[^MW_[GbeSFbd@`@CTHQwvQgkPHQwvQgGBBpOVF@w^Hb\ CsLR_xMcDARTHSTgCOCQTMbp{sMSHXdp{xTDe@CQTO_b_xRTeDB`CnMsA^MTPXVGGBD@w^HbCwM\ SDLSdXXVg_WFACaKrdTaP_XFAoxcPKnNx[^MTd[a?cKE@c[GQGfJBKxPTTaWwCOCQTCRd@YVWs[\ MSTRdp{xUTpdfbd@Tdd`fACrMUHeb`CnOC|^bp{sLRcyOddZVHCRJr|cfrdSUTp_b`CnOC|kcQ{\ oPca@CQTMSDtffBc|PTMPCqKnLhCRGAKiJr?uNs@EQCdcZfDsd@weMTd`_PCQHRpC`pogMSTF_P\ CdPCpPfA_jMSULFBdDSuaFFA_jMSTyfBc|PTLr]~");; # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/attr.tst:2309 # Input is: M := DigraphMaximumMatching(D);; IsMaximalMatching(D, M); # Expected output: true # But found: Error, Variable: 'DigraphMaximumMatching' must have a value Error, Variable: 'IsMaximalMatching' must have a value ######## ########> Diff in standard/attr.tst:2311 # Input is: Length(M); # Expected output: 63 # But found: Error, Variable: 'M' must have a value ######## ########> Diff in standard/attr.tst:2323 # Input is: M = M1; # Expected output: true # But found: Error, Variable: 'M' must have a value ######## ########> Diff in standard/attr.tst:2325 # Input is: D := DigraphFromDiSparse6String("\ .~?BG`WHawSbOT_wJbwYcOOcgCCS`d?SBkj?gedo_`sp?OOdSuCCC?o^bS[cwgdD?A[wdC}gofF\ [FGLJA_\\GhIi?uio_j?RF[bH|OaGyjgjjwOFdAHXYdhMbSQIDdE`KKTf?PalGh__jIKYHXPe@H\ gD]kLfdXcekPA`pmoSfslG[[n_CCGx_gpGd~CGdDhfic}IKBAhPbS@?XJJpnbogGHdg\\_kXslS\ aHeKJKaeXphhqk@pqOODABe[fKHgqoTfCKEPOrOSFxEHHqNQKr`qd@|cTc`YSqMb@G]CsRptl`h\ LSc@G`QrSZSS@?G~h`hPKD@X@GpTTLiMifSyjc@[NYUmq@PAOp[D?o]bG\\Gq[T|uiMvCq]Ryjv\ H^LUbchZKejUsoRC]mqga`}RaocpHH`wNczJ@WPY]hHPJ|DKa@OqHUK@DhMNYbij@axmQr@xCJ@\ KP@sVAcYAkA?wJboOcOOcgabSgBkjCsmCCMCkP_Sieo__cCb_ifWggGwdC}gofF[FGLJBhDHSMh\ oMi?uiONHSCH|U@w_fcocXNfhOaLBjwCAD`Dk~ILOkhKKTf?PSKThDLPbSoHKPGD]m@fkctaGUM\ LYmoSC{}LklG\\{CGxnw`K|SfsBAmCBp]L{gGHd_@BJ{jKDbg@bLSaHXKpgafS@BpijxpqOADAB\ eWycxHKHgNeUAmW@_qI@YhCSFxEHHqr`^MSgN@|cOokeSqMb@?WBoeaXHptl`hLSc@GdkRSZfxw\ pIc_gJGHEIiblHiMijc@CN[_OIGQCNOYJuWXBhERancXuuy^nSZCxis[VChZK`ddijvo]H@YLYV\ dPuaaohHKNCzJ@WKY]w`DOIH_GHDhzS\\TTlmQv");; # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/attr.tst:2338 # Input is: M := DigraphMaximumMatching(D);; IsMaximalMatching(D, M); # Expected output: true # But found: Error, Variable: 'DigraphMaximumMatching' must have a value Error, Variable: 'IsMaximalMatching' must have a value ######## ########> Diff in standard/attr.tst:2340 # Input is: Length(M); # Expected output: 96 # But found: Error, Variable: 'M' must have a value ######## ########> Diff in standard/attr.tst:2342 # Input is: D := DigraphFromDiSparse6String("\ .~?BZ_O?__B_SF?CE_kC_[A@[M@KP?sDACC@{M_OL`cJ`OV`GU`?T_{EA[DASCAKB_O]_GMBk?@\ g[b[JBSIBKHBCGA{FC{TCsDAcCAWc_WQ_OP_G`_?_`sL`_\\`W[D{IDsHBOl`?XDcFB?ja{U__g\ _WSC{AAWe_GQCgy_?PC_xa?w`waE{MCGuekKB{JBor`O\\ESH`?ZdxE_oXDpDb?lGcVD`B_WUDX\ A_OTDSSDH?_?RDCfFsPCo|cg{c_z`obFPR`gaFHQ`_wIK_ExO`O^H{HEhM`?\\Ecr_oZESDBOpH\ SCBGob?nHCVDpF_GUDhE_?TGh_a_jJ{idHAJkPD@@JcOCx?J[NCo~JSMFsLJCb`WaIsICGyIk_F\ HS`?wI[FBovL{uIKDB_tLkCBWsHxk_WYHpjhk@EHKLK?AwoHXgdxIK{THLdaWkGxcaOjK[PDPDK\ SODHCKKgGX_cxAJx}`geGL{`[ICXZ`GaJPx`?`NC_JC^FPVMsDBoxIpt__wIhs_W[ExrbWu_GY_\ ?XIKWEXOL{VEPNLqNaopHplPsTLaLa_nHaKaWmH[lHPhPSPPKODXfPCNDPFKshGpdOsgGhc`_fG\ aCgXaO[ICh`OScKCGCX?Jy?_waF{ECH\\NsDC?|J`|SCCBw{JX{R{BBozJQ]bhXNQ\\fHWNI[_?\ ZF@VNAZexUMyYbGuIhuRKWEhSMiWawsIXsQ{UIPrQsTEPPMQTa_pMIShyRaOnHpnaGmLqPdhKLi\ O`wkHXkP{MDXILYMU[LDPHLShHAp`WgGxgUCfPQn`GeGhePImchCPAlc`BKaFTcECXbOt@KQDTS\ CCH?KIhc?~KABTCAFp^OQf_G]Fh]Ss?Bg{OAdbacfPZNqbfHYNiajI`b@zSCVNREehUNI]WkTIh\ wWcSI`vRbBaWqIXuRZAaOpIPtRR@aGoIHsWCnI@rRA~dpNMQV`olHppQq|`gkHhoQi{`_jH`nV[\ JDPJLqRVSIDHILiQVKHD@HLcfQAvcpFPyu_pELIM_hDUfZ__B_o@_CE`WB_OJ_GI_CG_{EaWC_[\ A@k@@c?@[V`GUakFAcEaSCAKBACA@{@Bk?@g[`_Z`[I`GW`CFAof_oT_gd_cQC[AAGa_GOCK?@w\ _b{]`_\\ECJB_n`OZDsHBOl`?XDcFBCEAwi_gUDKTDCSf[@AOd_?Pa?bFCNCOvcGu`g_EkKBws`\ W]`O\\ESHB_pbWo_wYDxE_om_glGcCAwkG[BD[AAgiGK@GCRF{QFsPCsOCkNC_zfPR`gaFHQ`_`\ F@P`W_ExOepNbotHssHkFB`K_oqH\\IbHH_WWDxG_OVG{@Aold`DKCjGcRGX]aPAJkPGKOG@Z`w\ eF{MCg}JKLC_|JCKF`VcOz`O`FPT`G_IcGBww_wvIPn_o\\EpPLsDB`OLkZHxk_WrHpj_OXEPib\ C?H[UHSmKsSDhGKkRD`caPEaHDKSODHCKKND@BKCMNt]NkKCh?JkcFx[N[ICW}JXy`GaFhYNKGF\ `X_w_FXWM{EBwyIxu_g]FHUbhTMcBB_vI`r_OZEpRMS@BOtIPpbGsIHob?rI@nawqHxmaopHsTE\ @LLcSDxKLYKaXJLQJaOlHQIaGkHHgdXGK{NDQF`ohGqE`ggKaD`_fK[JCpa`OdGP`OSHC`@OKGJ\ {FCO~Jp~cG}Jh}fh[Ni___^JX{R{]FXYN[AFPX_G[FI[_?ZF@VR[YExUM{XEpTRKtIaWawsIYVa\ oragqQkpI@paWoHxoQ[QDxMLyQaGmHhmQKODhKLkND`JLaN`ojLYr`giHILUSKDHhPap`XFLAJ`\ OfGpfPQncpDKsGKiG_xBKaFTdAKYET[DCPa__`G@`Oah_W_KAg_O^JyAS{]Fi@Ss?F`\\OC[FX[\ NycbXZNqbbOxNkXF@{SKWExWSCuIxyR{UIpxWksIi\\WcrI`vRbBaXuRZAaPQMkPIIXa?nIAW`w\ mHxqQy}dhMMIUVkLD`LQkjH`nQdJQ[IDHlVKHD@HLaPVCGCxGL[FCpiUsEChELIMUkDC`DLALUf\ ");; # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/attr.tst:2371 # Input is: M := DigraphMaximumMatching(D);; IsMaximalMatching(D, M); # Expected output: true # But found: Error, Variable: 'DigraphMaximumMatching' must have a value Error, Variable: 'IsMaximalMatching' must have a value ######## ########> Diff in standard/attr.tst:2373 # Input is: Length(M); # Expected output: 109 # But found: Error, Variable: 'M' must have a value ######## ########> Diff in standard/attr.tst:2375 # Input is: D := DigraphFromDiSparse6String("\ .~?B]`?C`OFc?B`kbBcd@cf@si@sXeWDCswCczE{|A{~?wGgGRgWeF|E?tJBs_DtP??HC?le_xi\ `DipFj?kctZEozd\\LkGNGdbDT\\kxAh|BlWdlgHlwME[CapkcpAm_ompin?JeD{DD]ap[jeAAO\ kDpcOK@FX\\KxsN{SooKA}GE?zK[@G@Mp_@?x?fqA`?~GeO?gOA?kk{^B|CIMT?xWcpyP}ZE[TI\ [Ps@QNdyc@}R[He@^mLYh|xc`gNtpQ[XCgxGi^tgnNIgnMoBimbXHhYAep\\Lq\\uoYQ[YNUE_I\ YiDFf@zNsoG]~BPLc}EwW{OcSTUIoB@s|lV[NAG~skIFPA`PedGiIAOu[ByP[LyKpL\\lJGivJi\ xePSzJ{}H`zPAmuAoap]_HxYN]`gJbOTc?BcgKcKMbsjBKm?[r?kyDoqe{~?wG@|@A\\BF|KCCh\ iG?DlS?wXGlUAXF`czIDYBCzkGNGdbDT\\e\\fGTNlWdlgHgcA@omE[Yapkm_`mpi`wUnHHkD|J\ sUJeADpc_GWKxsN|XnCap?[E@H_MK?x?fpD`?fF{FB{DADfbw^geT?xNJEN`MXCU[AgUs@QOTyc\ AP`KoK\\_gdN_HxNLgmKXCgxGi^tgCJHxTEoBimhKDOSuJhmRk]M}uBPfQ[YNUE_IYvXFf@zNso\ G]~BPLc}ER|wocSPQiwq?x@lV[NAIrskyGQ|kshGhOxxFyHDNaTj`ny`\\lJGf@UcDVfX^fpKN\\ \qUD]nJP");; # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/attr.tst:2387 # Input is: M := DigraphMaximumMatching(D);; IsMaximalMatching(D, M); # Expected output: true # But found: Error, Variable: 'DigraphMaximumMatching' must have a value Error, Variable: 'IsMaximalMatching' must have a value ######## ########> Diff in standard/attr.tst:2389 # Input is: Length(M); # Expected output: 97 # But found: Error, Variable: 'M' must have a value ######## ########> Diff in standard/attr.tst:2391 # Input is: D := DigraphFromDiSparse6String("\ .~?B]_O?__B_S@`?E_kC_[A@[I_?H`CF_sD_cB@sA`c?@[IA{Y@CFAcE_gQ__Pc?A@{@BkLBcKB\ [J`SW`?VasEAge_gSCkC_WQC[AAGa_GOCK?CCp@g]eCJD{IBWm`Gl`?XDcwAwi_gUDKTDCBA_fa\ WeF[QCgy_?PCcOC[NCSMCK_`_^EcJBor`Oq`G[EKG_wn_om_gWDkCAwkG[BApA_OTDP@_GSDH?_\ ?RD?~cw}aGeFkO`wcF[MCWy`hQ`_w`W_E{IBxNbotHsGBhL_w[E[EBXJ_gYEHI__XECBB?nHCAA\ xFdhE_?TD`DKCSDXCJ{RDPBdHAJkPD@@JcOG@Z`{MCg}`gcFhW`_bF`V`WaF[y`KGBwwI[]ExQL\ {EBhPLsDEhO__ZE`NLcrHpj_OX_GWEHKLKVE@JLCnHPfdpHa_lH@dd`FKdbaGiKShG``dCMCxAJ\ {LCp|`_dJh{`W~J`z`ObFpZNSHCPx`?`F`X_w_J@vbwyIxuboxIptf@T_W[Exr_OZEpRMSYEhQM\ K?IHob?rI@nhyNhsoHhkPljPcmHXiP[QDhILIIaHHLAHhCiGxedHEKiE`ggGhcOlCKYCgXaO[IC\ hAKIA`GcKA@`?bG@^cP]_o`Fp\\_g|J`|SCCBw{JX{R{BNY]_O\\FPyRk@B_xNK?NAZbQYbKWEh\ SMkVE`RQ{UEXQQsqIHqQkSEHOMISaWoHxoQ[nHpnaHLLqPa?lHaO`xJLaNdXjPqr`hHLQLh@hPa\ p`WgLCICxfT{HGiHTsGChCKiGTkFC`BKak_obGPbT[aGHaOii__`G@`TKBC?~KABTC}JyAS{@Bo\ |Jq@_?{OAdb_zJ`~ScZFP}S[YFH|SSXF@XNa`exWNY_awuI{UIpxRrDe`TNBCa_rI`vRcRIXuRZ\ AaOpIPtWKPE@sRKODxOMYWV|NMQ}`olHqUVkkHhoQi{`_jH`nV[JDPJLsIDHlQQx`HHLaPVFWGx\ i_odGqMUkcLALUcbG`fPar_WaGXeURZgPdPQpZV]_O?__B_o@_CE_kK@[@@S?`CP?sDACC@{B@s\ A@k@@c?@[I`GU`?T_wS_oR_k^?WO_ONBs@@s?`cJBSIBKH`CFAof_oTCsDCkRCcBC[AAGa_K?@w\ _`o^bsKBgobcm`GY`?XDcFB?j_oVDSUDKCDCBC{AAWeF[@AOdFS?AGcFKOFCv`o`EsLC?t`_^Ec\ JE[\\b_p`?ZECYDxE_oXGkWDhC__kG[jGSAAgiGK@A_hGC?AWgaOffkOCg{c_zi[aFHQ`_`F@Pc\ @ObwuH{HBot`?sHlK_oZEPJbOpHTH_WnHCAAwm_GUDhEd`DKCSG`^dPBJsQDHAJkPD@@JcfG@Z`\ weFxY`odJKcFhW``V`WzIsICHT`G_FHS`?wI[FBovIPnbguIHmb_tLkCBWs_WYL[XEPLLS@B@KL\ K?AxJaonK{TKslKkRDcQDXEK[PDPDKSO`xBKCfGP^NsLCp@JsKG@\\NcJC_~J`z`ObFsHCO|JPx\ `?{JHw_w_F[EBxVMsDBoxIpt__\\IhsexSM\\R_GtISXE`oeXnawqHxmaopLiMahka_nH`jPcRH\ YJaOlPSPDcODXGKyG`wiGxeO{MGpdOtDKcKCxCOcJCpachAgH_OL^OCFCO~N{`Fp}_g_Fh|SCCF\ a^_W]FXYNY]bgyJLWRc?BWwIxwR[YExUMyYepTMqXb@SRCVE`RMcUIPrQsTEPPMSSe@NMARaPnQ\ SPDpLLqPdhKLiO`wkLcMHSLDPiUSKDHGPcJD@FLAJUCICxEKyIT{HCpeTsGChd_wcGYFTcEGPbO\ qj_gaGHaOii__`GACTKBC?~O[ABx^OS@Bp]OIe_?\\Ji?Sk[FX[NycbWyJ[YFHYNiaf@XNa`b?v\ JA_epVNQ^WstRrDagsIi\\WcrRbBePRMqZaOpRR@aHPMaXWCnMYWV{NDpNMQVVsMDhpVkLD`LMA\ TVcKHaSV[JDPmQYy`OhHPlVKHD@kQKGCxGLYOU{FCpFLQNUsEGphPsDC`DPkCKyKU[BPYqZ[ACH\ APRY");; # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/attr.tst:2420 # Input is: M := DigraphMaximumMatching(D);; IsMaximalMatching(D, M); # Expected output: true # But found: Error, Variable: 'DigraphMaximumMatching' must have a value Error, Variable: 'IsMaximalMatching' must have a value ######## ########> Diff in standard/attr.tst:2422 # Input is: Length(M); # Expected output: 111 # But found: Error, Variable: 'M' must have a value ######## ########> Diff in standard/attr.tst:2458 # Input is: DIGRAPHS_StopTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StopTest' must have a value ######## Digraphs package: standard/attr.tst msecs: 1153 false gap> ########> Diff in standard/cliques.tst:14 # Input is: DIGRAPHS_StartTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StartTest' must have a value ######## ########> Diff in standard/cliques.tst:17 # Input is: gr := CompleteDigraph(5);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/cliques.tst:18 # Input is: IsClique(gr, [6]); # Expected output: Error, the 2nd argument must be a duplicate-free list of vertices of \ \ the digraph that is the 1st argument, # But found: Error, Variable: 'IsClique' must have a value ######## ########> Diff in standard/cliques.tst:21 # Input is: IsClique(gr, []); # Expected output: true # But found: Error, Variable: 'IsClique' must have a value ######## ########> Diff in standard/cliques.tst:23 # Input is: IsClique(gr, [4]); # Expected output: true # But found: Error, Variable: 'IsClique' must have a value ######## ########> Diff in standard/cliques.tst:25 # Input is: IsClique(gr, [4, 3]); # Expected output: true # But found: Error, Variable: 'IsClique' must have a value ######## ########> Diff in standard/cliques.tst:27 # Input is: IsClique(gr, [4, 1, 3]); # Expected output: true # But found: Error, Variable: 'IsClique' must have a value ######## ########> Diff in standard/cliques.tst:29 # Input is: IsClique(gr, [4, 2, 3, 1]); # Expected output: true # But found: Error, Variable: 'IsClique' must have a value ######## ########> Diff in standard/cliques.tst:31 # Input is: IsClique(gr, [1, 5, 3, 4, 2]); # Expected output: true # But found: Error, Variable: 'IsClique' must have a value ######## ########> Diff in standard/cliques.tst:33 # Input is: IsClique(gr, [1, 1]); # Expected output: Error, the 2nd argument must be a duplicate-free list of vertices of \ \ the digraph that is the 1st argument, # But found: Error, Variable: 'IsClique' must have a value ######## ########> Diff in standard/cliques.tst:36 # Input is: gr := Digraph([ [2, 3, 4, 5, 7, 8, 11, 12], [1, 3, 4, 6, 7, 9, 11, 13], [1, 2, 5, 6, 8, 9, 12, 13], [1, 2, 5, 6, 7, 10, 11, 14], [1, 3, 4, 6, 8, 10, 12, 14], [2, 3, 4, 5, 9, 10, 13, 14], [1, 2, 4, 8, 9, 10, 11, 15], [1, 3, 5, 7, 9, 10, 12, 15], [2, 3, 6, 7, 8, 10, 13, 15], [4, 5, 6, 7, 8, 9, 14, 15], [1, 2, 4, 7, 12, 13, 14, 15], [1, 3, 5, 8, 11, 13, 14, 15], [2, 3, 6, 9, 11, 12, 14, 15], [4, 5, 6, 10, 11, 12, 13, 15], [7, 8, 9, 10, 11, 12, 13, 14]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/cliques.tst:46 # Input is: IsClique(gr, [1, 2, 4, 7, 11]); # Expected output: true # But found: Error, Variable: 'IsClique' must have a value ######## ########> Diff in standard/cliques.tst:48 # Input is: IsClique(gr, [1, 2, 3]); # Expected output: true # But found: Error, Variable: 'IsClique' must have a value ######## ########> Diff in standard/cliques.tst:50 # Input is: gr := Digraph([ [2, 3, 4, 5, 7, 8, 11, 12], [1, 3, 4, 6, 7, 9, 11, 13], [1, 2, 5, 6, 8, 9, 12, 13], [1, 2, 5, 6, 7, 10, 11, 14], [1, 3, 4, 6, 8, 10, 12, 14], [2, 3, 4, 5, 9, 10, 13, 14], [1, 2, 4, 8, 9, 10, 11, 15], [1, 3, 5, 7, 9, 10, 12, 15], [2, 3, 6, 7, 8, 10, 13, 15], [4, 5, 6, 7, 8, 9, 14, 15], [1, 2, 4, 7, 12, 13, 14, 15], [1, 3, 5, 8, 11, 13, 14, 15], [2, 3, 6, 9, 11, 12, 14, 15], [4, 5, 6, 10, 11, 12, 13, 15], [7, 8, 9, 10, 11, 12, 13, 14]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/cliques.tst:60 # Input is: IsMaximalClique(gr, [1, 2, 4, 7, 11]); # Expected output: true # But found: Error, Variable: 'IsMaximalClique' must have a value ######## ########> Diff in standard/cliques.tst:62 # Input is: IsMaximalClique(gr, [1, 2, 3]); # Expected output: true # But found: Error, Variable: 'IsMaximalClique' must have a value ######## ########> Diff in standard/cliques.tst:64 # Input is: IsMaximalClique(gr, [16]); # Expected output: Error, the 2nd argument must be a duplicate-free list of vertices of \ \ the digraph that is the 1st argument, # But found: Error, Variable: 'IsMaximalClique' must have a value ######## ########> Diff in standard/cliques.tst:67 # Input is: IsMaximalClique(gr, [1, 1]); # Expected output: Error, the 2nd argument must be a duplicate-free list of vertices of \ \ the digraph that is the 1st argument, # But found: Error, Variable: 'IsMaximalClique' must have a value ######## ########> Diff in standard/cliques.tst:70 # Input is: IsMaximalClique(gr, [1, 2, 4, 7, 11, 13]); # Expected output: false # But found: Error, Variable: 'IsMaximalClique' must have a value ######## ########> Diff in standard/cliques.tst:72 # Input is: gr := CompleteDigraph(5);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/cliques.tst:73 # Input is: IsMaximalClique(gr, [1]); # Expected output: false # But found: Error, Variable: 'IsMaximalClique' must have a value ######## ########> Diff in standard/cliques.tst:77 # Input is: gr := CycleDigraph(10);; # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/cliques.tst:78 # Input is: IsIndependentSet(gr, []); # Expected output: true # But found: Error, Variable: 'IsIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:80 # Input is: IsIndependentSet(gr, [1, 1]); # Expected output: Error, the 2nd argument must be a duplicate-free list of vertices of th\ \ e digraph that is the 1st argument, # But found: Error, Variable: 'IsIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:83 # Input is: IsIndependentSet(gr, [11]); # Expected output: Error, the 2nd argument must be a duplicate-free list of vertices of th\ \ e digraph that is the 1st argument, # But found: Error, Variable: 'IsIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:86 # Input is: IsIndependentSet(gr, [1, 2]); # Expected output: false # But found: Error, Variable: 'IsIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:88 # Input is: IsIndependentSet(gr, [1, 3]); # Expected output: true # But found: Error, Variable: 'IsIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:90 # Input is: IsMaximalIndependentSet(gr, []); # Expected output: false # But found: Error, Variable: 'IsMaximalIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:92 # Input is: IsMaximalIndependentSet(gr, [1, 2]); # Expected output: false # But found: Error, Variable: 'IsMaximalIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:94 # Input is: IsMaximalIndependentSet(gr, [1, 3]); # Expected output: false # But found: Error, Variable: 'IsMaximalIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:96 # Input is: gr := Digraph([[], [], [], [1, 2, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/cliques.tst:98 # Input is: IsIndependentSet(gr, [1, 2]); # Expected output: true # But found: Error, Variable: 'IsIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:100 # Input is: IsMaximalIndependentSet(gr, [1, 2]); # Expected output: false # But found: Error, Variable: 'IsMaximalIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:102 # Input is: IsIndependentSet(gr, [1, 2, 3]); # Expected output: true # But found: Error, Variable: 'IsIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:104 # Input is: IsMaximalIndependentSet(gr, [1, 2, 3]); # Expected output: true # But found: Error, Variable: 'IsMaximalIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:106 # Input is: gr := Digraph([[3], [3], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/cliques.tst:108 # Input is: IsMaximalIndependentSet(gr, [1, 2]); # Expected output: true # But found: Error, Variable: 'IsMaximalIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:112 # Input is: gr := Digraph([[3], [3], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/cliques.tst:114 # Input is: DigraphMaximalIndependentSet(); # Expected output: Error, at least 1 argument is required, # But found: Error, Variable: 'DigraphMaximalIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:116 # Input is: DigraphMaximalIndependentSet(3); # Expected output: Error, the 1st argument must be a digraph, # But found: Error, Variable: 'DigraphMaximalIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:118 # Input is: DigraphIndependentSet(); # Expected output: Error, at least 1 argument is required, # But found: Error, Variable: 'DigraphIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:120 # Input is: DigraphIndependentSet(3); # Expected output: Error, the 1st argument must be a digraph, # But found: Error, Variable: 'DigraphIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:122 # Input is: DigraphMaximalIndependentSet(gr); # Expected output: [ 3 ] # But found: Error, Variable: 'DigraphMaximalIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:124 # Input is: DigraphIndependentSet(gr); # Expected output: [ 3 ] # But found: Error, Variable: 'DigraphIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:126 # Input is: DigraphMaximalIndependentSet(gr, [], [], 2); # Expected output: [ 1, 2 ] # But found: Error, Variable: 'DigraphMaximalIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:128 # Input is: DigraphIndependentSet(gr, [], [], 3); # Expected output: fail # But found: Error, Variable: 'DigraphIndependentSet' must have a value ######## ########> Diff in standard/cliques.tst:132 # Input is: gr := EmptyDigraph(1);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/cliques.tst:133 # Input is: DigraphMaximalIndependentSetsReps(); # Expected output: Error, at least 1 argument is required, # But found: Error, Variable: 'DigraphMaximalIndependentSetsReps' must have a value ######## ########> Diff in standard/cliques.tst:135 # Input is: DigraphIndependentSetsReps(); # Expected output: Error, at least 1 argument is required, # But found: Error, Variable: 'DigraphIndependentSetsReps' must have a value ######## ########> Diff in standard/cliques.tst:137 # Input is: DigraphMaximalIndependentSets(); # Expected output: Error, at least 1 argument is required, # But found: Error, Variable: 'DigraphMaximalIndependentSets' must have a value ######## ########> Diff in standard/cliques.tst:139 # Input is: DigraphIndependentSets(); # Expected output: Error, at least 1 argument is required, # But found: Error, Variable: 'DigraphIndependentSets' must have a value ######## ########> Diff in standard/cliques.tst:141 # Input is: DigraphMaximalIndependentSetsReps(1); # Expected output: Error, the 1st argument must be a digraph, # But found: Error, Variable: 'DigraphMaximalIndependentSetsReps' must have a value ######## ########> Diff in standard/cliques.tst:143 # Input is: DigraphIndependentSetsReps(1); # Expected output: Error, the 1st argument must be a digraph, # But found: Error, Variable: 'DigraphIndependentSetsReps' must have a value ######## ########> Diff in standard/cliques.tst:145 # Input is: DigraphMaximalIndependentSets(1); # Expected output: Error, the 1st argument must be a digraph, # But found: Error, Variable: 'DigraphMaximalIndependentSets' must have a value ######## ########> Diff in standard/cliques.tst:147 # Input is: DigraphIndependentSets(1); # Expected output: Error, the 1st argument must be a digraph, # But found: Error, Variable: 'DigraphIndependentSets' must have a value ######## ########> Diff in standard/cliques.tst:149 # Input is: DigraphMaximalIndependentSetsReps(gr); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphMaximalIndependentSetsReps' must have a value ######## ########> Diff in standard/cliques.tst:151 # Input is: DigraphMaximalIndependentSetsReps(gr); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphMaximalIndependentSetsReps' must have a value ######## ########> Diff in standard/cliques.tst:153 # Input is: DigraphIndependentSetsReps(gr); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphIndependentSetsReps' must have a value ######## ########> Diff in standard/cliques.tst:155 # Input is: DigraphMaximalIndependentSets(gr); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphMaximalIndependentSets' must have a value ######## ########> Diff in standard/cliques.tst:157 # Input is: DigraphIndependentSets(gr); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphIndependentSets' must have a value ######## ########> Diff in standard/cliques.tst:159 # Input is: DigraphMaximalIndependentSetsReps(gr, []); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphMaximalIndependentSetsReps' must have a value ######## ########> Diff in standard/cliques.tst:161 # Input is: DigraphIndependentSetsReps(gr, []); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphIndependentSetsReps' must have a value ######## ########> Diff in standard/cliques.tst:163 # Input is: DigraphMaximalIndependentSets(gr, []); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphMaximalIndependentSets' must have a value ######## ########> Diff in standard/cliques.tst:165 # Input is: DigraphIndependentSets(gr, []); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphIndependentSets' must have a value ######## ########> Diff in standard/cliques.tst:167 # Input is: DigraphMaximalIndependentSetsReps(gr, [], []); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphMaximalIndependentSetsReps' must have a value ######## ########> Diff in standard/cliques.tst:169 # Input is: DigraphIndependentSetsReps(gr, [], []); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphIndependentSetsReps' must have a value ######## ########> Diff in standard/cliques.tst:171 # Input is: DigraphMaximalIndependentSets(gr, [], []); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphMaximalIndependentSets' must have a value ######## ########> Diff in standard/cliques.tst:173 # Input is: DigraphIndependentSets(gr, [], []); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphIndependentSets' must have a value ######## ########> Diff in standard/cliques.tst:175 # Input is: DigraphMaximalIndependentSetsReps(gr, [], [], 1); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphMaximalIndependentSetsReps' must have a value ######## ########> Diff in standard/cliques.tst:177 # Input is: DigraphIndependentSetsReps(gr, [], [], 1); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphIndependentSetsReps' must have a value ######## ########> Diff in standard/cliques.tst:179 # Input is: DigraphMaximalIndependentSets(gr, [], [], 1); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphMaximalIndependentSets' must have a value ######## ########> Diff in standard/cliques.tst:181 # Input is: DigraphIndependentSets(gr, [], [], 1); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphIndependentSets' must have a value ######## ########> Diff in standard/cliques.tst:183 # Input is: DigraphMaximalIndependentSetsReps(gr, [], [], 1, 1); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphMaximalIndependentSetsReps' must have a value ######## ########> Diff in standard/cliques.tst:185 # Input is: DigraphIndependentSetsReps(gr, [], [], 1, 1); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphIndependentSetsReps' must have a value ######## ########> Diff in standard/cliques.tst:187 # Input is: DigraphMaximalIndependentSets(gr, [], [], 1, 1); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphMaximalIndependentSets' must have a value ######## ########> Diff in standard/cliques.tst:189 # Input is: DigraphIndependentSets(gr, [], [], 1, 1); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphIndependentSets' must have a value ######## ########> Diff in standard/cliques.tst:191 # Input is: gr := CompleteDigraph(10);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/cliques.tst:192 # Input is: DigraphMaximalIndependentSetsRepsAttr(gr); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphMaximalIndependentSetsRepsAttr' must have a value ######## ########> Diff in standard/cliques.tst:194 # Input is: DigraphMaximalIndependentSetsAttr(gr); # Expected output: [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8 ], [ 9 ], [ 10 ] ] # But found: Error, Variable: 'DigraphMaximalIndependentSetsAttr' must have a value ######## ########> Diff in standard/cliques.tst:198 # Input is: gr := ChainDigraph(2);; # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/cliques.tst:199 # Input is: DigraphMaximalIndependentSets(gr); # Expected output: [ [ 1 ], [ 2 ] ] # But found: Error, Variable: 'DigraphMaximalIndependentSets' must have a value ######## ########> Diff in standard/cliques.tst:201 # Input is: gr := CompleteDigraph(2);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/cliques.tst:202 # Input is: DigraphMaximalIndependentSets(gr); # Expected output: [ [ 1 ], [ 2 ] ] # But found: Error, Variable: 'DigraphMaximalIndependentSets' must have a value ######## ########> Diff in standard/cliques.tst:204 # Input is: gr := DigraphFromDigraph6String("&FWsK?WSKC?"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/cliques.tst:206 # Input is: DigraphMaximalIndependentSetsReps(gr); # Expected output: [ [ 1, 4 ], [ 1, 5 ], [ 2, 5, 7 ] ] # But found: Error, Variable: 'DigraphMaximalIndependentSetsReps' must have a value ######## ########> Diff in standard/cliques.tst:208 # Input is: Set(DigraphMaximalIndependentSets(gr)); # Expected output: [ [ 1, 4 ], [ 1, 5 ], [ 1, 6 ], [ 2, 4 ], [ 2, 5, 7 ], [ 2, 6, 7 ], [ 3, 4 ], [ 3, 5, 7 ], [ 3, 6, 7 ] ] # But found: Error, Variable: 'DigraphMaximalIndependentSets' must have a value ######## ########> Diff in standard/cliques.tst:211 # Input is: Set(DigraphMaximalIndependentSets(gr)); # Expected output: [ [ 1, 4 ], [ 1, 5 ], [ 1, 6 ], [ 2, 4 ], [ 2, 5, 7 ], [ 2, 6, 7 ], [ 3, 4 ], [ 3, 5, 7 ], [ 3, 6, 7 ] ] # But found: Error, Variable: 'DigraphMaximalIndependentSets' must have a value ######## ########> Diff in standard/cliques.tst:214 # Input is: DigraphIndependentSetsReps(gr); # Expected output: [ [ 1 ], [ 1, 4 ], [ 1, 5 ], [ 2 ], [ 2, 5 ], [ 2, 5, 7 ], [ 2, 7 ], [ 7 ] ] # But found: Error, Variable: 'DigraphIndependentSetsReps' must have a value ######## ########> Diff in standard/cliques.tst:216 # Input is: Set(DigraphIndependentSets(gr)); # Expected output: [ [ 1 ], [ 1, 4 ], [ 1, 5 ], [ 1, 6 ], [ 2 ], [ 2, 4 ], [ 2, 5 ], [ 2, 5, 7 ], [ 2, 6 ], [ 2, 6, 7 ], [ 2, 7 ], [ 3 ], [ 3, 4 ], [ 3, 5 ], [ 3, 5, 7 ], [ 3, 6 ], [ 3, 6, 7 ], [ 3, 7 ], [ 4 ], [ 5 ], [ 5, 7 ], [ 6 ], [ 6, 7 ], [ 7 ] ] # But found: Error, Variable: 'DigraphIndependentSets' must have a value ######## ########> Diff in standard/cliques.tst:223 # Input is: gr := CompleteDigraph(5);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/cliques.tst:224 # Input is: DigraphMaximalClique(); # Expected output: Error, at least 1 argument is required, # But found: Error, Variable: 'DigraphMaximalClique' must have a value ######## ########> Diff in standard/cliques.tst:226 # Input is: DigraphClique(); # Expected output: Error, at least 1 argument is required, # But found: Error, Variable: 'DigraphClique' must have a value ######## ########> Diff in standard/cliques.tst:228 # Input is: DigraphMaximalClique(1); # Expected output: Error, the 1st argument must be a digraph by out-neighbours, # But found: Error, Variable: 'DigraphMaximalClique' must have a value ######## ########> Diff in standard/cliques.tst:230 # Input is: DigraphClique(1); # Expected output: Error, the 1st argument must be a digraph by out-neighbours, # But found: Error, Variable: 'DigraphClique' must have a value ######## ########> Diff in standard/cliques.tst:232 # Input is: DigraphMaximalClique(gr); # Expected output: [ 5, 4, 3, 2, 1 ] # But found: Error, Variable: 'DigraphMaximalClique' must have a value ######## ########> Diff in standard/cliques.tst:234 # Input is: DigraphClique(gr); # Expected output: [ 5, 4, 3, 2, 1 ] # But found: Error, Variable: 'DigraphClique' must have a value ######## ########> Diff in standard/cliques.tst:236 # Input is: DigraphMaximalClique(gr, [1, 1]); # Expected output: Error, the optional 2nd argument must be a duplicate-free list of ve\ \ rtices of the digraph that is the 1st argument, # But found: Error, Variable: 'DigraphMaximalClique' must have a value ######## ########> Diff in standard/cliques.tst:239 # Input is: DigraphMaximalClique(gr, [1], [1, 1]); # Expected output: Error, the optional 3rd argument must be a duplicate-free list of ve\ \ rtices of the digraph that is the 1st argument, # But found: Error, Variable: 'DigraphMaximalClique' must have a value ######## ########> Diff in standard/cliques.tst:242 # Input is: DigraphMaximalClique(gr, [1], [1], 0); # Expected output: Error, the optional 4th argument must be a positive integer, # But found: Error, Variable: 'DigraphMaximalClique' must have a value ######## ########> Diff in standard/cliques.tst:244 # Input is: gr := EmptyDigraph(5);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/cliques.tst:245 # Input is: DigraphMaximalClique(gr, [1, 2], [3]); # Expected output: fail # But found: Error, Variable: 'DigraphMaximalClique' must have a value ######## ########> Diff in standard/cliques.tst:247 # Input is: DigraphMaximalClique(gr, [1, 2], [2]); # Expected output: fail # But found: Error, Variable: 'DigraphMaximalClique' must have a value ######## ########> Diff in standard/cliques.tst:249 # Input is: DigraphMaximalClique(gr, [1, 2], [3]); # Expected output: fail # But found: Error, Variable: 'DigraphMaximalClique' must have a value ######## ########> Diff in standard/cliques.tst:251 # Input is: DigraphMaximalClique(gr, [1], [2]); # Expected output: [ 1 ] # But found: Error, Variable: 'DigraphMaximalClique' must have a value ######## ########> Diff in standard/cliques.tst:253 # Input is: DigraphClique(gr, [1], [1]); # Expected output: fail # But found: Error, Variable: 'DigraphClique' must have a value ######## ########> Diff in standard/cliques.tst:255 # Input is: DigraphMaximalClique(CompleteDigraph(5), [1, 2], [3]); # Expected output: fail # But found: Error, Variable: 'DigraphMaximalClique' must have a value ######## ########> Diff in standard/cliques.tst:257 # Input is: DigraphClique(CompleteDigraph(5), [1, 2], []); # Expected output: [ 1, 2, 5, 4, 3 ] # But found: Error, Variable: 'DigraphClique' must have a value ######## ########> Diff in standard/cliques.tst:261 # Input is: DigraphCliquesReps(); # Expected output: Error, there must be at least 1 argument, # But found: Error, Variable: 'DigraphCliquesReps' must have a value ######## ########> Diff in standard/cliques.tst:263 # Input is: DigraphCliques(); # Expected output: Error, there must be at least 1 argument, # But found: Error, Variable: 'DigraphCliques' must have a value ######## ########> Diff in standard/cliques.tst:265 # Input is: gr := EmptyDigraph(5);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/cliques.tst:266 # Input is: DigraphMaximalCliquesRepsAttr(gr); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphMaximalCliquesRepsAttr' must have a value ######## ########> Diff in standard/cliques.tst:268 # Input is: DigraphMaximalCliquesReps(); # Expected output: Error, there must be at least 1 argument, # But found: Error, Variable: 'DigraphMaximalCliquesReps' must have a value ######## ########> Diff in standard/cliques.tst:270 # Input is: DigraphMaximalCliquesReps(gr); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphMaximalCliquesReps' must have a value ######## ########> Diff in standard/cliques.tst:272 # Input is: DigraphMaximalCliquesAttr(gr); # Expected output: [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ] ] # But found: Error, Variable: 'DigraphMaximalCliquesAttr' must have a value ######## ########> Diff in standard/cliques.tst:274 # Input is: DigraphMaximalCliques(); # Expected output: Error, there must be at least 1 argument, # But found: Error, Variable: 'DigraphMaximalCliques' must have a value ######## ########> Diff in standard/cliques.tst:276 # Input is: DigraphMaximalCliques(gr); # Expected output: [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ] ] # But found: Error, Variable: 'DigraphMaximalCliques' must have a value ######## ########> Diff in standard/cliques.tst:278 # Input is: gr := EmptyDigraph(1);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/cliques.tst:279 # Input is: DigraphMaximalCliques(gr); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'DigraphMaximalCliques' must have a value ######## ########> Diff in standard/cliques.tst:281 # Input is: gr := DigraphFromDigraph6String("&DNNNF?"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/cliques.tst:283 # Input is: DigraphMaximalCliquesReps(gr); # Expected output: [ [ 1, 3 ] ] # But found: Error, Variable: 'DigraphMaximalCliquesReps' must have a value ######## ########> Diff in standard/cliques.tst:285 # Input is: Set(DigraphMaximalCliques(gr)); # Expected output: [ [ 1, 3 ], [ 1, 4 ], [ 2, 4 ], [ 2, 5 ], [ 3, 5 ] ] # But found: Error, Variable: 'DigraphMaximalCliques' must have a value ######## ########> Diff in standard/cliques.tst:287 # Input is: gr := DigraphFromGraph6String("N~~~~~~~wzmxufyZsvw"); # Expected output: # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/cliques.tst:289 # Input is: DigraphMaximalCliquesReps(gr); # Expected output: [ [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ], [ 1, 2, 3, 5, 8, 9, 14 ], [ 1, 2, 5, 13, 14 ], [ 1, 13, 14, 15 ], [ 11, 12, 13, 14, 15 ] ] # But found: Error, Variable: 'DigraphMaximalCliquesReps' must have a value ######## ########> Diff in standard/cliques.tst:292 # Input is: gr := DigraphFromGraph6String( "X~~~~~~~~~~~~~~~~~wvaSD{iLzBU{JJ}B]^FQn|gq~~Gb~TjF~"); # Expected output: # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/cliques.tst:295 # Input is: DigraphMaximalCliquesReps(gr); # Expected output: [ [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ], [ 1, 2, 3, 4, 5, 8, 12, 24 ], [ 2, 4, 12, 17, 24, 25 ], [ 4, 16, 17, 22, 23, 24, 25 ], [ 4, 7, 9, 16, 25 ], [ 3, 18, 19, 23, 24 ], [ 5, 16, 18, 22, 24 ], [ 16, 17, 18, 19, 20, 21, 22, 23, 24, 25 ] ] # But found: Error, Variable: 'DigraphMaximalCliquesReps' must have a value ######## ########> Diff in standard/cliques.tst:302 # Input is: CliquesFinder(Group(()), fail, fail, fail, fail, fail, fail, fail, fail); # Expected output: Error, the 1st argument must be a digraph, # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:304 # Input is: gr := CompleteDigraph(5);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/cliques.tst:305 # Input is: CliquesFinder(gr, [], fail, fail, fail, fail, fail, fail, fail); # Expected output: Error, the 2nd argument must be fail, or a function with 2 arguments, # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:308 # Input is: CliquesFinder(gr, f, fail, fail, fail, fail, fail, fail, fail); # Expected output: Error, the 2nd argument must be fail, or a function with 2 arguments, # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:310 # Input is: CliquesFinder(gr, fail, fail, fail, fail, fail, fail, fail, fail); # Expected output: Error, when the 2nd argument is fail, the 3rd argument mus\ \ t be a list, # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:314 # Input is: CliquesFinder(gr, f, fail, fail, fail, fail, fail, fail, fail); # Expected output: Error, the 4th argument must be infinity, or a positive integer, # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:316 # Input is: CliquesFinder(gr, fail, [], infinity, fail, fail, fail, fail, fail); # Expected output: Error, the 5th argument and the 6th argument must be (poss\ \ ibly empty) duplicate-free lists of vertices of the 1st argument # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:319 # Input is: CliquesFinder(gr, fail, [], infinity, [0, 'a'], fail, fail, fail, fail); # Expected output: Error, the 5th argument and the 6th argument must be (poss\ \ ibly empty) duplicate-free lists of vertices of the 1st argument # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:322 # Input is: CliquesFinder(gr, fail, [], infinity, [0], fail, fail, fail, fail); # Expected output: Error, the 5th argument and the 6th argument must be (poss\ \ ibly empty) duplicate-free lists of vertices of the 1st argument # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:325 # Input is: CliquesFinder(gr, fail, [], infinity, [1, 1], fail, fail, fail, fail); # Expected output: Error, the 5th argument and the 6th argument must be (poss\ \ ibly empty) duplicate-free lists of vertices of the 1st argument # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:328 # Input is: CliquesFinder(gr, fail, [], infinity, [1], fail, fail, fail, fail); # Expected output: Error, the 5th argument and the 6th argument must be (poss\ \ ibly empty) duplicate-free lists of vertices of the 1st argument # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:331 # Input is: CliquesFinder(gr, fail, [], infinity, [1], [0, 'a'], fail, fail, fail); # Expected output: Error, the 5th argument and the 6th argument must be (poss\ \ ibly empty) duplicate-free lists of vertices of the 1st argument # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:334 # Input is: CliquesFinder(gr, fail, [], infinity, [1], [0], fail, fail, fail); # Expected output: Error, the 5th argument and the 6th argument must be (poss\ \ ibly empty) duplicate-free lists of vertices of the 1st argument # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:337 # Input is: CliquesFinder(gr, fail, [], infinity, [1], [1, 1], fail, fail, fail); # Expected output: Error, the 5th argument and the 6th argument must be (poss\ \ ibly empty) duplicate-free lists of vertices of the 1st argument # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:340 # Input is: CliquesFinder(gr, fail, [], infinity, [1], [1], fail, fail, fail); # Expected output: Error, the 7th argument must be true or false, # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:342 # Input is: CliquesFinder(gr, fail, [], infinity, [1], [1], false, 0, fail); # Expected output: Error, the 8th argument must be fail, or a positive integer, # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:344 # Input is: CliquesFinder(gr, fail, [], infinity, [1], [1], false, 1, fail); # Expected output: Error, the 9th argument must be true or false, # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:346 # Input is: CliquesFinder(gr, fail, [], infinity, [1], [], false, 1, true); # Expected output: Error, if the 9th argument is true, then the 4th and 5th arguments and must be invariant under the action of the automorphism gro\ \ up of the maximal symmetric subdigraph without loops, # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:350 # Input is: CliquesFinder(gr, fail, [], infinity, [], [1], false, 1, true); # Expected output: Error, if the 9th argument is true, then the 4th and 5th arguments and must be invariant under the action of the automorphism gro\ \ up of the maximal symmetric subdigraph without loops, # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:354 # Input is: CliquesFinder(gr, fail, [], infinity, [1 .. 5], [1 .. 5], false, 1, true); # Expected output: [ ] # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:356 # Input is: CliquesFinder(gr, fail, [], infinity, [1], [1], false, 1, false); # Expected output: [ ] # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:360 # Input is: gr := ChainDigraph(5);; # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/cliques.tst:361 # Input is: CliquesFinder(gr, fail, [], infinity, [], [1 .. 4], false, 3, false); # Expected output: [ ] # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:363 # Input is: CliquesFinder(gr, fail, [], infinity, [1, 2], [], false, 3, false); # Expected output: [ ] # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:365 # Input is: gr := CompleteDigraph(5);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/cliques.tst:366 # Input is: CliquesFinder(gr, fail, [], infinity, [1 .. 5], [], false, 1, false); # Expected output: [ ] # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:368 # Input is: CliquesFinder(gr, fail, [], infinity, [1 .. 5], [1 .. 5], false, fail, false); # Expected output: [ ] # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:371 # Input is: CliquesFinder(gr, fail, [], infinity, [1], [], false, 1, false); # Expected output: [ [ 1 ] ] # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:373 # Input is: CliquesFinder(gr, fail, [], infinity, [], [], false, 1, false); # Expected output: [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ] ] # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:377 # Input is: gr := CompleteDigraph(5);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/cliques.tst:378 # Input is: CliquesFinder(gr, fail, [], infinity, [], [], true, 4, true); # Expected output: [ ] # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:380 # Input is: CliquesFinder(gr, fail, [], infinity, [], [], true, 5, true); # Expected output: [ [ 1, 2, 3, 4, 5 ] ] # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:382 # Input is: CliquesFinder(gr, fail, [], infinity, [], [], true, fail, true); # Expected output: [ [ 1, 2, 3, 4, 5 ] ] # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:384 # Input is: CliquesFinder(gr, fail, [], infinity, [], [], false, fail, true); # Expected output: [ [ 1 ], [ 1, 2 ], [ 1, 2, 3 ], [ 1, 2, 3, 4 ], [ 1, 2, 3, 4, 5 ] ] # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:386 # Input is: out := Set(CliquesFinder(gr, fail, [], infinity, [], [], false, fail, false)); # Expected output: [ [ 1 ], [ 1, 2 ], [ 1, 2, 3 ], [ 1, 2, 3, 4 ], [ 1, 2, 3, 4, 5 ], [ 1, 2, 3, 5 ], [ 1, 2, 4 ], [ 1, 2, 4, 5 ], [ 1, 2, 5 ], [ 1, 3 ], [ 1, 3, 4 ], [ 1, 3, 4, 5 ], [ 1, 3, 5 ], [ 1, 4 ], [ 1, 4, 5 ], [ 1, 5 ], [ 2 ], [ 2, 3 ], [ 2, 3, 4 ], [ 2, 3, 4, 5 ], [ 2, 3, 5 ], [ 2, 4 ], [ 2, 4, 5 ], [ 2, 5 ], [ 3 ], [ 3, 4 ], [ 3, 4, 5 ], [ 3, 5 ], [ 4 ], [ 4, 5 ], [ 5 ] ] # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:394 # Input is: Length(out); # Expected output: 31 # But found: Error, Variable: 'out' must have a value ######## ########> Diff in standard/cliques.tst:397 # Input is: Set(CliquesFinder(gr, fail, [], lim, [], [], false, fail, false)) = out; # Expected output: true # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:400 # Input is: out := Set(CliquesFinder(gr, fail, [], lim, [], [], false, fail, false)); # Expected output: [ [ 1 ], [ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 1, 5 ], [ 2 ], [ 2, 3 ], [ 2, 4 ], [ 2, 5 ], [ 3 ], [ 4 ], [ 5 ] ] # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:403 # Input is: Length(out) = lim; # Expected output: true # But found: Error, Variable: 'out' must have a value ######## ########> Diff in standard/cliques.tst:405 # Input is: out := Set(CliquesFinder(gr, fail, [], lim, [1, 4], [], false, fail, false)); # Expected output: [ [ 1, 2, 3, 4 ], [ 1, 2, 3, 4, 5 ], [ 1, 2, 4 ], [ 1, 2, 4, 5 ], [ 1, 3, 4 ], [ 1, 3, 4, 5 ], [ 1, 4 ], [ 1, 4, 5 ] ] # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:409 # Input is: out := Set(CliquesFinder(gr, fail, [], lim, [1, 4], [], false, 4, false)); # Expected output: [ [ 1, 2, 3, 4 ], [ 1, 2, 4, 5 ], [ 1, 3, 4, 5 ] ] # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:412 # Input is: out := CliquesFinder(gr, fail, [], lim, [2], [4, 5], false, fail, false); # Expected output: [ [ 2 ], [ 1, 2 ], [ 2, 3 ], [ 1, 2, 3 ] ] # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:414 # Input is: out := CliquesFinder(gr, fail, [], lim, [], [3, 4, 5], false, fail, false); # Expected output: [ [ 1 ], [ 2 ], [ 1, 2 ] ] # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:416 # Input is: out := CliquesFinder(gr, fail, [], lim, [], [3, 4, 5], false, 2, false); # Expected output: [ [ 1, 2 ] ] # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:418 # Input is: gr := DigraphSymmetricClosure(ChainDigraph(5));; # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/cliques.tst:419 # Input is: out := CliquesFinder(gr, fail, [], lim, [], [], true, 3, true); # Expected output: [ ] # But found: Error, Variable: 'CliquesFinder' must have a value ######## ########> Diff in standard/cliques.tst:423 # Input is: gr := DigraphFromGraph6String( "X~~~~~~~~~~~~~~~~~}EkpJK_vyRUwvH{fL^FFfzdo~tmB~cU^~"); # Expected output: # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/cliques.tst:426 # Input is: AutomorphismGroup(gr);; # Expected output: # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/cliques.tst:427 # Input is: c := DigraphMaximalCliques(gr);; # Expected output: # But found: Error, Variable: 'DigraphMaximalCliques' must have a value ######## ########> Diff in standard/cliques.tst:428 # Input is: Length(c); # Expected output: 52 # But found: Error, Variable: 'c' must have a value ######## ########> Diff in standard/cliques.tst:430 # Input is: gr := DigraphFromGraph6String(Concatenation( "b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~bx[^fbY^zbMznyvej^AX~", "v|Zf\\r~jXmr~}|LD~t}iF~ztlNV~_")); # Expected output: # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/cliques.tst:434 # Input is: AutomorphismGroup(gr);; # Expected output: # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/cliques.tst:435 # Input is: c := DigraphMaximalCliques(gr);; # Expected output: # But found: Error, Variable: 'DigraphMaximalCliques' must have a value ######## ########> Diff in standard/cliques.tst:436 # Input is: Length(c); # Expected output: 302 # But found: Error, Variable: 'c' must have a value ######## ########> Diff in standard/cliques.tst:438 # Input is: gr := DigraphFromGraph6String(Concatenation( "~?@O~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~", "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~", "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~", "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~", "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}NrN}}~~[F", "~X}H}jr~~t]~zwvmv\\zzy}n~y~m~Tzjy}M~{Jr^YZ~V|~~~V|uuu|^^Z|^w^emV|n~^}z~j", "uYz\\u~l~zz~~T|nllvb}~Z~~~~it~a}zvD~~j}tY~f~x~qn~~z~Z||{V]Sn~~~~z~jnfzod", "V~}nzn}}}~MFVn~z|F|F~|tNx~~~{")); # Expected output: # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/cliques.tst:448 # Input is: AutomorphismGroup(gr);; # Expected output: # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/cliques.tst:449 # Input is: c := DigraphMaximalCliques(gr);; # Expected output: # But found: Error, Variable: 'DigraphMaximalCliques' must have a value ######## ########> Diff in standard/cliques.tst:450 # Input is: Length(c); # Expected output: 12815 # But found: Error, Variable: 'c' must have a value ######## ########> Diff in standard/cliques.tst:454 # Input is: gr := DigraphFromSparse6String(":~?@c__EC?_F"); # Expected output: # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/cliques.tst:456 # Input is: DigraphMaximalCliquesReps(gr); # Expected output: [ [ 1 ], [ 2, 3, 5 ] ] # But found: Error, Variable: 'DigraphMaximalCliquesReps' must have a value ######## ########> Diff in standard/cliques.tst:458 # Input is: DigraphMaximalCliques(gr); # Expected output: [ [ 1 ], [ 4 ], [ 6 ], [ 7 ], [ 8 ], [ 9 ], [ 10 ], [ 11 ], [ 12 ], [ 13 ], [ 14 ], [ 15 ], [ 16 ], [ 17 ], [ 18 ], [ 19 ], [ 20 ], [ 21 ], [ 22 ], [ 23 ], [ 24 ], [ 25 ], [ 26 ], [ 27 ], [ 28 ], [ 29 ], [ 30 ], [ 31 ], [ 32 ], [ 33 ], [ 34 ], [ 35 ], [ 36 ], [ 37 ], [ 38 ], [ 39 ], [ 40 ], [ 41 ], [ 42 ], [ 43 ], [ 44 ], [ 45 ], [ 46 ], [ 47 ], [ 48 ], [ 49 ], [ 50 ], [ 51 ], [ 52 ], [ 53 ], [ 54 ], [ 55 ], [ 56 ], [ 57 ], [ 58 ], [ 59 ], [ 60 ], [ 61 ], [ 62 ], [ 63 ], [ 64 ], [ 65 ], [ 66 ], [ 67 ], [ 68 ], [ 69 ], [ 70 ], [ 71 ], [ 72 ], [ 73 ], [ 74 ], [ 75 ], [ 76 ], [ 77 ], [ 78 ], [ 79 ], [ 80 ], [ 81 ], [ 82 ], [ 83 ], [ 84 ], [ 85 ], [ 86 ], [ 87 ], [ 88 ], [ 89 ], [ 90 ], [ 91 ], [ 92 ], [ 93 ], [ 94 ], [ 95 ], [ 96 ], [ 97 ], [ 98 ], [ 99 ], [ 100 ], [ 2, 3, 5 ] ] # But found: Error, Variable: 'DigraphMaximalCliques' must have a value ######## ########> Diff in standard/cliques.tst:472 # Input is: CliqueNumber(NullDigraph(10)); # Expected output: 1 # But found: Error, Variable: 'CliqueNumber' must have a value ######## ########> Diff in standard/cliques.tst:474 # Input is: CliqueNumber(NullDigraph(0)); # Expected output: 0 # But found: Error, Variable: 'CliqueNumber' must have a value ######## ########> Diff in standard/cliques.tst:476 # Input is: CliqueNumber(CompleteDigraph(10)); # Expected output: 10 # But found: Error, Variable: 'CliqueNumber' must have a value ######## ########> Diff in standard/cliques.tst:478 # Input is: CliqueNumber(DigraphRemoveEdge(CompleteDigraph(10), [1, 2])); # Expected output: 9 # But found: Error, Variable: 'CliqueNumber' must have a value ######## ########> Diff in standard/cliques.tst:480 # Input is: CliqueNumber(JohnsonDigraph(10, 2)); # Expected output: 9 # But found: Error, Variable: 'CliqueNumber' must have a value ######## ########> Diff in standard/cliques.tst:482 # Input is: CliqueNumber(ChainDigraph(10)); # Expected output: 1 # But found: Error, Variable: 'CliqueNumber' must have a value ######## ########> Diff in standard/cliques.tst:484 # Input is: CliqueNumber(ChainDigraph(9)); # Expected output: 1 # But found: Error, Variable: 'CliqueNumber' must have a value ######## ########> Diff in standard/cliques.tst:486 # Input is: CliqueNumber(CycleDigraph(9)); # Expected output: 1 # But found: Error, Variable: 'CliqueNumber' must have a value ######## ########> Diff in standard/cliques.tst:488 # Input is: CliqueNumber(CycleDigraph(8)); # Expected output: 1 # But found: Error, Variable: 'CliqueNumber' must have a value ######## ########> Diff in standard/cliques.tst:490 # Input is: CliqueNumber(DigraphSymmetricClosure(CycleDigraph(8))); # Expected output: 2 # But found: Error, Variable: 'CliqueNumber' must have a value ######## ########> Diff in standard/cliques.tst:494 # Input is: D := Digraph(IsMutableDigraph, [[2, 3], [1, 3], [1, 2, 4], [3, 5, 6], [4, 6], [4, 5]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/cliques.tst:496 # Input is: cliques := DigraphMaximalCliquesReps(D); # Expected output: [ [ 1, 2, 3 ], [ 3, 4 ] ] # But found: Error, Variable: 'DigraphMaximalCliquesReps' must have a value ######## ########> Diff in standard/cliques.tst:498 # Input is: IsMutable(cliques) or ForAny(cliques, IsMutable); # Expected output: false # But found: Error, Variable: 'cliques' must have a value ######## ########> Diff in standard/cliques.tst:500 # Input is: cliques := DigraphMaximalCliques(D); # Expected output: [ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 3, 4 ] ] # But found: Error, Variable: 'DigraphMaximalCliques' must have a value ######## ########> Diff in standard/cliques.tst:502 # Input is: IsMutable(cliques) or ForAny(cliques, IsMutable); # Expected output: false # But found: Error, Variable: 'cliques' must have a value ######## ########> Diff in standard/cliques.tst:504 # Input is: cliques := DigraphMaximalCliques(D, [1]); # Expected output: [ [ 1, 2, 3 ] ] # But found: Error, Variable: 'DigraphMaximalCliques' must have a value ######## ########> Diff in standard/cliques.tst:506 # Input is: IsMutable(cliques) or ForAny(cliques, IsMutable); # Expected output: false # But found: Error, Variable: 'cliques' must have a value ######## ########> Diff in standard/cliques.tst:517 # Input is: DIGRAPHS_StopTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StopTest' must have a value ######## Digraphs package: standard/cliques.tst msecs: 191 false gap> ########> Diff in standard/constructors.tst:14 # Input is: DIGRAPHS_StartTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StartTest' must have a value ######## ########> Diff in standard/constructors.tst:25 # Input is: digraph := Digraph(group, [1 .. n], \^, adj); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/constructors.tst:27 # Input is: bddigraph := BipartiteDoubleDigraph(digraph); # Expected output: # But found: Error, Variable: 'BipartiteDoubleDigraph' must have a value ######## ########> Diff in standard/constructors.tst:29 # Input is: bdgroup := DigraphGroup(bddigraph); # Expected output: Group([ (1,2,3,4,5)(6,7,8,9,10), (1,6)(2,7)(3,8)(4,9)(5,10) ]) # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/constructors.tst:37 # Input is: digraph := Digraph(out); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/constructors.tst:39 # Input is: SetDigraphGroup(digraph, group); # Expected output: # But found: Error, Variable: 'SetDigraphGroup' must have a value ######## ########> Diff in standard/constructors.tst:40 # Input is: ddigraph := BipartiteDoubleDigraph(digraph); # Expected output: # But found: Error, Variable: 'BipartiteDoubleDigraph' must have a value ######## ########> Diff in standard/constructors.tst:42 # Input is: DigraphGroup(ddigraph); # Expected output: Group([ (2,3)(6,7), (2,4)(6,8), (1,5)(2,6)(3,7)(4,8) ]) # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/constructors.tst:44 # Input is: ddigraph := DoubleDigraph(digraph); # Expected output: # But found: Error, Variable: 'DoubleDigraph' must have a value ######## ########> Diff in standard/constructors.tst:46 # Input is: DigraphGroup(ddigraph); # Expected output: Group([ (2,3)(6,7), (2,4)(6,8), (1,5)(2,6)(3,7)(4,8) ]) # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/constructors.tst:50 # Input is: gr := Digraph([[2, 3], [1], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/constructors.tst:51 # Input is: gr2 := DoubleDigraph(gr); # Expected output: # But found: Error, Variable: 'DoubleDigraph' must have a value ######## ########> Diff in standard/constructors.tst:53 # Input is: OutNeighbours(gr2); # Expected output: [ [ 2, 3, 5, 6 ], [ 1, 4 ], [ ], [ 5, 6, 2, 3 ], [ 4, 1 ], [ ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/constructors.tst:55 # Input is: gr2 := BipartiteDoubleDigraph(gr); # Expected output: # But found: Error, Variable: 'BipartiteDoubleDigraph' must have a value ######## ########> Diff in standard/constructors.tst:57 # Input is: OutNeighbours(gr2); # Expected output: [ [ 5, 6 ], [ 4 ], [ ], [ 2, 3 ], [ 1 ], [ ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/constructors.tst:59 # Input is: gr := Digraph([[2, 2, 3], [1], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/constructors.tst:60 # Input is: gr2 := DoubleDigraph(gr); # Expected output: # But found: Error, Variable: 'DoubleDigraph' must have a value ######## ########> Diff in standard/constructors.tst:62 # Input is: OutNeighbours(gr2); # Expected output: [ [ 2, 2, 3, 5, 5, 6 ], [ 1, 4 ], [ ], [ 5, 5, 6, 2, 2, 3 ], [ 4, 1 ], [ ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/constructors.tst:64 # Input is: gr2 := BipartiteDoubleDigraph(gr); # Expected output: # But found: Error, Variable: 'BipartiteDoubleDigraph' must have a value ######## ########> Diff in standard/constructors.tst:66 # Input is: OutNeighbours(gr2); # Expected output: [ [ 5, 5, 6 ], [ 4 ], [ ], [ 2, 2, 3 ], [ 1 ], [ ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/constructors.tst:101 # Input is: digraph := Digraph(out); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/constructors.tst:103 # Input is: DigraphDiameter(digraph); # Expected output: 6 # But found: Error, Variable: 'DigraphDiameter' must have a value ######## ########> Diff in standard/constructors.tst:105 # Input is: DistanceDigraph(digraph, 4); # Expected output: # But found: Error, Variable: 'DistanceDigraph' must have a value ######## ########> Diff in standard/constructors.tst:107 # Input is: DistanceDigraph(digraph, [1, 3, 5]); # Expected output: # But found: Error, Variable: 'DistanceDigraph' must have a value ######## ########> Diff in standard/constructors.tst:109 # Input is: gr := DistanceDigraph(digraph, 0); # Expected output: # But found: Error, Variable: 'DistanceDigraph' must have a value ######## ########> Diff in standard/constructors.tst:111 # Input is: OutNeighbours(gr) = List([1 .. 126], x -> [x]); # Expected output: true # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/constructors.tst:115 # Input is: gr := Digraph([[1, 2], [], [2, 3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/constructors.tst:116 # Input is: DigraphGroup(gr) = Group((1, 3)); # Expected output: true # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/constructors.tst:118 # Input is: OutNeighbours(DistanceDigraph(gr, 0)); # Expected output: [ [ 1 ], [ 2 ], [ 3 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/constructors.tst:120 # Input is: OutNeighbours(DistanceDigraph(gr, 1)); # Expected output: [ [ 2 ], [ ], [ 2 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/constructors.tst:122 # Input is: OutNeighbours(DistanceDigraph(gr, 2)); # Expected output: [ [ ], [ ], [ ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/constructors.tst:126 # Input is: gr := Digraph([[1, 2], [2, 3], [4], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/constructors.tst:127 # Input is: DistanceDigraph(gr, -2); # Expected output: Error, the 2nd argument must be a non-negative integer, # But found: Error, Variable: 'DistanceDigraph' must have a value ######## ########> Diff in standard/constructors.tst:131 # Input is: gr := LineUndirectedDigraph(CompleteDigraph(3)); # Expected output: # But found: Error, Variable: 'LineUndirectedDigraph' must have a value ######## ########> Diff in standard/constructors.tst:133 # Input is: gr = CompleteDigraph(3); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/constructors.tst:135 # Input is: gr := LineDigraph(CompleteDigraph(3)); # Expected output: # But found: Error, Variable: 'LineDigraph' must have a value ######## ########> Diff in standard/constructors.tst:137 # Input is: OutNeighbours(gr); # Expected output: [ [ 3, 4 ], [ 5, 6 ], [ 1, 2 ], [ 6, 5 ], [ 2, 1 ], [ 4, 3 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/constructors.tst:139 # Input is: gr := LineUndirectedDigraph(CompleteDigraph(4));; # Expected output: # But found: Error, Variable: 'LineUndirectedDigraph' must have a value ######## ########> Diff in standard/constructors.tst:140 # Input is: OutNeighbours(gr); # Expected output: [ [ 2, 4, 5, 3 ], [ 3, 6, 4, 1 ], [ 5, 1, 2, 6 ], [ 5, 6, 2, 1 ], [ 1, 3, 6, 4 ], [ 2, 3, 5, 4 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/constructors.tst:143 # Input is: gr := Digraph([[2, 4], [1, 3, 4], [2, 4], [1, 2, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/constructors.tst:145 # Input is: gr2 := LineUndirectedDigraph(gr); # Expected output: # But found: Error, Variable: 'LineUndirectedDigraph' must have a value ######## ########> Diff in standard/constructors.tst:147 # Input is: OutNeighbours(gr2); # Expected output: [ [ 2, 3, 4 ], [ 1, 4, 5 ], [ 1, 4, 5 ], [ 1, 2, 3, 5 ], [ 2, 3, 4 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/constructors.tst:149 # Input is: gr := Digraph([[2, 4], [3], [1, 2, 4], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/constructors.tst:151 # Input is: gr2 := LineDigraph(gr); # Expected output: # But found: Error, Variable: 'LineDigraph' must have a value ######## ########> Diff in standard/constructors.tst:153 # Input is: OutNeighbours(gr2); # Expected output: [ [ 3 ], [ 7 ], [ 4, 5, 6 ], [ 1, 2 ], [ 3 ], [ 7 ], [ 4, 5, 6 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/constructors.tst:155 # Input is: gr := CompleteDigraph(6);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/constructors.tst:156 # Input is: gr2 := LineUndirectedDigraph(gr); # Expected output: # But found: Error, Variable: 'LineUndirectedDigraph' must have a value ######## ########> Diff in standard/constructors.tst:158 # Input is: DigraphGroup(gr) = SymmetricGroup(6); # Expected output: true # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/constructors.tst:160 # Input is: gr3 := LineUndirectedDigraph(gr); # Expected output: # But found: Error, Variable: 'LineUndirectedDigraph' must have a value ######## ########> Diff in standard/constructors.tst:162 # Input is: gr2 = gr3; # Expected output: true # But found: Error, Variable: 'gr2' must have a value ######## ########> Diff in standard/constructors.tst:164 # Input is: gr := CycleDigraph(8); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/constructors.tst:166 # Input is: gr2 := LineDigraph(gr); # Expected output: # But found: Error, Variable: 'LineDigraph' must have a value ######## ########> Diff in standard/constructors.tst:168 # Input is: DigraphGroup(gr); # Expected output: Group([ (1,2,3,4,5,6,7,8) ]) # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/constructors.tst:170 # Input is: gr3 := LineDigraph(gr); # Expected output: # But found: Error, Variable: 'LineDigraph' must have a value ######## ########> Diff in standard/constructors.tst:172 # Input is: gr2 = gr3; # Expected output: true # But found: Error, Variable: 'gr2' must have a value ######## ########> Diff in standard/constructors.tst:174 # Input is: gr := ChainDigraph(4); # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/constructors.tst:176 # Input is: LineUndirectedDigraph(gr); # Expected output: Error, the argument must be a symmetric digraph, # But found: Error, Variable: 'LineUndirectedDigraph' must have a value ######## ########> Diff in standard/constructors.tst:180 # Input is: DIGRAPHS_StopTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StopTest' must have a value ######## Digraphs package: standard/constructors.tst msecs: 87 false gap> ########> Diff in standard/display.tst:14 # Input is: DIGRAPHS_StartTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StartTest' must have a value ######## ########> Diff in standard/display.tst:17 # Input is: Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/display.tst:19 # Input is: Digraph([[]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/display.tst:21 # Input is: Digraph([[1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/display.tst:23 # Input is: Digraph([[2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/display.tst:25 # Input is: gr := Digraph([[1, 2], [2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/display.tst:27 # Input is: PrintString(gr); # Expected output: "DigraphFromDigraph6String(\"&Bq?\")" # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/display.tst:29 # Input is: String(gr); # Expected output: "DigraphFromDigraph6String(\"&Bq?\")" # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/display.tst:31 # Input is: gr := Digraph([[2], [1], [], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/display.tst:33 # Input is: PrintString(gr); # Expected output: "DigraphFromDigraph6String(\"&CQ?G\")" # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/display.tst:35 # Input is: String(gr); # Expected output: "DigraphFromDigraph6String(\"&CQ?G\")" # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/display.tst:40 # Input is: gr := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/display.tst:42 # Input is: PrintString(gr); # Expected output: "ChainDigraph(3)" # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/display.tst:44 # Input is: String(gr); # Expected output: "ChainDigraph(3)" # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/display.tst:50 # Input is: gr := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/display.tst:52 # Input is: dot := DotDigraph(gr);; # Expected output: # But found: Error, Variable: 'DotDigraph' must have a value ######## ########> Diff in standard/display.tst:53 # Input is: dot{[1 .. 50]}; # Expected output: "//dot\ndigraph hgn{\nnode [shape=circle]\n1\n2\n3\n1 -> " # But found: Error, Variable: 'dot' must have a value ######## ########> Diff in standard/display.tst:55 # Input is: dot{[51 .. 75]}; # Expected output: "1\n1 -> 2\n1 -> 2\n1 -> 3\n}\n" # But found: Error, Variable: 'dot' must have a value ######## ########> Diff in standard/display.tst:60 # Input is: gr1 := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/display.tst:62 # Input is: DotDigraph(gr1){[50 .. 109]}; # Expected output: "6\n7\n8\n1 -> 6\n1 -> 7\n2 -> 1\n2 -> 6\n3 -> 5\n4 -> 1\n4 -> 4\n4 -> " # But found: Error, Variable: 'DotDigraph' must have a value ######## ########> Diff in standard/display.tst:66 # Input is: gr2 := Digraph(adj); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/display.tst:68 # Input is: DotDigraph(gr2){[11 .. 75]}; # Expected output: "aph hgn{\nnode [shape=circle]\n1\n2\n3\n4\n1 -> 2\n2 -> 1\n2 -> 3\n3 -> 2\n" # But found: Error, Variable: 'DotDigraph' must have a value ######## ########> Diff in standard/display.tst:70 # Input is: DotSymmetricDigraph(gr2){[12 .. 70]}; # Expected output: " hgn{\nnode [shape=circle]\n\n1\n2\n3\n4\n1 -- 2\n2 -- 3\n3 -- 3\n3 -" # But found: Error, Variable: 'DotSymmetricDigraph' must have a value ######## ########> Diff in standard/display.tst:72 # Input is: DotSymmetricDigraph(gr1); # Expected output: Error, the argument must be a symmetric digraph, # But found: Error, Variable: 'DotSymmetricDigraph' must have a value ######## ########> Diff in standard/display.tst:78 # Input is: gr := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/display.tst:80 # Input is: dot := DotVertexLabelledDigraph(gr);; # Expected output: # But found: Error, Variable: 'DotVertexLabelledDigraph' must have a value ######## ########> Diff in standard/display.tst:81 # Input is: dot{[1 .. 50]}; # Expected output: "//dot\ndigraph hgn{\nnode [shape=circle]\n1 [label=\"1" # But found: Error, Variable: 'dot' must have a value ######## ########> Diff in standard/display.tst:83 # Input is: SetDigraphVertexLabel(gr, 1, 2); # Expected output: # But found: Error, Variable: 'SetDigraphVertexLabel' must have a value ######## ########> Diff in standard/display.tst:84 # Input is: dot := DotVertexLabelledDigraph(gr);; # Expected output: # But found: Error, Variable: 'DotVertexLabelledDigraph' must have a value ######## ########> Diff in standard/display.tst:85 # Input is: dot{[1 .. 50]}; # Expected output: "//dot\ndigraph hgn{\nnode [shape=circle]\n1 [label=\"2" # But found: Error, Variable: 'dot' must have a value ######## ########> Diff in standard/display.tst:111 # Input is: gr := Digraph([[1], [1, 2], [1, 3], [1, 4], [1 .. 5], [1 .. 6], [1, 2, 3, 4, 5, 7], [1, 8]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/display.tst:113 # Input is: Print(DotPartialOrderDigraph(gr)); # Expected output: //dot digraph hgn{ node [shape=circle] 1 2 3 4 5 6 7 8 2 -> 1 3 -> 1 4 -> 1 5 -> 2 5 -> 3 5 -> 4 6 -> 5 7 -> 5 8 -> 1 } # But found: Error, Variable: 'DotPartialOrderDigraph' must have a value ######## ########> Diff in standard/display.tst:135 # Input is: gr := Digraph([[1], [2], [1, 3], [2, 4], [1, 2, 3, 4, 5], [1, 2, 3, 6]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/display.tst:136 # Input is: Print(DotPartialOrderDigraph(gr)); # Expected output: //dot digraph hgn{ node [shape=circle] 1 2 3 4 5 6 3 -> 1 4 -> 2 5 -> 3 5 -> 4 6 -> 3 6 -> 2 } # But found: Error, Variable: 'DotPartialOrderDigraph' must have a value ######## ########> Diff in standard/display.tst:153 # Input is: gr := Digraph([[1], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/display.tst:154 # Input is: DotPartialOrderDigraph(gr); # Expected output: Error, the argument must be a partial order digraph, # But found: Error, Variable: 'DotPartialOrderDigraph' must have a value ######## ########> Diff in standard/display.tst:158 # Input is: gr := Digraph([[1], [1, 2], [1, 3], [1, 4], [1 .. 5], [1 .. 6], [1, 2, 3, 4, 5, 7], [1, 8]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/display.tst:160 # Input is: Print(DotPreorderDigraph(gr), "\n"); # Expected output: //dot digraph graphname { node [shape=Mrecord, height=0.5, fixedsize=true]ranksep=1; 1 [label="1", width=0.5] 2 [label="2", width=0.5] 3 [label="3", width=0.5] 4 [label="4", width=0.5] 5 [label="5", width=0.5] 6 [label="6", width=0.5] 7 [label="7", width=0.5] 8 [label="8", width=0.5] 2 -> 1 3 -> 1 4 -> 1 5 -> 2 5 -> 3 5 -> 4 6 -> 5 7 -> 5 8 -> 1 } # But found: Error, Variable: 'DotPreorderDigraph' must have a value ######## ########> Diff in standard/display.tst:184 # Input is: gr := DigraphFromDigraph6String(gr);; # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/display.tst:185 # Input is: Print(DotPreorderDigraph(gr){[1 .. 94]}, "\n"); # Expected output: //dot digraph graphname { node [shape=Mrecord, height=0.5, fixedsize=true]ranksep=1; 1 [label= # But found: Error, Variable: 'DotPreorderDigraph' must have a value ######## ########> Diff in standard/display.tst:190 # Input is: gr := DigraphDisjointUnion(CompleteDigraph(10), CompleteDigraph(5), CycleDigra\ ph(2));; # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/display.tst:191 # Input is: gr := DigraphReflexiveTransitiveClosure(DigraphAddEdge(gr, [10, 11]));; # Expected output: # But found: Error, Variable: 'DigraphReflexiveTransitiveClosure' must have a value ######## ########> Diff in standard/display.tst:192 # Input is: IsPreorderDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsPreorderDigraph' must have a value ######## ########> Diff in standard/display.tst:194 # Input is: Print(DotPreorderDigraph(gr), "\n"); # Expected output: //dot digraph graphname { node [shape=Mrecord, height=0.5, fixedsize=true]ranksep=1; 1 [label="11|12|13|14|15", width=2.5] 2 [label="1|2|3|4|5|6|7|8|9|10", width=5.] 3 [label="16|17", width=1.] 2 -> 1 } # But found: Error, Variable: 'DotPreorderDigraph' must have a value ######## ########> Diff in standard/display.tst:205 # Input is: gr := Digraph([[2, 3], [2], [1, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/display.tst:207 # Input is: Print(DotHighlightedDigraph(gr, [1, 2], "red", "black")); # Expected output: //dot digraph hgn{ subgraph lowverts{ node [shape=circle, color=black] edge [color=black] 3 } subgraph highverts{ node [shape=circle, color=red] edge [color=red] 1 2 } subgraph lowverts{ 3 -> 1 3 -> 3 } subgraph highverts{ 1 -> 2 1 -> 3 [color=black] 2 -> 2 } } # But found: Error, Variable: 'DotHighlightedDigraph' must have a value ######## ########> Diff in standard/display.tst:233 # Input is: Splash(DotDigraph(RandomDigraph(10)), rec(viewer := 1)); # Expected output: Error, the option `viewer` must be a string, not an integer, # But found: Error, Variable: 'Splash' must have a value ######## ########> Diff in standard/display.tst:235 # Input is: Splash(DotDigraph(RandomDigraph(10)), rec(viewer := "asdfasfa")); # Expected output: Error, the viewer "asdfasfa" specified in the option `viewer` is not available\ \ , # But found: Error, Variable: 'Splash' must have a value ######## ########> Diff in standard/display.tst:248 # Input is: DIGRAPHS_StopTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StopTest' must have a value ######## Digraphs package: standard/display.tst msecs: 80 false gap> ########> Diff in standard/examples.tst:14 # Input is: DIGRAPHS_StartTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StartTest' must have a value ######## ########> Diff in standard/examples.tst:17 # Input is: ChromaticNumber(PetersenGraph()); # Expected output: 3 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/examples.tst:19 # Input is: DigraphGirth(PetersenGraph()); # Expected output: 2 # But found: Error, Variable: 'DigraphGirth' must have a value ######## ########> Diff in standard/examples.tst:21 # Input is: PetersenGraph(IsMutableDigraph); # Expected output: # But found: Error, Variable: 'PetersenGraph' must have a value ######## ########> Diff in standard/examples.tst:25 # Input is: D := GeneralisedPetersenGraph(8, 3); # Expected output: # But found: Error, Variable: 'GeneralisedPetersenGraph' must have a value ######## ########> Diff in standard/examples.tst:27 # Input is: IsBipartiteDigraph(D); # Expected output: true # But found: Error, Variable: 'IsBipartiteDigraph' must have a value ######## ########> Diff in standard/examples.tst:29 # Input is: D := GeneralisedPetersenGraph(15, 7); # Expected output: # But found: Error, Variable: 'GeneralisedPetersenGraph' must have a value ######## ########> Diff in standard/examples.tst:31 # Input is: IsBipartiteDigraph(D); # Expected output: false # But found: Error, Variable: 'IsBipartiteDigraph' must have a value ######## ########> Diff in standard/examples.tst:33 # Input is: D := GeneralisedPetersenGraph(10, 2); # Expected output: # But found: Error, Variable: 'GeneralisedPetersenGraph' must have a value ######## ########> Diff in standard/examples.tst:35 # Input is: IsVertexTransitive(D); # Expected output: true # But found: Error, Variable: 'IsVertexTransitive' must have a value ######## ########> Diff in standard/examples.tst:37 # Input is: D := GeneralisedPetersenGraph(11, 2); # Expected output: # But found: Error, Variable: 'GeneralisedPetersenGraph' must have a value ######## ########> Diff in standard/examples.tst:39 # Input is: IsVertexTransitive(D); # Expected output: false # But found: Error, Variable: 'IsVertexTransitive' must have a value ######## ########> Diff in standard/examples.tst:41 # Input is: D := GeneralisedPetersenGraph(5, 2); # Expected output: # But found: Error, Variable: 'GeneralisedPetersenGraph' must have a value ######## ########> Diff in standard/examples.tst:43 # Input is: IsIsomorphicDigraph(D, PetersenGraph()); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/examples.tst:45 # Input is: G8_3 := DigraphFromGraph6String("OCQa`Q?OH?a@A@@?_OGB@"); # Expected output: # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/examples.tst:47 # Input is: D := GeneralisedPetersenGraph(8, 3); # Expected output: # But found: Error, Variable: 'GeneralisedPetersenGraph' must have a value ######## ########> Diff in standard/examples.tst:49 # Input is: IsIsomorphicDigraph(D, G8_3); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/examples.tst:53 # Input is: gr := CompleteDigraph(5); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/examples.tst:55 # Input is: AutomorphismGroup(gr) = SymmetricGroup(5); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/examples.tst:57 # Input is: CompleteDigraph(1) = EmptyDigraph(1); # Expected output: true # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/examples.tst:59 # Input is: CompleteDigraph(0); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/examples.tst:61 # Input is: CompleteDigraph(-1); # Expected output: Error, the argument must be a non-negative integer, # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/examples.tst:63 # Input is: CompleteDigraph(IsMutableDigraph, 10); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/examples.tst:67 # Input is: gr := EmptyDigraph(5); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/examples.tst:69 # Input is: AutomorphismGroup(gr) = SymmetricGroup(5); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/examples.tst:71 # Input is: EmptyDigraph(0); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/examples.tst:73 # Input is: EmptyDigraph(-1); # Expected output: Error, the argument must be a non-negative integer, # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/examples.tst:75 # Input is: EmptyDigraph(IsMutableDigraph, -1); # Expected output: Error, the argument must be a non-negative integer, # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/examples.tst:79 # Input is: gr := CycleDigraph(0); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `CycleDigraph' on 1 arguments # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/examples.tst:82 # Input is: gr := CycleDigraph(1); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/examples.tst:84 # Input is: AutomorphismGroup(gr) = Group(()); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/examples.tst:86 # Input is: gr := CycleDigraph(6);; # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/examples.tst:87 # Input is: AutomorphismGroup(gr) = Group((1, 2, 3, 4, 5, 6)); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/examples.tst:89 # Input is: DigraphEdges(gr); # Expected output: [ [ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 5, 6 ], [ 6, 1 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/examples.tst:91 # Input is: gr := CycleDigraph(1000); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/examples.tst:93 # Input is: gr := CycleDigraph(IsMutableDigraph, 6); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/examples.tst:97 # Input is: gr := ChainDigraph(0); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `ChainDigraph' on 1 arguments # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/examples.tst:100 # Input is: gr := ChainDigraph(1); # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/examples.tst:102 # Input is: IsEmptyDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsEmptyDigraph' must have a value ######## ########> Diff in standard/examples.tst:104 # Input is: gr = EmptyDigraph(1); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/examples.tst:106 # Input is: gr := ChainDigraph(2); # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/examples.tst:108 # Input is: AutomorphismGroup(gr) = Group(()); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/examples.tst:110 # Input is: HasIsTransitiveDigraph(gr); # Expected output: true # But found: Error, Variable: 'HasIsTransitiveDigraph' must have a value ######## ########> Diff in standard/examples.tst:112 # Input is: IsTransitiveDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsTransitiveDigraph' must have a value ######## ########> Diff in standard/examples.tst:114 # Input is: gr := ChainDigraph(10); # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/examples.tst:116 # Input is: OutNeighbours(gr); # Expected output: [ [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8 ], [ 9 ], [ 10 ], [ ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/examples.tst:118 # Input is: AutomorphismGroup(gr) = Group(()); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/examples.tst:120 # Input is: grrt := DigraphReflexiveTransitiveClosure(gr); # Expected output: # But found: Error, Variable: 'DigraphReflexiveTransitiveClosure' must have a value ######## ########> Diff in standard/examples.tst:122 # Input is: IsPartialOrderBinaryRelation(AsBinaryRelation(grrt)); # Expected output: true # But found: Error, Variable: 'grrt' must have a value ######## ########> Diff in standard/examples.tst:124 # Input is: IsAntisymmetricDigraph(grrt); # Expected output: true # But found: Error, Variable: 'IsAntisymmetricDigraph' must have a value ######## ########> Diff in standard/examples.tst:126 # Input is: grrt; # Expected output: # But found: Error, Variable: 'grrt' must have a value ######## ########> Diff in standard/examples.tst:128 # Input is: ChainDigraph(IsMutableDigraph, 10); # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/examples.tst:132 # Input is: gr := CompleteBipartiteDigraph(2, 0); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `CompleteBipartiteDigraph' on 2 argument\ \ s # But found: Error, Variable: 'CompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/examples.tst:136 # Input is: gr := CompleteBipartiteDigraph(0, 2); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `CompleteBipartiteDigraph' on 2 argument\ \ s # But found: Error, Variable: 'CompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/examples.tst:140 # Input is: gr := CompleteBipartiteDigraph(4, 3); # Expected output: # But found: Error, Variable: 'CompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/examples.tst:142 # Input is: AutomorphismGroup(gr) = Group((1, 2, 3, 4), (1, 2), (5, 6, 7), (5, 6)); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/examples.tst:144 # Input is: DigraphEdges(gr); # Expected output: [ [ 1, 5 ], [ 1, 6 ], [ 1, 7 ], [ 2, 5 ], [ 2, 6 ], [ 2, 7 ], [ 3, 5 ], [ 3, 6 ], [ 3, 7 ], [ 4, 5 ], [ 4, 6 ], [ 4, 7 ], [ 5, 1 ], [ 5, 2 ], [ 5, 3 ], [ 5, 4 ], [ 6, 1 ], [ 6, 2 ], [ 6, 3 ], [ 6, 4 ], [ 7, 1 ], [ 7, 2 ], [ 7, 3 ], [ 7, 4 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/examples.tst:149 # Input is: gr := CompleteBipartiteDigraph(4, 4); # Expected output: # But found: Error, Variable: 'CompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/examples.tst:151 # Input is: AutomorphismGroup(gr) = Group((1, 2, 3, 4), (1, 2), (5, 6, 7, 8), (5, 6), (1, 5)(2, 6)(3, 7)(4, 8)); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/examples.tst:156 # Input is: CompleteMultipartiteDigraph([5, 4, 2]); # Expected output: # But found: Error, Variable: 'CompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/examples.tst:158 # Input is: CompleteMultipartiteDigraph([5, 4, 2, 10, 1000]); # Expected output: # But found: Error, Variable: 'CompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/examples.tst:160 # Input is: CompleteMultipartiteDigraph([5]); # Expected output: # But found: Error, Variable: 'CompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/examples.tst:162 # Input is: CompleteMultipartiteDigraph([]); # Expected output: # But found: Error, Variable: 'CompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/examples.tst:164 # Input is: CompleteMultipartiteDigraph([5, 4, 2, 10, -5]); # Expected output: Error, the argument must be a list of positive integers, # But found: Error, Variable: 'CompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/examples.tst:166 # Input is: CompleteMultipartiteDigraph([5, 0, 2]); # Expected output: Error, the argument must be a list of positive integers, # But found: Error, Variable: 'CompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/examples.tst:168 # Input is: DigraphEdges(CompleteMultipartiteDigraph([3, 2])); # Expected output: [ [ 1, 4 ], [ 1, 5 ], [ 2, 4 ], [ 2, 5 ], [ 3, 4 ], [ 3, 5 ], [ 4, 1 ], [ 4, 2 ], [ 4, 3 ], [ 5, 1 ], [ 5, 2 ], [ 5, 3 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/examples.tst:171 # Input is: DigraphVertices(CompleteMultipartiteDigraph([2, 1, 2])); # Expected output: [ 1 .. 5 ] # But found: Error, Variable: 'DigraphVertices' must have a value ######## ########> Diff in standard/examples.tst:173 # Input is: DigraphEdges(CompleteMultipartiteDigraph([7, 8, 2])); # Expected output: [ [ 1, 8 ], [ 1, 9 ], [ 1, 10 ], [ 1, 11 ], [ 1, 12 ], [ 1, 13 ], [ 1, 14 ], [ 1, 15 ], [ 1, 16 ], [ 1, 17 ], [ 2, 8 ], [ 2, 9 ], [ 2, 10 ], [ 2, 11 ], [ 2, 12 ], [ 2, 13 ], [ 2, 14 ], [ 2, 15 ], [ 2, 16 ], [ 2, 17 ], [ 3, 8 ], [ 3, 9 ], [ 3, 10 ], [ 3, 11 ], [ 3, 12 ], [ 3, 13 ], [ 3, 14 ], [ 3, 15 ], [ 3, 16 ], [ 3, 17 ], [ 4, 8 ], [ 4, 9 ], [ 4, 10 ], [ 4, 11 ], [ 4, 12 ], [ 4, 13 ], [ 4, 14 ], [ 4, 15 ], [ 4, 16 ], [ 4, 17 ], [ 5, 8 ], [ 5, 9 ], [ 5, 10 ], [ 5, 11 ], [ 5, 12 ], [ 5, 13 ], [ 5, 14 ], [ 5, 15 ], [ 5, 16 ], [ 5, 17 ], [ 6, 8 ], [ 6, 9 ], [ 6, 10 ], [ 6, 11 ], [ 6, 12 ], [ 6, 13 ], [ 6, 14 ], [ 6, 15 ], [ 6, 16 ], [ 6, 17 ], [ 7, 8 ], [ 7, 9 ], [ 7, 10 ], [ 7, 11 ], [ 7, 12 ], [ 7, 13 ], [ 7, 14 ], [ 7, 15 ], [ 7, 16 ], [ 7, 17 ], [ 8, 1 ], [ 8, 2 ], [ 8, 3 ], [ 8, 4 ], [ 8, 5 ], [ 8, 6 ], [ 8, 7 ], [ 8, 16 ], [ 8, 17 ], [ 9, 1 ], [ 9, 2 ], [ 9, 3 ], [ 9, 4 ], [ 9, 5 ], [ 9, 6 ], [ 9, 7 ], [ 9, 16 ], [ 9, 17 ], [ 10, 1 ], [ 10, 2 ], [ 10, 3 ], [ 10, 4 ], [ 10, 5 ], [ 10, 6 ], [ 10, 7 ], [ 10, 16 ], [ 10, 17 ], [ 11, 1 ], [ 11, 2 ], [ 11, 3 ], [ 11, 4 ], [ 11, 5 ], [ 11, 6 ], [ 11, 7 ], [ 11, 16 ], [ 11, 17 ], [ 12, 1 ], [ 12, 2 ], [ 12, 3 ], [ 12, 4 ], [ 12, 5 ], [ 12, 6 ], [ 12, 7 ], [ 12, 16 ], [ 12, 17 ], [ 13, 1 ], [ 13, 2 ], [ 13, 3 ], [ 13, 4 ], [ 13, 5 ], [ 13, 6 ], [ 13, 7 ], [ 13, 16 ], [ 13, 17 ], [ 14, 1 ], [ 14, 2 ], [ 14, 3 ], [ 14, 4 ], [ 14, 5 ], [ 14, 6 ], [ 14, 7 ], [ 14, 16 ], [ 14, 17 ], [ 15, 1 ], [ 15, 2 ], [ 15, 3 ], [ 15, 4 ], [ 15, 5 ], [ 15, 6 ], [ 15, 7 ], [ 15, 16 ], [ 15, 17 ], [ 16, 1 ], [ 16, 2 ], [ 16, 3 ], [ 16, 4 ], [ 16, 5 ], [ 16, 6 ], [ 16, 7 ], [ 16, 8 ], [ 16, 9 ], [ 16, 10 ], [ 16, 11 ], [ 16, 12 ], [ 16, 13 ], [ 16, 14 ], [ 16, 15 ], [ 17, 1 ], [ 17, 2 ], [ 17, 3 ], [ 17, 4 ], [ 17, 5 ], [ 17, 6 ], [ 17, 7 ], [ 17, 8 ], [ 17, 9 ], [ 17, 10 ], [ 17, 11 ], [ 17, 12 ], [ 17, 13 ], [ 17, 14 ], [ 17, 15 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/examples.tst:203 # Input is: JohnsonDigraph(0, 4); # Expected output: # But found: Error, Variable: 'JohnsonDigraph' must have a value ######## ########> Diff in standard/examples.tst:205 # Input is: JohnsonDigraph(0, 0); # Expected output: # But found: Error, Variable: 'JohnsonDigraph' must have a value ######## ########> Diff in standard/examples.tst:207 # Input is: JohnsonDigraph(3, 0); # Expected output: # But found: Error, Variable: 'JohnsonDigraph' must have a value ######## ########> Diff in standard/examples.tst:209 # Input is: JohnsonDigraph(1, 0); # Expected output: # But found: Error, Variable: 'JohnsonDigraph' must have a value ######## ########> Diff in standard/examples.tst:211 # Input is: gr := JohnsonDigraph(3, 1); # Expected output: # But found: Error, Variable: 'JohnsonDigraph' must have a value ######## ########> Diff in standard/examples.tst:213 # Input is: OutNeighbours(gr); # Expected output: [ [ 2, 3 ], [ 1, 3 ], [ 1, 2 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/examples.tst:215 # Input is: gr := JohnsonDigraph(4, 2); # Expected output: # But found: Error, Variable: 'JohnsonDigraph' must have a value ######## ########> Diff in standard/examples.tst:217 # Input is: OutNeighbours(gr); # Expected output: [ [ 2, 3, 4, 5 ], [ 1, 3, 4, 6 ], [ 1, 2, 5, 6 ], [ 1, 2, 5, 6 ], [ 1, 3, 4, 6 ], [ 2, 3, 4, 5 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/examples.tst:220 # Input is: JohnsonDigraph(5, 1) = CompleteDigraph(5); # Expected output: true # But found: Error, Variable: 'JohnsonDigraph' must have a value ######## ########> Diff in standard/examples.tst:222 # Input is: JohnsonDigraph(3, -2); # Expected output: Error, the arguments and must be non-negative integers, # But found: Error, Variable: 'JohnsonDigraph' must have a value ######## ########> Diff in standard/examples.tst:224 # Input is: JohnsonDigraph(-1, 2); # Expected output: Error, the arguments and must be non-negative integers, # But found: Error, Variable: 'JohnsonDigraph' must have a value ######## ########> Diff in standard/examples.tst:226 # Input is: JohnsonDigraph(IsMutableDigraph, 4, 2); # Expected output: # But found: Error, Variable: 'JohnsonDigraph' must have a value ######## ########> Diff in standard/examples.tst:230 # Input is: DIGRAPHS_StopTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StopTest' must have a value ######## Digraphs package: standard/examples.tst msecs: 102 false gap> ########> Diff in standard/grahom.tst:14 # Input is: DIGRAPHS_StartTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StartTest' must have a value ######## ########> Diff in standard/grahom.tst:17 # Input is: HomomorphismDigraphsFinder(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0); # Expected output: Error, the 1st argument must be a digraph, not integer, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:19 # Input is: gr1 := ChainDigraph(2);; # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/grahom.tst:20 # Input is: gr2 := CompleteDigraph(3);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/grahom.tst:21 # Input is: HomomorphismDigraphsFinder(0, gr2, 0, 0, 0, 0, 0, 0, 0, 0, 0); # Expected output: Error, the 1st argument must be a digraph, not integer, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:23 # Input is: HomomorphismDigraphsFinder(gr1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0); # Expected output: Error, the 2nd argument must be a digraph, not integer, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:25 # Input is: HomomorphismDigraphsFinder(gr1, gr2, 0, 0, 0, 0, 0, 0, 0, 0, 0); # Expected output: Error, the 3rd argument must be a function with 2 arguments, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:27 # Input is: HomomorphismDigraphsFinder(gr2, gr1, 0, 0, 0, 0, 0, 0, 0, 0, 0); # Expected output: Error, the 3rd argument must be a function with 2 arguments, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:29 # Input is: gr1 := CompleteDigraph(2);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/grahom.tst:30 # Input is: HomomorphismDigraphsFinder(gr1, gr2, 0, 0, 0, 0, 0, 0, 0, 0, 0); # Expected output: Error, the 3rd argument must be a function with 2 arguments, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:32 # Input is: HomomorphismDigraphsFinder(gr1, gr2, IsTournament, 0, 0, 0, 0, 0, 0, 0, 0); # Expected output: Error, the 3rd argument must be a function with 2 arguments, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:34 # Input is: HomomorphismDigraphsFinder(gr1, gr2, fail, 0, 0, 0, 0, 0, 0, 0, 0); # Expected output: Error, the 3rd argument is fail and so the 4th argument must be a mutab\ \ le list, not integer, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:37 # Input is: HomomorphismDigraphsFinder(gr1, gr2, fail, "a", "a", 0, 0, 0, 0, 0, 0); # Expected output: Error, the 5th argument must be an integer or infinity, not list\ \ (string), # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:40 # Input is: HomomorphismDigraphsFinder(gr1, gr2, fail, "a", 1, 0, 0, 0, 0, 0, 0); # Expected output: Error, the 6th argument must be a positive integer, not 0, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:42 # Input is: HomomorphismDigraphsFinder(gr1, gr2, fail, "a", 5, 1, "b", 0, 0, 0, 0); # Expected output: Error, the 7th argument must be an integer or true or false, not l\ \ ist (string), # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:45 # Input is: HomomorphismDigraphsFinder(gr1, gr2, fail, "a", infinity, fail, -1, 0, 0, 0, 0); # Expected output: Error, the 7th argument must 0, 1, or 2, not -1, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:48 # Input is: HomomorphismDigraphsFinder(gr1, gr2, fail, "a", infinity, 2, 1, 0, 0, 0, 0); # Expected output: Error, the 8th argument must be a list or fail, not integer, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:61 # Input is: HomomorphismDigraphsFinder(gr1, gr2, fail, [], 1, 1, 1, [0, 1], 0, 0, 0); # Expected output: Error, the 8th argument must only contain positive integers, but found\ \ integer in position 1, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:65 # Input is: HomomorphismDigraphsFinder(gr1, gr2, fail, [], 1, 1, 1, [4, 4], 0, 0, 0); # Expected output: Error, in the 8th argument position 1 is out of range, must be in the \ \ range [1, 3], # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:69 # Input is: HomomorphismDigraphsFinder(gr2, gr1, fail, [], 1, 1, 1, [3], 0, 0, 0); # Expected output: Error, in the 8th argument position 1 is out of range, must be in the \ \ range [1, 2], # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:72 # Input is: HomomorphismDigraphsFinder(gr1, gr2, fail, [], 1, 1, 1, [3], 0, 0, 0); # Expected output: Error, the 9th argument must be a list or fail, not integer, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:74 # Input is: HomomorphismDigraphsFinder(gr1, gr2, fail, [], 1, 1, 1, [3], [1 .. 4], 0, 0); # Expected output: Error, the 9th argument is too long, must be at most 2, found 4, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:77 # Input is: HomomorphismDigraphsFinder(gr1, gr2, fail, [], 1, 1, 1, [], [1, 2, 3, 2], 0, 0); # Expected output: Error, the 9th argument is too long, must be at most 2, found 4, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:80 # Input is: HomomorphismDigraphsFinder(gr1, gr2, fail, [], 1, 1, 1, [1], [1], fail, fail); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:83 # Input is: HomomorphismDigraphsFinder(CompleteDigraph(2), CompleteDigraph(3), fail, # hook [], # user_param 1, # limit 2, # hint (rank 2) 1, # injective (yes) [1, 2], # only values 1 and 2 in the image [1], # 1 -> 1 fail, # no colours fail); # no colours # Expected output: [ IdentityTransformation ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:95 # Input is: HomomorphismDigraphsFinder(gr1, gr2, fail, [], 1, 3, 0, [1, 2], [1], fail, fail); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:98 # Input is: HomomorphismDigraphsFinder(gr2, gr1, fail, [], 1, 3, 0, [1, 2], [1], fail, fail); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:101 # Input is: HomomorphismDigraphsFinder(gr1, gr2, fail, [], 1, 1, 0, [], [], fail, fail); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:104 # Input is: HomomorphismDigraphsFinder(gr1, gr2, fail, [], 1, 1, 0, [1, 2], [], fail, fail); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:107 # Input is: HomomorphismDigraphsFinder(gr1, gr2, fail, [], 1, 1, 0, [1, 2], [], fail, fail); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:110 # Input is: HomomorphismDigraphsFinder(gr1, gr2, fail, [], 1, 2, 0, [1], [], fail, fail); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:113 # Input is: HomomorphismDigraphsFinder(gr1, gr1, fail, [], 1, 2, 0, [1, 2], [], fail, fail); # Expected output: [ IdentityTransformation ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:116 # Input is: HomomorphismDigraphsFinder(gr1, gr1, fail, [], 1, 2, 0, [1, 2], [], [[1, 2]], fail); # Expected output: Error, the 10th and 11th arguments and must both be lists \ \ or both be fail, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:120 # Input is: HomomorphismDigraphsFinder(gr1, gr1, fail, [], 1, 2, 0, [1, 2], [], fail, [[1, 2]]); # Expected output: Error, the 10th and 11th arguments and must both be lists \ \ or both be fail, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:124 # Input is: HomomorphismDigraphsFinder(gr1, gr1, fail, [], 1, 2, 0, [1, 2], [], [[1, 2]], [[1, 2]]); # Expected output: [ IdentityTransformation ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:127 # Input is: HomomorphismDigraphsFinder(gr1, gr1, fail, [], 1, 2, 0, [1, 2], [], [[1, 2], [2]], [[1, 2]]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 2], since it contains the vertex 2 more than once, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:131 # Input is: gr := CompleteDigraph(513);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/grahom.tst:132 # Input is: HomomorphismDigraphsFinder(gr, gr, fail, [], 1, fail, 0, [1 .. 513], [], fail, fail); # Expected output: Error, the 1st argument must have at most 512 vertices, found 513, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:135 # Input is: HomomorphismDigraphsFinder(gr1, gr1, fail, [], 1, 2, 0, [1, 2], [], [1, 2], [2, 1]); # Expected output: [ Transformation( [ 2, 1 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:138 # Input is: HomomorphismDigraphsFinder(gr1, gr1, fail, [], 1, 2, 0, [1, 2], [], [1, 2, 3], [2, 1]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 2 ]. The 2nd argument must have one of the following forms: 1. a list of length\ 2 consisting of every integer in the range [1 .. m], for some m <= 2; or 2. a list of non-empty disjoint lists whose union is [1 .. 2]. # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:146 # Input is: HomomorphismDigraphsFinder(gr1, gr1, fail, [], 1, 2, 0, [1, 2], [], [1, 3], [2, 1]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 2], since it contains the integer 3, which is greater than 2, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:150 # Input is: HomomorphismDigraphsFinder(gr1, gr1, fail, [], 1, 2, 0, [1, 2], [], [1, fail], [2, 1]); # Expected output: Error, the 2nd argument must be a homogeneous list, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:153 # Input is: gr := ChainDigraph(2); # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/grahom.tst:155 # Input is: GeneratorsOfEndomorphismMonoid(); # Expected output: Error, at least 1 argument expected, found 0, # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:157 # Input is: GeneratorsOfEndomorphismMonoid(Group(())); # Expected output: Error, the 1st argument must be a digraph, # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:159 # Input is: GeneratorsOfEndomorphismMonoid(gr); # Expected output: [ IdentityTransformation ] # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:161 # Input is: gr := DigraphTransitiveClosure(CompleteDigraph(2)); # Expected output: # But found: Error, Variable: 'DigraphTransitiveClosure' must have a value ######## ########> Diff in standard/grahom.tst:163 # Input is: DigraphHasLoops(gr); # Expected output: true # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/grahom.tst:165 # Input is: GeneratorsOfEndomorphismMonoid(gr); # Expected output: [ Transformation( [ 2, 1 ] ), IdentityTransformation, Transformation( [ 1, 1 ] ) ] # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:168 # Input is: gr := EmptyDigraph(2); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/grahom.tst:170 # Input is: GeneratorsOfEndomorphismMonoid(gr, Group(()), Group((1, 2))); # Expected output: Error, the 2nd argument must be a homogenous list, # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:172 # Input is: gr := EmptyDigraph(2);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/grahom.tst:173 # Input is: GeneratorsOfEndomorphismMonoid(gr, Group(())); # Expected output: Error, the 2nd argument must be a homogenous list, # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:175 # Input is: gr := EmptyDigraph(2);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/grahom.tst:176 # Input is: GeneratorsOfEndomorphismMonoid(gr, 1); # Expected output: [ Transformation( [ 2, 1 ] ) ] # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:178 # Input is: gr := EmptyDigraph(2);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/grahom.tst:179 # Input is: GeneratorsOfEndomorphismMonoid(gr, 2); # Expected output: [ Transformation( [ 2, 1 ] ), IdentityTransformation ] # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:181 # Input is: gr := EmptyDigraph(2);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/grahom.tst:182 # Input is: GeneratorsOfEndomorphismMonoidAttr(gr);; # Expected output: # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoidAttr' must have a value ######## ########> Diff in standard/grahom.tst:183 # Input is: GeneratorsOfEndomorphismMonoid(gr, 4) = last; # Expected output: true # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:185 # Input is: gens := GeneratorsOfEndomorphismMonoid(gr, 3); # Expected output: [ Transformation( [ 2, 1 ] ), IdentityTransformation, Transformation( [ 1, 1 ] ) ] # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:188 # Input is: IsFullTransformationSemigroup(Semigroup(gens)); # Expected output: true # But found: Error, Variable: 'gens' must have a value ######## ########> Diff in standard/grahom.tst:190 # Input is: Size(Semigroup(gens)); # Expected output: 4 # But found: Error, Variable: 'gens' must have a value ######## ########> Diff in standard/grahom.tst:192 # Input is: gr := CompleteDigraph(5);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/grahom.tst:193 # Input is: GeneratorsOfEndomorphismMonoid(gr, [1, 2, 3, 4, 5]); # Expected output: [ IdentityTransformation ] # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:195 # Input is: GeneratorsOfEndomorphismMonoid(gr); # Expected output: [ Transformation( [ 2, 3, 4, 5, 1 ] ), Transformation( [ 2, 1 ] ), IdentityTransformation ] # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:198 # Input is: GeneratorsOfEndomorphismMonoid(gr, [1, 1, 1, 2, 2]); # Expected output: [ Transformation( [ 1, 2, 3, 5, 4 ] ), Transformation( [ 1, 3, 2 ] ), Transformation( [ 2, 1 ] ), IdentityTransformation ] # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:201 # Input is: GeneratorsOfEndomorphismMonoid(gr, [1, 1, 1, 2, 2], 1); # Expected output: [ Transformation( [ 1, 2, 3, 5, 4 ] ), Transformation( [ 1, 3, 2 ] ), Transformation( [ 2, 1 ] ) ] # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:204 # Input is: GeneratorsOfEndomorphismMonoid(gr, [1, 1, 1, 2, 2], 0); # Expected output: Error, the 3rd argument must be a positive integer or infinity, # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:210 # Input is: gr := Digraph([[], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:212 # Input is: GeneratorsOfEndomorphismMonoid(gr); # Expected output: [ IdentityTransformation, Transformation( [ 2, 2 ] ) ] # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:216 # Input is: gr := Digraph([[2], [], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:218 # Input is: GeneratorsOfEndomorphismMonoid(gr); # Expected output: [ IdentityTransformation, Transformation( [ 3, 3, 3 ] ) ] # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:222 # Input is: gr := Digraph([[2], [1], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:224 # Input is: GeneratorsOfEndomorphismMonoid(gr); # Expected output: [ Transformation( [ 2, 1 ] ), IdentityTransformation, Transformation( [ 3, 3, 3 ] ) ] # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:229 # Input is: gr := Digraph([[2, 2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:231 # Input is: DigraphColouring(gr, 1); # Expected output: fail # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:233 # Input is: gr := EmptyDigraph(3); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/grahom.tst:235 # Input is: DigraphColouring(gr, 4); # Expected output: fail # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:237 # Input is: DigraphColouring(gr, 3); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:239 # Input is: DigraphColouring(gr, 2); # Expected output: Transformation( [ 1, 1, 2 ] ) # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:241 # Input is: DigraphColouring(gr, 1); # Expected output: Transformation( [ 1, 1, 1 ] ) # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:243 # Input is: gr := CompleteDigraph(3); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/grahom.tst:245 # Input is: DigraphColouring(gr, 1); # Expected output: fail # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:247 # Input is: DigraphColouring(gr, 2); # Expected output: fail # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:249 # Input is: DigraphColouring(gr, 3); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:251 # Input is: gr := EmptyDigraph(0); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/grahom.tst:253 # Input is: DigraphColouring(gr, 1); # Expected output: fail # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:255 # Input is: DigraphColouring(gr, 2); # Expected output: fail # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:257 # Input is: DigraphColouring(gr, 3); # Expected output: fail # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:259 # Input is: gr := EmptyDigraph(1); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/grahom.tst:261 # Input is: DigraphColouring(gr, 1); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:263 # Input is: DigraphColouring(gr, 2); # Expected output: fail # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:265 # Input is: gr := Digraph([[1, 2], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:266 # Input is: DigraphColouring(gr, -1); # Expected output: Error, the 2nd argument must be a non-negative integer, # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:268 # Input is: DigraphColouring(NullDigraph(0), 1); # Expected output: fail # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:270 # Input is: DigraphColouring(NullDigraph(0), 0); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:272 # Input is: DigraphColouring(CompleteDigraph(1), 0); # Expected output: fail # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:274 # Input is: DigraphColouring(Digraph([[1]]), 1); # Expected output: fail # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:276 # Input is: gr := DigraphFromDigraph6String(Concatenation( "+l??O?C?A_@???CE????GAAG?C??M?????@_?OO??G??@?IC???_C?G?o??C?AO???c_??A?", "A?S???OAA???OG???G_A??C?@?cC????_@G???S??C_?C???[??A?A?OA?O?@?A?@A???GGO", "??`?_O??G?@?A??G?@AH????AA?O@??_??b???Cg??C???_??W?G????d?G?C@A?C???GC?W", "?????K???__O[??????O?W???O@??_G?@?CG??G?@G?C??@G???_Q?O?O?c???OAO?C??C?G", "?O??A@??D??G?C_?A??O?_GA??@@?_?G???E?IW??????_@G?C??")); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/grahom.tst:283 # Input is: DigraphGreedyColouring(gr); # Expected output: Transformation( [ 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 3, 3, 2, 3, 3, 3, 2, 1, 4, 4, 2, 3, 3, 3, 3, 3, 1, 3, 4, 4, 3, 2, 1, 4, 3, 1 ] ) # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:287 # Input is: DigraphColouring(gr, 4); # Expected output: Transformation( [ 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 3, 3, 2, 3, 3, 3, 2, 1, 4, 4, 2, 3, 3, 3, 3, 3, 1, 3, 4, 4, 3, 2, 1, 4, 3, 1 ] ) # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:291 # Input is: D := Digraph([[4, 6, 8], [], [], [], [7], [2], [], [], [8], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:293 # Input is: DigraphColouring(D, 2); # Expected output: Transformation( [ 1, 1, 1, 2, 1, 2, 2, 2, 1, 1 ] ) # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:295 # Input is: DigraphColouring(Digraph([[1], []]), 2); # Expected output: fail # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:299 # Input is: DigraphGreedyColouring(EmptyDigraph(0)); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:301 # Input is: DigraphGreedyColouring(Digraph([[]])); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:303 # Input is: DigraphGreedyColouring(Digraph([[1]])); # Expected output: fail # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:305 # Input is: DigraphGreedyColouring(CycleDigraph(2)); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:307 # Input is: DigraphGreedyColouring(CycleDigraph(3)); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:309 # Input is: DigraphGreedyColouring(CycleDigraph(4)); # Expected output: Transformation( [ 1, 2, 1, 2 ] ) # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:311 # Input is: DigraphGreedyColouring(CycleDigraph(5)); # Expected output: Transformation( [ 1, 2, 1, 2, 3 ] ) # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:313 # Input is: DigraphGreedyColouring(CycleDigraph(6)); # Expected output: Transformation( [ 1, 2, 1, 2, 1, 2 ] ) # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:315 # Input is: DigraphGreedyColouring(CompleteDigraph(10)); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:317 # Input is: gr := CompleteDigraph(4);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/grahom.tst:318 # Input is: HasDigraphGreedyColouring(gr); # Expected output: false # But found: Error, Variable: 'HasDigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:320 # Input is: DigraphGreedyColouring(gr); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:322 # Input is: HasDigraphGreedyColouring(gr); # Expected output: true # But found: Error, Variable: 'HasDigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:324 # Input is: gr := CycleDigraph(4);; # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/grahom.tst:325 # Input is: HasDigraphGreedyColouring(gr); # Expected output: false # But found: Error, Variable: 'HasDigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:327 # Input is: DigraphGreedyColouring(gr); # Expected output: Transformation( [ 1, 2, 1, 2 ] ) # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:329 # Input is: HasDigraphGreedyColouring(gr); # Expected output: true # But found: Error, Variable: 'HasDigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:331 # Input is: DigraphGreedyColouring(ChainDigraph(10));; # Expected output: # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:332 # Input is: DigraphGreedyColouring(CompleteDigraph(10));; # Expected output: # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:333 # Input is: gr := DigraphFromSparse6String( ":]nA?LcB@_EDfEB`GIaHGdJIgEKcLK`?MdCHiFLaBJhFMkJM"); # Expected output: # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/grahom.tst:336 # Input is: DigraphGreedyColouring(gr);; # Expected output: # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:337 # Input is: DigraphGreedyColouring(EmptyDigraph(0)); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:339 # Input is: DigraphGreedyColouring(gr, [1 .. 10]); # Expected output: Error, the 2nd argument must be a permutation of [1 .. 30] # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:341 # Input is: DigraphGreedyColouring(gr, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, -1]); # Expected output: Error, the 2nd argument must be a permutation of [1 .. 30] # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:344 # Input is: DigraphGreedyColouring(gr, [1 .. 30]); # Expected output: Transformation( [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ] ) # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:347 # Input is: D := Digraph([[3, 4, 6, 8], [4, 6, 7, 8, 10], [2, 6, 7, 8, 9], [3, 5, 7], [1, 2, 3, 6, 9], [2, 6, 8, 10], [7], [1, 10], [2, 7, 8], [1, 2, 6, 8, 10]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:349 # Input is: DigraphHasLoops(D); # Expected output: true # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/grahom.tst:351 # Input is: DigraphGreedyColouring(D); # Expected output: fail # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:353 # Input is: DigraphColouring(D, 3); # Expected output: fail # But found: Error, Variable: 'DigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:355 # Input is: D := Digraph([[3], [], [2]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:356 # Input is: DigraphGreedyColouring(D, [1 .. 3]); # Expected output: Transformation( [ 1, 1, 2 ] ) # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:360 # Input is: DigraphGreedyColouring(EmptyDigraph(0), DigraphWelshPowellOrder); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:362 # Input is: DigraphGreedyColouring(Digraph([[]]), DigraphWelshPowellOrder); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:364 # Input is: DigraphGreedyColouring(Digraph([[1]]), DigraphWelshPowellOrder); # Expected output: fail # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:366 # Input is: DigraphGreedyColouring(CycleDigraph(2), DigraphWelshPowellOrder); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:368 # Input is: DigraphGreedyColouring(CycleDigraph(3), DigraphWelshPowellOrder); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:370 # Input is: DigraphGreedyColouring(CycleDigraph(4), DigraphWelshPowellOrder); # Expected output: Transformation( [ 1, 2, 1, 2 ] ) # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:372 # Input is: DigraphGreedyColouring(CycleDigraph(5), DigraphWelshPowellOrder); # Expected output: Transformation( [ 1, 2, 1, 2, 3 ] ) # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:374 # Input is: DigraphGreedyColouring(CycleDigraph(6), DigraphWelshPowellOrder); # Expected output: Transformation( [ 1, 2, 1, 2, 1, 2 ] ) # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:376 # Input is: DigraphGreedyColouring(CompleteDigraph(10), DigraphWelshPowellOrder); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:378 # Input is: gr := CompleteDigraph(4);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/grahom.tst:379 # Input is: HasDigraphGreedyColouring(gr); # Expected output: false # But found: Error, Variable: 'HasDigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:381 # Input is: DigraphGreedyColouring(gr, DigraphWelshPowellOrder); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:383 # Input is: HasDigraphGreedyColouring(gr); # Expected output: false # But found: Error, Variable: 'HasDigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:385 # Input is: gr := CycleDigraph(4);; # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/grahom.tst:386 # Input is: HasDigraphGreedyColouring(gr); # Expected output: false # But found: Error, Variable: 'HasDigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:388 # Input is: DigraphGreedyColouring(gr, DigraphWelshPowellOrder); # Expected output: Transformation( [ 1, 2, 1, 2 ] ) # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:390 # Input is: HasDigraphGreedyColouring(gr); # Expected output: false # But found: Error, Variable: 'HasDigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:392 # Input is: DigraphGreedyColouring(ChainDigraph(10), DigraphWelshPowellOrder); # Expected output: Transformation( [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1 ] ) # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:394 # Input is: DigraphGreedyColouring(CompleteDigraph(10), DigraphWelshPowellOrder); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:396 # Input is: gr := DigraphFromSparse6String( ":]nA?LcB@_EDfEB`GIaHGdJIgEKcLK`?MdCHiFLaBJhFMkJM"); # Expected output: # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/grahom.tst:399 # Input is: DigraphGreedyColouring(gr, DigraphWelshPowellOrder); # Expected output: Transformation( [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ] ) # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:402 # Input is: DigraphGreedyColouring(EmptyDigraph(0)); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:406 # Input is: order_func := D -> [1 .. DigraphNrVertices(D)];; # Expected output: # But found: Syntax warning: Unbound global variable in stream:1 order_func := D -> [1 .. DigraphNrVertices(D)];; ^^^^^^^^^^^^^^^^^ ######## ########> Diff in standard/grahom.tst:407 # Input is: DigraphGreedyColouring(EmptyDigraph(0), order_func); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:409 # Input is: DigraphGreedyColouring(Digraph([[]]), order_func); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:411 # Input is: DigraphGreedyColouring(Digraph([[1]]), order_func); # Expected output: fail # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:413 # Input is: DigraphGreedyColouring(CycleDigraph(2), order_func); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:415 # Input is: DigraphGreedyColouring(CycleDigraph(3), order_func); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:417 # Input is: DigraphGreedyColouring(CycleDigraph(4), order_func); # Expected output: Transformation( [ 1, 2, 1, 2 ] ) # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:419 # Input is: DigraphGreedyColouring(CycleDigraph(5), order_func); # Expected output: Transformation( [ 1, 2, 1, 2, 3 ] ) # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:421 # Input is: DigraphGreedyColouring(CycleDigraph(6), order_func); # Expected output: Transformation( [ 1, 2, 1, 2, 1, 2 ] ) # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:423 # Input is: DigraphGreedyColouring(CompleteDigraph(10), order_func); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:425 # Input is: gr := CompleteDigraph(4);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/grahom.tst:426 # Input is: HasDigraphGreedyColouring(gr); # Expected output: false # But found: Error, Variable: 'HasDigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:428 # Input is: DigraphGreedyColouring(gr, order_func); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:430 # Input is: HasDigraphGreedyColouring(gr); # Expected output: false # But found: Error, Variable: 'HasDigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:432 # Input is: gr := CycleDigraph(4);; # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/grahom.tst:433 # Input is: HasDigraphGreedyColouring(gr); # Expected output: false # But found: Error, Variable: 'HasDigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:435 # Input is: DigraphGreedyColouring(gr, order_func); # Expected output: Transformation( [ 1, 2, 1, 2 ] ) # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:437 # Input is: HasDigraphGreedyColouring(gr); # Expected output: false # But found: Error, Variable: 'HasDigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:439 # Input is: DigraphGreedyColouring(ChainDigraph(10), order_func); # Expected output: Transformation( [ 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ] ) # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:441 # Input is: DigraphGreedyColouring(CompleteDigraph(10), order_func); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:443 # Input is: gr := DigraphFromSparse6String( ":]nA?LcB@_EDfEB`GIaHGdJIgEKcLK`?MdCHiFLaBJhFMkJM"); # Expected output: # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/grahom.tst:446 # Input is: DigraphGreedyColouring(gr, order_func); # Expected output: Transformation( [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ] ) # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:449 # Input is: DigraphGreedyColouring(EmptyDigraph(0)); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphGreedyColouring' must have a value ######## ########> Diff in standard/grahom.tst:453 # Input is: gr := Digraph([[2, 3], [], [], [5], [], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:454 # Input is: gr := DigraphSymmetricClosure(gr);; # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/grahom.tst:456 # Input is: HomomorphismDigraphsFinder(gr, gr, fail, x, infinity, fail, 0, [1 .. 6], [], fail, fail); # Expected output: [ IdentityTransformation, Transformation( [ 1, 2, 3, 4, 5, 1 ] ), Transformation( [ 1, 2, 3, 4, 5, 2 ] ), Transformation( [ 1, 2, 3, 4, 5, 3 ] ), Transformation( [ 1, 2, 3, 4, 5, 4 ] ), Transformation( [ 1, 2, 3, 4, 5, 5 ] ), Transformation( [ 1, 2, 3, 1, 2, 4 ] ), Transformation( [ 1, 2, 3, 1, 2 ] ), Transformation( [ 1, 2, 3, 1, 2, 1 ] ), Transformation( [ 1, 2, 3, 1, 2, 2 ] ), Transformation( [ 1, 2, 3, 1, 2, 3 ] ), Transformation( [ 1, 2, 3, 1, 3, 4 ] ), Transformation( [ 1, 2, 3, 1, 3 ] ), Transformation( [ 1, 2, 3, 1, 3, 1 ] ), Transformation( [ 1, 2, 3, 1, 3, 2 ] ), Transformation( [ 1, 2, 3, 1, 3, 3 ] ), Transformation( [ 1, 2, 3, 2, 1, 4 ] ), Transformation( [ 1, 2, 3, 2, 1 ] ), Transformation( [ 1, 2, 3, 2, 1, 1 ] ), Transformation( [ 1, 2, 3, 2, 1, 2 ] ), Transformation( [ 1, 2, 3, 2, 1, 3 ] ), Transformation( [ 1, 2, 3, 3, 1, 4 ] ), Transformation( [ 1, 2, 3, 3, 1 ] ), Transformation( [ 1, 2, 3, 3, 1, 1 ] ), Transformation( [ 1, 2, 3, 3, 1, 2 ] ), Transformation( [ 1, 2, 3, 3, 1, 3 ] ), Transformation( [ 1, 2, 2, 3, 1, 4 ] ), Transformation( [ 1, 2, 2, 3, 1 ] ), Transformation( [ 1, 2, 2, 3, 1, 1 ] ), Transformation( [ 1, 2, 2, 3, 1, 2 ] ), Transformation( [ 1, 2, 2, 3, 1, 3 ] ), Transformation( [ 1, 2, 2, 4, 5, 3 ] ), Transformation( [ 1, 2, 2 ] ), Transformation( [ 1, 2, 2, 4, 5, 1 ] ), Transformation( [ 1, 2, 2, 4, 5, 2 ] ), Transformation( [ 1, 2, 2, 4, 5, 4 ] ), Transformation( [ 1, 2, 2, 4, 5, 5 ] ), Transformation( [ 1, 2, 2, 1, 3, 4 ] ), Transformation( [ 1, 2, 2, 1, 3 ] ), Transformation( [ 1, 2, 2, 1, 3, 1 ] ), Transformation( [ 1, 2, 2, 1, 3, 2 ] ), Transformation( [ 1, 2, 2, 1, 3, 3 ] ), Transformation( [ 1, 2, 2, 1, 2, 3 ] ), Transformation( [ 1, 2, 2, 1, 2, 4 ] ), Transformation( [ 1, 2, 2, 1, 2 ] ), Transformation( [ 1, 2, 2, 1, 2, 1 ] ), Transformation( [ 1, 2, 2, 1, 2, 2 ] ), Transformation( [ 1, 2, 2, 2, 1, 3 ] ), Transformation( [ 1, 2, 2, 2, 1, 4 ] ), Transformation( [ 1, 2, 2, 2, 1 ] ), Transformation( [ 1, 2, 2, 2, 1, 1 ] ), Transformation( [ 1, 2, 2, 2, 1, 2 ] ), Transformation( [ 2, 1, 1, 3, 1, 4 ] ), Transformation( [ 2, 1, 1, 3, 1 ] ), Transformation( [ 2, 1, 1, 3, 1, 1 ] ), Transformation( [ 2, 1, 1, 3, 1, 2 ] ), Transformation( [ 2, 1, 1, 3, 1, 3 ] ), Transformation( [ 2, 1, 1, 4, 5, 3 ] ), Transformation( [ 2, 1, 1 ] ), Transformation( [ 2, 1, 1, 4, 5, 1 ] ), Transformation( [ 2, 1, 1, 4, 5, 2 ] ), Transformation( [ 2, 1, 1, 4, 5, 4 ] ), Transformation( [ 2, 1, 1, 4, 5, 5 ] ), Transformation( [ 2, 1, 1, 1, 3, 4 ] ), Transformation( [ 2, 1, 1, 1, 3 ] ), Transformation( [ 2, 1, 1, 1, 3, 1 ] ), Transformation( [ 2, 1, 1, 1, 3, 2 ] ), Transformation( [ 2, 1, 1, 1, 3, 3 ] ), Transformation( [ 2, 1, 1, 1, 2, 3 ] ), Transformation( [ 2, 1, 1, 1, 2, 4 ] ), Transformation( [ 2, 1, 1, 1, 2 ] ), Transformation( [ 2, 1, 1, 1, 2, 1 ] ), Transformation( [ 2, 1, 1, 1, 2, 2 ] ), Transformation( [ 2, 1, 1, 2, 1, 3 ] ), Transformation( [ 2, 1, 1, 2, 1, 4 ] ), Transformation( [ 2, 1, 1, 2, 1 ] ), Transformation( [ 2, 1, 1, 2, 1, 1 ] ), Transformation( [ 2, 1, 1, 2, 1, 2 ] ), Transformation( [ 4, 5, 5, 1, 2, 3 ] ), Transformation( [ 4, 5, 5, 1, 2 ] ), Transformation( [ 4, 5, 5, 1, 2, 1 ] ), Transformation( [ 4, 5, 5, 1, 2, 2 ] ), Transformation( [ 4, 5, 5, 1, 2, 4 ] ), Transformation( [ 4, 5, 5, 1, 2, 5 ] ), Transformation( [ 4, 5, 5, 2, 1, 3 ] ), Transformation( [ 4, 5, 5, 2, 1 ] ), Transformation( [ 4, 5, 5, 2, 1, 1 ] ), Transformation( [ 4, 5, 5, 2, 1, 2 ] ), Transformation( [ 4, 5, 5, 2, 1, 4 ] ), Transformation( [ 4, 5, 5, 2, 1, 5 ] ), Transformation( [ 4, 5, 5, 4, 5, 1 ] ), Transformation( [ 4, 5, 5, 4, 5, 2 ] ), Transformation( [ 4, 5, 5, 4, 5 ] ), Transformation( [ 4, 5, 5, 4, 5, 4 ] ), Transformation( [ 4, 5, 5, 4, 5, 5 ] ), Transformation( [ 4, 5, 5, 5, 4, 1 ] ), Transformation( [ 4, 5, 5, 5, 4, 2 ] ), Transformation( [ 4, 5, 5, 5, 4 ] ), Transformation( [ 4, 5, 5, 5, 4, 4 ] ), Transformation( [ 4, 5, 5, 5, 4, 5 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:539 # Input is: Length(x); # Expected output: 100 # But found: 0 ######## ########> Diff in standard/grahom.tst:541 # Input is: HomomorphismDigraphsFinder(gr, gr, fail, x, infinity, fail, 0, [1 .. 6], [], fail, fail); # Expected output: [ IdentityTransformation, Transformation( [ 1, 2, 3, 4, 5, 1 ] ), Transformation( [ 1, 2, 3, 4, 5, 2 ] ), Transformation( [ 1, 2, 3, 4, 5, 3 ] ), Transformation( [ 1, 2, 3, 4, 5, 4 ] ), Transformation( [ 1, 2, 3, 4, 5, 5 ] ), Transformation( [ 1, 2, 3, 1, 2, 4 ] ), Transformation( [ 1, 2, 3, 1, 2 ] ), Transformation( [ 1, 2, 3, 1, 2, 1 ] ), Transformation( [ 1, 2, 3, 1, 2, 2 ] ), Transformation( [ 1, 2, 3, 1, 2, 3 ] ), Transformation( [ 1, 2, 3, 1, 3, 4 ] ), Transformation( [ 1, 2, 3, 1, 3 ] ), Transformation( [ 1, 2, 3, 1, 3, 1 ] ), Transformation( [ 1, 2, 3, 1, 3, 2 ] ), Transformation( [ 1, 2, 3, 1, 3, 3 ] ), Transformation( [ 1, 2, 3, 2, 1, 4 ] ), Transformation( [ 1, 2, 3, 2, 1 ] ), Transformation( [ 1, 2, 3, 2, 1, 1 ] ), Transformation( [ 1, 2, 3, 2, 1, 2 ] ), Transformation( [ 1, 2, 3, 2, 1, 3 ] ), Transformation( [ 1, 2, 3, 3, 1, 4 ] ), Transformation( [ 1, 2, 3, 3, 1 ] ), Transformation( [ 1, 2, 3, 3, 1, 1 ] ), Transformation( [ 1, 2, 3, 3, 1, 2 ] ), Transformation( [ 1, 2, 3, 3, 1, 3 ] ), Transformation( [ 1, 2, 2, 3, 1, 4 ] ), Transformation( [ 1, 2, 2, 3, 1 ] ), Transformation( [ 1, 2, 2, 3, 1, 1 ] ), Transformation( [ 1, 2, 2, 3, 1, 2 ] ), Transformation( [ 1, 2, 2, 3, 1, 3 ] ), Transformation( [ 1, 2, 2, 4, 5, 3 ] ), Transformation( [ 1, 2, 2 ] ), Transformation( [ 1, 2, 2, 4, 5, 1 ] ), Transformation( [ 1, 2, 2, 4, 5, 2 ] ), Transformation( [ 1, 2, 2, 4, 5, 4 ] ), Transformation( [ 1, 2, 2, 4, 5, 5 ] ), Transformation( [ 1, 2, 2, 1, 3, 4 ] ), Transformation( [ 1, 2, 2, 1, 3 ] ), Transformation( [ 1, 2, 2, 1, 3, 1 ] ), Transformation( [ 1, 2, 2, 1, 3, 2 ] ), Transformation( [ 1, 2, 2, 1, 3, 3 ] ), Transformation( [ 1, 2, 2, 1, 2, 3 ] ), Transformation( [ 1, 2, 2, 1, 2, 4 ] ), Transformation( [ 1, 2, 2, 1, 2 ] ), Transformation( [ 1, 2, 2, 1, 2, 1 ] ), Transformation( [ 1, 2, 2, 1, 2, 2 ] ), Transformation( [ 1, 2, 2, 2, 1, 3 ] ), Transformation( [ 1, 2, 2, 2, 1, 4 ] ), Transformation( [ 1, 2, 2, 2, 1 ] ), Transformation( [ 1, 2, 2, 2, 1, 1 ] ), Transformation( [ 1, 2, 2, 2, 1, 2 ] ), Transformation( [ 2, 1, 1, 3, 1, 4 ] ), Transformation( [ 2, 1, 1, 3, 1 ] ), Transformation( [ 2, 1, 1, 3, 1, 1 ] ), Transformation( [ 2, 1, 1, 3, 1, 2 ] ), Transformation( [ 2, 1, 1, 3, 1, 3 ] ), Transformation( [ 2, 1, 1, 4, 5, 3 ] ), Transformation( [ 2, 1, 1 ] ), Transformation( [ 2, 1, 1, 4, 5, 1 ] ), Transformation( [ 2, 1, 1, 4, 5, 2 ] ), Transformation( [ 2, 1, 1, 4, 5, 4 ] ), Transformation( [ 2, 1, 1, 4, 5, 5 ] ), Transformation( [ 2, 1, 1, 1, 3, 4 ] ), Transformation( [ 2, 1, 1, 1, 3 ] ), Transformation( [ 2, 1, 1, 1, 3, 1 ] ), Transformation( [ 2, 1, 1, 1, 3, 2 ] ), Transformation( [ 2, 1, 1, 1, 3, 3 ] ), Transformation( [ 2, 1, 1, 1, 2, 3 ] ), Transformation( [ 2, 1, 1, 1, 2, 4 ] ), Transformation( [ 2, 1, 1, 1, 2 ] ), Transformation( [ 2, 1, 1, 1, 2, 1 ] ), Transformation( [ 2, 1, 1, 1, 2, 2 ] ), Transformation( [ 2, 1, 1, 2, 1, 3 ] ), Transformation( [ 2, 1, 1, 2, 1, 4 ] ), Transformation( [ 2, 1, 1, 2, 1 ] ), Transformation( [ 2, 1, 1, 2, 1, 1 ] ), Transformation( [ 2, 1, 1, 2, 1, 2 ] ), Transformation( [ 4, 5, 5, 1, 2, 3 ] ), Transformation( [ 4, 5, 5, 1, 2 ] ), Transformation( [ 4, 5, 5, 1, 2, 1 ] ), Transformation( [ 4, 5, 5, 1, 2, 2 ] ), Transformation( [ 4, 5, 5, 1, 2, 4 ] ), Transformation( [ 4, 5, 5, 1, 2, 5 ] ), Transformation( [ 4, 5, 5, 2, 1, 3 ] ), Transformation( [ 4, 5, 5, 2, 1 ] ), Transformation( [ 4, 5, 5, 2, 1, 1 ] ), Transformation( [ 4, 5, 5, 2, 1, 2 ] ), Transformation( [ 4, 5, 5, 2, 1, 4 ] ), Transformation( [ 4, 5, 5, 2, 1, 5 ] ), Transformation( [ 4, 5, 5, 4, 5, 1 ] ), Transformation( [ 4, 5, 5, 4, 5, 2 ] ), Transformation( [ 4, 5, 5, 4, 5 ] ), Transformation( [ 4, 5, 5, 4, 5, 4 ] ), Transformation( [ 4, 5, 5, 4, 5, 5 ] ), Transformation( [ 4, 5, 5, 5, 4, 1 ] ), Transformation( [ 4, 5, 5, 5, 4, 2 ] ), Transformation( [ 4, 5, 5, 5, 4 ] ), Transformation( [ 4, 5, 5, 5, 4, 4 ] ), Transformation( [ 4, 5, 5, 5, 4, 5 ] ), IdentityTransformation, Transformation( [ 1, 2, 3, 4, 5, 1 ] ), Transformation( [ 1, 2, 3, 4, 5, 2 ] ), Transformation( [ 1, 2, 3, 4, 5, 3 ] ), Transformation( [ 1, 2, 3, 4, 5, 4 ] ), Transformation( [ 1, 2, 3, 4, 5, 5 ] ), Transformation( [ 1, 2, 3, 1, 2, 4 ] ), Transformation( [ 1, 2, 3, 1, 2 ] ), Transformation( [ 1, 2, 3, 1, 2, 1 ] ), Transformation( [ 1, 2, 3, 1, 2, 2 ] ), Transformation( [ 1, 2, 3, 1, 2, 3 ] ), Transformation( [ 1, 2, 3, 1, 3, 4 ] ), Transformation( [ 1, 2, 3, 1, 3 ] ), Transformation( [ 1, 2, 3, 1, 3, 1 ] ), Transformation( [ 1, 2, 3, 1, 3, 2 ] ), Transformation( [ 1, 2, 3, 1, 3, 3 ] ), Transformation( [ 1, 2, 3, 2, 1, 4 ] ), Transformation( [ 1, 2, 3, 2, 1 ] ), Transformation( [ 1, 2, 3, 2, 1, 1 ] ), Transformation( [ 1, 2, 3, 2, 1, 2 ] ), Transformation( [ 1, 2, 3, 2, 1, 3 ] ), Transformation( [ 1, 2, 3, 3, 1, 4 ] ), Transformation( [ 1, 2, 3, 3, 1 ] ), Transformation( [ 1, 2, 3, 3, 1, 1 ] ), Transformation( [ 1, 2, 3, 3, 1, 2 ] ), Transformation( [ 1, 2, 3, 3, 1, 3 ] ), Transformation( [ 1, 2, 2, 3, 1, 4 ] ), Transformation( [ 1, 2, 2, 3, 1 ] ), Transformation( [ 1, 2, 2, 3, 1, 1 ] ), Transformation( [ 1, 2, 2, 3, 1, 2 ] ), Transformation( [ 1, 2, 2, 3, 1, 3 ] ), Transformation( [ 1, 2, 2, 4, 5, 3 ] ), Transformation( [ 1, 2, 2 ] ), Transformation( [ 1, 2, 2, 4, 5, 1 ] ), Transformation( [ 1, 2, 2, 4, 5, 2 ] ), Transformation( [ 1, 2, 2, 4, 5, 4 ] ), Transformation( [ 1, 2, 2, 4, 5, 5 ] ), Transformation( [ 1, 2, 2, 1, 3, 4 ] ), Transformation( [ 1, 2, 2, 1, 3 ] ), Transformation( [ 1, 2, 2, 1, 3, 1 ] ), Transformation( [ 1, 2, 2, 1, 3, 2 ] ), Transformation( [ 1, 2, 2, 1, 3, 3 ] ), Transformation( [ 1, 2, 2, 1, 2, 3 ] ), Transformation( [ 1, 2, 2, 1, 2, 4 ] ), Transformation( [ 1, 2, 2, 1, 2 ] ), Transformation( [ 1, 2, 2, 1, 2, 1 ] ), Transformation( [ 1, 2, 2, 1, 2, 2 ] ), Transformation( [ 1, 2, 2, 2, 1, 3 ] ), Transformation( [ 1, 2, 2, 2, 1, 4 ] ), Transformation( [ 1, 2, 2, 2, 1 ] ), Transformation( [ 1, 2, 2, 2, 1, 1 ] ), Transformation( [ 1, 2, 2, 2, 1, 2 ] ), Transformation( [ 2, 1, 1, 3, 1, 4 ] ), Transformation( [ 2, 1, 1, 3, 1 ] ), Transformation( [ 2, 1, 1, 3, 1, 1 ] ), Transformation( [ 2, 1, 1, 3, 1, 2 ] ), Transformation( [ 2, 1, 1, 3, 1, 3 ] ), Transformation( [ 2, 1, 1, 4, 5, 3 ] ), Transformation( [ 2, 1, 1 ] ), Transformation( [ 2, 1, 1, 4, 5, 1 ] ), Transformation( [ 2, 1, 1, 4, 5, 2 ] ), Transformation( [ 2, 1, 1, 4, 5, 4 ] ), Transformation( [ 2, 1, 1, 4, 5, 5 ] ), Transformation( [ 2, 1, 1, 1, 3, 4 ] ), Transformation( [ 2, 1, 1, 1, 3 ] ), Transformation( [ 2, 1, 1, 1, 3, 1 ] ), Transformation( [ 2, 1, 1, 1, 3, 2 ] ), Transformation( [ 2, 1, 1, 1, 3, 3 ] ), Transformation( [ 2, 1, 1, 1, 2, 3 ] ), Transformation( [ 2, 1, 1, 1, 2, 4 ] ), Transformation( [ 2, 1, 1, 1, 2 ] ), Transformation( [ 2, 1, 1, 1, 2, 1 ] ), Transformation( [ 2, 1, 1, 1, 2, 2 ] ), Transformation( [ 2, 1, 1, 2, 1, 3 ] ), Transformation( [ 2, 1, 1, 2, 1, 4 ] ), Transformation( [ 2, 1, 1, 2, 1 ] ), Transformation( [ 2, 1, 1, 2, 1, 1 ] ), Transformation( [ 2, 1, 1, 2, 1, 2 ] ), Transformation( [ 4, 5, 5, 1, 2, 3 ] ), Transformation( [ 4, 5, 5, 1, 2 ] ), Transformation( [ 4, 5, 5, 1, 2, 1 ] ), Transformation( [ 4, 5, 5, 1, 2, 2 ] ), Transformation( [ 4, 5, 5, 1, 2, 4 ] ), Transformation( [ 4, 5, 5, 1, 2, 5 ] ), Transformation( [ 4, 5, 5, 2, 1, 3 ] ), Transformation( [ 4, 5, 5, 2, 1 ] ), Transformation( [ 4, 5, 5, 2, 1, 1 ] ), Transformation( [ 4, 5, 5, 2, 1, 2 ] ), Transformation( [ 4, 5, 5, 2, 1, 4 ] ), Transformation( [ 4, 5, 5, 2, 1, 5 ] ), Transformation( [ 4, 5, 5, 4, 5, 1 ] ), Transformation( [ 4, 5, 5, 4, 5, 2 ] ), Transformation( [ 4, 5, 5, 4, 5 ] ), Transformation( [ 4, 5, 5, 4, 5, 4 ] ), Transformation( [ 4, 5, 5, 4, 5, 5 ] ), Transformation( [ 4, 5, 5, 5, 4, 1 ] ), Transformation( [ 4, 5, 5, 5, 4, 2 ] ), Transformation( [ 4, 5, 5, 5, 4 ] ), Transformation( [ 4, 5, 5, 5, 4, 4 ] ), Transformation( [ 4, 5, 5, 5, 4, 5 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:705 # Input is: Length(x); # Expected output: 200 # But found: 0 ######## ########> Diff in standard/grahom.tst:707 # Input is: x{[1 .. 100]} = x{[101 .. 200]}; # Expected output: true # But found: Error, List Elements: [1] must have an assigned value ######## ########> Diff in standard/grahom.tst:711 # Input is: gr := Digraph([[2, 3], [], [], [5], [], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:713 # Input is: HomomorphismDigraphsFinder(gr, gr, fail, [], infinity, fail, 0, [1 .. 5], [], fail, fail); # Expected output: [ Transformation( [ 1, 2, 3, 4, 5, 1 ] ), Transformation( [ 1, 2, 3, 4, 5, 2 ] ), Transformation( [ 1, 2, 3, 4, 5, 3 ] ), Transformation( [ 1, 2, 3, 4, 5, 4 ] ), Transformation( [ 1, 2, 3, 4, 5, 5 ] ), Transformation( [ 1, 2, 3, 1, 2, 4 ] ), Transformation( [ 1, 2, 3, 1, 2, 5 ] ), Transformation( [ 1, 2, 3, 1, 2, 1 ] ), Transformation( [ 1, 2, 3, 1, 2, 2 ] ), Transformation( [ 1, 2, 3, 1, 2, 3 ] ), Transformation( [ 1, 2, 3, 1, 3, 4 ] ), Transformation( [ 1, 2, 3, 1, 3, 5 ] ), Transformation( [ 1, 2, 3, 1, 3, 1 ] ), Transformation( [ 1, 2, 3, 1, 3, 2 ] ), Transformation( [ 1, 2, 3, 1, 3, 3 ] ), Transformation( [ 1, 2, 2, 4, 5, 3 ] ), Transformation( [ 1, 2, 2, 4, 5, 1 ] ), Transformation( [ 1, 2, 2, 4, 5, 2 ] ), Transformation( [ 1, 2, 2, 4, 5, 4 ] ), Transformation( [ 1, 2, 2, 4, 5, 5 ] ), Transformation( [ 1, 2, 2, 1, 3, 4 ] ), Transformation( [ 1, 2, 2, 1, 3, 5 ] ), Transformation( [ 1, 2, 2, 1, 3, 1 ] ), Transformation( [ 1, 2, 2, 1, 3, 2 ] ), Transformation( [ 1, 2, 2, 1, 3, 3 ] ), Transformation( [ 1, 2, 2, 1, 2, 3 ] ), Transformation( [ 1, 2, 2, 1, 2, 4 ] ), Transformation( [ 1, 2, 2, 1, 2, 5 ] ), Transformation( [ 1, 2, 2, 1, 2, 1 ] ), Transformation( [ 1, 2, 2, 1, 2, 2 ] ), Transformation( [ 4, 5, 5, 1, 2, 3 ] ), Transformation( [ 4, 5, 5, 1, 2, 1 ] ), Transformation( [ 4, 5, 5, 1, 2, 2 ] ), Transformation( [ 4, 5, 5, 1, 2, 4 ] ), Transformation( [ 4, 5, 5, 1, 2, 5 ] ), Transformation( [ 4, 5, 5, 4, 5, 1 ] ), Transformation( [ 4, 5, 5, 4, 5, 2 ] ), Transformation( [ 4, 5, 5, 4, 5, 4 ] ), Transformation( [ 4, 5, 5, 4, 5, 5 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:754 # Input is: Length(last); # Expected output: 39 # But found: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `Length' on 1 arguments ######## ########> Diff in standard/grahom.tst:758 # Input is: gr := Digraph([[2, 3], [], [], [5], [], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:760 # Input is: HomomorphismDigraphsFinder(gr, gr, fail, [], infinity, fail, 0, [1 .. 6], [], fail, fail); # Expected output: [ IdentityTransformation, Transformation( [ 1, 2, 3, 4, 5, 1 ] ), Transformation( [ 1, 2, 3, 4, 5, 2 ] ), Transformation( [ 1, 2, 3, 4, 5, 3 ] ), Transformation( [ 1, 2, 3, 4, 5, 4 ] ), Transformation( [ 1, 2, 3, 4, 5, 5 ] ), Transformation( [ 1, 2, 3, 1, 2, 4 ] ), Transformation( [ 1, 2, 3, 1, 2, 5 ] ), Transformation( [ 1, 2, 3, 1, 2 ] ), Transformation( [ 1, 2, 3, 1, 2, 1 ] ), Transformation( [ 1, 2, 3, 1, 2, 2 ] ), Transformation( [ 1, 2, 3, 1, 2, 3 ] ), Transformation( [ 1, 2, 3, 1, 3, 4 ] ), Transformation( [ 1, 2, 3, 1, 3, 5 ] ), Transformation( [ 1, 2, 3, 1, 3 ] ), Transformation( [ 1, 2, 3, 1, 3, 1 ] ), Transformation( [ 1, 2, 3, 1, 3, 2 ] ), Transformation( [ 1, 2, 3, 1, 3, 3 ] ), Transformation( [ 1, 2, 2, 4, 5, 3 ] ), Transformation( [ 1, 2, 2 ] ), Transformation( [ 1, 2, 2, 4, 5, 1 ] ), Transformation( [ 1, 2, 2, 4, 5, 2 ] ), Transformation( [ 1, 2, 2, 4, 5, 4 ] ), Transformation( [ 1, 2, 2, 4, 5, 5 ] ), Transformation( [ 1, 2, 2, 1, 3, 4 ] ), Transformation( [ 1, 2, 2, 1, 3, 5 ] ), Transformation( [ 1, 2, 2, 1, 3 ] ), Transformation( [ 1, 2, 2, 1, 3, 1 ] ), Transformation( [ 1, 2, 2, 1, 3, 2 ] ), Transformation( [ 1, 2, 2, 1, 3, 3 ] ), Transformation( [ 1, 2, 2, 1, 2, 3 ] ), Transformation( [ 1, 2, 2, 1, 2, 4 ] ), Transformation( [ 1, 2, 2, 1, 2, 5 ] ), Transformation( [ 1, 2, 2, 1, 2 ] ), Transformation( [ 1, 2, 2, 1, 2, 1 ] ), Transformation( [ 1, 2, 2, 1, 2, 2 ] ), Transformation( [ 4, 5, 5, 1, 2, 3 ] ), Transformation( [ 4, 5, 5, 1, 2 ] ), Transformation( [ 4, 5, 5, 1, 2, 1 ] ), Transformation( [ 4, 5, 5, 1, 2, 2 ] ), Transformation( [ 4, 5, 5, 1, 2, 4 ] ), Transformation( [ 4, 5, 5, 1, 2, 5 ] ), Transformation( [ 4, 5, 5, 4, 5, 1 ] ), Transformation( [ 4, 5, 5, 4, 5, 2 ] ), Transformation( [ 4, 5, 5, 4, 5 ] ), Transformation( [ 4, 5, 5, 4, 5, 4 ] ), Transformation( [ 4, 5, 5, 4, 5, 5 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:801 # Input is: Length(last); # Expected output: 47 # But found: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `Length' on 1 arguments ######## ########> Diff in standard/grahom.tst:805 # Input is: gr := Digraph([[2, 3], [], [], [5], [], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:807 # Input is: gr := DigraphSymmetricClosure(gr); # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/grahom.tst:809 # Input is: HomomorphismDigraphsFinder(gr, gr, fail, [], infinity, fail, 0, [1 .. 6], [], fail, fail); # Expected output: [ IdentityTransformation, Transformation( [ 1, 2, 3, 4, 5, 1 ] ), Transformation( [ 1, 2, 3, 4, 5, 2 ] ), Transformation( [ 1, 2, 3, 4, 5, 3 ] ), Transformation( [ 1, 2, 3, 4, 5, 4 ] ), Transformation( [ 1, 2, 3, 4, 5, 5 ] ), Transformation( [ 1, 2, 3, 1, 2, 4 ] ), Transformation( [ 1, 2, 3, 1, 2 ] ), Transformation( [ 1, 2, 3, 1, 2, 1 ] ), Transformation( [ 1, 2, 3, 1, 2, 2 ] ), Transformation( [ 1, 2, 3, 1, 2, 3 ] ), Transformation( [ 1, 2, 3, 1, 3, 4 ] ), Transformation( [ 1, 2, 3, 1, 3 ] ), Transformation( [ 1, 2, 3, 1, 3, 1 ] ), Transformation( [ 1, 2, 3, 1, 3, 2 ] ), Transformation( [ 1, 2, 3, 1, 3, 3 ] ), Transformation( [ 1, 2, 3, 2, 1, 4 ] ), Transformation( [ 1, 2, 3, 2, 1 ] ), Transformation( [ 1, 2, 3, 2, 1, 1 ] ), Transformation( [ 1, 2, 3, 2, 1, 2 ] ), Transformation( [ 1, 2, 3, 2, 1, 3 ] ), Transformation( [ 1, 2, 3, 3, 1, 4 ] ), Transformation( [ 1, 2, 3, 3, 1 ] ), Transformation( [ 1, 2, 3, 3, 1, 1 ] ), Transformation( [ 1, 2, 3, 3, 1, 2 ] ), Transformation( [ 1, 2, 3, 3, 1, 3 ] ), Transformation( [ 1, 2, 2, 3, 1, 4 ] ), Transformation( [ 1, 2, 2, 3, 1 ] ), Transformation( [ 1, 2, 2, 3, 1, 1 ] ), Transformation( [ 1, 2, 2, 3, 1, 2 ] ), Transformation( [ 1, 2, 2, 3, 1, 3 ] ), Transformation( [ 1, 2, 2, 4, 5, 3 ] ), Transformation( [ 1, 2, 2 ] ), Transformation( [ 1, 2, 2, 4, 5, 1 ] ), Transformation( [ 1, 2, 2, 4, 5, 2 ] ), Transformation( [ 1, 2, 2, 4, 5, 4 ] ), Transformation( [ 1, 2, 2, 4, 5, 5 ] ), Transformation( [ 1, 2, 2, 1, 3, 4 ] ), Transformation( [ 1, 2, 2, 1, 3 ] ), Transformation( [ 1, 2, 2, 1, 3, 1 ] ), Transformation( [ 1, 2, 2, 1, 3, 2 ] ), Transformation( [ 1, 2, 2, 1, 3, 3 ] ), Transformation( [ 1, 2, 2, 1, 2, 3 ] ), Transformation( [ 1, 2, 2, 1, 2, 4 ] ), Transformation( [ 1, 2, 2, 1, 2 ] ), Transformation( [ 1, 2, 2, 1, 2, 1 ] ), Transformation( [ 1, 2, 2, 1, 2, 2 ] ), Transformation( [ 1, 2, 2, 2, 1, 3 ] ), Transformation( [ 1, 2, 2, 2, 1, 4 ] ), Transformation( [ 1, 2, 2, 2, 1 ] ), Transformation( [ 1, 2, 2, 2, 1, 1 ] ), Transformation( [ 1, 2, 2, 2, 1, 2 ] ), Transformation( [ 2, 1, 1, 3, 1, 4 ] ), Transformation( [ 2, 1, 1, 3, 1 ] ), Transformation( [ 2, 1, 1, 3, 1, 1 ] ), Transformation( [ 2, 1, 1, 3, 1, 2 ] ), Transformation( [ 2, 1, 1, 3, 1, 3 ] ), Transformation( [ 2, 1, 1, 4, 5, 3 ] ), Transformation( [ 2, 1, 1 ] ), Transformation( [ 2, 1, 1, 4, 5, 1 ] ), Transformation( [ 2, 1, 1, 4, 5, 2 ] ), Transformation( [ 2, 1, 1, 4, 5, 4 ] ), Transformation( [ 2, 1, 1, 4, 5, 5 ] ), Transformation( [ 2, 1, 1, 1, 3, 4 ] ), Transformation( [ 2, 1, 1, 1, 3 ] ), Transformation( [ 2, 1, 1, 1, 3, 1 ] ), Transformation( [ 2, 1, 1, 1, 3, 2 ] ), Transformation( [ 2, 1, 1, 1, 3, 3 ] ), Transformation( [ 2, 1, 1, 1, 2, 3 ] ), Transformation( [ 2, 1, 1, 1, 2, 4 ] ), Transformation( [ 2, 1, 1, 1, 2 ] ), Transformation( [ 2, 1, 1, 1, 2, 1 ] ), Transformation( [ 2, 1, 1, 1, 2, 2 ] ), Transformation( [ 2, 1, 1, 2, 1, 3 ] ), Transformation( [ 2, 1, 1, 2, 1, 4 ] ), Transformation( [ 2, 1, 1, 2, 1 ] ), Transformation( [ 2, 1, 1, 2, 1, 1 ] ), Transformation( [ 2, 1, 1, 2, 1, 2 ] ), Transformation( [ 4, 5, 5, 1, 2, 3 ] ), Transformation( [ 4, 5, 5, 1, 2 ] ), Transformation( [ 4, 5, 5, 1, 2, 1 ] ), Transformation( [ 4, 5, 5, 1, 2, 2 ] ), Transformation( [ 4, 5, 5, 1, 2, 4 ] ), Transformation( [ 4, 5, 5, 1, 2, 5 ] ), Transformation( [ 4, 5, 5, 2, 1, 3 ] ), Transformation( [ 4, 5, 5, 2, 1 ] ), Transformation( [ 4, 5, 5, 2, 1, 1 ] ), Transformation( [ 4, 5, 5, 2, 1, 2 ] ), Transformation( [ 4, 5, 5, 2, 1, 4 ] ), Transformation( [ 4, 5, 5, 2, 1, 5 ] ), Transformation( [ 4, 5, 5, 4, 5, 1 ] ), Transformation( [ 4, 5, 5, 4, 5, 2 ] ), Transformation( [ 4, 5, 5, 4, 5 ] ), Transformation( [ 4, 5, 5, 4, 5, 4 ] ), Transformation( [ 4, 5, 5, 4, 5, 5 ] ), Transformation( [ 4, 5, 5, 5, 4, 1 ] ), Transformation( [ 4, 5, 5, 5, 4, 2 ] ), Transformation( [ 4, 5, 5, 5, 4 ] ), Transformation( [ 4, 5, 5, 5, 4, 4 ] ), Transformation( [ 4, 5, 5, 5, 4, 5 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:892 # Input is: Length(last); # Expected output: 100 # But found: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `Length' on 1 arguments ######## ########> Diff in standard/grahom.tst:896 # Input is: gr1 := Digraph([[], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:897 # Input is: gr1 := DigraphSymmetricClosure(gr1);; # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/grahom.tst:898 # Input is: gr2 := Digraph([[], [1], [1, 3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:899 # Input is: gr2 := DigraphSymmetricClosure(gr2);; # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/grahom.tst:900 # Input is: HomomorphismDigraphsFinder(gr1, gr2, fail, [], infinity, fail, 1, [1, 2, 3], [], fail, fail); # Expected output: [ IdentityTransformation, Transformation( [ 1, 3, 3 ] ), Transformation( [ 2, 1 ] ), Transformation( [ 3, 1, 3 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:906 # Input is: HomomorphismDigraphsFinder(NullDigraph(4), CompleteDigraph(4), fail, [], infinity, fail, 1, [1 .. 4], [], fail, fail, Group(())); # Expected output: [ IdentityTransformation, Transformation( [ 1, 2, 4, 3 ] ), Transformation( [ 1, 3, 2 ] ), Transformation( [ 1, 3, 4, 2 ] ), Transformation( [ 1, 4, 2, 3 ] ), Transformation( [ 1, 4, 3, 2 ] ), Transformation( [ 2, 1 ] ), Transformation( [ 2, 1, 4, 3 ] ), Transformation( [ 2, 3, 1 ] ), Transformation( [ 2, 3, 4, 1 ] ), Transformation( [ 2, 4, 1, 3 ] ), Transformation( [ 2, 4, 3, 1 ] ), Transformation( [ 3, 1, 2 ] ), Transformation( [ 3, 1, 4, 2 ] ), Transformation( [ 3, 2, 1 ] ), Transformation( [ 3, 2, 4, 1 ] ), Transformation( [ 3, 4, 1, 2 ] ), Transformation( [ 3, 4, 2, 1 ] ), Transformation( [ 4, 1, 2, 3 ] ), Transformation( [ 4, 1, 3, 2 ] ), Transformation( [ 4, 2, 1, 3 ] ), Transformation( [ 4, 2, 3, 1 ] ), Transformation( [ 4, 3, 1, 2 ] ), Transformation( [ 4, 3, 2, 1 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:921 # Input is: HomomorphismDigraphsFinder(NullDigraph(4), CompleteDigraph(4), fail, [], infinity, fail, 1, [1 .. 4], [], fail, fail, Group((2, 3))); # Expected output: [ IdentityTransformation, Transformation( [ 1, 2, 4, 3 ] ), Transformation( [ 1, 4, 2, 3 ] ), Transformation( [ 2, 1 ] ), Transformation( [ 2, 1, 4, 3 ] ), Transformation( [ 2, 3, 1 ] ), Transformation( [ 2, 3, 4, 1 ] ), Transformation( [ 2, 4, 1, 3 ] ), Transformation( [ 2, 4, 3, 1 ] ), Transformation( [ 4, 1, 2, 3 ] ), Transformation( [ 4, 2, 1, 3 ] ), Transformation( [ 4, 2, 3, 1 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:930 # Input is: HomomorphismDigraphsFinder(NullDigraph(4), CompleteDigraph(4), fail, [], infinity, fail, 1, [1 .. 4], [], fail, fail, Group((1, 2, 3))); # Expected output: [ IdentityTransformation, Transformation( [ 1, 2, 4, 3 ] ), Transformation( [ 1, 3, 2 ] ), Transformation( [ 1, 3, 4, 2 ] ), Transformation( [ 1, 4, 2, 3 ] ), Transformation( [ 1, 4, 3, 2 ] ), Transformation( [ 4, 1, 2, 3 ] ), Transformation( [ 4, 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:937 # Input is: HomomorphismDigraphsFinder(NullDigraph(4), CompleteDigraph(4), fail, [], infinity, fail, 2, [1 .. 4], [], fail, fail, Group((2, 3))); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:941 # Input is: HomomorphismDigraphsFinder(NullDigraph(4), CompleteDigraph(4), fail, [], infinity, fail, 0, [1 .. 4], [], fail, fail, Group((1, 2), (2, 3))); # Expected output: [ IdentityTransformation, Transformation( [ 1, 2, 3, 1 ] ), Transformation( [ 1, 2, 3, 2 ] ), Transformation( [ 1, 2, 3, 3 ] ), Transformation( [ 1, 2, 4, 3 ] ), Transformation( [ 1, 2, 4, 1 ] ), Transformation( [ 1, 2, 4, 2 ] ), Transformation( [ 1, 2, 4, 4 ] ), Transformation( [ 1, 2, 1, 3 ] ), Transformation( [ 1, 2, 1 ] ), Transformation( [ 1, 2, 1, 1 ] ), Transformation( [ 1, 2, 1, 2 ] ), Transformation( [ 1, 2, 2, 3 ] ), Transformation( [ 1, 2, 2 ] ), Transformation( [ 1, 2, 2, 1 ] ), Transformation( [ 1, 2, 2, 2 ] ), Transformation( [ 1, 4, 2, 3 ] ), Transformation( [ 1, 4, 2, 1 ] ), Transformation( [ 1, 4, 2, 2 ] ), Transformation( [ 1, 4, 2, 4 ] ), Transformation( [ 1, 4, 1, 2 ] ), Transformation( [ 1, 4, 1, 1 ] ), Transformation( [ 1, 4, 1, 4 ] ), Transformation( [ 1, 4, 4, 2 ] ), Transformation( [ 1, 4, 4, 1 ] ), Transformation( [ 1, 4, 4, 4 ] ), Transformation( [ 1, 1, 2, 3 ] ), Transformation( [ 1, 1, 2 ] ), Transformation( [ 1, 1, 2, 1 ] ), Transformation( [ 1, 1, 2, 2 ] ), Transformation( [ 1, 1, 4, 2 ] ), Transformation( [ 1, 1, 4, 1 ] ), Transformation( [ 1, 1, 4, 4 ] ), Transformation( [ 1, 1, 1, 2 ] ), Transformation( [ 1, 1, 1 ] ), Transformation( [ 1, 1, 1, 1 ] ), Transformation( [ 4, 1, 2, 3 ] ), Transformation( [ 4, 1, 2, 1 ] ), Transformation( [ 4, 1, 2, 2 ] ), Transformation( [ 4, 1, 2, 4 ] ), Transformation( [ 4, 1, 1, 2 ] ), Transformation( [ 4, 1, 1, 1 ] ), Transformation( [ 4, 1, 1, 4 ] ), Transformation( [ 4, 1, 4, 2 ] ), Transformation( [ 4, 1, 4, 1 ] ), Transformation( [ 4, 1, 4, 4 ] ), Transformation( [ 4, 4, 1, 2 ] ), Transformation( [ 4, 4, 1, 1 ] ), Transformation( [ 4, 4, 1, 4 ] ), Transformation( [ 4, 4, 4, 1 ] ), Transformation( [ 4, 4, 4, 4 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:970 # Input is: HomomorphismDigraphsFinder(NullDigraph(4), CompleteDigraph(4), fail, [], infinity, fail, 0, [1 .. 4], [], fail, fail, Group((1, 2, 3, 4), (1, 2))); # Expected output: [ IdentityTransformation, Transformation( [ 1, 2, 3, 1 ] ), Transformation( [ 1, 2, 3, 2 ] ), Transformation( [ 1, 2, 3, 3 ] ), Transformation( [ 1, 2, 1, 3 ] ), Transformation( [ 1, 2, 1, 1 ] ), Transformation( [ 1, 2, 1, 2 ] ), Transformation( [ 1, 2, 2, 3 ] ), Transformation( [ 1, 2, 2, 1 ] ), Transformation( [ 1, 2, 2, 2 ] ), Transformation( [ 1, 1, 2, 3 ] ), Transformation( [ 1, 1, 2, 1 ] ), Transformation( [ 1, 1, 2, 2 ] ), Transformation( [ 1, 1, 1, 2 ] ), Transformation( [ 1, 1, 1, 1 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:981 # Input is: HomomorphismDigraphsFinder(NullDigraph(4), CompleteDigraph(4), fail, [], infinity, fail, 0, [1 .. 4], [], fail, fail); # Expected output: [ IdentityTransformation, Transformation( [ 1, 2, 3, 1 ] ), Transformation( [ 1, 2, 3, 2 ] ), Transformation( [ 1, 2, 3, 3 ] ), Transformation( [ 1, 2, 1, 3 ] ), Transformation( [ 1, 2, 1, 1 ] ), Transformation( [ 1, 2, 1, 2 ] ), Transformation( [ 1, 2, 2, 3 ] ), Transformation( [ 1, 2, 2, 1 ] ), Transformation( [ 1, 2, 2, 2 ] ), Transformation( [ 1, 1, 2, 3 ] ), Transformation( [ 1, 1, 2, 1 ] ), Transformation( [ 1, 1, 2, 2 ] ), Transformation( [ 1, 1, 1, 2 ] ), Transformation( [ 1, 1, 1, 1 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:991 # Input is: HomomorphismDigraphsFinder(CompleteDigraph(3), CompleteDigraph(3), fail, [], infinity, fail, 1, [1 .. 3], [], fail, fail, Group((1, 2, 3))); # Expected output: [ IdentityTransformation, Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:997 # Input is: gr1 := Digraph([[], [3], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:998 # Input is: gr2 := EmptyDigraph(10);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/grahom.tst:999 # Input is: DigraphHomomorphism(gr1, gr2); # Expected output: fail # But found: Error, Variable: 'DigraphHomomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1001 # Input is: gr2 := Digraph([[], [], [], [], [4], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1002 # Input is: DigraphHomomorphism(gr1, gr2); # Expected output: Transformation( [ 1, 5, 4, 4, 5 ] ) # But found: Error, Variable: 'DigraphHomomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1006 # Input is: gr1 := Digraph([[], [3], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1007 # Input is: gr2 := Digraph([[], [], [], [], [4], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1008 # Input is: HomomorphismsDigraphsRepresentatives(gr1, gr2); # Expected output: [ Transformation( [ 1, 5, 4, 4, 5 ] ), Transformation( [ 4, 5, 4, 4, 5 ] ), Transformation( [ 5, 5, 4, 4, 5 ] ) ] # But found: Error, Variable: 'HomomorphismsDigraphsRepresentatives' must have a value ######## ########> Diff in standard/grahom.tst:1011 # Input is: homos := HomomorphismsDigraphs(gr1, gr2); # Expected output: [ Transformation( [ 1, 5, 4, 4, 5, 2 ] ), Transformation( [ 1, 5, 4, 4, 5, 3 ] ), Transformation( [ 1, 5, 4, 4, 5 ] ), Transformation( [ 2, 5, 4, 4, 5, 1 ] ), Transformation( [ 2, 5, 4, 4, 5, 3 ] ), Transformation( [ 2, 5, 4, 4, 5 ] ), Transformation( [ 3, 5, 4, 4, 5, 1 ] ), Transformation( [ 3, 5, 4, 4, 5, 2 ] ), Transformation( [ 3, 5, 4, 4, 5 ] ), Transformation( [ 4, 5, 4, 4, 5, 1 ] ), Transformation( [ 4, 5, 4, 4, 5, 2 ] ), Transformation( [ 4, 5, 4, 4, 5, 3 ] ), Transformation( [ 4, 5, 4, 4, 5 ] ), Transformation( [ 5, 5, 4, 4, 5, 1 ] ), Transformation( [ 5, 5, 4, 4, 5, 2 ] ), Transformation( [ 5, 5, 4, 4, 5, 3 ] ), Transformation( [ 5, 5, 4, 4, 5 ] ), Transformation( [ 6, 5, 4, 4, 5, 1 ] ), Transformation( [ 6, 5, 4, 4, 5, 2 ] ), Transformation( [ 6, 5, 4, 4, 5, 3 ] ) ] # But found: Error, Variable: 'HomomorphismsDigraphs' must have a value ######## ########> Diff in standard/grahom.tst:1027 # Input is: edges := DigraphEdges(gr1);; # Expected output: # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/grahom.tst:1028 # Input is: mat := AdjacencyMatrix(gr2);; # Expected output: # But found: Error, Variable: 'AdjacencyMatrix' must have a value ######## ########> Diff in standard/grahom.tst:1029 # Input is: ForAll(homos, t -> ForAll(edges, e -> mat[e[1] ^ t][e[2] ^ t] = 1)); # Expected output: true # But found: Error, Variable: 'homos' must have a value Syntax warning: Unbound global variable in stream:1 ForAll(homos, t -> ForAll(edges, e -> mat[e[1] ^ t][e[2] ^ t] = 1)); ^^^^^ Syntax warning: Unbound global variable in stream:1 ForAll(homos, t -> ForAll(edges, e -> mat[e[1] ^ t][e[2] ^ t] = 1)); ^^^ ######## ########> Diff in standard/grahom.tst:1033 # Input is: gr1 := EmptyDigraph(1);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/grahom.tst:1034 # Input is: DigraphMonomorphism(gr1, gr1); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1036 # Input is: gr2 := EmptyDigraph(2);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/grahom.tst:1037 # Input is: DigraphMonomorphism(gr2, gr1); # Expected output: fail # But found: Error, Variable: 'DigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1039 # Input is: DigraphMonomorphism(gr1, gr2); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1041 # Input is: DigraphMonomorphism(CompleteDigraph(2), Digraph([[2], [1, 3], [2]])); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1045 # Input is: gr1 := ChainDigraph(2);; # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/grahom.tst:1046 # Input is: MonomorphismsDigraphs(gr1, EmptyDigraph(1)); # Expected output: [ ] # But found: Error, Variable: 'MonomorphismsDigraphs' must have a value ######## ########> Diff in standard/grahom.tst:1048 # Input is: gr2 := DigraphFromDigraph6String("&DZTAW?");; # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/grahom.tst:1049 # Input is: monos := MonomorphismsDigraphs(gr1, gr2); # Expected output: [ IdentityTransformation, Transformation( [ 1, 3, 3 ] ), Transformation( [ 1, 5, 3, 4, 5 ] ), Transformation( [ 2, 1 ] ), Transformation( [ 2, 3, 3 ] ), Transformation( [ 2, 5, 3, 4, 5 ] ), Transformation( [ 3, 2, 3 ] ), Transformation( [ 4, 2, 3, 4 ] ), Transformation( [ 4, 5, 3, 4, 5 ] ), Transformation( [ 5, 1, 3, 4, 5 ] ) ] # But found: Error, Variable: 'MonomorphismsDigraphs' must have a value ######## ########> Diff in standard/grahom.tst:1055 # Input is: monos = MonomorphismsDigraphsRepresentatives(gr1, gr2); # Expected output: true # But found: Error, Variable: 'monos' must have a value ######## ########> Diff in standard/grahom.tst:1057 # Input is: monos = HomomorphismsDigraphsRepresentatives(gr1, gr2); # Expected output: true # But found: Error, Variable: 'monos' must have a value ######## ########> Diff in standard/grahom.tst:1061 # Input is: gr1 := CycleDigraph(6);; # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/grahom.tst:1062 # Input is: gr2 := CycleDigraph(3);; # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/grahom.tst:1063 # Input is: DigraphEpimorphism(gr1, gr2); # Expected output: Transformation( [ 1, 2, 3, 1, 2, 3 ] ) # But found: Error, Variable: 'DigraphEpimorphism' must have a value ######## ########> Diff in standard/grahom.tst:1065 # Input is: DigraphEpimorphism(gr2, gr1); # Expected output: fail # But found: Error, Variable: 'DigraphEpimorphism' must have a value ######## ########> Diff in standard/grahom.tst:1069 # Input is: gr1 := CompleteDigraph(2);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/grahom.tst:1070 # Input is: gr2 := CompleteDigraph(3);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/grahom.tst:1071 # Input is: EpimorphismsDigraphs(gr1, gr2); # Expected output: [ ] # But found: Error, Variable: 'EpimorphismsDigraphs' must have a value ######## ########> Diff in standard/grahom.tst:1073 # Input is: gr1 := DigraphFromDigraph6String("&I@??HO???????A????");; # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/grahom.tst:1074 # Input is: DigraphEpimorphism(gr1, gr2); # Expected output: Transformation( [ 2, 1, 1, 2, 1, 3, 1, 2, 1, 1 ] ) # But found: Error, Variable: 'DigraphEpimorphism' must have a value ######## ########> Diff in standard/grahom.tst:1076 # Input is: epis := EpimorphismsDigraphsRepresentatives(gr1, gr2);; # Expected output: # But found: Error, Variable: 'EpimorphismsDigraphsRepresentatives' must have a value ######## ########> Diff in standard/grahom.tst:1077 # Input is: Length(epis); # Expected output: 972 # But found: Error, Variable: 'epis' must have a value ######## ########> Diff in standard/grahom.tst:1079 # Input is: epis := EpimorphismsDigraphs(gr1, gr2);; # Expected output: # But found: Error, Variable: 'EpimorphismsDigraphs' must have a value ######## ########> Diff in standard/grahom.tst:1080 # Input is: Length(epis); # Expected output: 5832 # But found: Error, Variable: 'epis' must have a value ######## ########> Diff in standard/grahom.tst:1082 # Input is: ForAll(epis, x -> RankOfTransformation(x, DigraphNrVertices(gr1)) = 3); # Expected output: true # But found: Error, Variable: 'epis' must have a value Syntax warning: Unbound global variable in stream:1 ForAll(epis, x -> RankOfTransformation(x, DigraphNrVertices(gr1)) = 3); ^^^^^^^^^^^^^^^^^ Syntax warning: Unbound global variable in stream:1 ForAll(epis, x -> RankOfTransformation(x, DigraphNrVertices(gr1)) = 3); ^^^ ######## ########> Diff in standard/grahom.tst:1086 # Input is: gr1 := CycleDigraph(3);; # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/grahom.tst:1087 # Input is: gr2 := CompleteBipartiteDigraph(4, 3);; # Expected output: # But found: Error, Variable: 'CompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/grahom.tst:1088 # Input is: DigraphEmbedding(gr1, gr2); # Expected output: fail # But found: Error, Variable: 'DigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1090 # Input is: gr2 := CompleteDigraph(4);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/grahom.tst:1091 # Input is: DigraphEmbedding(gr1, gr2); # Expected output: fail # But found: Error, Variable: 'DigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1093 # Input is: gr2 := Digraph([[2], [4, 1], [2], [3], [4]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1094 # Input is: DigraphEmbedding(gr1, gr2); # Expected output: Transformation( [ 2, 4, 3, 4 ] ) # But found: Error, Variable: 'DigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1096 # Input is: gr2 := CompleteDigraph(3);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/grahom.tst:1097 # Input is: DigraphEmbedding(gr1, gr2); # Expected output: fail # But found: Error, Variable: 'DigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1099 # Input is: DigraphEmbedding(gr1, gr1); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1101 # Input is: D := NullDigraph(2);; # Expected output: # But found: Error, Variable: 'NullDigraph' must have a value ######## ########> Diff in standard/grahom.tst:1102 # Input is: DD := DigraphFromDiSparse6String( ".~?C?_W@GN?e??@`W?wJ`cAG^?EG_@AEH?CacDWj@M??ga{Igq?WG_gbO?_J?}L_I_IFG~@?G_u_A\ \ AhBAiPOD`IB_QCEOxAck@HNB}KpK_KMhSBQ?`Hd[L?z`CIxY?}VOU`OGGteCVxHbcNXBd}JxO_uYo|\ \ bwVxmBiXxqEy\\ODf[SwOfwL`tgCOpncU`p~`e[WcA_JxYgsD@dg{Bpu`[bYRAc]hoHAd_BDIe@`hg\ \ Boed{ZwiaGOxFCs]HyeQ]XAbYL`}fmhogCSaYhEyTaR_?JAIdOYaTiwD@EEm@hFFObiqBSiYs@CQPK\ \ EaQWHBAMW]`Whw\\IIC?hAgPIKJQ[qjaciiTeYSP\\IWiXk_s[@pf?^BBa?SpkfiUwBAGRH[ck_zL@\ \ oJZNKq?PCGknHi_wciolS@O\\IuaGJLANx]LQD_]bW]J\\@_QPxK?uG@m?I_tCcnrDLMD@XKQLQ[b[\ \ cqX_?QA[e{]qlislBXjmGozLyXYTMQUQP_grj?aSkz^f{qrTiiQAtgWsrUhYXb@jsorreWbRCNAA_b\ \ IqSwxL}CQ_I_zru`sK@]GShrQNIziUes^K?`c?gSa?CGEaKDghAYEGkAmL_bbg@WHAyGHB?YPobcg@\ \ gHAuR_TdC?`D_KGhUAONxY@IVOC@IVpUDqVGkeKDW[B?KXf@MJGXdySg[e{YgfEiL`CCwSPUfKVpm`\ \ sH?ef[NgECY^?XfwB@u`SNiAEE[WD@uOiGCOSII@Y`Hk_W[yNDmGIQ?O\\iOeId_\\daCwOCgWGW@w\ \ Sp_hobyOb_]y_A{OpLhIJaO`wTydAOdhugQiPaikN@GIa\\HBGmJaIj?Xw@A?ZhC`ElOHj[@HsjgRA\ \ THqG@AF}PpJHyoQtkKM`bGenigk[oWNIokHH_{LaugGlbG_sJGZEkhWMA[gGPFusOcKEsoyEqtP~aG\ \ MPll_T`iKuBOWgIArIdAG@C`{PGGb]^Zb?ehwnKewWiLWwhPmUBjemsgGvIu{@RLIDrB`i{IQM]bBq\ \ cKyWLFcnzxKICIyKyEgI@g{XDeGbN");; # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/grahom.tst:1117 # Input is: DigraphEmbedding(D, DD); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1119 # Input is: D := DigraphDisjointUnion(CycleDigraph(3), CycleDigraph(5));; # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/grahom.tst:1120 # Input is: D := DigraphSymmetricClosure(D);; # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/grahom.tst:1121 # Input is: DigraphEmbedding(CycleDigraph(5), D); # Expected output: fail # But found: Error, Variable: 'DigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1123 # Input is: DigraphEmbedding(DigraphSymmetricClosure(CycleDigraph(5)), D); # Expected output: Transformation( [ 4, 5, 6, 7, 8, 6, 7, 8 ] ) # But found: Error, Variable: 'DigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1127 # Input is: gr := DigraphFromDigraph6String(Concatenation( "+U^{?A?BrwAHv_CNu@SMwHQm`GpyGbUYLAbfGTO?Enool[WrI", "HBSatQlC[TIC{iSBlo_VrO@u[_Eyk?]YS?")); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/grahom.tst:1131 # Input is: t := HomomorphismDigraphsFinder(gr, gr, fail, [], 1, fail, 0, [2, 6, 7, 11, 12, 13, 14, 15, 19, 20, 21], [], fail, fail)[1]; # Expected output: Transformation( [ 2, 13, 20, 19, 21, 19, 14, 13, 15, 14, 20, 6, 15, 21, 11, 12, 6, 7, 7, 12, 2, 11 ] ) # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1135 # Input is: ForAll(DigraphEdges(gr), e -> IsDigraphEdge(gr, e[1] ^ t, e[2] ^ t)); # Expected output: true # But found: Error, Variable: 'DigraphEdges' must have a value Syntax warning: Unbound global variable in stream:1 ForAll(DigraphEdges(gr), e -> IsDigraphEdge(gr, e[1] ^ t, e[2] ^ t)); ^^^^^^^^^^^^^ Syntax warning: Unbound global variable in stream:1 ForAll(DigraphEdges(gr), e -> IsDigraphEdge(gr, e[1] ^ t, e[2] ^ t)); ^^ Syntax warning: Unbound global variable in stream:1 ForAll(DigraphEdges(gr), e -> IsDigraphEdge(gr, e[1] ^ t, e[2] ^ t)); ^ Syntax warning: Unbound global variable in stream:1 ForAll(DigraphEdges(gr), e -> IsDigraphEdge(gr, e[1] ^ t, e[2] ^ t)); ^ ######## ########> Diff in standard/grahom.tst:1139 # Input is: gr := Digraph([[3, 4], [1, 3], [4], [1, 2, 3, 5], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1141 # Input is: ForAll(GeneratorsOfEndomorphismMonoid(gr), x -> IsDigraphEndomorphism(gr, x)); # Expected output: true # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value Syntax warning: Unbound global variable in stream:2 x -> IsDigraphEndomorphism(gr, x)); ^^^^^^^^^^^^^^^^^^^^^ Syntax warning: Unbound global variable in stream:2 x -> IsDigraphEndomorphism(gr, x)); ^^ ######## ########> Diff in standard/grahom.tst:1146 # Input is: IsDigraphEndomorphism(gr, x); # Expected output: false # But found: Error, Variable: 'IsDigraphEndomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1148 # Input is: IsDigraphHomomorphism(gr, gr, (1, 2)); # Expected output: false # But found: Error, Variable: 'IsDigraphHomomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1150 # Input is: gr := Digraph([[1, 1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1154 # Input is: IsDigraphEndomorphism(gr, x); # Expected output: Error, the 1st and 2nd arguments and must be digraphs with no mult\ \ iple edges, # But found: Error, Variable: 'IsDigraphEndomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1157 # Input is: IsDigraphEndomorphism(gr, ()); # Expected output: Error, the 1st and 2nd arguments and must not have multiple edges, # But found: Error, Variable: 'IsDigraphEndomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1159 # Input is: IsDigraphHomomorphism(gr, gr, ()); # Expected output: Error, the 1st and 2nd arguments and must be digraphs with no mult\ \ iple edges, # But found: Error, Variable: 'IsDigraphHomomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1162 # Input is: gr := DigraphTransitiveClosure(CompleteDigraph(2)); # Expected output: # But found: Error, Variable: 'DigraphTransitiveClosure' must have a value ######## ########> Diff in standard/grahom.tst:1164 # Input is: ForAll(GeneratorsOfEndomorphismMonoid(gr), x -> IsDigraphEndomorphism(gr, x)); # Expected output: true # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value Syntax warning: Unbound global variable in stream:2 x -> IsDigraphEndomorphism(gr, x)); ^^^^^^^^^^^^^^^^^^^^^ Syntax warning: Unbound global variable in stream:2 x -> IsDigraphEndomorphism(gr, x)); ^^ ######## ########> Diff in standard/grahom.tst:1168 # Input is: IsDigraphEndomorphism(gr, x); # Expected output: false # But found: Error, Variable: 'IsDigraphEndomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1171 # Input is: IsDigraphEndomorphism(gr, x); # Expected output: false # But found: Error, Variable: 'IsDigraphEndomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1173 # Input is: IsDigraphEndomorphism(gr, ()); # Expected output: true # But found: Error, Variable: 'IsDigraphEndomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1175 # Input is: IsDigraphEndomorphism(gr, (1, 2)); # Expected output: true # But found: Error, Variable: 'IsDigraphEndomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1177 # Input is: IsDigraphEndomorphism(gr, (1, 2)(3, 4)); # Expected output: false # But found: Error, Variable: 'IsDigraphEndomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1179 # Input is: IsDigraphEndomorphism(gr, (1, 2, 3, 4)); # Expected output: false # But found: Error, Variable: 'IsDigraphEndomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1181 # Input is: IsDigraphHomomorphism(NullDigraph(1), NullDigraph(3), Transformation([2, 2])); # Expected output: true # But found: Error, Variable: 'IsDigraphHomomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1187 # Input is: src := Digraph([[1], [1, 2], [1, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1189 # Input is: ran := Digraph([[1], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1191 # Input is: IsDigraphEpimorphism(src, ran, Transformation([1, 2, 2])); # Expected output: true # But found: Error, Variable: 'IsDigraphEpimorphism' must have a value ######## ########> Diff in standard/grahom.tst:1193 # Input is: IsDigraphEpimorphism(src, ran, Transformation([1, 2, 3])); # Expected output: false # But found: Error, Variable: 'IsDigraphEpimorphism' must have a value ######## ########> Diff in standard/grahom.tst:1195 # Input is: IsDigraphEpimorphism(src, src, Transformation([1, 2, 3])); # Expected output: true # But found: Error, Variable: 'IsDigraphEpimorphism' must have a value ######## ########> Diff in standard/grahom.tst:1197 # Input is: IsDigraphEpimorphism(src, src, Transformation([2, 2, 2])); # Expected output: false # But found: Error, Variable: 'IsDigraphEpimorphism' must have a value ######## ########> Diff in standard/grahom.tst:1199 # Input is: IsDigraphEpimorphism(src, ran, Transformation([2, 2, 2])); # Expected output: false # But found: Error, Variable: 'IsDigraphEpimorphism' must have a value ######## ########> Diff in standard/grahom.tst:1203 # Input is: src := Digraph([[1], [1, 2], [1, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1205 # Input is: ran := Digraph([[1], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1207 # Input is: IsDigraphEpimorphism(src, ran, ()); # Expected output: false # But found: Error, Variable: 'IsDigraphEpimorphism' must have a value ######## ########> Diff in standard/grahom.tst:1209 # Input is: IsDigraphEpimorphism(src, ran, (1, 2)); # Expected output: false # But found: Error, Variable: 'IsDigraphEpimorphism' must have a value ######## ########> Diff in standard/grahom.tst:1211 # Input is: IsDigraphEpimorphism(src, src, ()); # Expected output: true # But found: Error, Variable: 'IsDigraphEpimorphism' must have a value ######## ########> Diff in standard/grahom.tst:1213 # Input is: IsDigraphEpimorphism(src, src, (2, 3)); # Expected output: true # But found: Error, Variable: 'IsDigraphEpimorphism' must have a value ######## ########> Diff in standard/grahom.tst:1215 # Input is: IsDigraphEpimorphism(ran, src, ()); # Expected output: false # But found: Error, Variable: 'IsDigraphEpimorphism' must have a value ######## ########> Diff in standard/grahom.tst:1219 # Input is: src := Digraph([[1], [1, 2], [1, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1221 # Input is: ran := Digraph([[1], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1223 # Input is: IsDigraphMonomorphism(src, ran, Transformation([1, 2, 2])); # Expected output: false # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1225 # Input is: IsDigraphMonomorphism(src, ran, Transformation([1, 2, 3])); # Expected output: false # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1227 # Input is: IsDigraphMonomorphism(src, src, Transformation([1, 2, 3])); # Expected output: true # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1229 # Input is: IsDigraphMonomorphism(src, src, Transformation([2, 2, 2])); # Expected output: false # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1231 # Input is: IsDigraphMonomorphism(src, ran, Transformation([2, 2, 2])); # Expected output: false # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1233 # Input is: IsDigraphMonomorphism(ran, src, Transformation([2, 1])); # Expected output: false # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1235 # Input is: IsDigraphMonomorphism(ran, src, Transformation([1, 2])); # Expected output: true # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1239 # Input is: src := Digraph([[1], [1, 2], [1, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1241 # Input is: ran := Digraph([[1], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1243 # Input is: IsDigraphMonomorphism(src, ran, (1, 2)); # Expected output: false # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1245 # Input is: IsDigraphMonomorphism(src, ran, ()); # Expected output: false # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1247 # Input is: IsDigraphMonomorphism(src, src, ()); # Expected output: true # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1249 # Input is: IsDigraphMonomorphism(ran, src, (1, 2)); # Expected output: false # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1251 # Input is: IsDigraphMonomorphism(ran, src, ()); # Expected output: true # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1255 # Input is: src := Digraph([[1], [1, 2], [1, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1257 # Input is: ran := Digraph([[1], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1259 # Input is: IsDigraphEmbedding(src, ran, Transformation([1, 2, 2])); # Expected output: false # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1261 # Input is: IsDigraphEmbedding(src, ran, Transformation([1, 2, 3])); # Expected output: false # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1263 # Input is: IsDigraphEmbedding(src, src, Transformation([1, 2, 3])); # Expected output: true # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1265 # Input is: IsDigraphEmbedding(src, src, Transformation([2, 2, 2])); # Expected output: false # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1267 # Input is: IsDigraphEmbedding(src, ran, Transformation([2, 2, 2])); # Expected output: false # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1269 # Input is: IsDigraphEmbedding(ran, src, Transformation([2, 1])); # Expected output: false # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1271 # Input is: IsDigraphEmbedding(ran, src, Transformation([1, 2])); # Expected output: true # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1273 # Input is: src := Digraph([[1], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1275 # Input is: ran := Digraph([[1, 2], [1, 2], [1, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1277 # Input is: IsDigraphMonomorphism(src, ran, Transformation([1, 2])); # Expected output: true # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1279 # Input is: IsDigraphEmbedding(src, ran, Transformation([1, 2])); # Expected output: false # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1283 # Input is: src := Digraph([[1], [1, 2], [1, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1285 # Input is: ran := Digraph([[1], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1287 # Input is: IsDigraphEmbedding(src, ran, (1, 2)); # Expected output: false # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1289 # Input is: IsDigraphEmbedding(src, ran, ()); # Expected output: false # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1291 # Input is: IsDigraphEmbedding(src, src, ()); # Expected output: true # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1293 # Input is: IsDigraphEmbedding(ran, src, (1, 2)); # Expected output: false # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1295 # Input is: IsDigraphEmbedding(ran, src, ()); # Expected output: true # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1297 # Input is: src := Digraph([[1], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1299 # Input is: ran := Digraph([[1, 2], [1, 2], [1, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1301 # Input is: IsDigraphMonomorphism(src, ran, ()); # Expected output: true # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1303 # Input is: IsDigraphEmbedding(src, ran, ()); # Expected output: false # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1307 # Input is: D := JohnsonDigraph(5, 3); # Expected output: # But found: Error, Variable: 'JohnsonDigraph' must have a value ######## ########> Diff in standard/grahom.tst:1309 # Input is: IsDigraphColouring(D, [1, 2, 3, 3, 2, 1, 4, 5, 6, 7]); # Expected output: true # But found: Error, Variable: 'IsDigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:1311 # Input is: IsDigraphColouring(D, [1, 2, 3, 3, 2, 1, 2, 5, 6, 7]); # Expected output: false # But found: Error, Variable: 'IsDigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:1313 # Input is: IsDigraphColouring(D, [1, 2, 3, 3, 2, 1, 2, 5, 6, -1]); # Expected output: false # But found: Error, Variable: 'IsDigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:1315 # Input is: IsDigraphColouring(D, [1, 2, 3]); # Expected output: false # But found: Error, Variable: 'IsDigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:1317 # Input is: IsDigraphColouring(D, IdentityTransformation); # Expected output: true # But found: Error, Variable: 'IsDigraphColouring' must have a value ######## ########> Diff in standard/grahom.tst:1321 # Input is: D := Digraph([[2, 3], [], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1322 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit 3, # hint 0, # injective [1, 2, 3], # image [], # map [1, 2, 3], # colours1 [1, 3, 2]); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1336 # Input is: D := Digraph([[2, 3], [], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1337 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit 3, # hint 0, # injective [1, 2, 3], # image [,, 2], # map fail, # colours1 fail); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1349 # Input is: D := Digraph([[2, 3], [], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1350 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit 1, # hint 0, # injective [1, 2, 3], # image [, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1362 # Input is: D := Digraph([[2, 3], [], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1363 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit 2, # hint 0, # injective [1, 2, 3], # image [, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ Transformation( [ 1, 3, 3 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1375 # Input is: D := Digraph([[2, 3], [], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1376 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit 3, # hint 0, # injective [1, 2, 3], # image [, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1388 # Input is: D := Digraph([[2, 3], [], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1389 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 0, # injective [1, 2, 3], # image [, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1403 # Input is: D := Digraph([[2, 3], [], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1404 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 1, # injective [1, 2, 3], # image [, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1416 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 1, # injective [1, 2, 3], # image [3, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1428 # Input is: D := Digraph([[2, 3], [2], [3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1429 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 1, # injective [1, 2, 3], # image [, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1441 # Input is: D := Digraph([[2, 3], [2], [3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1442 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 1, # injective [1, 2, 3], # image [, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1454 # Input is: D := Digraph([[2, 3], [], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1455 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 1, # injective [1, 2, 3], # image [, 3], # map [1, 2, 3], # colours1 [1, 3, 2]); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1467 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 1, # injective [1, 2, 3], # image [], # map [1, 2, 3], # colours1 [1, 3, 2]); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1479 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 2, # injective [1, 2, 3], # image [, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1491 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 2, # injective [1, 2, 3], # image [3, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1505 # Input is: D := Digraph([[2, 3], [2], [3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1506 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 2, # injective [1, 2, 3], # image [, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1518 # Input is: D := Digraph([[2, 3], [2], [3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1519 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 2, # injective [1, 2, 3], # image [, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1531 # Input is: D := Digraph([[2, 3], [], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1532 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 2, # injective [1, 2, 3], # image [, 3], # map [1, 2, 3], # colours1 [1, 3, 2]); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1544 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 2, # injective [1, 2, 3], # image [], # map [1, 2, 3], # colours1 [1, 3, 2]); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1556 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 2, # injective [2, 3], # image [], # map [1, 2, 3], # colours1 [1, 3, 2]); # colours2 # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1568 # Input is: EmbeddingsDigraphsRepresentatives(NullDigraph(2), Digraph([[2, 3], [], []])); # Expected output: [ Transformation( [ 2, 3, 3 ] ) ] # But found: Error, Variable: 'EmbeddingsDigraphsRepresentatives' must have a value ######## ########> Diff in standard/grahom.tst:1573 # Input is: D1 := NullDigraph(2);; # Expected output: # But found: Error, Variable: 'NullDigraph' must have a value ######## ########> Diff in standard/grahom.tst:1574 # Input is: D2 := DigraphFromDiSparse6String( ".~?@c_oAN?xSA_XcBf?q^?YK?iooXja]oBJGlgZ_CLzgQoAn?kWjDIK[?P[c_qpNLM{{KFRMns`Wm\ \ tSNCuT^Z?a[rvOeCCdvGixXG`ZFc__AF?hKMg?IaGH]gGIAm?z?_lpGdmRUzMYQmoASkoKS]prafo[\ \ wws?[R_AcjsseVtaiXLcvXSwg`v@gfKBQ^KJc|n]D\\thb");; # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/grahom.tst:1578 # Input is: DigraphMonomorphism(D1, D2); # Expected output: IdentityTransformation # But found: Error, Variable: 'DigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1580 # Input is: D1 := CompleteDigraph(2);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/grahom.tst:1581 # Input is: DigraphMonomorphism(D1, D2); # Expected output: Transformation( [ 65, 66, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66 ] ) # But found: Error, Variable: 'DigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1586 # Input is: D := DigraphFromDigraph6String(Concatenation( "+U^{?A?BrwAHv_CNu@SMwHQm`GpyGbUYLAbfGTO?Enool[WrI", "HBSatQlC[TIC{iSBlo_VrO@u[_Eyk?]YS?"));; # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/grahom.tst:1589 # Input is: HomomorphismDigraphsFinder(D, D, fail, [], 1, fail, 1, [2, 6, 7, 11, 12, 13, 14, 15, 19, 20, 21], [], fail, fail); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1592 # Input is: D := Digraph([[2], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1593 # Input is: HomomorphismDigraphsFinder(D, D, fail, [], 1, fail, 1, [1], [], fail, fail); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1598 # Input is: D := Digraph([[2, 3], [1], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1599 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 1, # injective [1, 2, 3], # image [, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1611 # Input is: D := Digraph([[2, 3], [1], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1612 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 0, # injective [1, 2, 3], # image [, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1624 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 1, # injective [1, 2, 3], # image [3, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1636 # Input is: D := Digraph([[2, 3], [1, 2], [1, 3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1637 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 1, # injective [1, 2, 3], # image [, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1649 # Input is: D := Digraph([[2, 3], [1, 2], [1, 3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1650 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 1, # injective [1, 2, 3], # image [, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1662 # Input is: D := Digraph([[2, 3], [1], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1663 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 1, # injective [1, 2, 3], # image [, 3], # map [1, 2, 3], # colours1 [1, 3, 2]); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1675 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 1, # injective [1, 2, 3], # image [], # map [1, 2, 3], # colours1 [1, 3, 2]); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1687 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 2, # injective [1, 2, 3], # image [, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1699 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 2, # injective [1, 2, 3], # image [3, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1711 # Input is: D := DigraphAddAllLoops(Digraph([[2, 3], [1], [1], [], []]));; # Expected output: # But found: Error, Variable: 'DigraphAddAllLoops' must have a value ######## ########> Diff in standard/grahom.tst:1712 # Input is: EmbeddingsDigraphsRepresentatives(NullDigraph(2), D); # Expected output: [ Transformation( [ 1, 4, 3, 4 ] ), Transformation( [ 2, 3, 3 ] ), Transformation( [ 2, 4, 3, 4 ] ), Transformation( [ 4, 1, 3, 4 ] ), Transformation( [ 4, 2, 3, 4 ] ), Transformation( [ 4, 5, 3, 4, 5 ] ) ] # But found: Error, Variable: 'EmbeddingsDigraphsRepresentatives' must have a value ######## ########> Diff in standard/grahom.tst:1716 # Input is: D := Digraph([[2, 3], [1, 2], [1, 3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1717 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 1, # injective [1, 2, 3], # image [, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1729 # Input is: D := Digraph([[2, 3], [1, 2], [1, 3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1730 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 2, # injective [1, 2, 3], # image [, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1742 # Input is: D := Digraph([[2, 3], [1], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1743 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 2, # injective [1, 2, 3], # image [, 3], # map [1, 2, 3], # colours1 [1, 3, 2]); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1755 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 2, # injective [1, 2, 3], # image [], # map [1, 2, 3], # colours1 [1, 3, 2]); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1767 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 2, # injective [1, 2, 3], # image [, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ Transformation( [ 1, 3, 2 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1779 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 2, # injective [1, 2, 3], # image [3, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1791 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 2, # injective [2, 3], # image [, 3], # map fail, # colours1 fail); # colours2 # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1803 # Input is: D := DigraphAddAllLoops(Digraph([[2, 3], [1], [1], [], [5]]));; # Expected output: # But found: Error, Variable: 'DigraphAddAllLoops' must have a value ######## ########> Diff in standard/grahom.tst:1804 # Input is: EmbeddingsDigraphsRepresentatives(NullDigraph(2), D); # Expected output: [ Transformation( [ 1, 4, 3, 4 ] ), Transformation( [ 2, 3, 3 ] ), Transformation( [ 2, 4, 3, 4 ] ), Transformation( [ 4, 1, 3, 4 ] ), Transformation( [ 4, 2, 3, 4 ] ), Transformation( [ 4, 5, 3, 4, 5 ] ) ] # But found: Error, Variable: 'EmbeddingsDigraphsRepresentatives' must have a value ######## ########> Diff in standard/grahom.tst:1808 # Input is: EmbeddingsDigraphsRepresentatives(CompleteDigraph(2), D); # Expected output: [ IdentityTransformation, Transformation( [ 2, 1 ] ) ] # But found: Error, Variable: 'EmbeddingsDigraphsRepresentatives' must have a value ######## ########> Diff in standard/grahom.tst:1810 # Input is: MonomorphismsDigraphsRepresentatives(CompleteDigraph(2), D); # Expected output: [ IdentityTransformation, Transformation( [ 2, 1 ] ) ] # But found: Error, Variable: 'MonomorphismsDigraphsRepresentatives' must have a value ######## ########> Diff in standard/grahom.tst:1812 # Input is: D := Digraph([[3], [8], [9], [11], [2, 7, 8, 18], [18, 20], [1], [], [], [], [4, 8, 16], [13, 19], [], [4], [15], [1, 4, 6, 8], [], [7, 12], [], [8]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1815 # Input is: EmbeddingsDigraphsRepresentatives(CompleteDigraph(2), D); # Expected output: [ Transformation( [ 4, 11, 3, 4, 5, 6, 7, 8, 9, 10, 11 ] ), Transformation( [ 11, 4, 3, 4, 5, 6, 7, 8, 9, 10, 11 ] ) ] # But found: Error, Variable: 'EmbeddingsDigraphsRepresentatives' must have a value ######## ########> Diff in standard/grahom.tst:1818 # Input is: EmbeddingsDigraphs(CompleteDigraph(2), D); # Expected output: [ Transformation( [ 4, 11, 3, 4, 5, 6, 7, 8, 9, 10, 11 ] ), Transformation( [ 4, 11, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 19, 14, 15, 16, 17, 18, 13 ] ), Transformation( [ 4, 11, 3, 4, 5, 6, 7, 8, 9, 17, 11, 12, 13, 14, 15, 16, 10 ] ), Transformation( [ 4, 11, 3, 4, 5, 6, 7, 8, 9, 17, 11, 12, 19, 14, 15, 16, 10, 18, 13 ] ), Transformation( [ 11, 4, 3, 4, 5, 6, 7, 8, 9, 10, 11 ] ) , Transformation( [ 11, 4, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 19, 14, 15, 16, 17, 18, 13 ] ), Transformation( [ 11, 4, 3, 4, 5, 6, 7, 8, 9, 17, 11, 12, 13, 14, 15, 16, 10 ] ), Transformation( [ 11, 4, 3, 4, 5, 6, 7, 8, 9, 17, 11, 12, 19, 14, 15, 16, 10, 18, 13 ] ) ] # But found: Error, Variable: 'EmbeddingsDigraphs' must have a value ######## ########> Diff in standard/grahom.tst:1830 # Input is: D := DigraphAddAllLoops(Digraph([[2, 3], [1], [1], [], [5]]));; # Expected output: # But found: Error, Variable: 'DigraphAddAllLoops' must have a value ######## ########> Diff in standard/grahom.tst:1831 # Input is: HomomorphismDigraphsFinder(D, D, fail, # hook [], # user_param 1, # limit fail, # hint 2, # injective [1 .. 5], # image [1,, 4], # map fail, # colours1 fail); # colours2 # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1847 # Input is: D := Digraph(parts, {x, y} -> ForAll(x, z -> not z in y)); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:1849 # Input is: t := DigraphHomomorphism(CompleteDigraph(25), D); # Expected output: # But found: Error, Variable: 'DigraphHomomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1851 # Input is: tt := HomomorphismDigraphsFinder(CompleteDigraph(26), D, fail, # hook [], # user_param 1, # max_results fail, 0, [1 .. 280], OnTuples([2 .. 25], t), fail, fail)[1]; # Expected output: # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1863 # Input is: OnTuples([2 .. 25], t) = OnTuples([2 .. 25], tt); # Expected output: false # But found: Error, Variable: 't' must have a value ######## ########> Diff in standard/grahom.tst:1869 # Input is: D := DigraphSymmetricClosure(Digraph([[2, 3], [], [], [5], [], []]));; # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/grahom.tst:1870 # Input is: HomomorphismDigraphsFinder(D, D, hook, true, infinity, fail, 0, [1 .. 6], [], fail, fail); # Expected output: true # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1873 # Input is: found; # Expected output: 100 # But found: 0 ######## ########> Diff in standard/grahom.tst:1880 # Input is: D := DigraphSymmetricClosure(Digraph([[2, 3], [], [], [5], [], []]));; # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/grahom.tst:1881 # Input is: HomomorphismDigraphsFinder(D, D, hook, true, infinity, fail, 0, [1 .. 6], [], fail, fail); # Expected output: true # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1884 # Input is: found; # Expected output: 12 # But found: 0 ######## ########> Diff in standard/grahom.tst:1888 # Input is: D := DigraphDisjointUnion(CycleDigraph(3), CycleDigraph(5));; # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/grahom.tst:1889 # Input is: D := DigraphSymmetricClosure(D);; # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/grahom.tst:1890 # Input is: t := DigraphHomomorphism(DigraphSymmetricClosure(CycleDigraph(5)), D); # Expected output: Transformation( [ 1, 2, 3, 1, 2 ] ) # But found: Error, Variable: 'DigraphHomomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1892 # Input is: t := HomomorphismDigraphsFinder(DigraphSymmetricClosure(CycleDigraph(5)), D, fail, # hook [], # user_param 1, # max_results fail, 0, [1 .. 8], ListTransformation(t, 5), fail, fail)[1]; # Expected output: Transformation( [ 1, 2, 3, 1, 2 ] ) # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1904 # Input is: t := DigraphMonomorphism(DigraphSymmetricClosure(CycleDigraph(5)), D); # Expected output: Transformation( [ 4, 5, 6, 7, 8, 6, 7, 8 ] ) # But found: Error, Variable: 'DigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1906 # Input is: t := HomomorphismDigraphsFinder(DigraphSymmetricClosure(CycleDigraph(5)), D, fail, # hook [], # user_param 1, # max_results fail, 1, [1 .. 8], ListTransformation(t, 5), fail, fail); # Expected output: [ Transformation( [ 4, 5, 6, 7, 8, 6, 7, 8 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1918 # Input is: t := DigraphEmbedding(DigraphSymmetricClosure(CycleDigraph(5)), D); # Expected output: Transformation( [ 4, 5, 6, 7, 8, 6, 7, 8 ] ) # But found: Error, Variable: 'DigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:1920 # Input is: HomomorphismDigraphsFinder(DigraphSymmetricClosure(CycleDigraph(5)), D, fail, # hook [], # user_param 1, # max_results fail, 2, [1 .. 8], ListTransformation(t, 5), fail, fail); # Expected output: [ Transformation( [ 4, 5, 6, 7, 8, 6, 7, 8 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1932 # Input is: t := HomomorphismDigraphsFinder(DigraphSymmetricClosure(CycleDigraph(5)), D, fail, # hook [], # user_param 1, # max_results fail, 2, [1 .. 8], ListTransformation(t, 6), fail, fail); # Expected output: Error, the 9th argument is too long, must be at most 5, found 6, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1944 # Input is: t := HomomorphismDigraphsFinder(DigraphSymmetricClosure(CycleDigraph(5)), D, fail, # hook [], # user_param 1, # max_results fail, 0, [1 .. 8], [1, 1, 1, 1], fail, fail); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1956 # Input is: t := HomomorphismDigraphsFinder(DigraphSymmetricClosure(CycleDigraph(5)), D, fail, # hook [], # user_param 1, # max_results fail, 1, [1 .. 8], [1, 2, 3, 4], fail, fail); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1968 # Input is: t := HomomorphismDigraphsFinder(DigraphSymmetricClosure(CycleDigraph(5)), D, fail, # hook [], # user_param 2, # max_results fail, 1, [1 .. 8], [1, 1, 1, 1], fail, fail); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1980 # Input is: t := HomomorphismDigraphsFinder(DigraphSymmetricClosure(CycleDigraph(5)), D, fail, # hook [], # user_param 1, # max_results 2, 0, [1 .. 8], [4, 5, 6, 7], fail, fail); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:1994 # Input is: D := DigraphDisjointUnion(CycleDigraph(3), CycleDigraph(5));; # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/grahom.tst:1995 # Input is: t := DigraphHomomorphism(CycleDigraph(5), D); # Expected output: Transformation( [ 4, 5, 6, 7, 8, 6, 7, 8 ] ) # But found: Error, Variable: 'DigraphHomomorphism' must have a value ######## ########> Diff in standard/grahom.tst:1997 # Input is: t := HomomorphismDigraphsFinder(CycleDigraph(5), D, fail, # hook [], # user_param 1, # max_results fail, 0, [1 .. 8], ListTransformation(t, 5), fail, fail)[1]; # Expected output: Transformation( [ 4, 5, 6, 7, 8, 6, 7, 8 ] ) # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2009 # Input is: t := DigraphMonomorphism(CycleDigraph(5), D); # Expected output: Transformation( [ 4, 5, 6, 7, 8, 6, 7, 8 ] ) # But found: Error, Variable: 'DigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2011 # Input is: t := HomomorphismDigraphsFinder(CycleDigraph(5), D, fail, # hook [], # user_param 1, # max_results fail, 1, [1 .. 8], ListTransformation(t, 5), fail, fail); # Expected output: [ Transformation( [ 4, 5, 6, 7, 8, 6, 7, 8 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2023 # Input is: t := DigraphEmbedding(CycleDigraph(5), D); # Expected output: Transformation( [ 4, 5, 6, 7, 8, 6, 7, 8 ] ) # But found: Error, Variable: 'DigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:2025 # Input is: HomomorphismDigraphsFinder(CycleDigraph(5), D, fail, # hook [], # user_param 1, # max_results fail, 2, [1 .. 8], ListTransformation(t, 5), fail, fail); # Expected output: [ Transformation( [ 4, 5, 6, 7, 8, 6, 7, 8 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2037 # Input is: HomomorphismDigraphsFinder(CycleDigraph(5), D, fail, # hook [], # user_param 1, # max_results fail, 2, [1 .. 8], ListTransformation(t, 6), fail, fail); # Expected output: Error, the 9th argument is too long, must be at most 5, found 6, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2049 # Input is: D := DigraphDisjointUnion(CycleDigraph(3), CycleDigraph(5));; # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/grahom.tst:2050 # Input is: t := DigraphEmbedding(CycleDigraph(5), D); # Expected output: Transformation( [ 4, 5, 6, 7, 8, 6, 7, 8 ] ) # But found: Error, Variable: 'DigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:2052 # Input is: HomomorphismDigraphsFinder(CycleDigraph(5), D, fail, # hook [], # user_param 1, # max_results fail, 2, [1 .. 8], ListTransformation(t, 6), fail, fail); # Expected output: Error, the 9th argument is too long, must be at most 5, found 6, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2064 # Input is: HomomorphismDigraphsFinder(CycleDigraph(5), D, fail, # hook [], # user_param 1, # max_results fail, 0, [1 .. 8], [1, 1, 1, 1], fail, fail); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2076 # Input is: HomomorphismDigraphsFinder(CycleDigraph(5), D, fail, # hook [], # user_param 1, # max_results fail, 1, [1 .. 8], [1, 1, 1, 1], fail, fail); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2088 # Input is: HomomorphismDigraphsFinder(CycleDigraph(5), D, fail, # hook [], # user_param 1, # max_results fail, 2, [1 .. 8], [1, 1, 1, 1], fail, fail); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2100 # Input is: HomomorphismDigraphsFinder(CycleDigraph(5), D, fail, # hook [], # user_param 1, # max_results 2, 0, [1 .. 8], [4, 5, 6, 7], fail, fail); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2112 # Input is: HomomorphismDigraphsFinder(CycleDigraph(5), D, fail, # hook [], # user_param 1, # max_results 2, 0, [1 .. 8], [4, 5, 6, 7], fail, fail, [1, 3, 4, 5, 2]); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2125 # Input is: HomomorphismDigraphsFinder(CycleDigraph(5), D, fail, # hook [], # user_param 1, # max_results fail, 0, [1 .. 8], [4, 5, 6, 7], fail, fail, [1, 3, 4, 5, 2]); # Expected output: [ Transformation( [ 4, 5, 6, 7, 8, 6, 7, 8 ] ) ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2140 # Input is: HomomorphismDigraphsFinder(0); # Expected output: Error, there must be 11 or 12 arguments, found 1, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2142 # Input is: DigraphHomomorphism(NullDigraph(1), NullDigraph(513)); # Expected output: Error, the 2nd argument must have at most 512 vertices, found 513, # But found: Error, Variable: 'DigraphHomomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2144 # Input is: HomomorphismDigraphsFinder(NullDigraph(1), NullDigraph(510), fail, [], 1, false, 0, 0, 0, 0, 0); # Expected output: Error, the 6th argument must be an integer or fail, not boolean or fail\ \ , # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2148 # Input is: HomomorphismDigraphsFinder(NullDigraph(1), NullDigraph(510), fail, [], 1, fail, true, 0, 0, 0, 0); # Expected output: Error, the 8th argument must be a list or fail, not integer, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2151 # Input is: HomomorphismDigraphsFinder(NullDigraph(1), NullDigraph(510), fail, [], 1, fail, false, 0, 0, 0, 0); # Expected output: Error, the 8th argument must be a list or fail, not integer, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2154 # Input is: HomomorphismDigraphsFinder(NullDigraph(1), NullDigraph(510), fail, [], 1, fail, true, [1,, 3], 0, 0, 0); # Expected output: Error, the 8th argument must be a dense list, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2157 # Input is: HomomorphismDigraphsFinder(NullDigraph(1), NullDigraph(510), fail, [], 1, fail, true, [1, 1, 3], 0, 0, 0); # Expected output: Error, in the 8th argument position 2 is a duplicate, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2160 # Input is: HomomorphismDigraphsFinder(NullDigraph(1), NullDigraph(510), fail, [], 1, fail, true, [1, 2, 3], [5], 0, 0); # Expected output: Error, in the 9th argument the value 5 in position 1 does not be\ \ long to the 7th argument , # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2164 # Input is: HomomorphismDigraphsFinder(NullDigraph(1), NullDigraph(510), fail, [], 1, fail, true, [1, 2, 3], [1], true, 0); # Expected output: Error, the 10th argument must be a list or fail, not boolean or fail\ \ , # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2168 # Input is: HomomorphismDigraphsFinder(NullDigraph(1), NullDigraph(510), fail, [], 1, fail, true, [1, 2, 3], [1], fail, false); # Expected output: Error, the 11th argument must be a list or fail, not boolean or fail\ \ , # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2172 # Input is: HomomorphismDigraphsFinder(NullDigraph(1), NullDigraph(510), fail, [], 1, fail, true, [1, 2, 3], [1], fail, fail, true); # Expected output: Error, the 12th or 13th argument must be a permutation group or fail\ \ , not boolean or fail, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2176 # Input is: HomomorphismDigraphsFinder(NullDigraph(10), NullDigraph(510), fail, [], 1, fail, true, [1, 2, 3], [1], fail, fail, [1]); # Expected output: Error, the 12th argument must be a list of length 10, not 1, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2179 # Input is: HomomorphismDigraphsFinder(NullDigraph(1), NullDigraph(510), fail, [], 1, fail, true, [1, 2, 3], [1], fail, fail, "1"); # Expected output: Error, the 12th argument must consist of integers, but found list (str\ \ ing) in position 1, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2183 # Input is: HomomorphismDigraphsFinder(NullDigraph(2), NullDigraph(510), fail, [], 1, fail, true, [1, 2, 3], [1], fail, fail, [, 1]); # Expected output: Error, the 12th argument must be a dense list, but position 1 is not b\ \ ound, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2187 # Input is: HomomorphismDigraphsFinder(NullDigraph(3), NullDigraph(510), fail, [], 1, fail, true, [1, 2, 3], [1], fail, fail, [1, 3, 5]); # Expected output: Error, the 12th argument must consist of integers, in the range [1, 3]\ \ but found 5, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2191 # Input is: HomomorphismDigraphsFinder(NullDigraph(3), NullDigraph(510), fail, [], 1, fail, true, [1, 2, 3], [1], fail, fail, [1, 1, 3]); # Expected output: Error, the 12th argument must be duplicate-free, but the value 1 in po\ \ sition 2 is a duplicate, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2195 # Input is: HomomorphismDigraphsFinder(NullDigraph(3), NullDigraph(510), fail, [], 1, fail, true, [1, 2, 3], [1], fail, fail, 12); # Expected output: Error, the 12th or 13th argument must be a permutation group or fail\ \ , not integer, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2199 # Input is: HomomorphismDigraphsFinder(NullDigraph(3), NullDigraph(510), fail, [], 1, fail, true, [1, 2, 3], [1], fail, fail, true); # Expected output: Error, the 12th or 13th argument must be a permutation group or fail\ \ , not boolean or fail, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2203 # Input is: HomomorphismDigraphsFinder(NullDigraph(3), NullDigraph(510), fail, [], 1, fail, true, [1, 2, 3], [1], fail, fail, Group(MappingPermListList([1 .. 1000], [5 .. 1004]))); # Expected output: Error, expected group of automorphisms, but found a non-automorphism in positi\ \ on 1 of the group generators, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2208 # Input is: HomomorphismDigraphsFinder(NullDigraph(3), NullDigraph(510), fail, [], 1, fail, true, [1, 2, 3], [1], fail, fail, Group((1, 2), MappingPermListList([1 .. 1000], [5 .. 1004]))); # Expected output: Error, expected group of automorphisms, but found a non-automorphism in positi\ \ on 2 of the group generators, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2213 # Input is: HomomorphismDigraphsFinder(NullDigraph(3), ChainDigraph(3), fail, [], 1, fail, true, [1, 2, 3], [1], fail, fail, Group((1, 2, 3))); # Expected output: Error, expected group of automorphisms, but found a non-automorphism in positi\ \ on 1 of the group generators, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2217 # Input is: HomomorphismDigraphsFinder(NullDigraph(3), NullDigraph(3), fail, [], 1, fail, true, [1, 2, 3], [1], [1, 1, 1], [1, 2, 3], Group((1, 2, 3))); # Expected output: Error, expected group of automorphisms, but found a non-automorphism in positi\ \ on 1 of the group generators, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2221 # Input is: HomomorphismDigraphsFinder(NullDigraph(3), NullDigraph(3), fail, [], 1, fail, true, [1, 2, 3], [1], fail, fail, Group((1, 2, 3), (1, 2), (1, 3))); # Expected output: Error, expected at most 2 generators in the 12th or 13th argument but got 3, # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2227 # Input is: D1 := DigraphSymmetricClosure(Digraph([[2], [3], []]));; # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/grahom.tst:2228 # Input is: D2 := CompleteDigraph(3);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/grahom.tst:2229 # Input is: HomomorphismDigraphsFinder(D1, D2, fail, [], 1, fail, 2, [1, 2, 3], [1, 2, 3], fail, fail); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2232 # Input is: HomomorphismDigraphsFinder(D1, D2, fail, [], 1, fail, 2, [1, 2, 3], fail, fail, fail); # Expected output: [ ] # But found: Error, Variable: 'HomomorphismDigraphsFinder' must have a value ######## ########> Diff in standard/grahom.tst:2237 # Input is: DigraphSmallestLastOrder(D1); # Expected output: [ 3, 2, 1 ] # But found: Error, Variable: 'DigraphSmallestLastOrder' must have a value ######## ########> Diff in standard/grahom.tst:2239 # Input is: DigraphSmallestLastOrder(D2); # Expected output: [ 3, 2, 1 ] # But found: Error, Variable: 'DigraphSmallestLastOrder' must have a value ######## ########> Diff in standard/grahom.tst:2243 # Input is: D1 := DigraphFromGraph6String("E}hO"); # Expected output: # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/grahom.tst:2245 # Input is: D2 := DigraphFromGraph6String("E}h_"); # Expected output: # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/grahom.tst:2247 # Input is: mono := MonomorphismsDigraphs(D1, D2); # Expected output: [ ] # But found: Error, Variable: 'MonomorphismsDigraphs' must have a value ######## ########> Diff in standard/grahom.tst:2251 # Input is: gr := CompleteDigraph(5); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/grahom.tst:2253 # Input is: GeneratorsOfEndomorphismMonoid(gr); # Expected output: [ Transformation( [ 2, 3, 4, 5, 1 ] ), Transformation( [ 2, 1 ] ), IdentityTransformation ] # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:2256 # Input is: gr := CompleteDigraph(5); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/grahom.tst:2258 # Input is: GeneratorsOfEndomorphismMonoid(gr, [1, 1, 1, 2, 3]); # Expected output: [ Transformation( [ 1, 3, 2 ] ), Transformation( [ 2, 1 ] ), IdentityTransformation ] # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:2261 # Input is: GeneratorsOfEndomorphismMonoid(gr); # Expected output: [ Transformation( [ 2, 3, 4, 5, 1 ] ), Transformation( [ 2, 1 ] ), IdentityTransformation ] # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value ######## ########> Diff in standard/grahom.tst:2266 # Input is: gr1 := Digraph([[], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:2268 # Input is: gr2 := Digraph([[], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:2270 # Input is: IsDigraphAutomorphism(gr1, Transformation([1, 2])); # Expected output: true # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2272 # Input is: IsDigraphAutomorphism(gr1, Transformation([1, 2]), [1, 2]); # Expected output: true # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2274 # Input is: IsDigraphAutomorphism(gr2, Transformation([1, 2]), [1, 1]); # Expected output: true # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2276 # Input is: IsDigraphHomomorphism(gr1, gr2, Transformation([1, 2])); # Expected output: true # But found: Error, Variable: 'IsDigraphHomomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2278 # Input is: IsDigraphHomomorphism(gr1, gr2, Transformation([1, 2]), [1, 2], [1, 1]); # Expected output: false # But found: Error, Variable: 'IsDigraphHomomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2280 # Input is: IsDigraphHomomorphism(gr1, gr2, Transformation([1, 2]), [1, 1], [1, 1]); # Expected output: true # But found: Error, Variable: 'IsDigraphHomomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2282 # Input is: IsDigraphHomomorphism(gr1, gr2, Transformation([1, 2]), [1, 1], [1, 2]); # Expected output: false # But found: Error, Variable: 'IsDigraphHomomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2284 # Input is: gr1 := Digraph([[], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:2286 # Input is: gr1 := ChainDigraph(3); # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/grahom.tst:2288 # Input is: gr2 := ChainDigraph(6); # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/grahom.tst:2290 # Input is: IsDigraphHomomorphism(gr1, gr2, Transformation([1, 2, 3]), [1 .. 3], [1 .. 6])\ ; # Expected output: true # But found: Error, Variable: 'IsDigraphHomomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2292 # Input is: IsDigraphHomomorphism(gr1, gr2, Transformation([1, 2, 3]), [1 .. 3], [1, 1, 2,\ 3, 4, 5]); # Expected output: false # But found: Error, Variable: 'IsDigraphHomomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2294 # Input is: IsDigraphHomomorphism(gr1, gr2, Transformation([1, 2, 3]), [2, 2, 1], [2, 2, 1, 3, 4, 5]); # Expected output: true # But found: Error, Variable: 'IsDigraphHomomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2297 # Input is: IsDigraphHomomorphism(gr1, gr2, Transformation([1, 2, 3]), [2, 2, 1], [1, 1, 2, 3, 4, 5]); # Expected output: false # But found: Error, Variable: 'IsDigraphHomomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2300 # Input is: IsDigraphAutomorphism(gr1, Transformation([3, 2, 1]), [1, 2, 3]); # Expected output: false # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2302 # Input is: gr1 := CycleDigraph(6); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/grahom.tst:2308 # Input is: IsDigraphAutomorphism(gr1, x, [1 .. 6]); # Expected output: false # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2310 # Input is: IsDigraphAutomorphism(gr1, x, [1, 1, 2, 2, 3, 3]); # Expected output: false # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2312 # Input is: IsDigraphAutomorphism(gr1, x, [1, 1, 1, 1, 1, 1]); # Expected output: true # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2314 # Input is: IsDigraphAutomorphism(gr1, x, [1, 1, 2, 2, 3, 3]); # Expected output: false # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2316 # Input is: IsDigraphAutomorphism(gr1, x ^ 2, [1, 1, 2, 2, 3, 3]); # Expected output: false # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2318 # Input is: IsDigraphAutomorphism(gr1, x ^ 2, [1, 2, 2, 3, 4, 4]); # Expected output: false # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2320 # Input is: IsDigraphAutomorphism(gr1, x ^ 2, [1, 1, 1, 1, 1, 1]); # Expected output: true # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2322 # Input is: IsDigraphAutomorphism(gr1, x ^ 3, [1, 2, 2, 3, 4, 4]); # Expected output: false # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2324 # Input is: IsDigraphAutomorphism(gr1, x ^ 3, [1, 1, 1, 1, 1, 1]); # Expected output: true # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2326 # Input is: IsDigraphAutomorphism(gr1, t, [1 .. 6]); # Expected output: false # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2328 # Input is: IsDigraphAutomorphism(gr1, t, [1, 1, 2, 2, 3, 3]); # Expected output: false # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2330 # Input is: IsDigraphAutomorphism(gr1, t ^ 2, [1, 1, 2, 2, 3, 3]); # Expected output: false # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2332 # Input is: IsDigraphAutomorphism(gr1, t ^ 2, [1, 2, 2, 3, 4, 4]); # Expected output: false # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2334 # Input is: IsDigraphAutomorphism(gr1, t ^ 3, [1, 2, 2, 3, 4, 4]); # Expected output: false # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2336 # Input is: gr1 := DigraphFromDigraph6String("&D~~~~_"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/grahom.tst:2338 # Input is: ForAll(AutomorphismGroup(gr1), x -> x = () or not IsDigraphAutomorphism(gr1, x, [1 .. 5])); # Expected output: true # But found: Error, Variable: 'gr1' must have a value Syntax warning: Unbound global variable in stream:2 x -> x = () or not IsDigraphAutomorphism(gr1, x, [1 .. 5])); ^^^^^^^^^^^^^^^^^^^^^ Syntax warning: Unbound global variable in stream:2 x -> x = () or not IsDigraphAutomorphism(gr1, x, [1 .. 5])); ^^^ ######## ########> Diff in standard/grahom.tst:2341 # Input is: ForAll(AutomorphismGroup(gr1), x -> IsDigraphAutomorphism(gr1, x, [1, 1, 1, 1, 1])); # Expected output: true # But found: Error, Variable: 'gr1' must have a value Syntax warning: Unbound global variable in stream:2 x -> IsDigraphAutomorphism(gr1, x, [1, 1, 1, 1, 1])); ^^^^^^^^^^^^^^^^^^^^^ Syntax warning: Unbound global variable in stream:2 x -> IsDigraphAutomorphism(gr1, x, [1, 1, 1, 1, 1])); ^^^ ######## ########> Diff in standard/grahom.tst:2346 # Input is: gr1 := DigraphTransitiveClosure(CompleteDigraph(2)); # Expected output: # But found: Error, Variable: 'DigraphTransitiveClosure' must have a value ######## ########> Diff in standard/grahom.tst:2348 # Input is: IsDigraphEndomorphism(gr1, (1, 2), [1, 2]); # Expected output: false # But found: Error, Variable: 'IsDigraphEndomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2350 # Input is: IsDigraphEndomorphism(gr1, (1, 2), [1, 1]); # Expected output: true # But found: Error, Variable: 'IsDigraphEndomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2352 # Input is: IsDigraphEndomorphism(gr1, Transformation([1, 1]), [1, 2]); # Expected output: false # But found: Error, Variable: 'IsDigraphEndomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2354 # Input is: IsDigraphEndomorphism(gr1, Transformation([1, 1]), [1, 1]); # Expected output: true # But found: Error, Variable: 'IsDigraphEndomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2356 # Input is: ForAll(GeneratorsOfEndomorphismMonoid(gr1), x -> IsDigraphEndomorphism(gr1, x, [1, 1])); # Expected output: true # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value Syntax warning: Unbound global variable in stream:2 x -> IsDigraphEndomorphism(gr1, x, [1, 1])); ^^^^^^^^^^^^^^^^^^^^^ Syntax warning: Unbound global variable in stream:2 x -> IsDigraphEndomorphism(gr1, x, [1, 1])); ^^^ ######## ########> Diff in standard/grahom.tst:2359 # Input is: gr2 := Digraph([[3, 4], [1, 3], [4], [1, 2, 3, 5], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:2361 # Input is: ForAll(GeneratorsOfEndomorphismMonoid(gr2), x -> IsDigraphEndomorphism(gr2, x, [1, 1, 1, 1, 1])); # Expected output: true # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value Syntax warning: Unbound global variable in stream:2 x -> IsDigraphEndomorphism(gr2, x, [1, 1, 1, 1, 1])); ^^^^^^^^^^^^^^^^^^^^^ Syntax warning: Unbound global variable in stream:2 x -> IsDigraphEndomorphism(gr2, x, [1, 1, 1, 1, 1])); ^^^ ######## ########> Diff in standard/grahom.tst:2364 # Input is: gr1 := DigraphFromDigraph6String("&D~~~~_"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/grahom.tst:2366 # Input is: ForAll(GeneratorsOfEndomorphismMonoid(gr1), x -> IsDigraphEndomorphism(gr1, x, [1, 1, 1, 1, 1])); # Expected output: true # But found: Error, Variable: 'GeneratorsOfEndomorphismMonoid' must have a value Syntax warning: Unbound global variable in stream:2 x -> IsDigraphEndomorphism(gr1, x, [1, 1, 1, 1, 1])); ^^^^^^^^^^^^^^^^^^^^^ Syntax warning: Unbound global variable in stream:2 x -> IsDigraphEndomorphism(gr1, x, [1, 1, 1, 1, 1])); ^^^ ######## ########> Diff in standard/grahom.tst:2369 # Input is: ForAll(AutomorphismGroup(gr1), x -> IsDigraphEndomorphism(gr1, x, [1, 1, 1, 1, 1])); # Expected output: true # But found: Error, Variable: 'gr1' must have a value Syntax warning: Unbound global variable in stream:2 x -> IsDigraphEndomorphism(gr1, x, [1, 1, 1, 1, 1])); ^^^^^^^^^^^^^^^^^^^^^ Syntax warning: Unbound global variable in stream:2 x -> IsDigraphEndomorphism(gr1, x, [1, 1, 1, 1, 1])); ^^^ ######## ########> Diff in standard/grahom.tst:2374 # Input is: src := Digraph([[1], [1, 2], [1, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:2376 # Input is: ran := Digraph([[1], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:2378 # Input is: IsDigraphEpimorphism(src, ran, Transformation([1, 2, 2]), [1, 2, 2], [1, 2]); # Expected output: true # But found: Error, Variable: 'IsDigraphEpimorphism' must have a value ######## ########> Diff in standard/grahom.tst:2380 # Input is: IsDigraphEpimorphism(src, ran, Transformation([1, 2, 2]), [1, 2, 3], [1, 2]); # Expected output: false # But found: Error, Variable: 'IsDigraphEpimorphism' must have a value ######## ########> Diff in standard/grahom.tst:2382 # Input is: IsDigraphEpimorphism(src, src, Transformation([1, 2, 3]), [1, 1, 2], [1, 1, 2]); # Expected output: true # But found: Error, Variable: 'IsDigraphEpimorphism' must have a value ######## ########> Diff in standard/grahom.tst:2385 # Input is: IsDigraphEpimorphism(src, src, Transformation([1, 2, 3]), [1, 2, 3], [1, 1, 2]); # Expected output: false # But found: Error, Variable: 'IsDigraphEpimorphism' must have a value ######## ########> Diff in standard/grahom.tst:2388 # Input is: IsDigraphEpimorphism(src, src, (), [1, 2, 2], [1, 2, 2]); # Expected output: true # But found: Error, Variable: 'IsDigraphEpimorphism' must have a value ######## ########> Diff in standard/grahom.tst:2390 # Input is: IsDigraphEpimorphism(src, src, (2, 3), [1, 2, 3], [2, 3, 1]); # Expected output: false # But found: Error, Variable: 'IsDigraphEpimorphism' must have a value ######## ########> Diff in standard/grahom.tst:2392 # Input is: IsDigraphEpimorphism(src, src, (2, 3), [2, 1, 3], [2, 3, 1]); # Expected output: true # But found: Error, Variable: 'IsDigraphEpimorphism' must have a value ######## ########> Diff in standard/grahom.tst:2396 # Input is: src := Digraph([[1], [1, 2], [1, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:2398 # Input is: ran := Digraph([[1], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:2400 # Input is: IsDigraphMonomorphism(src, src, Transformation([1, 3, 2]), [2, 3, 1], [2, 1, 3]); # Expected output: true # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2403 # Input is: IsDigraphMonomorphism(src, src, Transformation([1, 3, 2]), [2, 3, 1], [2, 3, 1]); # Expected output: false # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2406 # Input is: IsDigraphMonomorphism(src, src, Transformation([1, 2, 3]), [2, 1, 1], [1, 2, 2]); # Expected output: false # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2409 # Input is: IsDigraphMonomorphism(src, src, Transformation([1, 2, 3]), [1, 2, 2], [1, 2, 2]); # Expected output: true # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2412 # Input is: IsDigraphMonomorphism(ran, src, Transformation([1, 2]), [2, 1], [1, 2, 1]); # Expected output: false # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2415 # Input is: IsDigraphMonomorphism(ran, src, Transformation([1, 2]), [2, 1], [1, 1, 1]); # Expected output: false # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2418 # Input is: IsDigraphMonomorphism(ran, src, Transformation([1, 2]), [1, 1], [1, 1, 2]); # Expected output: true # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2421 # Input is: IsDigraphMonomorphism(src, src, (), [1, 2, 2], [1, 2, 2]); # Expected output: true # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2423 # Input is: IsDigraphMonomorphism(src, src, (), [1, 1, 2], [1, 2, 2]); # Expected output: false # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2425 # Input is: IsDigraphMonomorphism(ran, src, (), [1, 1], [1, 1, 2]); # Expected output: true # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2427 # Input is: IsDigraphMonomorphism(ran, src, (), [1, 1], [2, 2, 1]); # Expected output: false # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2429 # Input is: IsDigraphMonomorphism(ran, src, (), [1, 2], [1, 2, 1]); # Expected output: true # But found: Error, Variable: 'IsDigraphMonomorphism' must have a value ######## ########> Diff in standard/grahom.tst:2433 # Input is: src := Digraph([[1], [1, 2], [1, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:2435 # Input is: ran := Digraph([[1], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grahom.tst:2437 # Input is: IsDigraphEmbedding(src, src, Transformation([1, 2, 3]), [1, 1, 1], [1, 1, 1]); # Expected output: true # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:2440 # Input is: IsDigraphEmbedding(src, src, Transformation([1, 2, 3]), [1, 1, 2], [1, 1, 2]); # Expected output: true # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:2443 # Input is: IsDigraphEmbedding(ran, src, Transformation([1, 2])); # Expected output: true # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:2445 # Input is: IsDigraphEmbedding(src, src, (), [1, 1, 1], [1, 1, 1]); # Expected output: true # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:2447 # Input is: IsDigraphEmbedding(src, src, (), [2, 1, 1], [1, 1, 1]); # Expected output: false # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:2449 # Input is: IsDigraphEmbedding(ran, src, (), [1, 1], [1, 1, 2]); # Expected output: true # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:2451 # Input is: IsDigraphEmbedding(ran, src, (), [2, 1], [1, 2, 2]); # Expected output: false # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:2453 # Input is: IsDigraphEmbedding(ran, src, (), [2, 1], [1, 1, 2]); # Expected output: false # But found: Error, Variable: 'IsDigraphEmbedding' must have a value ######## ########> Diff in standard/grahom.tst:2469 # Input is: DIGRAPHS_StopTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StopTest' must have a value ######## Digraphs package: standard/grahom.tst msecs: 944 false gap> ########> Diff in standard/grape.tst:14 # Input is: DIGRAPHS_StartTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StartTest' must have a value ######## ########> Diff in standard/grape.tst:19 # Input is: digraph := CayleyDigraph(group); # Expected output: # But found: Error, Variable: 'CayleyDigraph' must have a value ######## ########> Diff in standard/grape.tst:23 # Input is: digraph := CayleyDigraph(group); # Expected output: # But found: Error, Variable: 'CayleyDigraph' must have a value ######## ########> Diff in standard/grape.tst:25 # Input is: IsCayleyDigraph(digraph); # Expected output: true # But found: Error, Variable: 'IsCayleyDigraph' must have a value ######## ########> Diff in standard/grape.tst:27 # Input is: IsDigraph(digraph); # Expected output: true # But found: Error, Variable: 'IsDigraph' must have a value ######## ########> Diff in standard/grape.tst:29 # Input is: digraph := CayleyDigraph(group, [()]); # Expected output: # But found: Error, Variable: 'CayleyDigraph' must have a value ######## ########> Diff in standard/grape.tst:31 # Input is: GroupOfCayleyDigraph(digraph) = group; # Expected output: true # But found: Error, Variable: 'GroupOfCayleyDigraph' must have a value ######## ########> Diff in standard/grape.tst:33 # Input is: GeneratorsOfCayleyDigraph(digraph); # Expected output: [ () ] # But found: Error, Variable: 'GeneratorsOfCayleyDigraph' must have a value ######## ########> Diff in standard/grape.tst:35 # Input is: digraph := CayleyDigraph(group, [(1, 2, 3, 4), (2, 5)]); # Expected output: Error, the 2nd argument must consist of elements of the 1st argument, # But found: Error, Variable: 'CayleyDigraph' must have a value ######## ########> Diff in standard/grape.tst:38 # Input is: digraph := CayleyDigraph(group); # Expected output: Error, the 1st argument must be a finite group, # But found: Error, Variable: 'CayleyDigraph' must have a value ######## ########> Diff in standard/grape.tst:42 # Input is: digraph := NullDigraph(4); # Expected output: # But found: Error, Variable: 'NullDigraph' must have a value ######## ########> Diff in standard/grape.tst:44 # Input is: HasDigraphGroup(digraph); # Expected output: true # But found: Error, Variable: 'HasDigraphGroup' must have a value ######## ########> Diff in standard/grape.tst:46 # Input is: digraph := DigraphCopy(digraph); # Expected output: # But found: Error, Variable: 'DigraphCopy' must have a value ######## ########> Diff in standard/grape.tst:48 # Input is: HasDigraphGroup(digraph); # Expected output: false # But found: Error, Variable: 'HasDigraphGroup' must have a value ######## ########> Diff in standard/grape.tst:50 # Input is: SetDigraphGroup(digraph, Group((1, 3), (1, 2)(3, 4))); # Expected output: # But found: Error, Variable: 'SetDigraphGroup' must have a value ######## ########> Diff in standard/grape.tst:51 # Input is: digraph := DigraphAddEdgeOrbit(digraph, [4, 3]); # Expected output: # But found: Error, Variable: 'DigraphAddEdgeOrbit' must have a value ######## ########> Diff in standard/grape.tst:53 # Input is: Graph(digraph); # Expected output: rec( adjacencies := [ [ 2, 4 ] ], group := Group([ (1,3), (1,2)(3,4) ]), isGraph := true, names := [ 1 .. 4 ], order := 4, representatives := [ 1 ], schreierVector := [ -1, 2, 1, 2 ] ) # But found: Error, Variable: 'Graph' must have a value ######## ########> Diff in standard/grape.tst:57 # Input is: IsNullDigraph(DigraphRemoveEdgeOrbit(digraph, [4, 3])); # Expected output: true # But found: Error, Variable: 'IsNullDigraph' must have a value ######## ########> Diff in standard/grape.tst:61 # Input is: digraph := CompleteDigraph(4); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/grape.tst:63 # Input is: HasDigraphGroup(digraph); # Expected output: true # But found: Error, Variable: 'HasDigraphGroup' must have a value ######## ########> Diff in standard/grape.tst:65 # Input is: digraph := DigraphCopy(digraph); # Expected output: # But found: Error, Variable: 'DigraphCopy' must have a value ######## ########> Diff in standard/grape.tst:67 # Input is: HasDigraphGroup(digraph); # Expected output: false # But found: Error, Variable: 'HasDigraphGroup' must have a value ######## ########> Diff in standard/grape.tst:69 # Input is: SetDigraphGroup(digraph, Group((1, 3), (1, 2)(3, 4))); # Expected output: # But found: Error, Variable: 'SetDigraphGroup' must have a value ######## ########> Diff in standard/grape.tst:70 # Input is: digraph := DigraphRemoveEdgeOrbit(digraph, [1, 3]); # Expected output: # But found: Error, Variable: 'DigraphRemoveEdgeOrbit' must have a value ######## ########> Diff in standard/grape.tst:72 # Input is: IsCompleteDigraph(DigraphAddEdgeOrbit(digraph, [1, 3])); # Expected output: true # But found: Error, Variable: 'IsCompleteDigraph' must have a value ######## ########> Diff in standard/grape.tst:74 # Input is: Graph(digraph); # Expected output: rec( adjacencies := [ [ 2, 4 ] ], group := Group([ (1,3), (1,2)(3,4) ]), isGraph := true, names := [ 1 .. 4 ], order := 4, representatives := [ 1 ], schreierVector := [ -1, 2, 1, 2 ] ) # But found: Error, Variable: 'Graph' must have a value ######## ########> Diff in standard/grape.tst:80 # Input is: if DIGRAPHS_IsGrapeLoaded then gr := Digraph(JohnsonGraph(5, 3)); else gr := JohnsonDigraph(5, 3); SetDigraphGroup(gr, Group((1, 7, 10, 6, 3)(2, 8, 4, 9, 5), (4, 7)(5, 8)(6, 9))); fi; # Expected output: # But found: Error, Variable: 'DIGRAPHS_IsGrapeLoaded' must have a value ######## ########> Diff in standard/grape.tst:87 # Input is: HasDigraphGroup(gr); # Expected output: true # But found: Error, Variable: 'HasDigraphGroup' must have a value ######## ########> Diff in standard/grape.tst:89 # Input is: DigraphGroup(gr); # Expected output: Group([ (1,7,10,6,3)(2,8,4,9,5), (4,7)(5,8)(6,9) ]) # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/grape.tst:91 # Input is: if DIGRAPHS_IsGrapeLoaded then gr := Digraph(CompleteGraph(Group((1, 2, 3), (1, 2)))); else gr := Digraph([[2, 3], [1, 3], [1, 2]]); SetDigraphGroup(gr, Group((1, 2, 3), (1, 2))); fi; # Expected output: # But found: Error, Variable: 'DIGRAPHS_IsGrapeLoaded' must have a value ######## ########> Diff in standard/grape.tst:97 # Input is: HasDigraphGroup(gr); # Expected output: true # But found: Error, Variable: 'HasDigraphGroup' must have a value ######## ########> Diff in standard/grape.tst:99 # Input is: DigraphGroup(gr); # Expected output: Group([ (1,2,3), (1,2) ]) # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/grape.tst:101 # Input is: if DIGRAPHS_IsGrapeLoaded then gr := Digraph(Graph(Group([()]), [1, 2, 3], OnPoints, function(x, y) return x < y; end)); else gr := Digraph([[2, 3], [3], []]); fi; # Expected output: # But found: Error, Variable: 'DIGRAPHS_IsGrapeLoaded' must have a value ######## ########> Diff in standard/grape.tst:111 # Input is: HasDigraphGroup(gr); # Expected output: false # But found: Error, Variable: 'HasDigraphGroup' must have a value ######## ########> Diff in standard/grape.tst:113 # Input is: DigraphGroup(gr); # Expected output: Group(()) # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/grape.tst:115 # Input is: HasDigraphGroup(gr); # Expected output: true # But found: Error, Variable: 'HasDigraphGroup' must have a value ######## ########> Diff in standard/grape.tst:119 # Input is: digraph := EdgeOrbitsDigraph(Group((1, 3), (1, 2)(3, 4)), [[1, 2], [4, 5]], 5); # Expected output: # But found: Error, Variable: 'EdgeOrbitsDigraph' must have a value ######## ########> Diff in standard/grape.tst:122 # Input is: OutNeighbours(digraph); # Expected output: [ [ 2, 4, 5 ], [ 1, 3, 5 ], [ 2, 4, 5 ], [ 1, 3, 5 ], [ ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/grape.tst:124 # Input is: RepresentativeOutNeighbours(digraph); # Expected output: [ [ 2, 4, 5 ], [ ] ] # But found: Error, Variable: 'RepresentativeOutNeighbours' must have a value ######## ########> Diff in standard/grape.tst:126 # Input is: HasDigraphGroup(digraph); # Expected output: true # But found: Error, Variable: 'HasDigraphGroup' must have a value ######## ########> Diff in standard/grape.tst:128 # Input is: DigraphGroup(digraph) = Group((1, 3), (1, 2)(3, 4)); # Expected output: true # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/grape.tst:130 # Input is: digraph := EdgeOrbitsDigraph(Group(()), [3, 2], 3); # Expected output: # But found: Error, Variable: 'EdgeOrbitsDigraph' must have a value ######## ########> Diff in standard/grape.tst:132 # Input is: OutNeighbours(digraph); # Expected output: [ [ ], [ ], [ 2 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/grape.tst:134 # Input is: HasDigraphGroup(digraph); # Expected output: true # But found: Error, Variable: 'HasDigraphGroup' must have a value ######## ########> Diff in standard/grape.tst:136 # Input is: HasDigraphGroup(DigraphCopy(digraph)); # Expected output: false # But found: Error, Variable: 'HasDigraphGroup' must have a value ######## ########> Diff in standard/grape.tst:138 # Input is: digraph := EdgeOrbitsDigraph(Group(()), [3, 2]); # Expected output: # But found: Error, Variable: 'EdgeOrbitsDigraph' must have a value ######## ########> Diff in standard/grape.tst:140 # Input is: OutNeighbours(digraph); # Expected output: [ ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/grape.tst:142 # Input is: HasDigraphGroup(digraph); # Expected output: true # But found: Error, Variable: 'HasDigraphGroup' must have a value ######## ########> Diff in standard/grape.tst:144 # Input is: digraph := EdgeOrbitsDigraph(Group((1, 2)), [[1, 2], [3, 6, 5]]); # Expected output: Error, the 2nd argument must be a list of pairs of positive integers, # But found: Error, Variable: 'EdgeOrbitsDigraph' must have a value ######## ########> Diff in standard/grape.tst:146 # Input is: digraph := EdgeOrbitsDigraph(Group((1, 2)), [[1, 2], [3, -6]]); # Expected output: Error, the 2nd argument must be a list of pairs of positive integers, # But found: Error, Variable: 'EdgeOrbitsDigraph' must have a value ######## ########> Diff in standard/grape.tst:148 # Input is: digraph := EdgeOrbitsDigraph(Group((1, 2)), [[1, 2], [3, 6]], -1); # Expected output: Error, the 3rd argument must be a non-negative integer, # But found: Error, Variable: 'EdgeOrbitsDigraph' must have a value ######## ########> Diff in standard/grape.tst:152 # Input is: gr1 := CayleyDigraph(DihedralGroup(8)); # Expected output: # But found: Error, Variable: 'CayleyDigraph' must have a value ######## ########> Diff in standard/grape.tst:154 # Input is: gr2 := DigraphAddEdgeOrbit(gr1, [1, 8]); # Expected output: # But found: Error, Variable: 'DigraphAddEdgeOrbit' must have a value ######## ########> Diff in standard/grape.tst:156 # Input is: DigraphEdges(gr1); # Expected output: [ [ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 2, 1 ], [ 2, 8 ], [ 2, 6 ], [ 3, 5 ], [ 3, 4 ], [ 3, 7 ], [ 4, 6 ], [ 4, 7 ], [ 4, 1 ], [ 5, 3 ], [ 5, 2 ], [ 5, 8 ], [ 6, 4 ], [ 6, 5 ], [ 6, 2 ], [ 7, 8 ], [ 7, 1 ], [ 7, 3 ], [ 8, 7 ], [ 8, 6 ], [ 8, 5 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/grape.tst:161 # Input is: DigraphEdges(gr2); # Expected output: [ [ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 1, 8 ], [ 2, 1 ], [ 2, 8 ], [ 2, 6 ], [ 2, 3 ], [ 3, 5 ], [ 3, 4 ], [ 3, 7 ], [ 3, 2 ], [ 4, 6 ], [ 4, 7 ], [ 4, 1 ], [ 4, 5 ], [ 5, 3 ], [ 5, 2 ], [ 5, 8 ], [ 5, 4 ], [ 6, 4 ], [ 6, 5 ], [ 6, 2 ], [ 6, 7 ], [ 7, 8 ], [ 7, 1 ], [ 7, 3 ], [ 7, 6 ], [ 8, 7 ], [ 8, 6 ], [ 8, 5 ], [ 8, 1 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/grape.tst:167 # Input is: gr3 := DigraphRemoveEdgeOrbit(gr2, [1, 8]); # Expected output: # But found: Error, Variable: 'DigraphRemoveEdgeOrbit' must have a value ######## ########> Diff in standard/grape.tst:169 # Input is: gr3 = gr1; # Expected output: true # But found: Error, Variable: 'gr3' must have a value ######## ########> Diff in standard/grape.tst:171 # Input is: gr3 := DigraphRemoveEdgeOrbit(gr1, [1, 3]); # Expected output: # But found: Error, Variable: 'DigraphRemoveEdgeOrbit' must have a value ######## ########> Diff in standard/grape.tst:173 # Input is: gr3 := DigraphRemoveEdgeOrbit(gr3, [1, 2]); # Expected output: # But found: Error, Variable: 'DigraphRemoveEdgeOrbit' must have a value ######## ########> Diff in standard/grape.tst:175 # Input is: gr3 := DigraphRemoveEdgeOrbit(gr3, [1, 4]); # Expected output: # But found: Error, Variable: 'DigraphRemoveEdgeOrbit' must have a value ######## ########> Diff in standard/grape.tst:177 # Input is: DigraphAddEdgeOrbit(gr1, [0, 3]); # Expected output: Error, the 2nd argument must be a list of 2 positive integers, # But found: Error, Variable: 'DigraphAddEdgeOrbit' must have a value ######## ########> Diff in standard/grape.tst:179 # Input is: DigraphAddEdgeOrbit(gr1, [1, 2, 3]); # Expected output: Error, the 2nd argument must be a list of 2 positive integers, # But found: Error, Variable: 'DigraphAddEdgeOrbit' must have a value ######## ########> Diff in standard/grape.tst:181 # Input is: DigraphRemoveEdgeOrbit(gr1, [0, 3]); # Expected output: Error, the 2nd argument must be a pair of positive integers, # But found: Error, Variable: 'DigraphRemoveEdgeOrbit' must have a value ######## ########> Diff in standard/grape.tst:183 # Input is: DigraphRemoveEdgeOrbit(gr1, [1, 2, 3]); # Expected output: Error, the 2nd argument must be a pair of positive integers, # But found: Error, Variable: 'DigraphRemoveEdgeOrbit' must have a value ######## ########> Diff in standard/grape.tst:185 # Input is: gr2 := DigraphAddEdgeOrbit(gr1, [1, 4]); # Expected output: # But found: Error, Variable: 'DigraphAddEdgeOrbit' must have a value ######## ########> Diff in standard/grape.tst:187 # Input is: gr1 = gr2; # Expected output: true # But found: Error, Variable: 'gr1' must have a value ######## ########> Diff in standard/grape.tst:189 # Input is: DigraphAddEdgeOrbit(gr1, [3, 9]); # Expected output: Error, the 2nd argument must be a list of 2 vertices of the 1st argumen\ \ t , # But found: Error, Variable: 'DigraphAddEdgeOrbit' must have a value ######## ########> Diff in standard/grape.tst:192 # Input is: DigraphRemoveEdgeOrbit(gr1, [3, 9]); # Expected output: Error, the 2nd argument must be a pair of vertices of the 1st argument \ \ , # But found: Error, Variable: 'DigraphRemoveEdgeOrbit' must have a value ######## ########> Diff in standard/grape.tst:195 # Input is: gr2 := DigraphRemoveEdgeOrbit(gr1, [1, 8]); # Expected output: # But found: Error, Variable: 'DigraphRemoveEdgeOrbit' must have a value ######## ########> Diff in standard/grape.tst:197 # Input is: gr1 = gr2; # Expected output: true # But found: Error, Variable: 'gr1' must have a value ######## ########> Diff in standard/grape.tst:201 # Input is: gr := Digraph([[2, 2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grape.tst:203 # Input is: if DIGRAPHS_IsGrapeLoaded then Graph(gr); fi; # Expected output: # But found: Error, Variable: 'DIGRAPHS_IsGrapeLoaded' must have a value ######## ########> Diff in standard/grape.tst:208 # Input is: Digraph(SymmetricGroup(3), [1, 2, 3], OnPoints, {x, y} -> x <> y); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/grape.tst:212 # Input is: DIGRAPHS_StopTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StopTest' must have a value ######## Digraphs package: standard/grape.tst msecs: 150 false gap> ########> Diff in standard/io.tst:14 # Input is: DIGRAPHS_StartTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StartTest' must have a value ######## ########> Diff in standard/io.tst:17 # Input is: DigraphFromGraph6String("?"); # Expected output: # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/io.tst:19 # Input is: DigraphFromGraph6String("E?A?"); # Expected output: # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/io.tst:21 # Input is: DigraphFromGraph6String("@"); # Expected output: # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/io.tst:23 # Input is: gr := Digraph(300, [1, 2], [2, 1]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:25 # Input is: str := Graph6String(gr);; # Expected output: # But found: Error, Variable: 'Graph6String' must have a value ######## ########> Diff in standard/io.tst:26 # Input is: DigraphFromGraph6String(str) = gr; # Expected output: true # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/io.tst:28 # Input is: gr := Digraph([[2], [1, 4], [5], [2], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:30 # Input is: str := Graph6String(gr); # Expected output: "DaG" # But found: Error, Variable: 'Graph6String' must have a value ######## ########> Diff in standard/io.tst:32 # Input is: DigraphFromGraph6String(str); # Expected output: # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/io.tst:36 # Input is: List(l, x -> DigraphFromGraph6String(x)); # Expected output: [ , , , , , , , ] # But found: Syntax warning: Unbound global variable in stream:1 List(l, x -> DigraphFromGraph6String(x)); ^^^^^^^^^^^^^^^^^^^^^^^ Error, Variable: 'DigraphFromGraph6String' must have an assigned value ######## ########> Diff in standard/io.tst:45 # Input is: DigraphFromGraph6String(ListWithIdenticalEntries(500, '~')); # Expected output: Error, the 2nd argument is not a valid graph6 string, # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/io.tst:47 # Input is: D := DigraphFromGraph6String(IsMutableDigraph, "Dhc"); # Expected output: # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/io.tst:51 # Input is: str := Concatenation(DIGRAPHS_Dir(), "/data/graph5.g6.gz");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:52 # Input is: list := ReadDigraphs(str);; # Expected output: # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:53 # Input is: Size(list); # Expected output: 34 # But found: Error, Variable: 'list' must have a value ######## ########> Diff in standard/io.tst:55 # Input is: list2 := ReadDigraphs(str, DigraphFromGraph6String);; # Expected output: # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:56 # Input is: list = list2; # Expected output: true # But found: Error, Variable: 'list' must have a value ######## ########> Diff in standard/io.tst:58 # Input is: gr := ReadDigraphs(str, 10); # Expected output: # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:60 # Input is: list = gr; # Expected output: false # But found: Error, Variable: 'list' must have a value ######## ########> Diff in standard/io.tst:62 # Input is: list[10] = gr; # Expected output: true # But found: Error, Variable: 'list' must have a value ######## ########> Diff in standard/io.tst:64 # Input is: ReadDigraphs(34, DigraphFromGraph6String, 5); # Expected output: Error, the 1st argument must be a string or IO file object, # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:66 # Input is: ReadDigraphs(str, (1, 6, 5), 5); # Expected output: Error, the argument must be a function or fail, # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:68 # Input is: ReadDigraphs(str, DigraphFromGraph6String, 0); # Expected output: Error, the argument must be a positive integer or infinity # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:70 # Input is: str := Concatenation(DIGRAPHS_Dir(), "/data/tree9.4.txt");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:71 # Input is: list := ReadDigraphs(str);; # Expected output: # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:72 # Input is: list2 := ReadDigraphs(str, DigraphPlainTextLineDecoder(" ", " ", 1), infinity);; # Expected output: # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:75 # Input is: list = list2; # Expected output: true # But found: Error, Variable: 'list' must have a value ######## ########> Diff in standard/io.tst:77 # Input is: ReadDigraphs(str, 2, true, "elephant"); # Expected output: Error, there must be 1, 2, or 3 arguments, # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:80 # Input is: ReadDigraphs(badfilename, 3); # Expected output: Error, cannot open the file given as the 1st argument , # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:84 # Input is: DigraphFromSparse6String(":@"); # Expected output: # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/io.tst:86 # Input is: DigraphFromSparse6String(Concatenation(":[___dCfEcdFjCIideLhIfJ", "kLgkQge`RSbPTaOTbMNaS`QY")); # Expected output: # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/io.tst:89 # Input is: DigraphFromSparse6String(":I`ACWqHKhhccTF"); # Expected output: # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/io.tst:91 # Input is: DigraphFromSparse6String(":U___gFecGdHcEdFcFdE`GHbILaJKbNaM`RS"); # Expected output: # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/io.tst:93 # Input is: DigraphFromSparse6String(":U___fEcdcdIeHfGcFdE`GHbILaJKbNaM`RS"); # Expected output: # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/io.tst:95 # Input is: DigraphFromSparse6String(":U___fEcdGcdeJfIcFdEbLNaKM`H`GbIRaJQ"); # Expected output: # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/io.tst:97 # Input is: gr := Digraph([[2], [1, 4], [5], [2], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:99 # Input is: str := Sparse6String(gr); # Expected output: ":Dapj" # But found: Error, Variable: 'Sparse6String' must have a value ######## ########> Diff in standard/io.tst:101 # Input is: DigraphFromSparse6String(str); # Expected output: # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/io.tst:103 # Input is: gr := Digraph(231, [1, 1, 3, 4], [3, 4, 1, 1]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:105 # Input is: str := Sparse6String(gr); # Expected output: ":~?Bf_O?_F" # But found: Error, Variable: 'Sparse6String' must have a value ######## ########> Diff in standard/io.tst:107 # Input is: DigraphFromSparse6String(str); # Expected output: # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/io.tst:109 # Input is: gr := Digraph(rec(DigraphNrVertices := 2 ^ 17, DigraphSource := [1, 1, 3, 4, 1\ 0, 100], DigraphRange := [3, 4, 1, 1, 100, 10])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:112 # Input is: str := Sparse6String(gr); # Expected output: ":~_??_?A???_??_@b??H" # But found: Error, Variable: 'Sparse6String' must have a value ######## ########> Diff in standard/io.tst:114 # Input is: DigraphFromSparse6String(str); # Expected output: # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/io.tst:116 # Input is: DigraphFromSparse6String(IsMutableDigraph, ":Sa?dBDf?aiH`El@AjK_@gqBIp"); # Expected output: # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/io.tst:120 # Input is: gr := Digraph([[5], [1, 2, 5], [1], [2], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:122 # Input is: str := Digraph6String(gr); # Expected output: "&DBeA@?" # But found: Error, Variable: 'Digraph6String' must have a value ######## ########> Diff in standard/io.tst:124 # Input is: gr = DigraphFromDigraph6String("+DWg?[?"); # deprecated format # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/io.tst:126 # Input is: DigraphFromDigraph6String(str); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/io.tst:128 # Input is: gr := Digraph(231, [1 .. 100], [1 .. 100] * 0 + 200); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:130 # Input is: str := Digraph6String(gr);; # Expected output: # But found: Error, Variable: 'Digraph6String' must have a value ######## ########> Diff in standard/io.tst:131 # Input is: DigraphFromDigraph6String(str); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/io.tst:133 # Input is: D := DigraphFromDigraph6String(IsMutableDigraph, "&DOOOW?"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/io.tst:137 # Input is: gr := Digraph([[1, 4], [2, 3, 4], [2, 4], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:139 # Input is: str := DiSparse6String(gr); # Expected output: ".CgXoHe@J" # But found: Error, Variable: 'DiSparse6String' must have a value ######## ########> Diff in standard/io.tst:141 # Input is: DigraphFromDiSparse6String(str) = gr; # Expected output: true # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/io.tst:143 # Input is: gr := Digraph(rec(DigraphNrVertices := 1617, DigraphSource := [1 .. 100], DigraphRange := Concatenation([1 .. 50], [1 .. 50] * 0 + 51))); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:146 # Input is: str := DiSparse6String(gr);; # Expected output: # But found: Error, Variable: 'DiSparse6String' must have a value ######## ########> Diff in standard/io.tst:147 # Input is: DigraphFromDiSparse6String(str) = gr; # Expected output: true # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/io.tst:149 # Input is: gr := Digraph(rec(DigraphNrVertices := 2 ^ 17, DigraphSource := [1 .. 100], DigraphRange := Concatenation([50 .. 98], [-1050 .. -1000] * -1))); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:152 # Input is: str := DiSparse6String(gr);; # Expected output: # But found: Error, Variable: 'DiSparse6String' must have a value ######## ########> Diff in standard/io.tst:153 # Input is: DigraphFromDiSparse6String(str) = gr; # Expected output: true # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/io.tst:155 # Input is: gr := Digraph([[1, 1, 4], [2, 3, 4], [2, 4], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:157 # Input is: str := DiSparse6String(gr); # Expected output: ".CgXo?eWCn" # But found: Error, Variable: 'DiSparse6String' must have a value ######## ########> Diff in standard/io.tst:159 # Input is: gr = DigraphFromDiSparse6String(str); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/io.tst:161 # Input is: gr := Digraph(rec(DigraphNrVertices := 7890, DigraphSource := [1 .. 100] * 0 +\ 1000, DigraphRange := [1 .. 100] * 0 + 2000)); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:164 # Input is: str := DiSparse6String(gr);; # Expected output: # But found: Error, Variable: 'DiSparse6String' must have a value ######## ########> Diff in standard/io.tst:165 # Input is: gr = DigraphFromDiSparse6String(str); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/io.tst:167 # Input is: DigraphFromDiSparse6String(IsMutableDigraph, ".IoCuh?oR"); # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/io.tst:172 # Input is: gr[1] := Digraph(2 ^ 16, [1, 1, 3, 4, 7, 10, 100], [3, 4, 1, 1, 3, 100, 10]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:175 # Input is: gr[2] := Digraph(1000, [1 .. 1000], Concatenation([2 .. 1000], [1])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:179 # Input is: gr[3] := Digraph([[1, 1, 4], [2, 3, 4], [2, 4], [2], [1, 3, 3, 5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:181 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/test.ds6");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:182 # Input is: WriteDigraphs(filename, gr, "w"); # Expected output: IO_OK # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:184 # Input is: ReadDigraphs(filename); # Expected output: [ , , ] # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:188 # Input is: gr[1] := Digraph([[5], [1, 2, 5], [1], [2], [4]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:189 # Input is: gr[2] := Digraph(rec(DigraphNrVertices := 105, DigraphSource := [1 .. 100], DigraphRange := [1 .. 100] * 0 + 52));; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:191 # Input is: gr[3] := EmptyDigraph(0);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/io.tst:192 # Input is: gr[4] := Digraph([[6, 7], [6, 9], [1, 3, 4, 5, 8, 9], [1, 2, 3, 4, 5, 6, 7, 10], [1, 5, 6, 7, 10], [2, 4, 5, 9, 10], [3, 4, 5, 6, 7, 8, 9, 10], [1, 3, 5, 7, 8, 9], [1, 2, 5], [1, 2]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:195 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/test.d6");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:196 # Input is: WriteDigraphs(filename, gr, "w"); # Expected output: IO_OK # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:198 # Input is: ReadDigraphs(filename); # Expected output: [ , , , ] # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:203 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/test.txt");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:204 # Input is: WriteDigraphs(filename, CompleteDigraph(2), DigraphPlainTextLineEncoder(" ", " ", -1)); # Expected output: IO_OK # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:208 # Input is: gr[1] := Digraph([[5], [1, 2, 5], [1], [2], [4]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:209 # Input is: DigraphGroup(gr[1]); # Expected output: Group(()) # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/io.tst:211 # Input is: gr[2] := Digraph(rec(DigraphNrVertices := 105, DigraphSource := [1 .. 100], DigraphRange := [1 .. 100] * 0 + 52));; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:213 # Input is: gr[3] := EmptyDigraph(0);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/io.tst:214 # Input is: gr[4] := Digraph([[6, 7], [6, 9], [1, 3, 4, 5, 8, 9], [1, 2, 3, 4, 5, 6, 7, 10], [1, 5, 6, 7, 10], [2, 4, 5, 9, 10], [3, 4, 5, 6, 7, 8, 9, 10], [1, 3, 5, 7, 8, 9], [1, 2, 5], [1, 2]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:217 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/test.p");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:218 # Input is: WriteDigraphs(filename, gr, "w"); # Expected output: IO_OK # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:220 # Input is: ReadDigraphs(filename); # Expected output: [ , , , ] # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:225 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/test.txt");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:226 # Input is: WriteDigraphs(filename, gr, "w"); # Expected output: IO_OK # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:232 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/test.txt");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:233 # Input is: ReadDigraphs(filename); # Expected output: [ , , , ] # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:238 # Input is: gr := [CompleteDigraph(30)];; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/io.tst:239 # Input is: DigraphGroup(gr[1]) = SymmetricGroup(30); # Expected output: true # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/io.tst:241 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/test.p");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:242 # Input is: WriteDigraphs(filename, gr, "w"); # Expected output: IO_OK # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:244 # Input is: ReadDigraphs(filename); # Expected output: [ ] # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:247 # Input is: gr[1] := Digraph(30, [1, 2], [2, 1]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:249 # Input is: gr[2] := Digraph([[2], [1, 4], [5], [2], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:251 # Input is: gr[3] := Digraph([[2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:253 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/test.g6");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:254 # Input is: WriteDigraphs(filename, gr, "w"); # Expected output: IO_OK # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:256 # Input is: rdgr := ReadDigraphs(filename);; # Expected output: # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:257 # Input is: gr = rdgr; # Expected output: true # But found: Error, Variable: 'rdgr' must have a value ######## ########> Diff in standard/io.tst:259 # Input is: WriteDigraphs(filename, gr, Graph6String, "w"); # Expected output: IO_OK # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:261 # Input is: gr = ReadDigraphs(filename); # Expected output: true # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:263 # Input is: gr[3] := Digraph([[1, 2], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:265 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/test.s6.bz2");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:266 # Input is: WriteDigraphs(filename, gr, "w"); # Expected output: IO_OK # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:268 # Input is: rdgr := ReadDigraphs(filename);; # Expected output: # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:269 # Input is: gr = rdgr; # Expected output: true # But found: Error, Variable: 'rdgr' must have a value ######## ########> Diff in standard/io.tst:271 # Input is: newfilename := Concatenation(DIGRAPHS_Dir(), "/tst/out/test.bz2");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:272 # Input is: IO_rename(filename, newfilename); # Expected output: true # But found: Error, Variable: 'IO_rename' must have a value ######## ########> Diff in standard/io.tst:274 # Input is: rdgr := ReadDigraphs(newfilename); # Expected output: Error, cannot determine the file format, # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:276 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/test.h6.bz2");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:277 # Input is: IO_rename(newfilename, filename); # Expected output: true # But found: Error, Variable: 'IO_rename' must have a value ######## ########> Diff in standard/io.tst:279 # Input is: rdgr := ReadDigraphs(filename); # Expected output: Error, cannot determine the file format, # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:283 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/helloworld.g6");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:284 # Input is: f := DigraphFile(filename, "w");; # Expected output: # But found: Error, Variable: 'DigraphFile' must have a value ######## ########> Diff in standard/io.tst:285 # Input is: WriteDigraphs(f, List([1 .. 5], CompleteDigraph)); # Expected output: IO_OK # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:287 # Input is: f := DigraphFile(filename, "r");; # Expected output: # But found: Error, Variable: 'DigraphFile' must have a value ######## ########> Diff in standard/io.tst:288 # Input is: ReadDigraphs(f); # Expected output: [ , , , , ] # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:294 # Input is: f := DigraphFile(filename, "a");; # Expected output: # But found: Error, Variable: 'DigraphFile' must have a value ######## ########> Diff in standard/io.tst:295 # Input is: WriteDigraphs(f, CycleDigraph(5)); # Expected output: Error, the argument must be a symmetric digraph with no loops or multiple \ \ edges, # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:298 # Input is: WriteDigraphs(f, JohnsonDigraph(6, 3)); # Expected output: IO_OK # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:300 # Input is: f := DigraphFile(filename, "r");; # Expected output: # But found: Error, Variable: 'DigraphFile' must have a value ######## ########> Diff in standard/io.tst:301 # Input is: ReadDigraphs(f); # Expected output: [ , , , , , ] # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:308 # Input is: newfilename := Concatenation(DIGRAPHS_Dir(), "/tst/out/hello2.g6");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:309 # Input is: IO_rename(filename, newfilename); # Expected output: true # But found: Error, Variable: 'IO_rename' must have a value ######## ########> Diff in standard/io.tst:311 # Input is: ReadDigraphs(f); # Expected output: [ ] # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:313 # Input is: it := IteratorFromDigraphFile(newfilename); # Expected output: # But found: Error, Variable: 'IteratorFromDigraphFile' must have a value ######## ########> Diff in standard/io.tst:315 # Input is: NextIterator(it); # Expected output: # But found: Error, Variable: 'it' must have a value ######## ########> Diff in standard/io.tst:317 # Input is: NextIterator(it); # Expected output: # But found: Error, Variable: 'it' must have a value ######## ########> Diff in standard/io.tst:319 # Input is: it := IteratorFromDigraphFile(newfilename, DigraphFromGraph6String); # Expected output: # But found: Error, Variable: 'IteratorFromDigraphFile' must have a value ######## ########> Diff in standard/io.tst:321 # Input is: NextIterator(it); # Expected output: # But found: Error, Variable: 'it' must have a value ######## ########> Diff in standard/io.tst:323 # Input is: IsDoneIterator(it); # Expected output: false # But found: Error, Variable: 'it' must have a value ######## ########> Diff in standard/io.tst:325 # Input is: NextIterator(it); # Expected output: # But found: Error, Variable: 'it' must have a value ######## ########> Diff in standard/io.tst:327 # Input is: NextIterator(it); # Expected output: # But found: Error, Variable: 'it' must have a value ######## ########> Diff in standard/io.tst:329 # Input is: NextIterator(it); # Expected output: # But found: Error, Variable: 'it' must have a value ######## ########> Diff in standard/io.tst:331 # Input is: NextIterator(it); # Expected output: # But found: Error, Variable: 'it' must have a value ######## ########> Diff in standard/io.tst:333 # Input is: NextIterator(it); # Expected output: # But found: Error, Variable: 'it' must have a value ######## ########> Diff in standard/io.tst:335 # Input is: NextIterator(it); # Expected output: IO_Nothing # But found: Error, Variable: 'it' must have a value ######## ########> Diff in standard/io.tst:337 # Input is: NextIterator(it); # Expected output: IO_Nothing # But found: Error, Variable: 'it' must have a value ######## ########> Diff in standard/io.tst:339 # Input is: IsDoneIterator(it); # Expected output: true # But found: Error, Variable: 'it' must have a value ######## ########> Diff in standard/io.tst:341 # Input is: it := ShallowCopy(it); # Expected output: # But found: Error, Variable: 'it' must have a value ######## ########> Diff in standard/io.tst:343 # Input is: NextIterator(it); # Expected output: # But found: Error, Variable: 'it' must have a value ######## ########> Diff in standard/io.tst:345 # Input is: IteratorFromDigraphFile(1, 2, 3); # Expected output: Error, there must be 1 or 2 arguments, # But found: Error, Variable: 'IteratorFromDigraphFile' must have a value ######## ########> Diff in standard/io.tst:347 # Input is: IteratorFromDigraphFile(1, 2); # Expected output: Error, the 1st argument must be a string, # But found: Error, Variable: 'IteratorFromDigraphFile' must have a value ######## ########> Diff in standard/io.tst:349 # Input is: IteratorFromDigraphFile("happy", "happy"); # Expected output: Error, the 2nd argument must be a function or fail, # But found: Error, Variable: 'IteratorFromDigraphFile' must have a value ######## ########> Diff in standard/io.tst:351 # Input is: f := DigraphFile(Concatenation(DIGRAPHS_Dir(), "/data/test-1.d6"));; # Expected output: # But found: Error, Variable: 'DigraphFile' must have a value ######## ########> Diff in standard/io.tst:352 # Input is: IO_Close(f); # Expected output: true # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:354 # Input is: f := DigraphFile(Concatenation(DIGRAPHS_Dir(), "/data/test-1.d6"), Digraph6String);; # Expected output: # But found: Error, Variable: 'DigraphFile' must have a value ######## ########> Diff in standard/io.tst:356 # Input is: IO_Close(f); # Expected output: true # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:358 # Input is: f := DigraphFile(1, 2, 3, 4); # Expected output: Error, there must be 1, 2, or 3 arguments, # But found: Error, Variable: 'DigraphFile' must have a value ######## ########> Diff in standard/io.tst:360 # Input is: DigraphFile(Concatenation(DIGRAPHS_Dir(), "/data/test-1.d6"), Digraph6String, "wtf");; # Expected output: Error, the 3rd argument must be one of "a", "w", or "r" # But found: Error, Variable: 'DigraphFile' must have a value ######## ########> Diff in standard/io.tst:363 # Input is: ReadDigraphs(f); # Expected output: Error, the 1st argument is a closed file, # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:365 # Input is: f := DigraphFile(Concatenation(DIGRAPHS_Dir(), "/tst/out/test.d6"), Digraph6String, "w");; # Expected output: # But found: Error, Variable: 'DigraphFile' must have a value ######## ########> Diff in standard/io.tst:367 # Input is: ReadDigraphs(f); # Expected output: Error, the mode of the 1st argument must be "r", # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:369 # Input is: IO_Close(f); # Expected output: true # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:373 # Input is: gr := Digraph([[1, 2], [2, 3], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:375 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/plain.txt");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:376 # Input is: WritePlainTextDigraph(1, 2, 3, 4); # Expected output: Error, the 1st argument must be a string, # But found: Error, Variable: 'WritePlainTextDigraph' must have a value ######## ########> Diff in standard/io.tst:378 # Input is: WritePlainTextDigraph(".", gr, ",", -2); # Expected output: Error, cannot open the file given as the 1st argument , # But found: Error, Variable: 'WritePlainTextDigraph' must have a value ######## ########> Diff in standard/io.tst:380 # Input is: WritePlainTextDigraph(filename, gr, ",", -3); # Expected output: # But found: Error, Variable: 'WritePlainTextDigraph' must have a value ######## ########> Diff in standard/io.tst:381 # Input is: WritePlainTextDigraph(filename, gr, ",", -1); # Expected output: # But found: Error, Variable: 'WritePlainTextDigraph' must have a value ######## ########> Diff in standard/io.tst:382 # Input is: ReadPlainTextDigraph(1, 2, 3, 4); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `ReadPlainTextDigraph' on 4 arguments # But found: Error, Variable: 'ReadPlainTextDigraph' must have a value ######## ########> Diff in standard/io.tst:385 # Input is: ReadPlainTextDigraph(filename, ",", 1, "i"); # Expected output: # But found: Error, Variable: 'ReadPlainTextDigraph' must have a value ######## ########> Diff in standard/io.tst:390 # Input is: ReadPlainTextDigraph(filename, ",", 1, "i"); # Expected output: Error, cannot open the file given as the 2nd argument , # But found: Error, Variable: 'ReadPlainTextDigraph' must have a value ######## ########> Diff in standard/io.tst:392 # Input is: WritePlainTextDigraph(filename, gr, ',', -1); # Expected output: Error, the 3rd argument must be a string, # But found: Error, Variable: 'WritePlainTextDigraph' must have a value ######## ########> Diff in standard/io.tst:394 # Input is: WritePlainTextDigraph(1, gr, ',', -1); # Expected output: Error, the 1st argument must be a string, # But found: Error, Variable: 'WritePlainTextDigraph' must have a value ######## ########> Diff in standard/io.tst:396 # Input is: WritePlainTextDigraph(1, gr, ",", "a"); # Expected output: Error, the 1st argument must be a string, # But found: Error, Variable: 'WritePlainTextDigraph' must have a value ######## ########> Diff in standard/io.tst:400 # Input is: gr := TournamentLineDecoder("101001"); # Expected output: # But found: Error, Variable: 'TournamentLineDecoder' must have a value ######## ########> Diff in standard/io.tst:402 # Input is: OutNeighbours(gr); # Expected output: [ [ 2, 4 ], [ ], [ 1, 2, 4 ], [ 2 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/io.tst:404 # Input is: gr := TournamentLineDecoder(""); # Expected output: # But found: Error, Variable: 'TournamentLineDecoder' must have a value ######## ########> Diff in standard/io.tst:408 # Input is: gr := AdjacencyMatrixUpperTriangleLineDecoder("100101"); # Expected output: # But found: Error, Variable: 'AdjacencyMatrixUpperTriangleLineDecoder' must have a value ######## ########> Diff in standard/io.tst:410 # Input is: OutNeighbours(gr); # Expected output: [ [ 2 ], [ 3 ], [ 4 ], [ ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/io.tst:412 # Input is: gr := AdjacencyMatrixUpperTriangleLineDecoder("11y111x111"); # Expected output: # But found: Error, Variable: 'AdjacencyMatrixUpperTriangleLineDecoder' must have a value ######## ########> Diff in standard/io.tst:414 # Input is: OutNeighbours(gr); # Expected output: [ [ 2, 3, 5 ], [ 3, 4 ], [ 4, 5 ], [ 5 ], [ ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/io.tst:416 # Input is: gr := AdjacencyMatrixUpperTriangleLineDecoder(""); # Expected output: # But found: Error, Variable: 'AdjacencyMatrixUpperTriangleLineDecoder' must have a value ######## ########> Diff in standard/io.tst:420 # Input is: gr := TCodeDecoder("3 2 0 2 2 1"); # Expected output: # But found: Error, Variable: 'TCodeDecoder' must have a value ######## ########> Diff in standard/io.tst:422 # Input is: OutNeighbours(gr); # Expected output: [ [ 3 ], [ ], [ 2 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/io.tst:424 # Input is: gr = TCodeDecoderNC("3 2 0 2 2 1"); # Expected output: true # But found: Error, Variable: 'TCodeDecoderNC' must have a value ######## ########> Diff in standard/io.tst:426 # Input is: gr := TCodeDecoder("12 3 0 10 6 2 8 8"); # Expected output: # But found: Error, Variable: 'TCodeDecoder' must have a value ######## ########> Diff in standard/io.tst:428 # Input is: OutNeighbours(gr); # Expected output: [ [ 11 ], [ ], [ ], [ ], [ ], [ ], [ 3 ], [ ], [ 9 ], [ ], [ ], [ ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/io.tst:430 # Input is: gr := TCodeDecoder(3); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `TCodeDecoder' on 1 arguments # But found: Error, Variable: 'TCodeDecoder' must have a value ######## ########> Diff in standard/io.tst:433 # Input is: gr := TCodeDecoder("gr 5"); # Expected output: Error, the 2nd argument must be a string of space-separated non-negative i\ \ ntegers, # But found: Error, Variable: 'TCodeDecoder' must have a value ######## ########> Diff in standard/io.tst:436 # Input is: gr := TCodeDecoder("10"); # Expected output: Error, the 2nd argument must be a string of at least two integers, # But found: Error, Variable: 'TCodeDecoder' must have a value ######## ########> Diff in standard/io.tst:438 # Input is: gr := TCodeDecoder("2 2 0 4 1 2"); # Expected output: Error, the 2nd argument must be a string consisting of integers in the ran\ \ ge [0 .. 2], # But found: Error, Variable: 'TCodeDecoder' must have a value ######## ########> Diff in standard/io.tst:441 # Input is: gr := TCodeDecoder("3 2 0 2"); # Expected output: Error, the 2nd argument must be a string of length at least 6 # But found: Error, Variable: 'TCodeDecoder' must have a value ######## ########> Diff in standard/io.tst:443 # Input is: gr := TCodeDecoderNC("100 5 0 12 48 49 99 1 54 49 49 49"); # Expected output: # But found: Error, Variable: 'TCodeDecoderNC' must have a value ######## ########> Diff in standard/io.tst:447 # Input is: DigraphFromGraph6String(""); # Expected output: Error, the 2nd argument must be a non-empty string, # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/io.tst:449 # Input is: DigraphFromDigraph6String(""); # Expected output: Error, the 2nd argument must be a non-empty string, # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/io.tst:451 # Input is: DigraphFromSparse6String(""); # Expected output: Error, the 2nd argument must be a non-empty string, # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/io.tst:453 # Input is: DigraphFromDiSparse6String(""); # Expected output: Error, the 2nd argument must be a non-empty string, # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/io.tst:457 # Input is: DigraphFromDiSparse6String("I'm a string"); # Expected output: Error, the 2nd argument is not a valid disparse6 string, # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/io.tst:459 # Input is: DigraphFromDiSparse6String(".~~"); # Expected output: Error, the 2nd argument is not a valid disparse6 string, # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/io.tst:461 # Input is: DigraphFromDiSparse6String(".~~??@???o??N"); # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/io.tst:463 # Input is: DigraphFromDiSparse6String(".~??"); # Expected output: Error, the 2nd argument is not a valid disparse6 string, # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/io.tst:465 # Input is: DiSparse6String(CompleteDigraph(1)); # Expected output: ".@~" # But found: Error, Variable: 'DiSparse6String' must have a value ######## ########> Diff in standard/io.tst:467 # Input is: DigraphFromDiSparse6String(".@~"); # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/io.tst:469 # Input is: gr := Digraph([[], [], [1, 2]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:470 # Input is: DiSparse6String(gr); # Expected output: ".BoN" # But found: Error, Variable: 'DiSparse6String' must have a value ######## ########> Diff in standard/io.tst:474 # Input is: gr := CompleteDigraph(3); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/io.tst:476 # Input is: str := PlainTextString(gr); # Expected output: "0 1 0 2 1 0 1 2 2 0 2 1" # But found: Error, Variable: 'PlainTextString' must have a value ######## ########> Diff in standard/io.tst:478 # Input is: gr2 := DigraphFromPlainTextString(str); # Expected output: # But found: Error, Variable: 'DigraphFromPlainTextString' must have a value ######## ########> Diff in standard/io.tst:480 # Input is: gr = gr2; # Expected output: true # But found: Error, Variable: 'gr2' must have a value ######## ########> Diff in standard/io.tst:482 # Input is: D := DigraphFromPlainTextString(IsMutableDigraph, "0 1 1 2 2 3 3 4 4 0"); # Expected output: # But found: Error, Variable: 'DigraphFromPlainTextString' must have a value ######## ########> Diff in standard/io.tst:487 # Input is: DigraphFromGraph6String("~llk"); # Expected output: Error, the 2nd argument is not a valid graph6 string, # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/io.tst:489 # Input is: DigraphFromDigraph6String("&~llk"); # Expected output: Error, the 2nd argument is not a valid digraph6 string, # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/io.tst:491 # Input is: DigraphFromSparse6String(":~~l"); # Expected output: Error, the 2nd argument is not a valid sparse6 string, # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/io.tst:493 # Input is: DigraphFromSparse6String(":~hl"); # Expected output: Error, the 2nd argument is not a valid sparse6 string, # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/io.tst:495 # Input is: DigraphFromDiSparse6String(".~~l"); # Expected output: Error, the 2nd argument is not a valid disparse6 string, # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/io.tst:499 # Input is: DigraphFromDigraph6String("x"); # Expected output: Error, the 2nd argument is not a valid digraph6 string, # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/io.tst:501 # Input is: DigraphFromSparse6String("y"); # Expected output: Error, the 2nd argument is not a valid sparse6 string, # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/io.tst:503 # Input is: DigraphFromDiSparse6String("z"); # Expected output: Error, the 2nd argument is not a valid disparse6 string, # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/io.tst:507 # Input is: Sparse6String(ChainDigraph(3)); # Expected output: Error, the argument must be a symmetric digraph, # But found: Error, Variable: 'Sparse6String' must have a value ######## ########> Diff in standard/io.tst:509 # Input is: Sparse6String(CompleteDigraph(1)); # Expected output: ":@" # But found: Error, Variable: 'Sparse6String' must have a value ######## ########> Diff in standard/io.tst:511 # Input is: gr := Digraph([[1], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:512 # Input is: Sparse6String(gr); # Expected output: ":AF" # But found: Error, Variable: 'Sparse6String' must have a value ######## ########> Diff in standard/io.tst:516 # Input is: DigraphFromSparse6String(":TdBkJ`Kq?x"); # Expected output: # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/io.tst:518 # Input is: Sparse6String(last); # Expected output: ":TdBkJ`Kq?" # But found: Error, Variable: 'Sparse6String' must have a value ######## ########> Diff in standard/io.tst:522 # Input is: DigraphPlainTextLineDecoder(" ", " ", 1, "."); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphPlainTextLineDecoder' on 4 argum\ \ ents # But found: Error, Variable: 'DigraphPlainTextLineDecoder' must have a value ######## ########> Diff in standard/io.tst:528 # Input is: list := [CompleteDigraph(4), CycleDigraph(8), "hello world"];; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/io.tst:529 # Input is: WriteDigraphs(72, list, "w"); # Expected output: Error, the 1st argument must be a string or a file, # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:531 # Input is: WriteDigraphs("mylist", list, "w"); # Expected output: Error, the 2nd argument must be a digraph or list of digraphs, # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:533 # Input is: WriteDigraphs(1, 2, 3, 4, 5); # Expected output: Error, there must be 2, 3, or 4 arguments, # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:535 # Input is: WriteDigraphs(filename, CompleteDigraph(2), 3, "w"); # Expected output: Error, the argument must be a function or fail, # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:537 # Input is: WriteDigraphs(filename, CompleteDigraph(2), Graph6String, "r"); # Expected output: Error, the argument must be "a" or "w", # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:539 # Input is: filename := DigraphFile(Concatenation(DIGRAPHS_Dir(), "/tst/out/test.g6"));; # Expected output: # But found: Error, Variable: 'DigraphFile' must have a value ######## ########> Diff in standard/io.tst:541 # Input is: gr := CompleteDigraph(1);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/io.tst:542 # Input is: WriteDigraphs(filename, gr, "w"); # Expected output: Error, the 1st argument is a file, and so there must only be 2 argu\ \ ments, # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:545 # Input is: WriteDigraphs(filename, gr, fail, "w"); # Expected output: Error, the 1st argument is a file, and so there must only be 2 argu\ \ ments, # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:548 # Input is: IO_Close(filename); # Expected output: true # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:550 # Input is: WriteDigraphs(filename, gr); # Expected output: Error, the 1st argument is closed, # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:552 # Input is: f := DigraphFile(Concatenation(DIGRAPHS_Dir(), "/tst/out/test.d6"), Digraph6String, "r");; # Expected output: # But found: Error, Variable: 'DigraphFile' must have a value ######## ########> Diff in standard/io.tst:554 # Input is: WriteDigraphs(f, EmptyDigraph(4)); # Expected output: Error, the mode of the 1st argument must be "w" or "a", # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:556 # Input is: IO_Close(f); # Expected output: true # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:560 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/choose.gz");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:561 # Input is: list := [CompleteDigraph(5), EmptyDigraph(100), CompleteDigraph(3)];; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/io.tst:562 # Input is: ForAll(list, IsSymmetricDigraph); # Expected output: true # But found: Error, Variable: 'list' must have a value ######## ########> Diff in standard/io.tst:564 # Input is: WriteDigraphs(filename, list, "w"); # Expected output: IO_OK # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:566 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/choose.s6.gz");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:567 # Input is: list2 := ReadDigraphs(filename);; # Expected output: # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:568 # Input is: list = list2; # Expected output: true # But found: Error, Variable: 'list' must have a value ######## ########> Diff in standard/io.tst:570 # Input is: mult := Digraph([[1, 2], [1, 1, 3], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:571 # Input is: list := [CompleteDigraph(5), EmptyDigraph(100), mult];; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/io.tst:572 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/choosemult.gz");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:573 # Input is: WriteDigraphs(filename, list, "w"); # Expected output: IO_OK # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:575 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/choosemult.ds6.gz");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:576 # Input is: list2 := ReadDigraphs(filename);; # Expected output: # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:577 # Input is: list = list2; # Expected output: true # But found: Error, Variable: 'list' must have a value ######## ########> Diff in standard/io.tst:579 # Input is: list := [CompleteDigraph(3), CycleDigraph(100), EmptyDigraph(2)];; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/io.tst:580 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/choose");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:581 # Input is: WriteDigraphs(filename, list, "w"); # Expected output: IO_OK # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:583 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/choose.ds6");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:584 # Input is: list2 := ReadDigraphs(filename);; # Expected output: # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:585 # Input is: list = list2; # Expected output: true # But found: Error, Variable: 'list' must have a value ######## ########> Diff in standard/io.tst:587 # Input is: gr := Digraph([[2, 2], [1, 1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:588 # Input is: IsSymmetricDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/io.tst:590 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/alone");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:591 # Input is: WriteDigraphs(filename, [gr], "w"); # Expected output: IO_OK # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:593 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/alone.ds6");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:594 # Input is: list2 := ReadDigraphs(filename); # Expected output: [ ] # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:596 # Input is: list2[1] = gr; # Expected output: true # But found: Error, Variable: 'list2' must have a value ######## ########> Diff in standard/io.tst:598 # Input is: list := [CompleteDigraph(10), CompleteDigraph(15)];; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/io.tst:599 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/dense.bz2");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:600 # Input is: WriteDigraphs(filename, list, "w"); # Expected output: IO_OK # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:602 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/dense.g6.bz2");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:603 # Input is: list2 := ReadDigraphs(filename);; # Expected output: # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:604 # Input is: list = list2; # Expected output: true # But found: Error, Variable: 'list' must have a value ######## ########> Diff in standard/io.tst:606 # Input is: gr := [Digraph([[1, 2, 3, 4], [1, 2, 3, 4], [1, 3, 4], [1, 2, 3, 4]])]; # Expected output: [ ] # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:608 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/dense");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:609 # Input is: WriteDigraphs(filename, gr, "w"); # Expected output: IO_OK # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:611 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/dense.d6");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:612 # Input is: list2 := ReadDigraphs(filename);; # Expected output: # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:613 # Input is: gr = list2; # Expected output: true # But found: Error, Variable: 'list2' must have a value ######## ########> Diff in standard/io.tst:616 # Input is: WriteDigraphs(filename, gr, "w"); # Expected output: Error, cannot open the file given as the 1st argument , # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:620 # Input is: Graph6String(ChainDigraph(4)); # Expected output: Error, the argument must be a symmetric digraph with no loops or multiple \ \ edges, # But found: Error, Variable: 'Graph6String' must have a value ######## ########> Diff in standard/io.tst:623 # Input is: DIGRAPHS_Graph6Length(-1); # Expected output: fail # But found: Error, Variable: 'DIGRAPHS_Graph6Length' must have a value ######## ########> Diff in standard/io.tst:625 # Input is: DIGRAPHS_Graph6Length(68719476737); # Expected output: fail # But found: Error, Variable: 'DIGRAPHS_Graph6Length' must have a value ######## ########> Diff in standard/io.tst:627 # Input is: DIGRAPHS_Graph6Length(258748); # Expected output: [ 63, 63, 0, 0, 0, 63, 10, 60 ] # But found: Error, Variable: 'DIGRAPHS_Graph6Length' must have a value ######## ########> Diff in standard/io.tst:629 # Input is: WriteDigraphs(1, 1, "w"); # Expected output: Error, the 1st argument must be a string or a file, # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:631 # Input is: WriteDigraphs("string", [1], "w"); # Expected output: Error, the 2nd argument must be a digraph or list of digraphs, # But found: Error, Variable: 'WriteDigraphs' must have a value ######## ########> Diff in standard/io.tst:633 # Input is: Sparse6String(EmptyDigraph(2 ^ 20)); # Expected output: ":~~??C???" # But found: Error, Variable: 'Sparse6String' must have a value ######## ########> Diff in standard/io.tst:635 # Input is: DigraphFromSparse6String(":~~??C???"); # Expected output: # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/io.tst:640 # Input is: gr := EmptyDigraph(0);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/io.tst:642 # Input is: WriteDIMACSDigraph(filename, 0); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `WriteDIMACSDigraph' on 2 arguments # But found: Error, Variable: 'WriteDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:645 # Input is: WriteDIMACSDigraph(0, gr); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `WriteDIMACSDigraph' on 2 arguments # But found: Error, Variable: 'WriteDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:648 # Input is: WriteDIMACSDigraph(gr, filename); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `WriteDIMACSDigraph' on 2 arguments # But found: Error, Variable: 'WriteDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:651 # Input is: WriteDIMACSDigraph("file", ChainDigraph(2)); # Expected output: Error, the 2nd argument must be a symmetric digraph, # But found: Error, Variable: 'WriteDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:653 # Input is: WriteDIMACSDigraph(filename, gr); # Expected output: Error, cannot open the file given as the 1st argument , # But found: Error, Variable: 'WriteDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:656 # Input is: D := CompleteDigraph(3); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/io.tst:658 # Input is: SetDigraphVertexLabels(D, ["a", "b", "c"]); # Expected output: # But found: Error, Variable: 'SetDigraphVertexLabels' must have a value ######## ########> Diff in standard/io.tst:659 # Input is: WriteDIMACSDigraph(filename, CompleteDigraph(3)); # Expected output: IO_OK # But found: Error, Variable: 'WriteDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:664 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/loops.dimacs");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:665 # Input is: gr := EmptyDigraph(1); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/io.tst:667 # Input is: DigraphHasLoops(gr); # Expected output: false # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/io.tst:669 # Input is: HasDigraphHasLoops(gr); # Expected output: true # But found: Error, Variable: 'HasDigraphHasLoops' must have a value ######## ########> Diff in standard/io.tst:671 # Input is: WriteDIMACSDigraph(filename, gr); # Expected output: IO_OK # But found: Error, Variable: 'WriteDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:673 # Input is: gr := Digraph([[1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:675 # Input is: DigraphHasLoops(gr); # Expected output: true # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/io.tst:677 # Input is: HasDigraphHasLoops(gr); # Expected output: true # But found: Error, Variable: 'HasDigraphHasLoops' must have a value ######## ########> Diff in standard/io.tst:679 # Input is: WriteDIMACSDigraph(filename, gr); # Expected output: IO_OK # But found: Error, Variable: 'WriteDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:681 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/loops.dimacs.gz");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:682 # Input is: gr := Digraph([[2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:684 # Input is: HasDigraphHasLoops(gr); # Expected output: false # But found: Error, Variable: 'HasDigraphHasLoops' must have a value ######## ########> Diff in standard/io.tst:686 # Input is: WriteDIMACSDigraph(filename, gr); # Expected output: IO_OK # But found: Error, Variable: 'WriteDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:690 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/labels.dimacs");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:691 # Input is: gr := Digraph([[2], [1, 3], [2]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:692 # Input is: SetDigraphVertexLabels(gr, Elements(CyclicGroup(3))); # Expected output: # But found: Error, Variable: 'SetDigraphVertexLabels' must have a value ######## ########> Diff in standard/io.tst:693 # Input is: WriteDIMACSDigraph(filename, gr); # Expected output: IO_OK # But found: Error, Variable: 'WriteDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:697 # Input is: ReadDIMACSDigraph("does/not/exist.gz"); # Expected output: Error, cannot open the file given as the 2nd argument , # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:699 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/bad.dimacs");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:702 # Input is: file := IO_CompressedFile(UserHomeExpand(filename), "w");; # Expected output: # But found: Error, Variable: 'IO_CompressedFile' must have a value ######## ########> Diff in standard/io.tst:703 # Input is: IO_WriteLine(file, "file for testing purposes");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:704 # Input is: IO_Close(file);; # Expected output: # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:705 # Input is: ReadDIMACSDigraph(filename); # Expected output: Error, the format of the file given as the 2nd argument cannot be deter\ \ mined, # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:710 # Input is: file := IO_CompressedFile(UserHomeExpand(filename), "w");; # Expected output: # But found: Error, Variable: 'IO_CompressedFile' must have a value ######## ########> Diff in standard/io.tst:711 # Input is: IO_WriteLine(file, "c file for testing purposes");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:712 # Input is: IO_WriteLine(file, "p edge 'a' 1");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:713 # Input is: IO_Close(file);; # Expected output: # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:714 # Input is: ReadDIMACSDigraph(filename); # Expected output: Error, the format of the file given as the 2nd argument cannot be deter\ \ mined, # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:717 # Input is: file := IO_CompressedFile(UserHomeExpand(filename), "w");; # Expected output: # But found: Error, Variable: 'IO_CompressedFile' must have a value ######## ########> Diff in standard/io.tst:718 # Input is: IO_WriteLine(file, "p edge 2 -1");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:719 # Input is: IO_Close(file);; # Expected output: # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:720 # Input is: ReadDIMACSDigraph(filename); # Expected output: Error, the format of the file given as the 2nd argument cannot be deter\ \ mined, # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:723 # Input is: file := IO_CompressedFile(UserHomeExpand(filename), "w");; # Expected output: # But found: Error, Variable: 'IO_CompressedFile' must have a value ######## ########> Diff in standard/io.tst:724 # Input is: IO_WriteLine(file, "p edge 1 1");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:725 # Input is: IO_WriteLine(file, "p edge 1 1");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:726 # Input is: IO_Close(file);; # Expected output: # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:727 # Input is: ReadDIMACSDigraph(filename); # Expected output: Error, the format of the file given as the 2nd argument cannot be deter\ \ mined, # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:730 # Input is: file := IO_CompressedFile(UserHomeExpand(filename), "w");; # Expected output: # But found: Error, Variable: 'IO_CompressedFile' must have a value ######## ########> Diff in standard/io.tst:731 # Input is: IO_WriteLine(file, "p edge 1");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:732 # Input is: IO_Close(file);; # Expected output: # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:733 # Input is: ReadDIMACSDigraph(filename); # Expected output: Error, the format of the file given as the 2nd argument cannot be deter\ \ mined, # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:736 # Input is: file := IO_CompressedFile(UserHomeExpand(filename), "w");; # Expected output: # But found: Error, Variable: 'IO_CompressedFile' must have a value ######## ########> Diff in standard/io.tst:737 # Input is: IO_WriteLine(file, "p fail 1 1");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:738 # Input is: IO_Close(file);; # Expected output: # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:739 # Input is: ReadDIMACSDigraph(filename); # Expected output: Error, the format of the file given as the 2nd argument cannot be deter\ \ mined, # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:742 # Input is: file := IO_CompressedFile(UserHomeExpand(filename), "w");; # Expected output: # But found: Error, Variable: 'IO_CompressedFile' must have a value ######## ########> Diff in standard/io.tst:743 # Input is: IO_WriteLine(file, "c empty file");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:744 # Input is: IO_Close(file);; # Expected output: # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:745 # Input is: ReadDIMACSDigraph(filename); # Expected output: Error, the format of the file given as the 2nd argument cannot be deter\ \ mined, # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:750 # Input is: file := IO_CompressedFile(UserHomeExpand(filename), "w");; # Expected output: # But found: Error, Variable: 'IO_CompressedFile' must have a value ######## ########> Diff in standard/io.tst:751 # Input is: IO_WriteLine(file, "e 1 1");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:752 # Input is: IO_Close(file);; # Expected output: # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:753 # Input is: ReadDIMACSDigraph(filename); # Expected output: Error, the format of the file given as the 2nd argument cannot be deter\ \ mined, # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:758 # Input is: file := IO_CompressedFile(UserHomeExpand(filename), "w");; # Expected output: # But found: Error, Variable: 'IO_CompressedFile' must have a value ######## ########> Diff in standard/io.tst:759 # Input is: IO_WriteLine(file, "p edge 2 1");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:760 # Input is: IO_WriteLine(file, "n 2");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:761 # Input is: IO_Close(file);; # Expected output: # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:762 # Input is: ReadDIMACSDigraph(filename); # Expected output: Error, the format of the file given as the 2nd argument cannot be deter\ \ mined, # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:765 # Input is: file := IO_CompressedFile(UserHomeExpand(filename), "w");; # Expected output: # But found: Error, Variable: 'IO_CompressedFile' must have a value ######## ########> Diff in standard/io.tst:766 # Input is: IO_WriteLine(file, "p edge 2 1");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:767 # Input is: IO_WriteLine(file, "n 3 1");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:768 # Input is: IO_Close(file);; # Expected output: # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:769 # Input is: ReadDIMACSDigraph(filename); # Expected output: Error, the format of the file given as the 2nd argument cannot be deter\ \ mined, # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:772 # Input is: file := IO_CompressedFile(UserHomeExpand(filename), "w");; # Expected output: # But found: Error, Variable: 'IO_CompressedFile' must have a value ######## ########> Diff in standard/io.tst:773 # Input is: IO_WriteLine(file, "p edge 2 1");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:774 # Input is: IO_WriteLine(file, "n 2 a");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:775 # Input is: IO_Close(file);; # Expected output: # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:776 # Input is: ReadDIMACSDigraph(filename); # Expected output: Error, the format of the file given as the 2nd argument cannot be deter\ \ mined, # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:781 # Input is: file := IO_CompressedFile(UserHomeExpand(filename), "w");; # Expected output: # But found: Error, Variable: 'IO_CompressedFile' must have a value ######## ########> Diff in standard/io.tst:782 # Input is: IO_WriteLine(file, "p edge 2 1");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:783 # Input is: IO_WriteLine(file, "e 2 1 3");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:784 # Input is: IO_Close(file);; # Expected output: # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:785 # Input is: ReadDIMACSDigraph(filename); # Expected output: Error, the format of the file given as the 2nd argument cannot be deter\ \ mined, # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:788 # Input is: file := IO_CompressedFile(UserHomeExpand(filename), "w");; # Expected output: # But found: Error, Variable: 'IO_CompressedFile' must have a value ######## ########> Diff in standard/io.tst:789 # Input is: IO_WriteLine(file, "p edge 2 1");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:790 # Input is: IO_WriteLine(file, "e 2 a");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:791 # Input is: IO_Close(file);; # Expected output: # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:792 # Input is: ReadDIMACSDigraph(filename); # Expected output: Error, the format of the file given as the 2nd argument cannot be deter\ \ mined, # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:795 # Input is: file := IO_CompressedFile(UserHomeExpand(filename), "w");; # Expected output: # But found: Error, Variable: 'IO_CompressedFile' must have a value ######## ########> Diff in standard/io.tst:796 # Input is: IO_WriteLine(file, "p edge 2 1");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:797 # Input is: IO_WriteLine(file, "e 3 1");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:798 # Input is: IO_Close(file);; # Expected output: # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:799 # Input is: ReadDIMACSDigraph(filename); # Expected output: Error, the format of the file given as the 2nd argument cannot be deter\ \ mined, # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:802 # Input is: file := IO_CompressedFile(UserHomeExpand(filename), "w");; # Expected output: # But found: Error, Variable: 'IO_CompressedFile' must have a value ######## ########> Diff in standard/io.tst:803 # Input is: IO_WriteLine(file, "p edge 2 1");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:804 # Input is: IO_WriteLine(file, "e 1 3");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:805 # Input is: IO_Close(file);; # Expected output: # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:806 # Input is: ReadDIMACSDigraph(filename); # Expected output: Error, the format of the file given as the 2nd argument cannot be deter\ \ mined, # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:811 # Input is: file := IO_CompressedFile(UserHomeExpand(filename), "w");; # Expected output: # But found: Error, Variable: 'IO_CompressedFile' must have a value ######## ########> Diff in standard/io.tst:812 # Input is: IO_WriteLine(file, "p edge 2 1");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:813 # Input is: IO_WriteLine(file, "d");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:814 # Input is: IO_WriteLine(file, "v");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:815 # Input is: IO_WriteLine(file, "x");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:816 # Input is: IO_WriteLine(file, "j");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:817 # Input is: IO_Close(file);; # Expected output: # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:818 # Input is: ReadDIMACSDigraph(filename); # Expected output: Error, the format of the file given as the 2nd argument cannot be deter\ \ mined, # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:823 # Input is: file := IO_CompressedFile(UserHomeExpand(filename), "w");; # Expected output: # But found: Error, Variable: 'IO_CompressedFile' must have a value ######## ########> Diff in standard/io.tst:824 # Input is: IO_WriteLine(file, "p edge 2 1");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:825 # Input is: IO_WriteLine(file, "e 1 2");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:826 # Input is: IO_Close(file);; # Expected output: # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:827 # Input is: ReadDIMACSDigraph(filename); # Expected output: # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:829 # Input is: file := IO_CompressedFile(UserHomeExpand(filename), "w");; # Expected output: # But found: Error, Variable: 'IO_CompressedFile' must have a value ######## ########> Diff in standard/io.tst:830 # Input is: IO_WriteLine(file, "p edge 2 2");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:831 # Input is: IO_WriteLine(file, "e 1 2");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:832 # Input is: IO_Close(file);; # Expected output: # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:833 # Input is: ReadDIMACSDigraph(filename); # Expected output: # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:835 # Input is: file := IO_CompressedFile(UserHomeExpand(filename), "w");; # Expected output: # But found: Error, Variable: 'IO_CompressedFile' must have a value ######## ########> Diff in standard/io.tst:836 # Input is: IO_WriteLine(file, "p edge 2 3");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:837 # Input is: IO_WriteLine(file, "e 1 2");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:838 # Input is: IO_Close(file);; # Expected output: # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:839 # Input is: ReadDIMACSDigraph(filename); # Expected output: # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:841 # Input is: file := IO_CompressedFile(UserHomeExpand(filename), "w");; # Expected output: # But found: Error, Variable: 'IO_CompressedFile' must have a value ######## ########> Diff in standard/io.tst:842 # Input is: IO_WriteLine(file, "p edge 2 6");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:843 # Input is: IO_WriteLine(file, "e 1 1");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:844 # Input is: IO_WriteLine(file, "e 1 2");; # Expected output: # But found: Error, Variable: 'IO_WriteLine' must have a value ######## ########> Diff in standard/io.tst:845 # Input is: IO_Close(file);; # Expected output: # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:846 # Input is: ReadDIMACSDigraph(filename); # Expected output: # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:850 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/good.dimacs");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:851 # Input is: gr := Digraph([[2], [1, 3, 4], [2, 3], [2], [5], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:853 # Input is: SetDigraphVertexLabels(gr, [2, 3, 5, 7, 11, 13]);; # Expected output: # But found: Error, Variable: 'SetDigraphVertexLabels' must have a value ######## ########> Diff in standard/io.tst:854 # Input is: WriteDIMACSDigraph(filename, gr); # Expected output: IO_OK # But found: Error, Variable: 'WriteDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:856 # Input is: read := ReadDIMACSDigraph(filename); # Expected output: # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:858 # Input is: gr = read; # Expected output: true # But found: Error, Variable: 'read' must have a value ######## ########> Diff in standard/io.tst:860 # Input is: DigraphVertexLabels(read); # Expected output: [ 2, 3, 5, 7, 11, 13 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/io.tst:862 # Input is: gr := Digraph([[2], [1, 3, 3], [2, 3, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:864 # Input is: DigraphVertexLabels(gr); # Expected output: [ 1 .. 3 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/io.tst:866 # Input is: WriteDIMACSDigraph(filename, gr); # Expected output: IO_OK # But found: Error, Variable: 'WriteDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:868 # Input is: read := ReadDIMACSDigraph(filename); # Expected output: # But found: Error, Variable: 'ReadDIMACSDigraph' must have a value ######## ########> Diff in standard/io.tst:870 # Input is: gr = read; # Expected output: true # But found: Error, Variable: 'read' must have a value ######## ########> Diff in standard/io.tst:872 # Input is: DigraphVertexLabels(gr); # Expected output: [ 1 .. 3 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/io.tst:876 # Input is: DIGRAPHS_ChooseFileDecoder(1); # Expected output: Error, the argument must be a string, # But found: Error, Variable: 'DIGRAPHS_ChooseFileDecoder' must have a value ######## ########> Diff in standard/io.tst:878 # Input is: DIGRAPHS_ChooseFileEncoder(1); # Expected output: Error, the argument must be a string, # But found: Error, Variable: 'DIGRAPHS_ChooseFileEncoder' must have a value ######## ########> Diff in standard/io.tst:882 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/good.dimacs");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:883 # Input is: file := IO_File(filename, "r");; # Expected output: # But found: Error, Variable: 'IO_File' must have a value ######## ########> Diff in standard/io.tst:884 # Input is: gr := CompleteDigraph(2); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/io.tst:886 # Input is: DigraphGroup(gr); # Expected output: Sym( [ 1 .. 2 ] ) # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/io.tst:888 # Input is: IO_Pickle(file, gr); # Expected output: IO_Error # But found: Error, Variable: 'IO_Pickle' must have a value ######## ########> Diff in standard/io.tst:890 # Input is: gr := Digraph([[2], [3], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/io.tst:892 # Input is: HasDigraphGroup(gr); # Expected output: false # But found: Error, Variable: 'HasDigraphGroup' must have a value ######## ########> Diff in standard/io.tst:894 # Input is: IO_Pickle(file, gr); # Expected output: IO_Error # But found: Error, Variable: 'IO_Pickle' must have a value ######## ########> Diff in standard/io.tst:896 # Input is: IO_Close(file); # Expected output: true # But found: Error, Variable: 'IO_Close' must have a value ######## ########> Diff in standard/io.tst:900 # Input is: DigraphFile(10); # Expected output: Error, the 1st argument must be a string, # But found: Error, Variable: 'DigraphFile' must have a value ######## ########> Diff in standard/io.tst:902 # Input is: DigraphFile("tmp", false); # Expected output: Error, the 2nd argument must be a function or fail, # But found: Error, Variable: 'DigraphFile' must have a value ######## ########> Diff in standard/io.tst:904 # Input is: filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/test.p");; # Expected output: # But found: Error, Variable: 'DIGRAPHS_Dir' must have a value ######## ########> Diff in standard/io.tst:905 # Input is: ReadDigraphs(filename, IO_Unpickle); # Expected output: [ ] # But found: Error, Variable: 'ReadDigraphs' must have a value ######## ########> Diff in standard/io.tst:926 # Input is: DIGRAPHS_StopTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StopTest' must have a value ######## Digraphs package: standard/io.tst msecs: 479 false gap> ########> Diff in standard/isomorph.tst:14 # Input is: DIGRAPHS_StartTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StartTest' must have a value ######## ########> Diff in standard/isomorph.tst:20 # Input is: gr := CompleteDigraph(n); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:22 # Input is: AutomorphismGroup(gr) = SymmetricGroup(n); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:24 # Input is: not DIGRAPHS_NautyAvailable or NautyAutomorphismGroup(gr) = SymmetricGroup(n); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:30 # Input is: gr := EmptyDigraph(n); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:32 # Input is: AutomorphismGroup(gr) = SymmetricGroup(n); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:34 # Input is: not DIGRAPHS_NautyAvailable or NautyAutomorphismGroup(gr) = SymmetricGroup(n); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:40 # Input is: gr := ChainDigraph(n); # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:42 # Input is: IsTrivial(AutomorphismGroup(gr)); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:44 # Input is: not DIGRAPHS_NautyAvailable or IsTrivial(NautyAutomorphismGroup(gr)); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:46 # Input is: gr := DigraphCopy(ChainDigraph(n));; # Expected output: # But found: Error, Variable: 'DigraphCopy' must have a value ######## ########> Diff in standard/isomorph.tst:47 # Input is: not DIGRAPHS_NautyAvailable or IsTrivial(NautyAutomorphismGroup(gr)); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:49 # Input is: not DIGRAPHS_NautyAvailable or IsTrivial(NautyAutomorphismGroup(gr, [1, 2, 3, 1, 2])); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:55 # Input is: gr := CycleDigraph(n); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:57 # Input is: IsCyclic(AutomorphismGroup(gr)); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:59 # Input is: Size(AutomorphismGroup(gr)) = n; # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:61 # Input is: not DIGRAPHS_NautyAvailable or Size(NautyAutomorphismGroup(gr)) = n; # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:68 # Input is: gr := CompleteBipartiteDigraph(m, n); # Expected output: # But found: Error, Variable: 'CompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:70 # Input is: G := AutomorphismGroup(gr);; # Expected output: # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:71 # Input is: G = DirectProduct(SymmetricGroup(m), SymmetricGroup(n)); # Expected output: true # But found: Error, Variable: 'G' must have a value ######## ########> Diff in standard/isomorph.tst:73 # Input is: G := NautyAutomorphismGroup(gr);; # Expected output: # But found: Error, Variable: 'NautyAutomorphismGroup' must have a value ######## ########> Diff in standard/isomorph.tst:74 # Input is: not DIGRAPHS_NautyAvailable or G = DirectProduct(SymmetricGroup(m), SymmetricGroup(n)); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:79 # Input is: gr := Digraph([[2], [], [2], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:81 # Input is: AutomorphismGroup(gr) = SymmetricGroup([1, 3, 4]); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:83 # Input is: not DIGRAPHS_NautyAvailable or NautyAutomorphismGroup(gr) = SymmetricGroup([1, 3, 4]); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:90 # Input is: gr := Digraph([[2], [], [2], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:92 # Input is: gr = gr; # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:94 # Input is: IsIsomorphicDigraph(gr, gr); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:96 # Input is: gr1 := OnDigraphs(gr, (1, 3, 4)); # Expected output: # But found: Error, Variable: 'OnDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:98 # Input is: gr = gr1; # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:100 # Input is: IsIsomorphicDigraph(gr, gr1); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:102 # Input is: gr2 := OnDigraphs(gr, (1, 3)(2, 4)); # Expected output: # But found: Error, Variable: 'OnDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:104 # Input is: not DIGRAPHS_NautyAvailable or NautyCanonicalLabelling(gr2) = (1, 2, 3, 4); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:106 # Input is: gr = gr2; # Expected output: false # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:108 # Input is: IsIsomorphicDigraph(gr, gr2); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:110 # Input is: gr3 := DigraphReverseEdge(gr, [4, 2]); # Expected output: # But found: Error, Variable: 'DigraphReverseEdge' must have a value ######## ########> Diff in standard/isomorph.tst:112 # Input is: gr = gr3; # Expected output: false # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:114 # Input is: IsIsomorphicDigraph(gr, gr3); # Expected output: false # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:118 # Input is: gr4 := DigraphAddEdge(gr, [1, 3]); # Expected output: # But found: Error, Variable: 'DigraphAddEdge' must have a value ######## ########> Diff in standard/isomorph.tst:120 # Input is: gr = gr4; # Expected output: false # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:122 # Input is: IsIsomorphicDigraph(gr, gr4); # Expected output: false # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:126 # Input is: gr5 := DigraphAddVertex(gr); # Expected output: # But found: Error, Variable: 'DigraphAddVertex' must have a value ######## ########> Diff in standard/isomorph.tst:128 # Input is: gr = gr5; # Expected output: false # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:130 # Input is: IsIsomorphicDigraph(gr, gr5); # Expected output: false # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:134 # Input is: gr := Digraph([ [10], [4, 8], [3, 9], [7, 13, 16, 20], [5, 10, 14, 18], [14], [], [1, 6], [16], [6, 12], [8], [2, 14], [2, 12], [17], [4, 20], [1, 5, 6, 14, 18], [3], [5, 7], [4], [6, 11]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:141 # Input is: gr1 := OnDigraphs(gr, p); # Expected output: # But found: Error, Variable: 'OnDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:143 # Input is: gr = gr1; # Expected output: false # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:145 # Input is: IsIsomorphicDigraph(gr, gr1); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:147 # Input is: gr2 := OnDigraphs(gr, Transformation([1, 1])); # Expected output: # But found: Error, Variable: 'OnDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:149 # Input is: gr = gr2; # Expected output: false # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:151 # Input is: IsIsomorphicDigraph(gr, gr2); # Expected output: false # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:157 # Input is: gr1 := Digraph([[1, 2, 3, 2], [1, 3], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:159 # Input is: gr2 := Digraph([[1, 2, 3, 2], [1, 3], [3], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:161 # Input is: IsIsomorphicDigraph(gr1, gr2); # Expected output: false # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:165 # Input is: gr1 := Digraph([[1, 2, 3, 2], [1, 3], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:167 # Input is: gr2 := Digraph([[1, 2, 3, 2], [1, 3], [3, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:169 # Input is: IsIsomorphicDigraph(gr1, gr2); # Expected output: false # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:173 # Input is: gr1 := Digraph([[1, 2, 3, 2], [1, 3], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:175 # Input is: gr2 := Digraph([[1, 2, 3], [1, 2, 3], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:177 # Input is: IsIsomorphicDigraph(gr1, gr2); # Expected output: false # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:181 # Input is: gr1 := Digraph([[2, 2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:183 # Input is: gr2 := CompleteDigraph(2); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:185 # Input is: IsIsomorphicDigraph(gr1, gr2, [1, 1], [1, 1]); # Expected output: false # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:187 # Input is: IsIsomorphicDigraph(gr2, gr1, [1, 1], [1, 1]); # Expected output: false # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:189 # Input is: IsIsomorphicDigraph(gr1, gr1, [1, 1], [1, 1]); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:191 # Input is: IsIsomorphicDigraph(gr2, gr2, [], [1, 1]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 2 ]. The 2nd argument must have one of the following forms: 1. a list of length\ 2 consisting of every integer in the range [1 .. m], for some m <= 2; or 2. a list of non-empty disjoint lists whose union is [1 .. 2]. # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:198 # Input is: IsIsomorphicDigraph(gr2, gr2, [2, 2], []); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 2], since it contains the colour 2, but it lacks the colour 1 . A colouring must use precisely the colours [1 .. m], for some positive inte\ g\ er m <= 2, # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:204 # Input is: IsIsomorphicDigraph(EmptyDigraph(1), EmptyDigraph(2), [1], [1, 1]); # Expected output: false # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:206 # Input is: IsIsomorphicDigraph(EmptyDigraph(1), Digraph([[1]]), [1], [1]); # Expected output: false # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:208 # Input is: IsIsomorphicDigraph(EmptyDigraph(2), EmptyDigraph(2), [1, 1], [1, 2]); # Expected output: false # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:210 # Input is: IsIsomorphicDigraph(EmptyDigraph(2), EmptyDigraph(2), [1, 1], [1, 1]); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:212 # Input is: IsIsomorphicDigraph(gr2, gr2, [1, 1], [2, 2]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 2], since it contains the colour 2, but it lacks the colour 1 . A colouring must use precisely the colours [1 .. m], for some positive inte\ g\ er m <= 2, # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:218 # Input is: IsIsomorphicDigraph(gr2, gr2, [1, 2], [2, 1]); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:220 # Input is: gr1 := CycleDigraph(4); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:222 # Input is: gr2 := DigraphDisjointUnion(CycleDigraph(2), CycleDigraph(2)); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/isomorph.tst:224 # Input is: IsIsomorphicDigraph(gr1, gr2, [1, 1, 1, 1], [1, 1, 1, 1]); # Expected output: false # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:226 # Input is: IsIsomorphicDigraph(gr1, gr1, [1, 1, 2, 2], [1, 1, 1, 2]); # Expected output: false # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:232 # Input is: gr1 := EmptyDigraph(3); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:234 # Input is: gr2 := ChainDigraph(3); # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:236 # Input is: IsomorphismDigraphs(gr1, gr2); # Expected output: fail # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:238 # Input is: IsomorphismDigraphs(gr2, gr1); # Expected output: fail # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:240 # Input is: IsIsomorphicDigraph(gr1, gr2); # Expected output: false # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:244 # Input is: gr := Digraph([[3], [2, 3, 4], [1, 3], [], [1, 4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:246 # Input is: IsomorphismDigraphs(gr, gr); # Expected output: () # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:248 # Input is: not DIGRAPHS_NautyAvailable or NautyCanonicalLabelling(gr) = (1, 2, 5, 4); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:250 # Input is: for i in SymmetricGroup(DigraphNrVertices(gr)) do new := OnDigraphs(gr, i); if not IsomorphismDigraphs(gr, new) = i and IsomorphismDigraphs(new, gr) = i ^ -1 then Print("fail"); fi; od; # Expected output: # But found: Error, Variable: 'DigraphNrVertices' must have an assigned value ######## ########> Diff in standard/isomorph.tst:259 # Input is: gr := Digraph([[3], [2, 3, 4], [1, 3], [], [1, 4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:261 # Input is: IsomorphismDigraphs(gr, gr); # Expected output: () # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:263 # Input is: for i in SymmetricGroup(DigraphNrVertices(gr)) do new := OnDigraphs(gr, i); if not IsomorphismDigraphs(gr, new) = i and IsomorphismDigraphs(new, gr) = i ^ -1 then Print("fail"); fi; od; # Expected output: # But found: Error, Variable: 'DigraphNrVertices' must have an assigned value ######## ########> Diff in standard/isomorph.tst:272 # Input is: gr1 := Digraph([[], [2, 3, 4], [1, 3], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:273 # Input is: gr2 := OnDigraphs(gr1, (1, 2, 3));; # Expected output: # But found: Error, Variable: 'OnDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:274 # Input is: gr1 <> gr2; # Expected output: true # But found: Error, Variable: 'gr1' must have a value ######## ########> Diff in standard/isomorph.tst:276 # Input is: IsMultiDigraph(gr1); # Expected output: false # But found: Error, Variable: 'IsMultiDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:278 # Input is: not DIGRAPHS_NautyAvailable or NautyCanonicalLabelling(gr1) = (1, 2, 4); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:280 # Input is: HasBlissCanonicalLabelling(gr1) and HasBlissCanonicalLabelling(gr2); # Expected output: false # But found: Error, Variable: 'HasBlissCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:282 # Input is: not DIGRAPHS_NautyAvailable or HasNautyCanonicalLabelling(gr1) and NautyCanonicalLabelling(gr1) <> fail; # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:285 # Input is: not DIGRAPHS_NautyAvailable or not HasNautyCanonicalLabelling(gr2); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:287 # Input is: IsomorphismDigraphs(gr1, gr2);; # Expected output: # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:290 # Input is: gr1 := Digraph([[2, 2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:292 # Input is: gr2 := CompleteDigraph(2); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:294 # Input is: IsomorphismDigraphs(gr1, gr2, [1, 1], [1, 1]); # Expected output: fail # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:296 # Input is: IsomorphismDigraphs(gr2, gr1, [1, 1], [1, 1]); # Expected output: fail # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:298 # Input is: IsomorphismDigraphs(gr1, gr1, [1, 1], [1, 1]); # Expected output: [ (), () ] # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:300 # Input is: IsomorphismDigraphs(gr2, gr2, [], [1, 1]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 2 ]. The 2nd argument must have one of the following forms: 1. a list of length\ 2 consisting of every integer in the range [1 .. m], for some m <= 2; or 2. a list of non-empty disjoint lists whose union is [1 .. 2]. # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:307 # Input is: IsomorphismDigraphs(gr2, gr2, [2, 2], []); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 2], since it contains the colour 2, but it lacks the colour 1 . A colouring must use precisely the colours [1 .. m], for some positive inte\ g\ er m <= 2, # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:313 # Input is: IsomorphismDigraphs(EmptyDigraph(1), EmptyDigraph(2), [1], [1, 1]); # Expected output: fail # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:315 # Input is: IsomorphismDigraphs(EmptyDigraph(1), Digraph([[1]]), [1], [1]); # Expected output: fail # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:317 # Input is: IsomorphismDigraphs(EmptyDigraph(2), EmptyDigraph(2), [1, 1], [1, 2]); # Expected output: fail # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:319 # Input is: IsomorphismDigraphs(EmptyDigraph(2), EmptyDigraph(2), [1, 1], [1, 1]); # Expected output: () # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:321 # Input is: IsomorphismDigraphs(gr2, gr2, [1, 1], [[1, 2]]); # Expected output: () # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:323 # Input is: IsomorphismDigraphs(gr2, gr2, [1, 2], [2, 1]); # Expected output: (1,2) # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:325 # Input is: gr1 := CycleDigraph(4); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:327 # Input is: gr2 := DigraphDisjointUnion(CycleDigraph(2), CycleDigraph(2)); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/isomorph.tst:329 # Input is: IsomorphismDigraphs(gr1, gr2, [1, 1, 1, 1], [1, 1, 1, 1]); # Expected output: fail # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:331 # Input is: gr1 := CompleteDigraph(3);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:332 # Input is: IsomorphismDigraphs(gr1, gr1, [1, 2, 2], [[1, 3], [2]]); # Expected output: fail # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:338 # Input is: gr := Digraph([[2], [3, 5, 6], [3], [4, 6], [1, 4], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:340 # Input is: BlissCanonicalLabelling(gr); # Expected output: (1,2,6,3)(4,5) # But found: Error, Variable: 'BlissCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:342 # Input is: not DIGRAPHS_NautyAvailable or NautyCanonicalLabelling(gr) = (1, 3, 2, 6)(4, 5); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:345 # Input is: canon := OutNeighbours(BlissCanonicalDigraph(gr)); # Expected output: [ [ 1 ], [ 6 ], [ 5 ], [ 2, 5 ], [ 5, 3 ], [ 1, 4, 3 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/isomorph.tst:347 # Input is: for i in SymmetricGroup(DigraphNrVertices(gr)) do new := OnDigraphs(gr, i); if not OutNeighbours(OnDigraphs(new, BlissCanonicalLabelling(new))) = canon then Print("fail\n"); fi; od; # Expected output: # But found: Error, Variable: 'DigraphNrVertices' must have an assigned value ######## ########> Diff in standard/isomorph.tst:354 # Input is: gr1 := DigraphReverseEdge(gr, [2, 5]); # Expected output: # But found: Error, Variable: 'DigraphReverseEdge' must have a value ######## ########> Diff in standard/isomorph.tst:356 # Input is: gr = gr1; # Expected output: false # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:358 # Input is: IsIsomorphicDigraph(gr, gr1); # Expected output: false # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:360 # Input is: canon = OnDigraphs(gr1, BlissCanonicalLabelling(gr1)); # Expected output: false # But found: Error, Variable: 'canon' must have a value ######## ########> Diff in standard/isomorph.tst:362 # Input is: canon := NautyCanonicalDigraph(gr);; # Expected output: # But found: Error, Variable: 'NautyCanonicalDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:363 # Input is: canon = fail or OutNeighbours(canon) = [[5], [2], [6], [3, 5], [5, 1], [2, 4, 1]]; # Expected output: true # But found: Error, Variable: 'canon' must have a value ######## ########> Diff in standard/isomorph.tst:366 # Input is: if canon <> fail then for i in SymmetricGroup(DigraphNrVertices(gr)) do new := OnDigraphs(gr, i); if OnDigraphs(new, NautyCanonicalLabelling(new)) <> canon then Print("fail\n"); fi; od; fi; # Expected output: # But found: Error, Variable: 'canon' must have a value ######## ########> Diff in standard/isomorph.tst:376 # Input is: G := Digraph(10, [1, 1, 3, 4, 4, 5, 8, 8], [6, 3, 3, 9, 10, 9, 4, 10]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:377 # Input is: BlissCanonicalLabelling(G, [[1 .. 5], [6 .. 10]]); # Expected output: (1,5,2)(6,9)(8,10) # But found: Error, Variable: 'BlissCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:379 # Input is: not DIGRAPHS_NautyAvailable or NautyCanonicalLabelling(G, [[1 .. 5], [6 .. 10]]) = (1, 5, 3, 4)(6, 8, 10)(7, 9); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:383 # Input is: BlissCanonicalLabelling(G, [1, 1, 1, 1, 1, 2, 2, 2, 2, 2]); # Expected output: (1,5,2)(6,9)(8,10) # But found: Error, Variable: 'BlissCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:385 # Input is: not DIGRAPHS_NautyAvailable or NautyCanonicalLabelling(G, [1, 1, 1, 1, 1, 2, 2, 2, 2, 2]) = (1, 5, 3, 4)(6, 8, 10)(7, 9); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:391 # Input is: gr := CompleteBipartiteDigraph(4, 4); # Expected output: # But found: Error, Variable: 'CompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:393 # Input is: AutomorphismGroup(gr) = Group([ (7, 8), (6, 7), (5, 6), (3, 4), (2, 3), (1, 2), (1, 5)(2, 6)(3, 7)(4, 8)]); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:396 # Input is: AutomorphismGroup(gr, [[1 .. 4], [5 .. 8]]); # Expected output: Group([ (7,8), (6,7), (5,6), (3,4), (2,3), (1,2) ]) # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:398 # Input is: AutomorphismGroup(gr, [1 .. 8]); # Expected output: Group(()) # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:402 # Input is: gr := CompleteBipartiteDigraph(4, 4); # Expected output: # But found: Error, Variable: 'CompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:404 # Input is: AutomorphismGroup(gr, [[1 .. 4], [5 .. 9]]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 8], since the entry in position 2 contains 9 which is not an integer in the range [1 .. 8], # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:408 # Input is: AutomorphismGroup(gr, ["a", "b"]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 8], since the entry in position 1 contains 'a' which is not an integer in the range [1 .. 8], # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:412 # Input is: AutomorphismGroup(gr, [1 .. 10]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 8 ]. The 2nd argument must have one of the following forms: 1. a list of length\ 8 consisting of every integer in the range [1 .. m], for some m <= 8; or 2. a list of non-empty disjoint lists whose union is [1 .. 8]. # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:419 # Input is: AutomorphismGroup(gr, [-1 .. -10]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 8 ]. The 2nd argument must have one of the following forms: 1. a list of length\ 8 consisting of every integer in the range [1 .. m], for some m <= 8; or 2. a list of non-empty disjoint lists whose union is [1 .. 8]. # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:428 # Input is: gr := CompleteBipartiteDigraph(4, 4); # Expected output: # But found: Error, Variable: 'CompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:430 # Input is: BlissCanonicalLabelling(gr); # Expected output: (1,8,4)(2,3)(5,7) # But found: Error, Variable: 'BlissCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:432 # Input is: not DIGRAPHS_NautyAvailable or NautyCanonicalLabelling(gr) = (2, 6, 3, 7, 4, 8, 5); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:435 # Input is: not DIGRAPHS_NautyAvailable or NautyCanonicalLabelling(gr, [1 .. 8]) = (); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:438 # Input is: BlissCanonicalLabelling(gr, [[1 .. 4], [5 .. 8]]); # Expected output: (1,4)(2,3)(5,8)(6,7) # But found: Error, Variable: 'BlissCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:440 # Input is: not DIGRAPHS_NautyAvailable or NautyCanonicalLabelling(gr, [[1 .. 4], [5 .. 8]]) = (); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:445 # Input is: gr := ChainDigraph(5); # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:447 # Input is: BlissCanonicalLabelling(gr); # Expected output: (1,5)(2,4) # But found: Error, Variable: 'BlissCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:449 # Input is: BlissCanonicalLabelling(BlissCanonicalDigraph(gr)); # Expected output: () # But found: Error, Variable: 'BlissCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:453 # Input is: gr := CompleteBipartiteDigraph(4, 4); # Expected output: # But found: Error, Variable: 'CompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:455 # Input is: BlissCanonicalLabelling(gr, [[1 .. 4], [5 .. 9]]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 8], since the entry in position 2 contains 9 which is not an integer in the range [1 .. 8], # But found: Error, Variable: 'BlissCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:459 # Input is: BlissCanonicalLabelling(gr, ["a", "b"]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 8], since the entry in position 1 contains 'a' which is not an integer in the range [1 .. 8], # But found: Error, Variable: 'BlissCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:463 # Input is: BlissCanonicalLabelling(gr, [1 .. 10]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 8 ]. The 2nd argument must have one of the following forms: 1. a list of length\ 8 consisting of every integer in the range [1 .. m], for some m <= 8; or 2. a list of non-empty disjoint lists whose union is [1 .. 8]. # But found: Error, Variable: 'BlissCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:470 # Input is: BlissCanonicalLabelling(gr, [-1 .. -10]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 8 ]. The 2nd argument must have one of the following forms: 1. a list of length\ 8 consisting of every integer in the range [1 .. m], for some m <= 8; or 2. a list of non-empty disjoint lists whose union is [1 .. 8]. # But found: Error, Variable: 'BlissCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:479 # Input is: DIGRAPHS_ValidateVertexColouring(); # Expected output: Error, Function: number of arguments must be 2 (not 0) # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:481 # Input is: DIGRAPHS_ValidateVertexColouring(fail); # Expected output: Error, Function: number of arguments must be 2 (not 1) # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:483 # Input is: DIGRAPHS_ValidateVertexColouring(fail, fail); # Expected output: Error, the 1st argument must be a non-negative integer, # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:485 # Input is: DIGRAPHS_ValidateVertexColouring(0, fail); # Expected output: Error, the 2nd argument must be a homogeneous list, # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:487 # Input is: DIGRAPHS_ValidateVertexColouring(fail, []); # Expected output: Error, the 1st argument must be a non-negative integer, # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:489 # Input is: DIGRAPHS_ValidateVertexColouring(0, [], fail); # Expected output: Error, Function: number of arguments must be 2 (not 3) # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:493 # Input is: DIGRAPHS_ValidateVertexColouring(0, []); # Expected output: [ ] # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:495 # Input is: DIGRAPHS_ValidateVertexColouring(0, [2]); # Expected output: Error, the only valid partition of the vertices of the digraph with 0 vertices\ \ is the empty list, # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:498 # Input is: DIGRAPHS_ValidateVertexColouring(1, []); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 1 ]. The 2nd argument must have one of the following forms: 1. a list of length\ 1 consisting of every integer in the range [1 .. m], for some m <= 1; or 2. a list of non-empty disjoint lists whose union is [1 .. 1]. # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:505 # Input is: DIGRAPHS_ValidateVertexColouring(1, [fail]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 1 ]. The 2nd argument must have one of the following forms: 1. a list of length\ 1 consisting of every integer in the range [1 .. m], for some m <= 1; or 2. a list of non-empty disjoint lists whose union is [1 .. 1]. # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:512 # Input is: DIGRAPHS_ValidateVertexColouring(1, [1, 1]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 1 ]. The 2nd argument must have one of the following forms: 1. a list of length\ 1 consisting of every integer in the range [1 .. m], for some m <= 1; or 2. a list of non-empty disjoint lists whose union is [1 .. 1]. # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:519 # Input is: DIGRAPHS_ValidateVertexColouring(2, [1, -1]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 2], since it contains the element -1, which is not a positive integer, # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:522 # Input is: DIGRAPHS_ValidateVertexColouring(2, [2, 3]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 2], since it contains the integer 3, which is greater than 2, # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:525 # Input is: DIGRAPHS_ValidateVertexColouring(2, [2, 0]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 2], since it contains the element 0, which is not a positive integer, # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:528 # Input is: DIGRAPHS_ValidateVertexColouring(2, [[]]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 2], since it does not assign a colour to the vertex 1, # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:531 # Input is: DIGRAPHS_ValidateVertexColouring(1, [[1, 1]]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 1], since it contains the vertex 1 more than once, # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:534 # Input is: DIGRAPHS_ValidateVertexColouring(1, [[0, 1]]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 1], since the entry in position 1 contains 0 which is not an integer in the range [1 .. 1], # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:538 # Input is: DIGRAPHS_ValidateVertexColouring(1, [[2]]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 1], since the entry in position 1 contains 2 which is not an integer in the range [1 .. 1], # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:542 # Input is: DIGRAPHS_ValidateVertexColouring(4, [[3], [2, 1], [4]]); # Expected output: [ 2, 2, 1, 3 ] # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:544 # Input is: DIGRAPHS_ValidateVertexColouring(4, [1, 1, 3, 4]); # Expected output: Error, the 2nd argument does not define a colouring of the vertice\ \ s [1 .. 4], since it contains the colour 4, but it lacks the colour 2 . A colouring must use precisely the colours [1 .. m], for some positive inte\ g\ er m <= 4, # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:550 # Input is: DIGRAPHS_ValidateVertexColouring(4, [1, 1, 3, 2]); # Expected output: [ 1, 1, 3, 2 ] # But found: Error, Variable: 'DIGRAPHS_ValidateVertexColouring' must have a value ######## ########> Diff in standard/isomorph.tst:554 # Input is: D := ChainDigraph(3);; # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:555 # Input is: DIGRAPHS_ValidateEdgeColouring(3, 3); # Expected output: Error, the 1st argument must be a digraph, # But found: Error, Variable: 'DIGRAPHS_ValidateEdgeColouring' must have a value ######## ########> Diff in standard/isomorph.tst:557 # Input is: DIGRAPHS_ValidateEdgeColouring(D, 3); # Expected output: Error, the 2nd argument must be a list of the same shape as OutNeighbours(grap\ \ h), where graph is the 1st argument, # But found: Error, Variable: 'DIGRAPHS_ValidateEdgeColouring' must have a value ######## ########> Diff in standard/isomorph.tst:560 # Input is: DIGRAPHS_ValidateEdgeColouring(D, [3]); # Expected output: Error, the 2nd argument must be a list of the same shape as OutNeighbours(grap\ \ h), where graph is the 1st argument, # But found: Error, Variable: 'DIGRAPHS_ValidateEdgeColouring' must have a value ######## ########> Diff in standard/isomorph.tst:563 # Input is: DIGRAPHS_ValidateEdgeColouring(D, [[1], [], [2]]); # Expected output: Error, the 2nd argument must be a list of the same shape as OutNeighbours(grap\ \ h), where graph is the 1st argument, # But found: Error, Variable: 'DIGRAPHS_ValidateEdgeColouring' must have a value ######## ########> Diff in standard/isomorph.tst:566 # Input is: DIGRAPHS_ValidateEdgeColouring(D, [[-1], [2], []]); # Expected output: Error, the 2nd argument should be a list of lists of positive integers, # But found: Error, Variable: 'DIGRAPHS_ValidateEdgeColouring' must have a value ######## ########> Diff in standard/isomorph.tst:568 # Input is: DIGRAPHS_ValidateEdgeColouring(D, [[3], [2], []]); # Expected output: Error, the 2nd argument should be a list of lists whose union is [1 .. number \ \ of colours], # But found: Error, Variable: 'DIGRAPHS_ValidateEdgeColouring' must have a value ######## ########> Diff in standard/isomorph.tst:571 # Input is: DIGRAPHS_ValidateEdgeColouring(D, fail); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_ValidateEdgeColouring' must have a value ######## ########> Diff in standard/isomorph.tst:575 # Input is: gr1 := Digraph([[1, 2], [1, 2], [2, 3], [1, 2, 3], [5]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:576 # Input is: gr2 := Digraph([[1, 3], [2, 3], [2, 3], [1, 2, 3], [5]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:577 # Input is: BlissCanonicalDigraph(gr1) = BlissCanonicalDigraph(gr2); # Expected output: true # But found: Error, Variable: 'BlissCanonicalDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:579 # Input is: gr3 := Digraph([[2, 3], [2, 3], [1, 3], [1, 2, 3], [5]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:580 # Input is: BlissCanonicalDigraph(gr1) = BlissCanonicalDigraph(gr3); # Expected output: false # But found: Error, Variable: 'BlissCanonicalDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:582 # Input is: BlissCanonicalDigraph(gr3, [1, 1, 1, 1, 1]); # Expected output: # But found: Error, Variable: 'BlissCanonicalDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:584 # Input is: BlissCanonicalDigraph(Digraph([[1], [2], [3], [3], [2], [1]])) = BlissCanonicalDigraph(Digraph([[1], [2], [3], [1], [2], [3]])); # Expected output: true # But found: Error, Variable: 'BlissCanonicalDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:589 # Input is: gr1 := Digraph([[1, 2], [1, 2], [2, 3], [1, 2, 3], [5]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:590 # Input is: gr2 := Digraph([[1, 3], [2, 3], [2, 3], [1, 2, 3], [5]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:591 # Input is: NautyCanonicalDigraph(gr1) = NautyCanonicalDigraph(gr2); # Expected output: true # But found: Error, Variable: 'NautyCanonicalDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:593 # Input is: gr3 := Digraph([[2, 3], [2, 3], [1, 3], [1, 2, 3], [5]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:594 # Input is: not DIGRAPHS_NautyAvailable or NautyCanonicalDigraph(gr1) <> NautyCanonicalDigraph(gr3); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:597 # Input is: gr7 := NautyCanonicalDigraph(gr3, [1, 1, 1, 1, 1]);; # Expected output: # But found: Error, Variable: 'NautyCanonicalDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:598 # Input is: not DIGRAPHS_NautyAvailable or NautyCanonicalDigraph(gr3, [1, 2, 1, 2, 1]) = NautyCanonicalDigraph(gr3, [[1, 3, 5], [2, 4]]); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:602 # Input is: gr7 = fail or gr7 = NautyCanonicalDigraph(gr7); # Expected output: true # But found: Error, Variable: 'gr7' must have a value ######## ########> Diff in standard/isomorph.tst:604 # Input is: not DIGRAPHS_NautyAvailable or NautyCanonicalDigraph(Digraph([[1], [2], [3], [3], [2], [1]])) = NautyCanonicalDigraph(Digraph([[1], [2], [3], [1], [2], [3]])); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:608 # Input is: gr4 := Digraph([[3, 4], [2, 2, 3], [2, 2, 4], [2, 2, 3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:609 # Input is: gr5 := NautyCanonicalDigraph(gr4); # Expected output: fail # But found: Error, Variable: 'NautyCanonicalDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:611 # Input is: gr5 := NautyCanonicalDigraph(gr4, [1, 2, 3, 4]); # Expected output: fail # But found: Error, Variable: 'NautyCanonicalDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:615 # Input is: not DIGRAPHS_NautyAvailable or NautyAutomorphismGroup(NullDigraph(0)) = Group(()); # Expected output: true # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:620 # Input is: nauty := not DIGRAPHS_UsingBliss;; # Expected output: # But found: Error, Variable: 'DIGRAPHS_UsingBliss' must have a value ######## ########> Diff in standard/isomorph.tst:621 # Input is: DigraphsUseNauty(); # Expected output: # But found: Error, Variable: 'DigraphsUseNauty' must have a value ######## ########> Diff in standard/isomorph.tst:622 # Input is: DigraphsUseBliss(); # Expected output: # But found: Error, Variable: 'DigraphsUseBliss' must have a value ######## ########> Diff in standard/isomorph.tst:623 # Input is: p := DIGRAPHS_NautyAvailable;; # Expected output: # But found: Error, Variable: 'DIGRAPHS_NautyAvailable' must have a value ######## ########> Diff in standard/isomorph.tst:624 # Input is: MakeReadWriteGlobal("DIGRAPHS_NautyAvailable"); # Expected output: # But found: #I MakeReadWriteGlobal: DIGRAPHS_NautyAvailable already read-write ######## ########> Diff in standard/isomorph.tst:626 # Input is: DigraphsUseNauty(); # Expected output: # But found: Error, Variable: 'DigraphsUseNauty' must have a value ######## ########> Diff in standard/isomorph.tst:629 # Input is: if not nauty then DigraphsUseBliss(); fi; # Expected output: # But found: Error, Variable: 'nauty' must have a value ######## ########> Diff in standard/isomorph.tst:634 # Input is: gr1 := Digraph([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:636 # Input is: IsDigraphAutomorphism(gr1, (1, 2, 3)); # Expected output: false # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:638 # Input is: IsDigraphAutomorphism(gr1, (2, 3)); # Expected output: true # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:640 # Input is: IsDigraphAutomorphism(gr1, ()); # Expected output: true # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:642 # Input is: gr2 := Digraph([[1], [1, 2], [1, 3], [1, 4], [1, 5], [1, 2, 3, 4, 5, 6]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:644 # Input is: IsDigraphAutomorphism(gr2, (2, 3, 4, 5)); # Expected output: true # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:646 # Input is: IsDigraphAutomorphism(gr2, (1, 6)); # Expected output: false # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:648 # Input is: IsDigraphAutomorphism(gr2, (2, 3, 6)); # Expected output: false # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:650 # Input is: IsDigraphAutomorphism(Digraph([[1, 1], [1, 1, 2], [1, 2, 2, 3]]), ()); # Expected output: Error, the 1st and 2nd arguments and must not have multiple edges, # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:654 # Input is: gr1 := Digraph([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:656 # Input is: IsDigraphAutomorphism(gr1, AsTransformation((1, 2, 3))); # Expected output: false # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:658 # Input is: IsDigraphAutomorphism(gr1, AsTransformation((2, 3))); # Expected output: true # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:660 # Input is: IsDigraphAutomorphism(gr1, AsTransformation(())); # Expected output: true # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:662 # Input is: gr2 := Digraph([[1], [1, 2], [1, 3], [1, 4], [1, 5], [1, 2, 3, 4, 5, 6]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:664 # Input is: IsDigraphAutomorphism(gr2, AsTransformation((2, 3, 4, 5))); # Expected output: true # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:666 # Input is: IsDigraphAutomorphism(gr2, AsTransformation((1, 6))); # Expected output: false # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:668 # Input is: IsDigraphAutomorphism(gr2, AsTransformation((2, 3, 6))); # Expected output: false # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:670 # Input is: IsDigraphAutomorphism(gr2, Transformation([1, 1, 2, 3])); # Expected output: false # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:672 # Input is: IsDigraphAutomorphism(Digraph([[1, 1], [1, 1, 2], [1, 2, 2, 3]]), AsTransformation(())); # Expected output: Error, the 1st and 2nd arguments and must not have multiple edges, # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:677 # Input is: AutomorphismGroup(Digraph([]), [], []); # Expected output: Group(()) # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:679 # Input is: AutomorphismGroup(Digraph([[]]), [1], [[]]); # Expected output: Group(()) # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:681 # Input is: AutomorphismGroup(Digraph([[], []]), [1, 1], [[], []]); # Expected output: Group([ (1,2) ]) # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:683 # Input is: AutomorphismGroup(Digraph([[], []]), [1, 2], [[], []]); # Expected output: Group(()) # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:685 # Input is: AutomorphismGroup(Digraph([[2], [1]]), [1, 1], [[1], [1]]); # Expected output: Group([ (1,2) ]) # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:687 # Input is: AutomorphismGroup(Digraph([[2], [1]]), [1, 2], [[1], [1]]); # Expected output: Group(()) # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:689 # Input is: AutomorphismGroup(Digraph([[2], [1]]), [1, 1], [[2], [1]]); # Expected output: Group(()) # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:691 # Input is: AutomorphismGroup(Digraph([[2, 2], [1, 1]]), [1, 1], [[2, 1], [1, 2]]); # Expected output: Group([ (1,2), () ]) # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:693 # Input is: D := Digraph([[2, 3, 3, 4], [3, 4, 4, 1], [4, 1, 1, 2], [1, 2, 2, 3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:696 # Input is: AutomorphismGroup(D, vc, ec); # Expected output: Group([ (1,2)(3,4), (1,3)(2,4), () ]) # But found: Error, Variable: 'D' must have a value ######## ########> Diff in standard/isomorph.tst:699 # Input is: AutomorphismGroup(D, vc, ec); # Expected output: Group([ (1,2)(3,4), () ]) # But found: Error, Variable: 'D' must have a value ######## ########> Diff in standard/isomorph.tst:705 # Input is: gr := DigraphEdgeUnion(CompleteDigraph(4), CompleteDigraph(4)); # Expected output: # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/isomorph.tst:707 # Input is: G := AutomorphismGroup(gr);; # Expected output: # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:708 # Input is: Image(Projection(G, 1)) = SymmetricGroup(4); # Expected output: true # But found: Error, Variable: 'G' must have a value ######## ########> Diff in standard/isomorph.tst:710 # Input is: StructureDescription(Image(Projection(G, 2))); # Expected output: "C2 x C2 x C2 x C2 x C2 x C2 x C2 x C2 x C2 x C2 x C2 x C2" # But found: Error, Variable: 'G' must have a value ######## ########> Diff in standard/isomorph.tst:714 # Input is: D := Digraph([[2, 2, 4], [3], [2], [1, 2, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:718 # Input is: G := AutomorphismGroup(D, v_cols, e_cols); # Expected output: Group([ (1,2), (3,4), (5,6) ]) # But found: Error, Variable: 'D' must have a value ######## ########> Diff in standard/isomorph.tst:720 # Input is: Range(Projection(G, 1)); # Expected output: Group([ (1,4) ]) # But found: Error, Variable: 'G' must have a value ######## ########> Diff in standard/isomorph.tst:722 # Input is: Range(Projection(G, 2)); # Expected output: Group([ (1,2), (7,8) ]) # But found: Error, Variable: 'G' must have a value ######## ########> Diff in standard/isomorph.tst:726 # Input is: gr := Digraph([[2], [1, 3], [], [3, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:728 # Input is: G := AutomorphismGroup(gr); # Expected output: Group([ (), (1,2) ]) # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:730 # Input is: IsTrivial(Image(Projection(G, 1))); # Expected output: true # But found: Error, Variable: 'G' must have a value ######## ########> Diff in standard/isomorph.tst:732 # Input is: Image(Projection(G, 2)); # Expected output: Group([ (4,5) ]) # But found: Error, Variable: 'G' must have a value ######## ########> Diff in standard/isomorph.tst:736 # Input is: gr := Digraph([ [5, 7, 8, 4, 6, 1], [3, 1, 7, 2, 7, 9], [1, 5, 2, 3, 9], [1, 3, 3, 9, 9], [6, 3, 5, 7, 9], [3, 9], [8, 3, 6, 8, 8, 7, 7, 8, 9], [6, 1, 6, 7, 8, 4, 2, 5, 4], [1, 5, 2, 3, 9]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:742 # Input is: G := AutomorphismGroup(gr);; # Expected output: # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:743 # Input is: Size(G); # Expected output: 3072 # But found: Error, Variable: 'G' must have a value ######## ########> Diff in standard/isomorph.tst:745 # Input is: Image(Projection(G, 1)) = Group((3, 9)); # Expected output: true # But found: Error, Variable: 'G' must have a value ######## ########> Diff in standard/isomorph.tst:747 # Input is: Image(Projection(G, 2)) = Group([(21, 22), (34, 37), (35, 36), (39, 41), (44, 47), (9, 11)(33, 37, 34), (19, 20)(30, 34)(33, 37)]); # Expected output: true # But found: Error, Variable: 'G' must have a value ######## ########> Diff in standard/isomorph.tst:750 # Input is: BlissCanonicalLabelling(gr) = BlissCanonicalLabelling(DigraphCopy(gr)); # Expected output: true # But found: Error, Variable: 'BlissCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:755 # Input is: gr := Digraph([ [5, 7, 8, 4, 6, 1], [3, 1, 7, 2, 7, 9], [1, 5, 2, 3, 9], [1, 3, 3, 9, 9], [6, 3, 5, 7, 9], [3, 9], [8, 3, 6, 8, 8, 7, 7, 8, 9], [6, 1, 6, 7, 8, 4, 2, 5, 4], [1, 5, 2, 3, 9]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:761 # Input is: IsIsomorphicDigraph(gr, gr); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:763 # Input is: gr1 := OnDigraphs(gr, (3, 9)(1, 2, 7, 5));; # Expected output: # But found: Error, Variable: 'OnDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:764 # Input is: IsIsomorphicDigraph(gr, gr1); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:766 # Input is: gr2 := OnDigraphs(gr, (3, 9));; # Expected output: # But found: Error, Variable: 'OnDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:767 # Input is: IsIsomorphicDigraph(gr, gr2); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:771 # Input is: gr1 := Digraph([[2, 1, 2], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:772 # Input is: gr2 := Digraph([[], [2, 1, 1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:773 # Input is: IsIsomorphicDigraph(gr1, gr1, [1, 1], [1, 1]); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:775 # Input is: IsIsomorphicDigraph(gr1, gr1, [1, 1], [1, 2]); # Expected output: false # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:777 # Input is: IsIsomorphicDigraph(gr1, gr2, [1, 2], [2, 1]); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:779 # Input is: IsIsomorphicDigraph(gr1, gr2, [1, 2], [1, 2]); # Expected output: false # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:785 # Input is: gr := Digraph([ [5, 7, 8, 4, 6, 1], [3, 1, 7, 2, 7, 9], [1, 5, 2, 3, 9], [1, 3, 3, 9, 9], [6, 3, 5, 7, 9], [3, 9], [8, 3, 6, 8, 8, 7, 7, 8, 9], [6, 1, 6, 7, 8, 4, 2, 5, 4], [1, 5, 2, 3, 9]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:791 # Input is: IsomorphismDigraphs(gr, gr); # Expected output: [ (), () ] # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:793 # Input is: BlissCanonicalLabelling(gr); # Expected output: [ (1,9,5,7,4)(2,3,6), () ] # But found: Error, Variable: 'BlissCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:795 # Input is: NautyCanonicalLabelling(gr); # Expected output: fail # But found: Error, Variable: 'NautyCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:797 # Input is: AutomorphismGroup(gr); # Expected output: # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:800 # Input is: gr1 := OnDigraphs(gr, p); # Expected output: # But found: Error, Variable: 'OnDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:802 # Input is: iso := IsomorphismDigraphs(gr, gr1); # Expected output: [ (1,8,2)(3,5,4,9,7), () ] # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:804 # Input is: OnMultiDigraphs(gr, iso) = gr1; # Expected output: true # But found: Error, Variable: 'OnMultiDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:806 # Input is: iso[1] = p; # Expected output: true # But found: Error, Variable: 'iso' must have a value ######## ########> Diff in standard/isomorph.tst:809 # Input is: gr1 := OnDigraphs(gr, p); # Expected output: # But found: Error, Variable: 'OnDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:811 # Input is: iso := IsomorphismDigraphs(gr, gr1); # Expected output: [ (1,7,8,4)(2,6,5), () ] # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:813 # Input is: OnMultiDigraphs(gr, iso) = gr1; # Expected output: true # But found: Error, Variable: 'OnMultiDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:815 # Input is: iso[1] = p; # Expected output: true # But found: Error, Variable: 'iso' must have a value ######## ########> Diff in standard/isomorph.tst:819 # Input is: gr1 := Digraph([[2, 1, 2], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:820 # Input is: gr2 := Digraph([[], [2, 1, 1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:821 # Input is: IsomorphismDigraphs(gr1, gr1, [1, 1], [1, 1]); # Expected output: [ (), () ] # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:823 # Input is: IsomorphismDigraphs(gr1, gr1, [1, 1], [1, 2]); # Expected output: fail # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:825 # Input is: IsomorphismDigraphs(gr1, gr2, [1, 2], [2, 1]); # Expected output: [ (1,2), () ] # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:827 # Input is: IsomorphismDigraphs(gr1, gr2, [1, 2], [1, 2]); # Expected output: fail # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:829 # Input is: IsomorphismDigraphs(gr1, gr2, [1, 1], [1, 1]); # Expected output: [ (1,2), () ] # But found: Error, Variable: 'IsomorphismDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:835 # Input is: gr := Digraph([[2, 2], [1, 1], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:837 # Input is: BlissCanonicalLabelling(gr); # Expected output: [ (), () ] # But found: Error, Variable: 'BlissCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:839 # Input is: canon := OutNeighbours(OnMultiDigraphs(gr, last)); # Expected output: [ [ 2, 2 ], [ 1, 1 ], [ 2 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/isomorph.tst:841 # Input is: for i in SymmetricGroup(DigraphNrVertices(gr)) do for j in SymmetricGroup(DigraphNrEdges(gr)) do new := OnMultiDigraphs(gr, [i, j]); if not OutNeighbours(OnMultiDigraphs(new, BlissCanonicalLabelling(new))) = canon then Print("fail"); fi; od; od; # Expected output: # But found: Error, Variable: 'DigraphNrVertices' must have an assigned value ######## ########> Diff in standard/isomorph.tst:849 # Input is: gr1 := Digraph([[2, 2], [1, 3], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:851 # Input is: gr = gr1; # Expected output: false # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:853 # Input is: IsIsomorphicDigraph(gr, gr1); # Expected output: false # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:855 # Input is: canon = OnMultiDigraphs(gr1, BlissCanonicalLabelling(gr1)); # Expected output: false # But found: Error, Variable: 'canon' must have a value ######## ########> Diff in standard/isomorph.tst:857 # Input is: NautyCanonicalLabelling(gr); # Expected output: fail # But found: Error, Variable: 'NautyCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:861 # Input is: gr := Digraph([[2, 2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:863 # Input is: AutomorphismGroup(gr, [1, 2]); # Expected output: Group([ (), (1,2) ]) # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:865 # Input is: NautyAutomorphismGroup(gr); # Expected output: fail # But found: Error, Variable: 'NautyAutomorphismGroup' must have a value ######## ########> Diff in standard/isomorph.tst:867 # Input is: NautyAutomorphismGroup(gr, [1, 2]); # Expected output: fail # But found: Error, Variable: 'NautyAutomorphismGroup' must have a value ######## ########> Diff in standard/isomorph.tst:871 # Input is: gr := Digraph([[2, 2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:873 # Input is: BlissCanonicalLabelling(gr, [1, 2]); # Expected output: [ (), () ] # But found: Error, Variable: 'BlissCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:875 # Input is: NautyCanonicalLabelling(gr, [1, 2]); # Expected output: fail # But found: Error, Variable: 'NautyCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:879 # Input is: gr4 := Digraph([[3, 4], [2, 2, 3], [2, 2, 4], [2, 2, 3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:880 # Input is: gr5 := BlissCanonicalDigraph(gr4);; # Expected output: # But found: Error, Variable: 'BlissCanonicalDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:881 # Input is: gr5 = gr4; # Expected output: false # But found: Error, Variable: 'gr5' must have a value ######## ########> Diff in standard/isomorph.tst:883 # Input is: IsIsomorphicDigraph(gr4, gr5); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:885 # Input is: gr5 = BlissCanonicalDigraph(gr4, [1, 1, 1, 1]); # Expected output: true # But found: Error, Variable: 'gr5' must have a value ######## ########> Diff in standard/isomorph.tst:887 # Input is: BlissCanonicalDigraph(gr4, [1, 2, 1, 2]) = BlissCanonicalDigraph(gr4, [[1, 3], [2, 4]]); # Expected output: true # But found: Error, Variable: 'BlissCanonicalDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:890 # Input is: gr5 = BlissCanonicalDigraph(gr5); # Expected output: true # But found: Error, Variable: 'gr5' must have a value ######## ########> Diff in standard/isomorph.tst:892 # Input is: gr6 := OnMultiDigraphs(gr4, [(1, 2), (5, 6)]);; # Expected output: # But found: Error, Variable: 'OnMultiDigraphs' must have a value ######## ########> Diff in standard/isomorph.tst:893 # Input is: IsIsomorphicDigraph(gr4, gr6); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:895 # Input is: gr5 = BlissCanonicalDigraph(gr6); # Expected output: true # But found: Error, Variable: 'gr5' must have a value ######## ########> Diff in standard/isomorph.tst:901 # Input is: gr := Digraph([ [5, 7, 8, 4, 6, 1], [3, 1, 7, 2, 7, 9], [1, 5, 2, 3, 9], [1, 3, 3, 9, 9], [6, 3, 5, 7, 9], [3, 9], [8, 3, 6, 8, 8, 7, 7, 8, 9], [6, 1, 6, 7, 8, 4, 2, 5, 4], [1, 5, 2, 3, 9]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:907 # Input is: G := AutomorphismGroup(gr);; # Expected output: # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/isomorph.tst:908 # Input is: HasBlissCanonicalLabelling(gr); # Expected output: true # But found: Error, Variable: 'HasBlissCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:910 # Input is: BlissCanonicalLabelling(gr); # Expected output: [ (1,9,5,7,4)(2,3,6), () ] # But found: Error, Variable: 'BlissCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:912 # Input is: BlissCanonicalLabelling(gr) = BlissCanonicalLabelling(DigraphCopy(gr)); # Expected output: true # But found: Error, Variable: 'BlissCanonicalLabelling' must have a value ######## ########> Diff in standard/isomorph.tst:916 # Input is: gr := Digraph([[2, 2, 4, 4], [1, 1, 3], [2], [1, 1, 5], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:918 # Input is: DigraphGroup(gr); # Expected output: Group([ (2,4)(3,5) ]) # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/isomorph.tst:920 # Input is: DigraphDiameter(gr); # Expected output: 4 # But found: Error, Variable: 'DigraphDiameter' must have a value ######## ########> Diff in standard/isomorph.tst:922 # Input is: DigraphUndirectedGirth(gr); # Expected output: 2 # But found: Error, Variable: 'DigraphUndirectedGirth' must have a value ######## ########> Diff in standard/isomorph.tst:924 # Input is: gr := EmptyDigraph(0);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:925 # Input is: DigraphUndirectedGirth(gr); # Expected output: infinity # But found: Error, Variable: 'DigraphUndirectedGirth' must have a value ######## ########> Diff in standard/isomorph.tst:927 # Input is: DigraphDiameter(gr); # Expected output: fail # But found: Error, Variable: 'DigraphDiameter' must have a value ######## ########> Diff in standard/isomorph.tst:931 # Input is: gr := Digraph([[1, 2, 2], [], [2, 2, 3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:932 # Input is: DigraphGroup(gr) = Group((1, 3)); # Expected output: true # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/isomorph.tst:934 # Input is: OutNeighbours(DistanceDigraph(gr, 0)); # Expected output: [ [ 1 ], [ 2 ], [ 3 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/isomorph.tst:936 # Input is: OutNeighbours(DistanceDigraph(gr, 1)); # Expected output: [ [ 2 ], [ ], [ 2 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/isomorph.tst:938 # Input is: OutNeighbours(DistanceDigraph(gr, 2)); # Expected output: [ [ ], [ ], [ ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/isomorph.tst:942 # Input is: gr := Digraph([[2], [1, 3], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:944 # Input is: BlissAutomorphismGroup(gr, false, []); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 2nd choice method found for `BlissAutomorphismGroup' on 3 arguments # But found: Error, Variable: 'BlissAutomorphismGroup' must have a value ######## ########> Diff in standard/isomorph.tst:947 # Input is: BlissAutomorphismGroup(gr, fail, []); # Expected output: Error, the 2nd argument must be a list of the same shape as OutNeighbours(grap\ \ h), where graph is the 1st argument, # But found: Error, Variable: 'BlissAutomorphismGroup' must have a value ######## ########> Diff in standard/isomorph.tst:950 # Input is: BlissAutomorphismGroup(gr, fail, [[1], [1, 1], [1]]) = Group([(1, 3)]); # Expected output: true # But found: Error, Variable: 'BlissAutomorphismGroup' must have a value ######## ########> Diff in standard/isomorph.tst:954 # Input is: gr1 := Digraph([[2, 3, 4], [1, 3, 4], [1, 2], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:956 # Input is: IsDigraphIsomorphism(gr1, gr1, (1, 2)); # Expected output: true # But found: Error, Variable: 'IsDigraphIsomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:958 # Input is: IsDigraphIsomorphism(gr1, gr1, (1, 2)(3, 4)); # Expected output: true # But found: Error, Variable: 'IsDigraphIsomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:960 # Input is: gr2 := Digraph([[2, 3, 4, 4], [1, 3, 4], [1, 2], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/isomorph.tst:962 # Input is: IsDigraphIsomorphism(gr1, gr2, (1, 2)); # Expected output: Error, the 1st and 2nd arguments and must not have multiple edges, # But found: Error, Variable: 'IsDigraphIsomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:964 # Input is: IsDigraphIsomorphism(gr2, gr1, (1, 2)); # Expected output: Error, the 1st and 2nd arguments and must not have multiple edges, # But found: Error, Variable: 'IsDigraphIsomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:966 # Input is: IsDigraphIsomorphism(gr1, gr1, Transformation([2, 1, 4, 3, 6, 5])); # Expected output: true # But found: Error, Variable: 'IsDigraphIsomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:968 # Input is: IsDigraphIsomorphism(gr1, gr1, Transformation([2, 1, 3, 5, 4, 6])); # Expected output: false # But found: Error, Variable: 'IsDigraphIsomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:970 # Input is: gr := NullDigraph(5);; # Expected output: # But found: Error, Variable: 'NullDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:971 # Input is: ForAll(AutomorphismGroup(gr), x -> IsDigraphAutomorphism(gr, x, [1, 1, 1, 1, 1])); # Expected output: true # But found: Error, Variable: 'gr' must have a value Syntax warning: Unbound global variable in stream:2 x -> IsDigraphAutomorphism(gr, x, [1, 1, 1, 1, 1])); ^^^^^^^^^^^^^^^^^^^^^ Syntax warning: Unbound global variable in stream:2 x -> IsDigraphAutomorphism(gr, x, [1, 1, 1, 1, 1])); ^^ ######## ########> Diff in standard/isomorph.tst:974 # Input is: Number(AutomorphismGroup(gr), x -> IsDigraphAutomorphism(gr, x, [1, 2, 3, 4, 5])); # Expected output: 1 # But found: Error, Variable: 'gr' must have a value Syntax warning: Unbound global variable in stream:2 x -> IsDigraphAutomorphism(gr, x, [1, 2, 3, 4, 5])); ^^^^^^^^^^^^^^^^^^^^^ Syntax warning: Unbound global variable in stream:2 x -> IsDigraphAutomorphism(gr, x, [1, 2, 3, 4, 5])); ^^ ######## ########> Diff in standard/isomorph.tst:977 # Input is: gr2 := CycleDigraph(6); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:981 # Input is: ForAll([1 .. 6], i -> IsDigraphAutomorphism(gr2, t ^ i, [1, 1, 1, 1, 1, 1])); # Expected output: true # But found: Syntax warning: Unbound global variable in stream:2 i -> IsDigraphAutomorphism(gr2, ^^^^^^^^^^^^^^^^^^^^^ Syntax warning: Unbound global variable in stream:2 i -> IsDigraphAutomorphism(gr2, ^^^ Error, Variable: 'IsDigraphAutomorphism' must have an assigned value ######## ########> Diff in standard/isomorph.tst:986 # Input is: ForAll([2, 4, 6], i -> IsDigraphAutomorphism(gr2, t ^ i, [1, 2, 1, 2, 1, 2])); # Expected output: true # But found: Syntax warning: Unbound global variable in stream:2 i -> IsDigraphAutomorphism(gr2, ^^^^^^^^^^^^^^^^^^^^^ Syntax warning: Unbound global variable in stream:2 i -> IsDigraphAutomorphism(gr2, ^^^ Error, Variable: 'IsDigraphAutomorphism' must have an assigned value ######## ########> Diff in standard/isomorph.tst:991 # Input is: IsDigraphAutomorphism(gr2, t ^ 3, [1, 2, 3, 1, 2, 3]); # Expected output: true # But found: Error, Variable: 'IsDigraphAutomorphism' must have a value ######## ########> Diff in standard/isomorph.tst:993 # Input is: gr3 := CycleDigraph(5);; # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/isomorph.tst:994 # Input is: Number(FullTransformationMonoid(5), t -> IsDigraphAutomorphism(gr3, t, [1, 1, 1, 1, 1])); # Expected output: 5 # But found: Syntax warning: Unbound global variable in stream:2 t -> IsDigraphAutomorphism(gr3, ^^^^^^^^^^^^^^^^^^^^^ Syntax warning: Unbound global variable in stream:2 t -> IsDigraphAutomorphism(gr3, ^^^ Error, Variable: 'IsDigraphAutomorphism' must have an assigned value ######## ########> Diff in standard/isomorph.tst:1020 # Input is: DIGRAPHS_StopTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StopTest' must have a value ######## Digraphs package: standard/isomorph.tst msecs: 437 false gap> ########> Diff in standard/labels.tst:14 # Input is: DIGRAPHS_StartTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StartTest' must have a value ######## ########> Diff in standard/labels.tst:17 # Input is: gr := RandomDigraph(10);; # Expected output: # But found: Error, Variable: 'RandomDigraph' must have a value ######## ########> Diff in standard/labels.tst:18 # Input is: DigraphVertexLabels(gr); # Expected output: [ 1 .. 10 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/labels.tst:20 # Input is: SetDigraphVertexLabels(gr, ["a", "b", 10]); # Expected output: Error, the 2nd arument must be a list with length equal to the number \ \ of vertices of the digraph that is the 1st argument, # But found: Error, Variable: 'SetDigraphVertexLabels' must have a value ######## ########> Diff in standard/labels.tst:23 # Input is: gr := RandomDigraph(3);; # Expected output: # But found: Error, Variable: 'RandomDigraph' must have a value ######## ########> Diff in standard/labels.tst:24 # Input is: SetDigraphVertexLabels(gr, ["a", "b", 10]); # Expected output: # But found: Error, Variable: 'SetDigraphVertexLabels' must have a value ######## ########> Diff in standard/labels.tst:25 # Input is: DigraphVertexLabels(gr); # Expected output: [ "a", "b", 10 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/labels.tst:27 # Input is: DigraphVertexLabel(gr, 1); # Expected output: "a" # But found: Error, Variable: 'DigraphVertexLabel' must have a value ######## ########> Diff in standard/labels.tst:29 # Input is: DigraphVertexLabel(gr, 2); # Expected output: "b" # But found: Error, Variable: 'DigraphVertexLabel' must have a value ######## ########> Diff in standard/labels.tst:31 # Input is: DigraphVertexLabel(gr, 10); # Expected output: Error, the 2nd argument has no label or is not a vertex of the digraph \ \ that is the 1st argument # But found: Error, Variable: 'DigraphVertexLabel' must have a value ######## ########> Diff in standard/labels.tst:34 # Input is: DigraphVertexLabel(gr, 3); # Expected output: 10 # But found: Error, Variable: 'DigraphVertexLabel' must have a value ######## ########> Diff in standard/labels.tst:36 # Input is: SetDigraphVertexLabel(gr, 3, 3); # Expected output: # But found: Error, Variable: 'SetDigraphVertexLabel' must have a value ######## ########> Diff in standard/labels.tst:37 # Input is: DigraphVertexLabel(gr, 3); # Expected output: 3 # But found: Error, Variable: 'DigraphVertexLabel' must have a value ######## ########> Diff in standard/labels.tst:39 # Input is: ClearDigraphVertexLabels(gr); # Expected output: # But found: Error, Variable: 'ClearDigraphVertexLabels' must have a value ######## ########> Diff in standard/labels.tst:40 # Input is: DigraphVertexLabels(gr); # Expected output: [ 1 .. 3 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/labels.tst:42 # Input is: gr := RandomDigraph(5);; # Expected output: # But found: Error, Variable: 'RandomDigraph' must have a value ######## ########> Diff in standard/labels.tst:43 # Input is: SetDigraphVertexLabel(gr, 6, (1, 3, 2, 5, 4)); # Expected output: Error, the 2nd argument is not a vertex of the digraph that is the 1st\ \ argument, # But found: Error, Variable: 'SetDigraphVertexLabel' must have a value ######## ########> Diff in standard/labels.tst:46 # Input is: SetDigraphVertexLabel(gr, 2, (1, 3, 2, 5, 4)); # Expected output: # But found: Error, Variable: 'SetDigraphVertexLabel' must have a value ######## ########> Diff in standard/labels.tst:47 # Input is: DigraphVertexLabel(gr, 2); # Expected output: (1,3,2,5,4) # But found: Error, Variable: 'DigraphVertexLabel' must have a value ######## ########> Diff in standard/labels.tst:49 # Input is: gr := RandomDigraph(3);; # Expected output: # But found: Error, Variable: 'RandomDigraph' must have a value ######## ########> Diff in standard/labels.tst:50 # Input is: DigraphVertexLabel(gr, 2); # Expected output: 2 # But found: Error, Variable: 'DigraphVertexLabel' must have a value ######## ########> Diff in standard/labels.tst:52 # Input is: gr := RandomDigraph(10);; # Expected output: # But found: Error, Variable: 'RandomDigraph' must have a value ######## ########> Diff in standard/labels.tst:53 # Input is: gr := InducedSubdigraph(gr, [1, 2, 3, 5, 7]);; # Expected output: # But found: Error, Variable: 'InducedSubdigraph' must have a value ######## ########> Diff in standard/labels.tst:54 # Input is: DigraphVertexLabels(gr); # Expected output: [ 1, 2, 3, 5, 7 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/labels.tst:56 # Input is: DigraphVertices(gr); # Expected output: [ 1 .. 5 ] # But found: Error, Variable: 'DigraphVertices' must have a value ######## ########> Diff in standard/labels.tst:58 # Input is: gr := Digraph([[4, 8], [4, 9], [5], [9], [6], [3, 5], [], [6], [1, 3], [10]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/labels.tst:61 # Input is: x := DigraphVertexLabels(gr); # Expected output: [ 1 .. 10 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/labels.tst:63 # Input is: x[1] := "a"; # Expected output: "a" # But found: Error, Variable: 'x' must have a value ######## ########> Diff in standard/labels.tst:65 # Input is: x; # Expected output: [ "a", 2, 3, 4, 5, 6, 7, 8, 9, 10 ] # But found: Error, Variable: 'x' must have a value ######## ########> Diff in standard/labels.tst:67 # Input is: DigraphVertexLabels(gr); # Expected output: [ 1 .. 10 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/labels.tst:69 # Input is: SetDigraphVertexLabel(gr, 2, []); # Expected output: # But found: Error, Variable: 'SetDigraphVertexLabel' must have a value ######## ########> Diff in standard/labels.tst:70 # Input is: x := DigraphVertexLabel(gr, 2); # Expected output: [ ] # But found: Error, Variable: 'DigraphVertexLabel' must have a value ######## ########> Diff in standard/labels.tst:72 # Input is: Add(x, 1); # Expected output: # But found: Error, Variable: 'x' must have a value ######## ########> Diff in standard/labels.tst:73 # Input is: x; # Expected output: [ 1 ] # But found: Error, Variable: 'x' must have a value ######## ########> Diff in standard/labels.tst:75 # Input is: DigraphVertexLabels(gr); # Expected output: [ 1, [ ], 3, 4, 5, 6, 7, 8, 9, 10 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/labels.tst:77 # Input is: RemoveDigraphVertexLabel(gr, 2); # Expected output: # But found: Error, Variable: 'RemoveDigraphVertexLabel' must have a value ######## ########> Diff in standard/labels.tst:78 # Input is: DigraphVertexLabels(gr); # Expected output: [ 1, 3, 4, 5, 6, 7, 8, 9, 10 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/labels.tst:80 # Input is: D := NullDigraph(5);; # Expected output: # But found: Error, Variable: 'NullDigraph' must have a value ######## ########> Diff in standard/labels.tst:81 # Input is: RemoveDigraphVertexLabel(D, 6); # Expected output: # But found: Error, Variable: 'RemoveDigraphVertexLabel' must have a value ######## ########> Diff in standard/labels.tst:84 # Input is: gr := Digraph([[2, 3], [3], [1, 5], [], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/labels.tst:86 # Input is: DigraphEdgeLabels(gr); # Expected output: [ [ 1, 1 ], [ 1 ], [ 1, 1 ], [ ], [ 1 ] ] # But found: Error, Variable: 'DigraphEdgeLabels' must have a value ######## ########> Diff in standard/labels.tst:88 # Input is: SetDigraphEdgeLabels(gr, [1, 2]); # Expected output: Error, the 2nd argument must be a list with the same shape as the out\ \ -neighbours of the digraph that is the 1st argument, # But found: Error, Variable: 'SetDigraphEdgeLabels' must have a value ######## ########> Diff in standard/labels.tst:91 # Input is: SetDigraphEdgeLabel(gr, 2, 4, "banana"); # Expected output: Error, there is no edge from 2 to 4 in the digraph that is the 1st argument, # But found: Error, Variable: 'SetDigraphEdgeLabel' must have a value ######## ########> Diff in standard/labels.tst:94 # Input is: SetDigraphEdgeLabels(gr, function(x, y) return x + y; end); # Expected output: # But found: Error, Variable: 'SetDigraphEdgeLabels' must have a value ######## ########> Diff in standard/labels.tst:95 # Input is: DigraphEdgeLabels(gr); # Expected output: [ [ 3, 4 ], [ 5 ], [ 4, 8 ], [ ], [ 9 ] ] # But found: Error, Variable: 'DigraphEdgeLabels' must have a value ######## ########> Diff in standard/labels.tst:97 # Input is: SetDigraphEdgeLabels(gr, [["a", "b"], ["c"], [42, []], [], [1]]); # Expected output: # But found: Error, Variable: 'SetDigraphEdgeLabels' must have a value ######## ########> Diff in standard/labels.tst:99 # Input is: DigraphEdgeLabels(gr); # Expected output: [ [ "a", "b" ], [ "c" ], [ 42, [ ] ], [ ], [ 1 ] ] # But found: Error, Variable: 'DigraphEdgeLabels' must have a value ######## ########> Diff in standard/labels.tst:101 # Input is: DigraphEdgeLabel(gr, 1, 2); # Expected output: "a" # But found: Error, Variable: 'DigraphEdgeLabel' must have a value ######## ########> Diff in standard/labels.tst:103 # Input is: SetDigraphEdgeLabel(gr, 1, 2, "23"); # Expected output: # But found: Error, Variable: 'SetDigraphEdgeLabel' must have a value ######## ########> Diff in standard/labels.tst:104 # Input is: DigraphEdgeLabel(gr, 1, 2); # Expected output: "23" # But found: Error, Variable: 'DigraphEdgeLabel' must have a value ######## ########> Diff in standard/labels.tst:106 # Input is: DigraphEdgeLabels(gr); # Expected output: [ [ "23", "b" ], [ "c" ], [ 42, [ ] ], [ ], [ 1 ] ] # But found: Error, Variable: 'DigraphEdgeLabels' must have a value ######## ########> Diff in standard/labels.tst:108 # Input is: x := DigraphEdgeLabel(gr, 3, 5); # Expected output: [ ] # But found: Error, Variable: 'DigraphEdgeLabel' must have a value ######## ########> Diff in standard/labels.tst:110 # Input is: Add(x, "hello, world"); # Expected output: # But found: Error, Variable: 'x' must have a value ######## ########> Diff in standard/labels.tst:111 # Input is: x; # Expected output: [ "hello, world" ] # But found: Error, Variable: 'x' must have a value ######## ########> Diff in standard/labels.tst:113 # Input is: DigraphEdgeLabels(gr); # Expected output: [ [ "23", "b" ], [ "c" ], [ 42, [ ] ], [ ], [ 1 ] ] # But found: Error, Variable: 'DigraphEdgeLabels' must have a value ######## ########> Diff in standard/labels.tst:115 # Input is: gr := Digraph([[3], [1, 3, 5], [1], [1, 2, 4], [2, 3, 5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/labels.tst:117 # Input is: l := DigraphEdgeLabels(gr); # Expected output: [ [ 1 ], [ 1, 1, 1 ], [ 1 ], [ 1, 1, 1 ], [ 1, 1, 1 ] ] # But found: Error, Variable: 'DigraphEdgeLabels' must have a value ######## ########> Diff in standard/labels.tst:119 # Input is: MakeImmutable(l); # Expected output: [ [ 1 ], [ 1, 1, 1 ], [ 1 ], [ 1, 1, 1 ], [ 1, 1, 1 ] ] # But found: Error, Variable: 'l' must have a value ######## ########> Diff in standard/labels.tst:121 # Input is: SetDigraphEdgeLabels(gr, l); # Expected output: # But found: Error, Variable: 'SetDigraphEdgeLabels' must have a value ######## ########> Diff in standard/labels.tst:122 # Input is: SetDigraphEdgeLabel(gr, 2, 1, "Hello, banana"); # Expected output: # But found: Error, Variable: 'SetDigraphEdgeLabel' must have a value ######## ########> Diff in standard/labels.tst:123 # Input is: DigraphEdgeLabels(gr); # Expected output: [ [ 1 ], [ "Hello, banana", 1, 1 ], [ 1 ], [ 1, 1, 1 ], [ 1, 1, 1 ] ] # But found: Error, Variable: 'DigraphEdgeLabels' must have a value ######## ########> Diff in standard/labels.tst:125 # Input is: gr := Digraph([[2, 2], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/labels.tst:126 # Input is: SetDigraphEdgeLabels(gr, [[5, infinity], []]); # Expected output: Error, the argument must be a digraph with no multiple edges, edge labels \ \ are not supported on digraphs with multiple edges, # But found: Error, Variable: 'SetDigraphEdgeLabels' must have a value ######## ########> Diff in standard/labels.tst:129 # Input is: DigraphEdgeLabels(gr); # Expected output: Error, the argument must be a digraph with no multiple edges, edge labels \ \ are not supported on digraphs with multiple edges, # But found: Error, Variable: 'DigraphEdgeLabels' must have a value ######## ########> Diff in standard/labels.tst:132 # Input is: SetDigraphEdgeLabel(gr, 1, 2, infinity); # Expected output: Error, the 1st argument must be a digraph with no multiple edges, edge lab\ \ els are not supported on digraphs with multiple edges, # But found: Error, Variable: 'SetDigraphEdgeLabel' must have a value ######## ########> Diff in standard/labels.tst:135 # Input is: gr := Digraph([[2, 3], [3], [1, 5], [], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/labels.tst:137 # Input is: SetDigraphEdgeLabel(gr, 2, 3, "banana"); # Expected output: # But found: Error, Variable: 'SetDigraphEdgeLabel' must have a value ######## ########> Diff in standard/labels.tst:138 # Input is: D := Digraph(IsMutableDigraph, [[2, 3], [3], [1, 5], [], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/labels.tst:140 # Input is: DigraphEdgeLabels(D); # Expected output: [ [ 1, 1 ], [ 1 ], [ 1, 1 ], [ ], [ 1 ] ] # But found: Error, Variable: 'DigraphEdgeLabels' must have a value ######## ########> Diff in standard/labels.tst:142 # Input is: DigraphAddVertex(D); # Expected output: # But found: Error, Variable: 'DigraphAddVertex' must have a value ######## ########> Diff in standard/labels.tst:144 # Input is: DigraphAddEdge(D, 6, 1); # Expected output: # But found: Error, Variable: 'DigraphAddEdge' must have a value ######## ########> Diff in standard/labels.tst:146 # Input is: SetDigraphEdgeLabel(D, 6, 1, "banana"); # Expected output: # But found: Error, Variable: 'SetDigraphEdgeLabel' must have a value ######## ########> Diff in standard/labels.tst:147 # Input is: DigraphEdgeLabels(D); # Expected output: [ [ 1, 1 ], [ 1 ], [ 1, 1 ], [ ], [ 1 ], [ "banana" ] ] # But found: Error, Variable: 'DigraphEdgeLabels' must have a value ######## ########> Diff in standard/labels.tst:149 # Input is: DigraphAddEdge(D, 6, 1); # Expected output: # But found: Error, Variable: 'DigraphAddEdge' must have a value ######## ########> Diff in standard/labels.tst:151 # Input is: DigraphEdgeLabel(D, 6, 1); # Expected output: Error, the 1st argument must be a digraph with no multiple edges, edge lab\ \ els are not supported on digraphs with multiple edges, # But found: Error, Variable: 'DigraphEdgeLabel' must have a value ######## ########> Diff in standard/labels.tst:154 # Input is: SetDigraphEdgeLabels(D, ReturnFail); # Expected output: Error, the argument must be a digraph with no multiple edges, edge labels \ \ are not supported on digraphs with multiple edges, # But found: Error, Variable: 'SetDigraphEdgeLabels' must have a value ######## ########> Diff in standard/labels.tst:157 # Input is: D := Digraph(IsMutableDigraph, [[2, 3], [3], [1, 5], [], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/labels.tst:159 # Input is: DigraphEdgeLabel(D, 1, 5); # Expected output: Error, there is no edge from 1 to 5 in the digraph that is the 1st argument, # But found: Error, Variable: 'DigraphEdgeLabel' must have a value ######## ########> Diff in standard/labels.tst:162 # Input is: gr := Digraph(IsMutableDigraph, [[2, 3], [3], [1, 5], [], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/labels.tst:164 # Input is: SetDigraphEdgeLabel(gr, 1, 2, "bab"); # Expected output: # But found: Error, Variable: 'SetDigraphEdgeLabel' must have a value ######## ########> Diff in standard/labels.tst:165 # Input is: DigraphAddVertex(gr); # Expected output: # But found: Error, Variable: 'DigraphAddVertex' must have a value ######## ########> Diff in standard/labels.tst:167 # Input is: DigraphAddEdge(gr, 6, 1); # Expected output: # But found: Error, Variable: 'DigraphAddEdge' must have a value ######## ########> Diff in standard/labels.tst:169 # Input is: SetDigraphEdgeLabel(gr, 6, 1, "bab"); # Expected output: # But found: Error, Variable: 'SetDigraphEdgeLabel' must have a value ######## ########> Diff in standard/labels.tst:170 # Input is: RemoveDigraphEdgeLabel(gr, 6, 1); # Expected output: # But found: Error, Variable: 'RemoveDigraphEdgeLabel' must have a value ######## ########> Diff in standard/labels.tst:171 # Input is: ClearDigraphEdgeLabels(gr); # Expected output: # But found: Error, Variable: 'ClearDigraphEdgeLabels' must have a value ######## ########> Diff in standard/labels.tst:172 # Input is: DigraphEdgeLabel(gr, 6, 1); # Expected output: 1 # But found: Error, Variable: 'DigraphEdgeLabel' must have a value ######## ########> Diff in standard/labels.tst:176 # Input is: gr := Digraph([[2, 2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/labels.tst:178 # Input is: DigraphEdgeLabel(gr, 1, 2); # Expected output: Error, the 1st argument must be a digraph with no multiple edges, edge lab\ \ els are not supported on digraphs with multiple edges, # But found: Error, Variable: 'DigraphEdgeLabel' must have a value ######## ########> Diff in standard/labels.tst:181 # Input is: SetDigraphEdgeLabels(gr, ReturnFalse); # Expected output: Error, the argument must be a digraph with no multiple edges, edge labels \ \ are not supported on digraphs with multiple edges, # But found: Error, Variable: 'SetDigraphEdgeLabels' must have a value ######## ########> Diff in standard/labels.tst:184 # Input is: gr := Digraph([[2, 1], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/labels.tst:186 # Input is: DigraphEdgeLabel(gr, 2, 2); # Expected output: Error, there is no edge from 2 to 2 in the digraph that is the 1st argument, # But found: Error, Variable: 'DigraphEdgeLabel' must have a value ######## ########> Diff in standard/labels.tst:189 # Input is: SetDigraphEdgeLabel(gr, 2, 2, "a"); # Expected output: Error, there is no edge from 2 to 2 in the digraph that is the 1st argument, # But found: Error, Variable: 'SetDigraphEdgeLabel' must have a value ######## ########> Diff in standard/labels.tst:194 # Input is: DIGRAPHS_StopTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StopTest' must have a value ######## Digraphs package: standard/labels.tst msecs: 125 false gap> ########> Diff in standard/oper.tst:15 # Input is: DIGRAPHS_StartTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StartTest' must have a value ######## ########> Diff in standard/oper.tst:18 # Input is: gr := DigraphFromDigraph6String("&EhxPC?@"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/oper.tst:20 # Input is: DigraphRemoveLoops(gr); # Expected output: # But found: Error, Variable: 'DigraphRemoveLoops' must have a value ######## ########> Diff in standard/oper.tst:22 # Input is: gr := DigraphFromDigraph6String("&EhxPC?@"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/oper.tst:24 # Input is: HasDigraphHasLoops(gr); # Expected output: false # But found: Error, Variable: 'HasDigraphHasLoops' must have a value ######## ########> Diff in standard/oper.tst:26 # Input is: DigraphHasLoops(gr); # Expected output: true # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/oper.tst:28 # Input is: gr1 := DigraphRemoveLoops(gr); # Expected output: # But found: Error, Variable: 'DigraphRemoveLoops' must have a value ######## ########> Diff in standard/oper.tst:30 # Input is: HasDigraphHasLoops(gr1); # Expected output: true # But found: Error, Variable: 'HasDigraphHasLoops' must have a value ######## ########> Diff in standard/oper.tst:32 # Input is: DigraphHasLoops(gr1); # Expected output: false # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/oper.tst:36 # Input is: gr := Digraph([[2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:38 # Input is: DigraphRemoveEdges(gr, [[2, 1]]); # Expected output: # But found: Error, Variable: 'DigraphRemoveEdges' must have a value ######## ########> Diff in standard/oper.tst:40 # Input is: last = gr; # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/oper.tst:42 # Input is: DigraphRemoveEdges(gr, [[1, 2]]); # Expected output: # But found: Error, Variable: 'DigraphRemoveEdges' must have a value ######## ########> Diff in standard/oper.tst:44 # Input is: gr := DigraphFromDigraph6String("&DtGsw_"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/oper.tst:46 # Input is: Set(DigraphEdges(gr)) = Set( [[1, 2], [1, 1], [1, 4], [2, 1], [2, 4], [3, 4], [3, 3], [4, 1], [4, 5], [4, 4], [5, 1], [5, 5]]); # Expected output: true # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:50 # Input is: gr1 := DigraphRemoveEdges(gr, [[1, 4], [4, 5], [5, 5]]); # Expected output: # But found: Error, Variable: 'DigraphRemoveEdges' must have a value ######## ########> Diff in standard/oper.tst:52 # Input is: DigraphEdges(gr1); # Expected output: [ [ 1, 2 ], [ 1, 1 ], [ 2, 1 ], [ 2, 4 ], [ 3, 4 ], [ 3, 3 ], [ 4, 1 ], [ 4, 4 ], [ 5, 1 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:55 # Input is: gr := Digraph([[2, 2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:57 # Input is: DigraphRemoveEdges(gr, [[1, 2]]); # Expected output: Error, the 1st argument must be a digraph with no multiple edges, # But found: Error, Variable: 'DigraphRemoveEdges' must have a value ######## ########> Diff in standard/oper.tst:61 # Input is: gr := Digraph([[1, 1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:63 # Input is: DigraphRemoveEdge(gr, [1, 1]); # Expected output: Error, the 1st argument must be a digraph with no multiple edges, # But found: Error, Variable: 'DigraphRemoveEdge' must have a value ######## ########> Diff in standard/oper.tst:65 # Input is: gr := Digraph([[2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:67 # Input is: DigraphRemoveEdge(gr, [1, 1, 1]); # Expected output: Error, the 2nd argument must be a list of length 2, # But found: Error, Variable: 'DigraphRemoveEdge' must have a value ######## ########> Diff in standard/oper.tst:69 # Input is: DigraphRemoveEdge(gr, [Group(()), Group(())]); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphRemoveEdge' on 3 arguments # But found: Error, Variable: 'DigraphRemoveEdge' must have a value ######## ########> Diff in standard/oper.tst:72 # Input is: DigraphRemoveEdge(gr, [1, Group(())]); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphRemoveEdge' on 3 arguments # But found: Error, Variable: 'DigraphRemoveEdge' must have a value ######## ########> Diff in standard/oper.tst:75 # Input is: DigraphRemoveEdge(gr, [3, 1]); # Expected output: Error, the 2nd argument must be a vertex of the digraph that is the \ \ 1st argument, # But found: Error, Variable: 'DigraphRemoveEdge' must have a value ######## ########> Diff in standard/oper.tst:78 # Input is: DigraphRemoveEdge(gr, [1, 3]); # Expected output: Error, the 3rd argument must be a vertex of the digraph that is the \ \ 1st argument, # But found: Error, Variable: 'DigraphRemoveEdge' must have a value ######## ########> Diff in standard/oper.tst:81 # Input is: gr := DigraphRemoveEdge(gr, [2, 1]); # Expected output: # But found: Error, Variable: 'DigraphRemoveEdge' must have a value ######## ########> Diff in standard/oper.tst:83 # Input is: DigraphEdges(gr); # Expected output: [ [ 1, 2 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:87 # Input is: gr := Digraph([[2], [1], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:89 # Input is: DigraphEdges(gr); # Expected output: [ [ 1, 2 ], [ 2, 1 ], [ 3, 3 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:93 # Input is: OnDigraphs(gr, g); # Expected output: # But found: Error, Variable: 'OnDigraphs' must have a value ######## ########> Diff in standard/oper.tst:95 # Input is: DigraphEdges(last); # Expected output: [ [ 1, 1 ], [ 2, 3 ], [ 3, 2 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:99 # Input is: OnDigraphs(gr, h); # Expected output: Error, the 2nd argument

must be a permutation that permutes of the digraph\ \ that is the 1st argument, # But found: Error, Variable: 'OnDigraphs' must have a value ######## ########> Diff in standard/oper.tst:102 # Input is: gr := Digraph([[1, 1, 1, 3, 5], [], [3, 2, 4, 5], [2, 5], [1, 2, 1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:104 # Input is: DigraphEdges(gr); # Expected output: [ [ 1, 1 ], [ 1, 1 ], [ 1, 1 ], [ 1, 3 ], [ 1, 5 ], [ 3, 3 ], [ 3, 2 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 4, 5 ], [ 5, 1 ], [ 5, 2 ], [ 5, 1 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:109 # Input is: OnDigraphs(gr, p1); # Expected output: Error, the 2nd argument

must be a permutation that permutes of the digraph\ \ that is the 1st argument, # But found: Error, Variable: 'OnDigraphs' must have a value ######## ########> Diff in standard/oper.tst:114 # Input is: OnDigraphs(gr, p2); # Expected output: # But found: Error, Variable: 'OnDigraphs' must have a value ######## ########> Diff in standard/oper.tst:116 # Input is: DigraphEdges(last); # Expected output: [ [ 2, 1 ], [ 2, 5 ], [ 3, 3 ], [ 3, 3 ], [ 3, 3 ], [ 3, 4 ], [ 3, 5 ], [ 4, 4 ], [ 4, 1 ], [ 4, 2 ], [ 4, 5 ], [ 5, 3 ], [ 5, 1 ], [ 5, 3 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:119 # Input is: gr := DigraphFromDiSparse6String(".CaoJG_hF"); # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/oper.tst:121 # Input is: DigraphEdges(gr); # Expected output: [ [ 1, 2 ], [ 1, 3 ], [ 2, 1 ], [ 2, 4 ], [ 2, 4 ], [ 3, 3 ], [ 4, 1 ], [ 4, 3 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:126 # Input is: OnDigraphs(gr, p1); # Expected output: Error, the 2nd argument

must be a permutation that permutes of the digraph\ \ that is the 1st argument, # But found: Error, Variable: 'OnDigraphs' must have a value ######## ########> Diff in standard/oper.tst:131 # Input is: OnDigraphs(gr, p2); # Expected output: # But found: Error, Variable: 'OnDigraphs' must have a value ######## ########> Diff in standard/oper.tst:133 # Input is: DigraphEdges(last); # Expected output: [ [ 1, 4 ], [ 1, 2 ], [ 2, 2 ], [ 3, 4 ], [ 3, 1 ], [ 3, 1 ], [ 4, 3 ], [ 4, 2 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:138 # Input is: gr := Digraph([[2], [1, 3], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:140 # Input is: OutNeighbours(gr); # Expected output: [ [ 2 ], [ 1, 3 ], [ ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/oper.tst:143 # Input is: OnDigraphs(gr, t); # Expected output: Error, the 2nd argument must be a transformation that maps every vertex of\ \ the digraph that is the 1st argument, to another vertex. # But found: Error, Variable: 'OnDigraphs' must have a value ######## ########> Diff in standard/oper.tst:147 # Input is: gr := OnDigraphs(gr, t); # Expected output: # But found: Error, Variable: 'OnDigraphs' must have a value ######## ########> Diff in standard/oper.tst:149 # Input is: OutNeighbours(gr); # Expected output: [ [ 2 ], [ 1, 1 ], [ ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/oper.tst:153 # Input is: gr1 := CompleteDigraph(3); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:155 # Input is: DigraphEdges(gr1); # Expected output: [ [ 1, 2 ], [ 1, 3 ], [ 2, 1 ], [ 2, 3 ], [ 3, 1 ], [ 3, 2 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:157 # Input is: gr2 := OnMultiDigraphs(gr1, (1, 3), (3, 6));; # Expected output: # But found: Error, Variable: 'OnMultiDigraphs' must have a value ######## ########> Diff in standard/oper.tst:158 # Input is: DigraphEdges(gr1);; # Expected output: # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:159 # Input is: OnMultiDigraphs(gr1, [(1, 3)]); # Expected output: Error, the 2nd argument must be a pair of permutations, # But found: Error, Variable: 'OnMultiDigraphs' must have a value ######## ########> Diff in standard/oper.tst:161 # Input is: OnMultiDigraphs(gr1, [(1, 3), (1, 7)]); # Expected output: Error, the 2nd entry of the 2nd argument must permute the edges of the\ \ digraph that is the 1st argument, # But found: Error, Variable: 'OnMultiDigraphs' must have a value ######## ########> Diff in standard/oper.tst:166 # Input is: gr := DigraphFromDiSparse6String(".IgBGLQ?Apkc"); # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/oper.tst:168 # Input is: InNeighborsOfVertex(gr, 7); # Expected output: [ 7 ] # But found: Error, Variable: 'InNeighborsOfVertex' must have a value ######## ########> Diff in standard/oper.tst:170 # Input is: InNeighboursOfVertex(gr, 7); # Expected output: [ 7 ] # But found: Error, Variable: 'InNeighboursOfVertex' must have a value ######## ########> Diff in standard/oper.tst:172 # Input is: InDegreeOfVertex(gr, 7); # Expected output: 1 # But found: Error, Variable: 'InDegreeOfVertex' must have a value ######## ########> Diff in standard/oper.tst:174 # Input is: InNeighboursOfVertex(gr, 11); # Expected output: Error, the 2nd argument is not a vertex of the 1st argument , # But found: Error, Variable: 'InNeighboursOfVertex' must have a value ######## ########> Diff in standard/oper.tst:176 # Input is: InDegreeOfVertex(gr, 11); # Expected output: Error, the 2nd argument is not a vertex of the 1st argument , # But found: Error, Variable: 'InDegreeOfVertex' must have a value ######## ########> Diff in standard/oper.tst:178 # Input is: gr := DigraphFromDiSparse6String(".CgXo?eWCaJ"); # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/oper.tst:180 # Input is: InNeighboursOfVertex(gr, 3); # Expected output: [ 2 ] # But found: Error, Variable: 'InNeighboursOfVertex' must have a value ######## ########> Diff in standard/oper.tst:182 # Input is: InDegreeOfVertex(gr, 3); # Expected output: 1 # But found: Error, Variable: 'InDegreeOfVertex' must have a value ######## ########> Diff in standard/oper.tst:184 # Input is: InNeighbours(gr); # Expected output: [ [ 1, 1 ], [ 2, 3, 4 ], [ 2 ], [ 1, 2, 3, 3, 3 ] ] # But found: Error, Variable: 'InNeighbours' must have a value ######## ########> Diff in standard/oper.tst:186 # Input is: InNeighboursOfVertex(gr, 4); # Expected output: [ 1, 2, 3, 3, 3 ] # But found: Error, Variable: 'InNeighboursOfVertex' must have a value ######## ########> Diff in standard/oper.tst:188 # Input is: InDegreeOfVertex(gr, 4); # Expected output: 5 # But found: Error, Variable: 'InDegreeOfVertex' must have a value ######## ########> Diff in standard/oper.tst:190 # Input is: InDegrees(gr); # Expected output: [ 2, 3, 1, 5 ] # But found: Error, Variable: 'InDegrees' must have a value ######## ########> Diff in standard/oper.tst:192 # Input is: InDegreeOfVertex(gr, 2); # Expected output: 3 # But found: Error, Variable: 'InDegreeOfVertex' must have a value ######## ########> Diff in standard/oper.tst:196 # Input is: gr := DigraphFromDiSparse6String(".Ig??OaDgDQ~"); # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/oper.tst:198 # Input is: OutNeighborsOfVertex(gr, 2); # Expected output: [ ] # But found: Error, Variable: 'OutNeighborsOfVertex' must have a value ######## ########> Diff in standard/oper.tst:200 # Input is: OutNeighboursOfVertex(gr, 2); # Expected output: [ ] # But found: Error, Variable: 'OutNeighboursOfVertex' must have a value ######## ########> Diff in standard/oper.tst:202 # Input is: OutDegreeOfVertex(gr, 2); # Expected output: 0 # But found: Error, Variable: 'OutDegreeOfVertex' must have a value ######## ########> Diff in standard/oper.tst:204 # Input is: OutNeighboursOfVertex(gr, 5); # Expected output: [ 1, 1, 2, 2, 3, 3 ] # But found: Error, Variable: 'OutNeighboursOfVertex' must have a value ######## ########> Diff in standard/oper.tst:206 # Input is: OutDegreeOfVertex(gr, 5); # Expected output: 6 # But found: Error, Variable: 'OutDegreeOfVertex' must have a value ######## ########> Diff in standard/oper.tst:208 # Input is: OutNeighboursOfVertex(gr, 12); # Expected output: Error, the 2nd argument is not a vertex of the 1st argument , # But found: Error, Variable: 'OutNeighboursOfVertex' must have a value ######## ########> Diff in standard/oper.tst:210 # Input is: OutDegreeOfVertex(gr, 12); # Expected output: Error, the 2nd argument is not a vertex of the 1st argument , # But found: Error, Variable: 'OutDegreeOfVertex' must have a value ######## ########> Diff in standard/oper.tst:212 # Input is: gr := Digraph([[2, 2, 2, 2], [2, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:214 # Input is: OutNeighboursOfVertex(gr, 2); # Expected output: [ 2, 2 ] # But found: Error, Variable: 'OutNeighboursOfVertex' must have a value ######## ########> Diff in standard/oper.tst:216 # Input is: OutDegreeOfVertex(gr, 2); # Expected output: 2 # But found: Error, Variable: 'OutDegreeOfVertex' must have a value ######## ########> Diff in standard/oper.tst:218 # Input is: OutDegrees(gr); # Expected output: [ 4, 2 ] # But found: Error, Variable: 'OutDegrees' must have a value ######## ########> Diff in standard/oper.tst:220 # Input is: OutDegreeOfVertex(gr, 1); # Expected output: 4 # But found: Error, Variable: 'OutDegreeOfVertex' must have a value ######## ########> Diff in standard/oper.tst:227 # Input is: gr := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:229 # Input is: InducedSubdigraph(gr, [-1]); # Expected output: Error, the 2nd argument must be a duplicate-free subset of the vertices\ \ of the digraph that is the 1st argument, # But found: Error, Variable: 'InducedSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:232 # Input is: InducedSubdigraph(gr, [1 .. 9]); # Expected output: Error, the 2nd argument must be a duplicate-free subset of the vertices\ \ of the digraph that is the 1st argument, # But found: Error, Variable: 'InducedSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:235 # Input is: InducedSubdigraph(gr, []); # Expected output: # But found: Error, Variable: 'InducedSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:237 # Input is: InducedSubdigraph(gr, [2 .. 6]); # Expected output: # But found: Error, Variable: 'InducedSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:239 # Input is: InducedSubdigraph(gr, [8]); # Expected output: # But found: Error, Variable: 'InducedSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:241 # Input is: i1 := InducedSubdigraph(gr, [1, 4, 3]); # Expected output: # But found: Error, Variable: 'InducedSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:243 # Input is: OutNeighbours(i1); # Expected output: [ [ 1, 1, 3, 3, 2 ], [ ], [ 2 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/oper.tst:245 # Input is: i2 := InducedSubdigraph(gr, [3, 4, 3, 1]); # Expected output: Error, the 2nd argument must be a duplicate-free subset of the vertices\ \ of the digraph that is the 1st argument, # But found: Error, Variable: 'InducedSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:250 # Input is: gr := Digraph(adj); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:252 # Input is: InducedSubdigraph(gr, ["a"]); # Expected output: Error, the 2nd argument must be a duplicate-free subset of the vertices\ \ of the digraph that is the 1st argument, # But found: Error, Variable: 'InducedSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:255 # Input is: InducedSubdigraph(gr, [0]); # Expected output: Error, the 2nd argument must be a duplicate-free subset of the vertices\ \ of the digraph that is the 1st argument, # But found: Error, Variable: 'InducedSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:258 # Input is: InducedSubdigraph(gr, [2 .. 9]); # Expected output: Error, the 2nd argument must be a duplicate-free subset of the vertices\ \ of the digraph that is the 1st argument, # But found: Error, Variable: 'InducedSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:261 # Input is: InducedSubdigraph(gr, []); # Expected output: # But found: Error, Variable: 'InducedSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:263 # Input is: i1 := InducedSubdigraph(gr, [1, 3, 5, 7]); # Expected output: # But found: Error, Variable: 'InducedSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:265 # Input is: OutNeighbours(i1); # Expected output: [ [ 2, 3, 4 ], [ ], [ 1, 2, 3, 4 ], [ 1 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/oper.tst:267 # Input is: i2 := InducedSubdigraph(gr, [7, 5, 3, 1]); # Expected output: # But found: Error, Variable: 'InducedSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:269 # Input is: i1 = i2; # Expected output: false # But found: Error, Variable: 'i1' must have a value ######## ########> Diff in standard/oper.tst:271 # Input is: IsIsomorphicDigraph(i1, i2); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/oper.tst:273 # Input is: InducedSubdigraph(gr, [2 .. 8]); # Expected output: # But found: Error, Variable: 'InducedSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:275 # Input is: InducedSubdigraph(gr, [8]); # Expected output: # But found: Error, Variable: 'InducedSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:277 # Input is: InducedSubdigraph(gr, [7, 8]); # Expected output: # But found: Error, Variable: 'InducedSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:279 # Input is: gr := Digraph([[2, 4], [4, 5], [2, 5, 5], [5, 5], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:281 # Input is: gri := InducedSubdigraph(gr, [4, 2, 5]); # Expected output: # But found: Error, Variable: 'InducedSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:283 # Input is: DigraphVertexLabels(gri); # Expected output: [ 4, 2, 5 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:285 # Input is: OutNeighbours(gri); # Expected output: [ [ 3, 3 ], [ 1, 3 ], [ ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/oper.tst:289 # Input is: gr := CompleteDigraph(2); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:291 # Input is: DigraphEdges(gr); # Expected output: [ [ 1, 2 ], [ 2, 1 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:293 # Input is: qr := QuotientDigraph(gr, [[1, 2]]); # Expected output: # But found: Error, Variable: 'QuotientDigraph' must have a value ######## ########> Diff in standard/oper.tst:295 # Input is: DigraphEdges(qr); # Expected output: [ [ 1, 1 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:297 # Input is: QuotientDigraph(EmptyDigraph(0), []); # Expected output: # But found: Error, Variable: 'QuotientDigraph' must have a value ######## ########> Diff in standard/oper.tst:299 # Input is: QuotientDigraph(EmptyDigraph(0), [[1]]); # Expected output: Error, the 2nd argument should be an empty list, which is the only\ \ valid partition of the vertices of 1st argument because it has no vertice\ \ s, # But found: Error, Variable: 'QuotientDigraph' must have a value ######## ########> Diff in standard/oper.tst:303 # Input is: gr := Digraph([[1, 2, 3, 2], [1, 3, 2], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:305 # Input is: DigraphEdges(gr); # Expected output: [ [ 1, 1 ], [ 1, 2 ], [ 1, 3 ], [ 1, 2 ], [ 2, 1 ], [ 2, 3 ], [ 2, 2 ], [ 3, 1 ], [ 3, 2 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:308 # Input is: qr := QuotientDigraph(gr, [[1, 3], [2]]); # Expected output: # But found: Error, Variable: 'QuotientDigraph' must have a value ######## ########> Diff in standard/oper.tst:310 # Input is: DigraphEdges(qr); # Expected output: [ [ 1, 1 ], [ 1, 2 ], [ 2, 1 ], [ 2, 2 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:312 # Input is: QuotientDigraph(gr, [3]); # Expected output: Error, the 2nd argument is not a valid partition of the vertices [\ \ 1 .. 3] of the 1st argument , # But found: Error, Variable: 'QuotientDigraph' must have a value ######## ########> Diff in standard/oper.tst:315 # Input is: QuotientDigraph(gr, []); # Expected output: Error, the 2nd argument is not a valid partition of the vertices [\ \ 1 .. 3] of the 1st argument , # But found: Error, Variable: 'QuotientDigraph' must have a value ######## ########> Diff in standard/oper.tst:318 # Input is: QuotientDigraph(gr, [[], []]); # Expected output: Error, the 2nd argument is not a valid partition of the vertices [\ \ 1 .. 3] of the 1st argument , # But found: Error, Variable: 'QuotientDigraph' must have a value ######## ########> Diff in standard/oper.tst:321 # Input is: QuotientDigraph(gr, [[0], [1]]); # Expected output: Error, the 2nd argument is not a valid partition of the vertices [\ \ 1 .. 3] of the 1st argument , # But found: Error, Variable: 'QuotientDigraph' must have a value ######## ########> Diff in standard/oper.tst:324 # Input is: QuotientDigraph(gr, [[1], [2], [0]]); # Expected output: Error, the 2nd argument is not a valid partition of the vertices [\ \ 1 .. 3] of the 1st argument , # But found: Error, Variable: 'QuotientDigraph' must have a value ######## ########> Diff in standard/oper.tst:327 # Input is: QuotientDigraph(gr, [[1], [2, 4]]); # Expected output: Error, the 2nd argument is not a valid partition of the vertices [\ \ 1 .. 3] of the 1st argument , # But found: Error, Variable: 'QuotientDigraph' must have a value ######## ########> Diff in standard/oper.tst:330 # Input is: QuotientDigraph(gr, [[1, 2], [2]]); # Expected output: Error, the 2nd argument is not a valid partition of the vertices [\ \ 1 .. 3] of the 1st argument , # But found: Error, Variable: 'QuotientDigraph' must have a value ######## ########> Diff in standard/oper.tst:333 # Input is: QuotientDigraph(gr, [[1], [2]]); # Expected output: Error, the 2nd argument is not a valid partition of the vertices [\ \ 1 .. 3] of the 1st argument , # But found: Error, Variable: 'QuotientDigraph' must have a value ######## ########> Diff in standard/oper.tst:336 # Input is: gr := Digraph(rec( DigraphNrVertices := 8, DigraphSource := [1, 1, 2, 2, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 7, 7, 7, 7, 7, 8, \ 8], DigraphRange := [6, 7, 1, 6, 5, 1, 4, 8, 1, 3, 4, 6, 7, 7, 1, 4, 5, 6, 7, 5, 6\ ])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:341 # Input is: qr := QuotientDigraph(gr, [[1], [2, 3, 5, 7], [4, 6, 8]]); # Expected output: # But found: Error, Variable: 'QuotientDigraph' must have a value ######## ########> Diff in standard/oper.tst:343 # Input is: OutNeighbours(qr); # Expected output: [ [ 2, 3 ], [ 1, 2, 3 ], [ 1, 2, 3 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/oper.tst:347 # Input is: gr := Digraph([[2, 2, 2, 2, 2], [1, 1, 1, 1], [1], [3, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:349 # Input is: DigraphInEdges(gr, 1); # Expected output: [ [ 2, 1 ], [ 2, 1 ], [ 2, 1 ], [ 2, 1 ], [ 3, 1 ] ] # But found: Error, Variable: 'DigraphInEdges' must have a value ######## ########> Diff in standard/oper.tst:351 # Input is: DigraphOutEdges(gr, 3); # Expected output: [ [ 3, 1 ] ] # But found: Error, Variable: 'DigraphOutEdges' must have a value ######## ########> Diff in standard/oper.tst:353 # Input is: DigraphOutEdges(gr, 5); # Expected output: Error, the 2nd argument is not a vertex of the 1st argument , # But found: Error, Variable: 'DigraphOutEdges' must have a value ######## ########> Diff in standard/oper.tst:355 # Input is: DigraphInEdges(gr, 1000); # Expected output: Error, the 2nd argument is not a vertex of the 1st argument , # But found: Error, Variable: 'DigraphInEdges' must have a value ######## ########> Diff in standard/oper.tst:357 # Input is: gr := Digraph(rec(DigraphVertices := ["a", "b", "c"], DigraphSource := ["a", "\ a", "b"], DigraphRange := ["b", "b", "c"])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:360 # Input is: DigraphInEdges(gr, 1); # Expected output: [ ] # But found: Error, Variable: 'DigraphInEdges' must have a value ######## ########> Diff in standard/oper.tst:362 # Input is: DigraphInEdges(gr, 2); # Expected output: [ [ 1, 2 ], [ 1, 2 ] ] # But found: Error, Variable: 'DigraphInEdges' must have a value ######## ########> Diff in standard/oper.tst:364 # Input is: DigraphOutEdges(gr, 1); # Expected output: [ [ 1, 2 ], [ 1, 2 ] ] # But found: Error, Variable: 'DigraphOutEdges' must have a value ######## ########> Diff in standard/oper.tst:368 # Input is: gr := Digraph([[2, 4], [], [2, 6], [1, 3], [2, 3], [5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:370 # Input is: DigraphStronglyConnectedComponent(gr, 1); # Expected output: [ 1, 4 ] # But found: Error, Variable: 'DigraphStronglyConnectedComponent' must have a value ######## ########> Diff in standard/oper.tst:372 # Input is: DigraphStronglyConnectedComponent(gr, 2); # Expected output: [ 2 ] # But found: Error, Variable: 'DigraphStronglyConnectedComponent' must have a value ######## ########> Diff in standard/oper.tst:374 # Input is: DigraphStronglyConnectedComponent(gr, 3); # Expected output: [ 3, 6, 5 ] # But found: Error, Variable: 'DigraphStronglyConnectedComponent' must have a value ######## ########> Diff in standard/oper.tst:376 # Input is: DigraphStronglyConnectedComponent(gr, 7); # Expected output: Error, the 2nd argument is not a vertex of the 1st argument , # But found: Error, Variable: 'DigraphStronglyConnectedComponent' must have a value ######## ########> Diff in standard/oper.tst:380 # Input is: gr := Digraph([[2, 4], [], [2, 6], [1, 3], [2, 3], [5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:382 # Input is: DigraphConnectedComponent(gr, 3); # Expected output: [ 1, 2, 3, 4, 5, 6 ] # But found: Error, Variable: 'DigraphConnectedComponent' must have a value ######## ########> Diff in standard/oper.tst:384 # Input is: DigraphConnectedComponent(gr, 7); # Expected output: Error, the 2nd argument is not a vertex of the 1st argument , # But found: Error, Variable: 'DigraphConnectedComponent' must have a value ######## ########> Diff in standard/oper.tst:390 # Input is: gr := CycleDigraph(1000); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/oper.tst:392 # Input is: IsDigraphEdge(gr, [1]); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:394 # Input is: IsDigraphEdge(gr, ["a", 2]); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:396 # Input is: IsDigraphEdge(gr, [1, "a"]); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:398 # Input is: IsDigraphEdge(gr, [1001, 1]); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:400 # Input is: IsDigraphEdge(gr, [1, 1001]); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:402 # Input is: IsDigraphEdge(gr, [100, 101]); # Expected output: true # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:404 # Input is: IsDigraphEdge(gr, [1000, 1]); # Expected output: true # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:406 # Input is: IsDigraphEdge(gr, [1000, 600]); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:412 # Input is: gr := Digraph(out); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:414 # Input is: IsDigraphEdge(gr, [1]); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:416 # Input is: IsDigraphEdge(gr, ["a", 2]); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:418 # Input is: IsDigraphEdge(gr, [1, "a"]); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:420 # Input is: IsDigraphEdge(gr, [1001, 1]); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:422 # Input is: IsDigraphEdge(gr, [1, 1001]); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:424 # Input is: IsDigraphEdge(gr, [100, 101]); # Expected output: true # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:426 # Input is: IsDigraphEdge(gr, [1000, 1]); # Expected output: true # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:428 # Input is: IsDigraphEdge(gr, [1000, 600]); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:430 # Input is: gr := Digraph(rec(DigraphNrVertices := 2, DigraphSource := [1], DigraphRange :\ = [2])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:432 # Input is: IsDigraphEdge(gr, [2, 1]); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:434 # Input is: IsDigraphEdge(gr, [1, 1]); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:438 # Input is: gr := CompleteDigraph(500); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:440 # Input is: IsDigraphEdge(gr, [200, 199]); # Expected output: true # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:442 # Input is: IsDigraphEdge(gr, [499, 499]); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:444 # Input is: IsDigraphEdge(gr, [249, 251]); # Expected output: true # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:446 # Input is: gr := EmptyDigraph(1000000); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/oper.tst:448 # Input is: IsDigraphEdge(gr, [9999, 9999]); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:450 # Input is: gr := CompleteDigraph(10); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:452 # Input is: mat := AdjacencyMatrix(gr);; # Expected output: # But found: Error, Variable: 'AdjacencyMatrix' must have a value ######## ########> Diff in standard/oper.tst:453 # Input is: IsDigraphEdge(gr, [5, 5]); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:455 # Input is: IsDigraphEdge(gr, [5, 6]); # Expected output: true # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:457 # Input is: gr := Digraph([[1, 1], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:459 # Input is: mat := AdjacencyMatrix(gr);; # Expected output: # But found: Error, Variable: 'AdjacencyMatrix' must have a value ######## ########> Diff in standard/oper.tst:460 # Input is: IsDigraphEdge(gr, [1, 1]); # Expected output: true # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:462 # Input is: IsDigraphEdge(gr, [1, 2]); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:468 # Input is: gr := Digraph([1 .. 20], adj);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:469 # Input is: IsDigraphEdge(gr, [1, 4]); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:471 # Input is: IsDigraphEdge(gr, 3, 6); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:473 # Input is: IsDigraphEdge(gr, 12, 6); # Expected output: true # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:475 # Input is: IsDigraphEdge(gr, 26, 13); # Expected output: false # But found: Error, Variable: 'IsDigraphEdge' must have a value ######## ########> Diff in standard/oper.tst:479 # Input is: gr := RandomDigraph(100);; # Expected output: # But found: Error, Variable: 'RandomDigraph' must have a value ######## ########> Diff in standard/oper.tst:480 # Input is: DigraphAddEdges(gr, []);; # Expected output: # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/oper.tst:481 # Input is: gr = last; # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/oper.tst:483 # Input is: DigraphAddEdges(gr, [12]); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphAddEdge' on 2 arguments # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/oper.tst:486 # Input is: DigraphAddEdges(gr, [[12]]); # Expected output: Error, the 2nd argument must be a list of length 2, # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/oper.tst:488 # Input is: DigraphAddEdges(gr, [[12, 13, 14], [11, 10]]); # Expected output: Error, the 2nd argument must be a list of length 2, # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/oper.tst:490 # Input is: DigraphAddEdges(gr, [[-2, 3], ["a"]]); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphAddEdge' on 3 arguments # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/oper.tst:493 # Input is: DigraphAddEdges(gr, [[11, 10], [12, 13, 14]]); # Expected output: Error, the 2nd argument must be a list of length 2, # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/oper.tst:495 # Input is: DigraphAddEdges(gr, [[4, 5], [1, 120], [1, 1]]); # Expected output: Error, the 2nd argument must be a vertex of the digraph that is the \ \ 1st argument, # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/oper.tst:498 # Input is: DigraphAddEdges(gr, [[4, 5], [120, 1], [1, 1]]); # Expected output: Error, the 2nd argument must be a vertex of the digraph that is the \ \ 1st argument, # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/oper.tst:501 # Input is: gr := Digraph([[2, 2], [1, 3, 2], [2, 1], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:503 # Input is: DigraphEdges(gr); # Expected output: [ [ 1, 2 ], [ 1, 2 ], [ 2, 1 ], [ 2, 3 ], [ 2, 2 ], [ 3, 2 ], [ 3, 1 ], [ 4, 1 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:506 # Input is: gr2 := DigraphAddEdges(gr, [[2, 1], [3, 3], [2, 4], [3, 3]]); # Expected output: # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/oper.tst:508 # Input is: DigraphEdges(gr2); # Expected output: [ [ 1, 2 ], [ 1, 2 ], [ 2, 1 ], [ 2, 3 ], [ 2, 2 ], [ 2, 1 ], [ 2, 4 ], [ 3, 2 ], [ 3, 1 ], [ 3, 3 ], [ 3, 3 ], [ 4, 1 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:511 # Input is: gr3 := Digraph(rec(DigraphNrVertices := DigraphNrVertices(gr), DigraphSource := ShallowCopy(DigraphSource(gr)), DigraphRange := ShallowCopy(DigraphRange(gr)))); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:515 # Input is: gr4 := DigraphAddEdges(gr3, [[2, 1], [3, 3], [2, 4], [3, 3]]); # Expected output: # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/oper.tst:517 # Input is: gr2 = gr4; # Expected output: true # But found: Error, Variable: 'gr2' must have a value ######## ########> Diff in standard/oper.tst:519 # Input is: gr := Digraph([[1, 2], [], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:521 # Input is: gr1 := DigraphAddEdges(gr, []); # Expected output: # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/oper.tst:523 # Input is: gr = gr1; # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/oper.tst:525 # Input is: DigraphAddEdges(gr, [3]); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphAddEdge' on 2 arguments # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/oper.tst:528 # Input is: DigraphAddEdges(gr, [[3]]); # Expected output: Error, the 2nd argument must be a list of length 2, # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/oper.tst:530 # Input is: DigraphAddEdges(gr, ["ab"]); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphAddEdge' on 3 arguments # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/oper.tst:533 # Input is: DigraphAddEdges(gr, [[-1, -2]]); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphAddEdge' on 3 arguments # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/oper.tst:536 # Input is: DigraphAddEdges(gr, [[1, 2], [1, 2, 3]]); # Expected output: Error, the 2nd argument must be a list of length 2, # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/oper.tst:538 # Input is: DigraphAddEdges(gr, [[4, 2]]); # Expected output: Error, the 2nd argument must be a vertex of the digraph that is the \ \ 1st argument, # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/oper.tst:541 # Input is: DigraphAddEdges(gr, [[2, 4]]); # Expected output: Error, the 2nd argument must be a vertex of the digraph that is the \ \ 1st argument, # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/oper.tst:544 # Input is: DigraphAddEdges(gr, [[2, 3], [2, 3]]); # Expected output: # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/oper.tst:546 # Input is: DigraphEdges(last); # Expected output: [ [ 1, 1 ], [ 1, 2 ], [ 2, 3 ], [ 2, 3 ], [ 3, 1 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:548 # Input is: DigraphEdges(gr); # Expected output: [ [ 1, 1 ], [ 1, 2 ], [ 3, 1 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:552 # Input is: gr := RandomDigraph(10);; # Expected output: # But found: Error, Variable: 'RandomDigraph' must have a value ######## ########> Diff in standard/oper.tst:553 # Input is: DigraphAddEdge(gr, [1, 2, 3]); # Expected output: Error, the 2nd argument must be a list of length 2, # But found: Error, Variable: 'DigraphAddEdge' must have a value ######## ########> Diff in standard/oper.tst:555 # Input is: DigraphAddEdge(gr, ["a", "a"]); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphAddEdge' on 3 arguments # But found: Error, Variable: 'DigraphAddEdge' must have a value ######## ########> Diff in standard/oper.tst:558 # Input is: DigraphAddEdge(gr, [1, "a"]); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphAddEdge' on 3 arguments # But found: Error, Variable: 'DigraphAddEdge' must have a value ######## ########> Diff in standard/oper.tst:561 # Input is: DigraphAddEdge(gr, [11, 1]); # Expected output: Error, the 2nd argument must be a vertex of the digraph that is the \ \ 1st argument, # But found: Error, Variable: 'DigraphAddEdge' must have a value ######## ########> Diff in standard/oper.tst:564 # Input is: DigraphAddEdge(gr, [1, 11]); # Expected output: Error, the 2nd argument must be a vertex of the digraph that is the \ \ 1st argument, # But found: Error, Variable: 'DigraphAddEdge' must have a value ######## ########> Diff in standard/oper.tst:567 # Input is: gr := EmptyDigraph(2); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/oper.tst:569 # Input is: DigraphAddEdge(gr, [1, 2]); # Expected output: # But found: Error, Variable: 'DigraphAddEdge' must have a value ######## ########> Diff in standard/oper.tst:571 # Input is: DigraphEdges(last); # Expected output: [ [ 1, 2 ] ] # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:575 # Input is: gr := Digraph([[1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:576 # Input is: gr2 := DigraphAddVertices(gr, 3); # Expected output: # But found: Error, Variable: 'DigraphAddVertices' must have a value ######## ########> Diff in standard/oper.tst:578 # Input is: DigraphVertices(gr2); # Expected output: [ 1 .. 4 ] # But found: Error, Variable: 'DigraphVertices' must have a value ######## ########> Diff in standard/oper.tst:580 # Input is: DigraphEdges(gr) = DigraphEdges(gr2); # Expected output: true # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:582 # Input is: gr2 := DigraphAddVertices(gr, [SymmetricGroup(2), Group(())]); # Expected output: # But found: Error, Variable: 'DigraphAddVertices' must have a value ######## ########> Diff in standard/oper.tst:584 # Input is: DigraphVertices(gr2); # Expected output: [ 1 .. 3 ] # But found: Error, Variable: 'DigraphVertices' must have a value ######## ########> Diff in standard/oper.tst:586 # Input is: DigraphEdges(gr) = DigraphEdges(gr2); # Expected output: true # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:588 # Input is: DigraphVertexLabels(gr2); # Expected output: [ 1, Sym( [ 1 .. 2 ] ), Group(()) ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:590 # Input is: gr := Digraph([[1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:591 # Input is: SetDigraphVertexLabels(gr, [AlternatingGroup(5)]); # Expected output: # But found: Error, Variable: 'SetDigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:592 # Input is: gr2 := DigraphAddVertices(gr, [SymmetricGroup(2), Group(())]); # Expected output: # But found: Error, Variable: 'DigraphAddVertices' must have a value ######## ########> Diff in standard/oper.tst:594 # Input is: DigraphVertexLabels(gr2); # Expected output: [ Alt( [ 1 .. 5 ] ), Sym( [ 1 .. 2 ] ), Group(()) ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:596 # Input is: gr := Digraph(rec(DigraphNrVertices := 1, DigraphSource := [1], DigraphRange :\ = [1])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:598 # Input is: gr2 := DigraphAddVertices(gr, 2); # Expected output: # But found: Error, Variable: 'DigraphAddVertices' must have a value ######## ########> Diff in standard/oper.tst:600 # Input is: DigraphVertexLabels(gr2); # Expected output: [ 1, 2, 3 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:602 # Input is: SetDigraphVertexLabels(gr, [true]); # Expected output: # But found: Error, Variable: 'SetDigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:603 # Input is: gr2 := DigraphAddVertices(gr, 2); # Expected output: # But found: Error, Variable: 'DigraphAddVertices' must have a value ######## ########> Diff in standard/oper.tst:605 # Input is: DigraphVertexLabels(gr2); # Expected output: [ true, 2, 3 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:607 # Input is: gr := Digraph(rec(DigraphNrVertices := 1, DigraphSource := [1], DigraphRange :\ = [1]));; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:608 # Input is: gr2 := DigraphAddVertices(gr, [SymmetricGroup(2), Group(())]); # Expected output: # But found: Error, Variable: 'DigraphAddVertices' must have a value ######## ########> Diff in standard/oper.tst:610 # Input is: DigraphVertexLabels(gr2); # Expected output: [ 1, Sym( [ 1 .. 2 ] ), Group(()) ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:612 # Input is: gr := Digraph(rec(DigraphNrVertices := 1, DigraphSource := [1], DigraphRange :\ = [1]));; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:613 # Input is: SetDigraphVertexLabels(gr, [AlternatingGroup(5)]); # Expected output: # But found: Error, Variable: 'SetDigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:614 # Input is: gr2 := DigraphAddVertices(gr, [SymmetricGroup(2), Group(())]); # Expected output: # But found: Error, Variable: 'DigraphAddVertices' must have a value ######## ########> Diff in standard/oper.tst:616 # Input is: DigraphVertexLabels(gr2); # Expected output: [ Alt( [ 1 .. 5 ] ), Sym( [ 1 .. 2 ] ), Group(()) ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:618 # Input is: DigraphAddVertices(gr2, -1); # Expected output: Error, the 2nd argument must be a non-negative integer, # But found: Error, Variable: 'DigraphAddVertices' must have a value ######## ########> Diff in standard/oper.tst:620 # Input is: gr3 := DigraphAddVertices(gr2, 0); # Expected output: # But found: Error, Variable: 'DigraphAddVertices' must have a value ######## ########> Diff in standard/oper.tst:622 # Input is: IsIdenticalObj(gr2, gr3); # Expected output: false # But found: Error, Variable: 'gr2' must have a value ######## ########> Diff in standard/oper.tst:624 # Input is: gr2 = gr3; # Expected output: true # But found: Error, Variable: 'gr2' must have a value ######## ########> Diff in standard/oper.tst:626 # Input is: gr3 := DigraphAddVertices(gr2, []); # Expected output: # But found: Error, Variable: 'DigraphAddVertices' must have a value ######## ########> Diff in standard/oper.tst:628 # Input is: IsIdenticalObj(gr2, gr3); # Expected output: false # But found: Error, Variable: 'gr2' must have a value ######## ########> Diff in standard/oper.tst:630 # Input is: gr2 = gr3; # Expected output: true # But found: Error, Variable: 'gr2' must have a value ######## ########> Diff in standard/oper.tst:634 # Input is: D := Digraph([[1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:636 # Input is: DigraphVertexLabels(D); # Expected output: [ 1 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:638 # Input is: DigraphAddVertices(D, 2, [fail]); # Expected output: Error, the list (3rd argument) must have length (2nd argument), # But found: Error, Variable: 'DigraphAddVertices' must have a value ######## ########> Diff in standard/oper.tst:640 # Input is: D := DigraphAddVertices(D, 2, [fail, true]); # Expected output: # But found: Error, Variable: 'DigraphAddVertices' must have a value ######## ########> Diff in standard/oper.tst:642 # Input is: DigraphVertexLabels(D); # Expected output: [ 1, fail, true ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:646 # Input is: gr := CompleteDigraph(1); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:648 # Input is: DigraphVertices(gr); # Expected output: [ 1 ] # But found: Error, Variable: 'DigraphVertices' must have a value ######## ########> Diff in standard/oper.tst:650 # Input is: gr2 := DigraphAddVertex(gr); # Expected output: # But found: Error, Variable: 'DigraphAddVertex' must have a value ######## ########> Diff in standard/oper.tst:652 # Input is: DigraphVertices(gr2); # Expected output: [ 1, 2 ] # But found: Error, Variable: 'DigraphVertices' must have a value ######## ########> Diff in standard/oper.tst:654 # Input is: DigraphEdges(gr) = DigraphEdges(gr2); # Expected output: true # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:656 # Input is: gr := DigraphAddEdge(gr, [1, 1]); # Expected output: # But found: Error, Variable: 'DigraphAddEdge' must have a value ######## ########> Diff in standard/oper.tst:658 # Input is: DigraphVertices(gr); # Expected output: [ 1 ] # But found: Error, Variable: 'DigraphVertices' must have a value ######## ########> Diff in standard/oper.tst:660 # Input is: gr2 := DigraphAddVertex(gr); # Expected output: # But found: Error, Variable: 'DigraphAddVertex' must have a value ######## ########> Diff in standard/oper.tst:662 # Input is: DigraphVertices(gr2); # Expected output: [ 1, 2 ] # But found: Error, Variable: 'DigraphVertices' must have a value ######## ########> Diff in standard/oper.tst:664 # Input is: DigraphEdges(gr) = DigraphEdges(gr2); # Expected output: true # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:666 # Input is: gr2 := DigraphAddVertex(gr, SymmetricGroup(2)); # Expected output: # But found: Error, Variable: 'DigraphAddVertex' must have a value ######## ########> Diff in standard/oper.tst:668 # Input is: DigraphVertices(gr2); # Expected output: [ 1, 2 ] # But found: Error, Variable: 'DigraphVertices' must have a value ######## ########> Diff in standard/oper.tst:670 # Input is: DigraphEdges(gr) = DigraphEdges(gr2); # Expected output: true # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:672 # Input is: DigraphVertexLabels(gr); # Expected output: [ 1 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:674 # Input is: DigraphVertexLabels(gr2); # Expected output: [ 1, Sym( [ 1 .. 2 ] ) ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:678 # Input is: gr := DigraphFromDigraph6String("&MU?GAa?SDCFStK`???d?@LWOq[{DECO?U?"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/oper.tst:680 # Input is: DigraphRemoveVertex(gr, "a"); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphRemoveVertex' on 2 arguments # But found: Error, Variable: 'DigraphRemoveVertex' must have a value ######## ########> Diff in standard/oper.tst:683 # Input is: DigraphRemoveVertex(gr, 0); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphRemoveVertex' on 2 arguments # But found: Error, Variable: 'DigraphRemoveVertex' must have a value ######## ########> Diff in standard/oper.tst:686 # Input is: DigraphRemoveVertex(gr, 15); # Expected output: # But found: Error, Variable: 'DigraphRemoveVertex' must have a value ######## ########> Diff in standard/oper.tst:688 # Input is: gr2 := DigraphRemoveVertex(gr, 10);; # Expected output: # But found: Error, Variable: 'DigraphRemoveVertex' must have a value ######## ########> Diff in standard/oper.tst:689 # Input is: DigraphNrVertices(gr2); # Expected output: 13 # But found: Error, Variable: 'DigraphNrVertices' must have a value ######## ########> Diff in standard/oper.tst:691 # Input is: DigraphNrEdges(gr2) = DigraphNrEdges(gr) - OutDegreeOfVertex(gr, 10) - InDegreeOfVertex(gr, 10); # Expected output: true # But found: Error, Variable: 'DigraphNrEdges' must have a value ######## ########> Diff in standard/oper.tst:694 # Input is: D := CycleDigraph(IsMutableDigraph, 5); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/oper.tst:696 # Input is: DigraphRemoveVertex(D, 1); # Expected output: # But found: Error, Variable: 'DigraphRemoveVertex' must have a value ######## ########> Diff in standard/oper.tst:698 # Input is: DigraphVertexLabels(D); # Expected output: [ 2, 3, 4, 5 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:702 # Input is: gr := CompleteDigraph(4); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:704 # Input is: gr2 := DigraphRemoveVertices(gr, []); # Expected output: # But found: Error, Variable: 'DigraphRemoveVertices' must have a value ######## ########> Diff in standard/oper.tst:706 # Input is: gr = gr2; # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/oper.tst:708 # Input is: gr2 := DigraphRemoveVertices(gr, [0]); # Expected output: Error, the 2nd argument must be a duplicate-free list of positive integ\ \ ers, # But found: Error, Variable: 'DigraphRemoveVertices' must have a value ######## ########> Diff in standard/oper.tst:711 # Input is: gr2 := DigraphRemoveVertices(gr, [1, "a"]); # Expected output: Error, the 2nd argument must be a duplicate-free list of positive integ\ \ ers, # But found: Error, Variable: 'DigraphRemoveVertices' must have a value ######## ########> Diff in standard/oper.tst:714 # Input is: gr2 := DigraphRemoveVertices(gr, [1, 1]); # Expected output: Error, the 2nd argument must be a duplicate-free list of positive integ\ \ ers, # But found: Error, Variable: 'DigraphRemoveVertices' must have a value ######## ########> Diff in standard/oper.tst:717 # Input is: gr2 := DigraphRemoveVertices(gr, [1, 0]); # Expected output: Error, the 2nd argument must be a duplicate-free list of positive integ\ \ ers, # But found: Error, Variable: 'DigraphRemoveVertices' must have a value ######## ########> Diff in standard/oper.tst:720 # Input is: gr2 := DigraphRemoveVertices(gr, [1, 5]); # Expected output: # But found: Error, Variable: 'DigraphRemoveVertices' must have a value ######## ########> Diff in standard/oper.tst:722 # Input is: gr2 := DigraphRemoveVertices(gr, [1, 3]); # Expected output: # But found: Error, Variable: 'DigraphRemoveVertices' must have a value ######## ########> Diff in standard/oper.tst:724 # Input is: IsCompleteDigraph(gr2); # Expected output: true # But found: Error, Variable: 'IsCompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:726 # Input is: DigraphVertexLabels(gr2); # Expected output: [ 2, 4 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:728 # Input is: gr3 := DigraphRemoveVertices(gr, [1 .. 4]); # Expected output: # But found: Error, Variable: 'DigraphRemoveVertices' must have a value ######## ########> Diff in standard/oper.tst:730 # Input is: gr := Digraph(rec(DigraphNrVertices := 4, DigraphSource := [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4], DigraphRange := [1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:734 # Input is: IsCompleteDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsCompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:736 # Input is: SetDigraphVertexLabels(gr, [(), (1, 2), (1, 2, 3), (1, 2, 3, 4)]); # Expected output: # But found: Error, Variable: 'SetDigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:737 # Input is: gr2 := DigraphRemoveVertices(gr, [1 .. 4]); # Expected output: # But found: Error, Variable: 'DigraphRemoveVertices' must have a value ######## ########> Diff in standard/oper.tst:739 # Input is: gr3 := DigraphRemoveVertices(gr, [2, 3]); # Expected output: # But found: Error, Variable: 'DigraphRemoveVertices' must have a value ######## ########> Diff in standard/oper.tst:741 # Input is: DigraphVertexLabels(gr3); # Expected output: [ (), (1,2,3,4) ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:743 # Input is: gr4 := DigraphRemoveVertices(gr, []); # Expected output: # But found: Error, Variable: 'DigraphRemoveVertices' must have a value ######## ########> Diff in standard/oper.tst:745 # Input is: gr = gr4; # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/oper.tst:747 # Input is: gr := Digraph([[1, 10], [], [], [3], [3, 4, 10], [1, 3, 8], [9], [9], [3], [3, 5, 10]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:750 # Input is: DigraphSinks(gr); # Expected output: [ 2, 3 ] # But found: Error, Variable: 'DigraphSinks' must have a value ######## ########> Diff in standard/oper.tst:752 # Input is: DigraphRemoveVertices(gr, DigraphSinks(gr)); # Expected output: # But found: Error, Variable: 'DigraphRemoveVertices' must have a value ######## ########> Diff in standard/oper.tst:756 # Input is: gr := Digraph([[1, 1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:758 # Input is: DigraphReverseEdges(gr, [[2, 2]]); # Expected output: Error, the 1st argument must be a digraph with no multiple edges, # But found: Error, Variable: 'DigraphReverseEdges' must have a value ######## ########> Diff in standard/oper.tst:760 # Input is: DigraphReverseEdges(gr, [2]); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphReverseEdge' on 2 arguments # But found: Error, Variable: 'DigraphReverseEdges' must have a value ######## ########> Diff in standard/oper.tst:763 # Input is: gr := CompleteDigraph(100); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:765 # Input is: DigraphReverseEdges(gr, "a"); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphReverseEdge' on 2 arguments # But found: Error, Variable: 'DigraphReverseEdges' must have a value ######## ########> Diff in standard/oper.tst:768 # Input is: DigraphReverseEdges(gr, Group(())); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphReverseEdges' on 2 arguments # But found: Error, Variable: 'DigraphReverseEdges' must have a value ######## ########> Diff in standard/oper.tst:771 # Input is: DigraphReverseEdges(gr, [0, 0]); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphReverseEdge' on 2 arguments # But found: Error, Variable: 'DigraphReverseEdges' must have a value ######## ########> Diff in standard/oper.tst:774 # Input is: DigraphReverseEdges(gr, [[0]]); # Expected output: Error, the 2nd argument must be a list of length 2, # But found: Error, Variable: 'DigraphReverseEdges' must have a value ######## ########> Diff in standard/oper.tst:776 # Input is: DigraphReverseEdges(gr, [[1], [1]]); # Expected output: Error, the 2nd argument must be a list of length 2, # But found: Error, Variable: 'DigraphReverseEdges' must have a value ######## ########> Diff in standard/oper.tst:778 # Input is: edges := ShallowCopy(DigraphEdges(gr));; # Expected output: # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:779 # Input is: gr = DigraphReverseEdges(gr, edges); # Expected output: Error, the 1st argument must be a digraph with no multiple edges, # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/oper.tst:781 # Input is: gr = DigraphReverseEdges(gr, [1 .. DigraphNrEdges(gr)]); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphReverseEdge' on 2 arguments # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/oper.tst:784 # Input is: DigraphReverseEdge(gr, 2) = DigraphReverseEdge(gr, [1, 3]); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphReverseEdge' on 2 arguments # But found: Error, Variable: 'DigraphReverseEdge' must have a value ######## ########> Diff in standard/oper.tst:787 # Input is: gr = DigraphReverseEdges(gr, []); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/oper.tst:789 # Input is: gr := CycleDigraph(100); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/oper.tst:791 # Input is: edges := ShallowCopy(DigraphEdges(gr));; # Expected output: # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:792 # Input is: gr = DigraphReverseEdges(gr, edges); # Expected output: false # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/oper.tst:794 # Input is: gr2 := DigraphReverseEdges(gr, edges); # Expected output: # But found: Error, Variable: 'DigraphReverseEdges' must have a value ######## ########> Diff in standard/oper.tst:796 # Input is: gr = gr2; # Expected output: false # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/oper.tst:798 # Input is: edges2 := ShallowCopy(DigraphEdges(gr2));; # Expected output: # But found: Error, Variable: 'DigraphEdges' must have a value ######## ########> Diff in standard/oper.tst:799 # Input is: gr = DigraphReverseEdges(gr2, edges2); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/oper.tst:801 # Input is: gr = DigraphReverseEdges(gr, [1 .. DigraphNrEdges(gr)]); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphReverseEdge' on 2 arguments # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/oper.tst:804 # Input is: DigraphReverseEdge(gr, 1) = DigraphReverseEdge(gr, [1, 2]); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `DigraphReverseEdge' on 2 arguments # But found: Error, Variable: 'DigraphReverseEdge' must have a value ######## ########> Diff in standard/oper.tst:807 # Input is: gr = DigraphReverseEdges(gr, []); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/oper.tst:817 # Input is: gr := Digraph( [[1, 2, 4, 5, 7], [1, 2], [3, 7], [2, 10], [2, 6], [2, 7], [], [3, 4], [1, 10], [1, 3, 9]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:821 # Input is: rtclosure := DigraphFloydWarshall(gr, func, 0, 1);; # Expected output: # But found: Error, Variable: 'DigraphFloydWarshall' must have a value ######## ########> Diff in standard/oper.tst:822 # Input is: grrt := DigraphByAdjacencyMatrix(rtclosure); # Expected output: # But found: Error, Variable: 'DigraphByAdjacencyMatrix' must have a value ######## ########> Diff in standard/oper.tst:824 # Input is: grrt = DigraphReflexiveTransitiveClosure(gr); # Expected output: true # But found: Error, Variable: 'grrt' must have a value ######## ########> Diff in standard/oper.tst:832 # Input is: gr := Digraph(rec( DigraphNrVertices := 10, DigraphSource := [1, 2, 2, 3, 4, 5, 6, 7, 10, 10, 10], DigraphRange := [6, 9, 5, 7, 3, 4, 8, 4, 7, 9, 8])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:837 # Input is: tclosure := DigraphFloydWarshall(gr, func, 0, 1);; # Expected output: # But found: Error, Variable: 'DigraphFloydWarshall' must have a value ######## ########> Diff in standard/oper.tst:838 # Input is: grt := DigraphByAdjacencyMatrix(tclosure); # Expected output: # But found: Error, Variable: 'DigraphByAdjacencyMatrix' must have a value ######## ########> Diff in standard/oper.tst:840 # Input is: grt = DigraphTransitiveClosure(gr); # Expected output: true # But found: Error, Variable: 'grt' must have a value ######## ########> Diff in standard/oper.tst:848 # Input is: gr := Digraph( [[1, 2, 4, 5, 7], [1, 2], [3, 7], [2, 10], [2, 6], [2, 7], [], [3, 4], [1, 10], [1, 3, 9]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:852 # Input is: rtclosure := DigraphFloydWarshall(gr, func, 0, 1);; # Expected output: # But found: Error, Variable: 'DigraphFloydWarshall' must have a value ######## ########> Diff in standard/oper.tst:853 # Input is: grrt := DigraphByAdjacencyMatrix(rtclosure); # Expected output: # But found: Error, Variable: 'DigraphByAdjacencyMatrix' must have a value ######## ########> Diff in standard/oper.tst:855 # Input is: grrt = DigraphReflexiveTransitiveClosure(gr); # Expected output: true # But found: Error, Variable: 'grrt' must have a value ######## ########> Diff in standard/oper.tst:863 # Input is: gr := DigraphFromDigraph6String("&I???@?A`?G?GCCS@??"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/oper.tst:865 # Input is: tclosure := DigraphFloydWarshall(gr, func, 0, 1);; # Expected output: # But found: Error, Variable: 'DigraphFloydWarshall' must have a value ######## ########> Diff in standard/oper.tst:866 # Input is: grt := DigraphByAdjacencyMatrix(tclosure); # Expected output: # But found: Error, Variable: 'DigraphByAdjacencyMatrix' must have a value ######## ########> Diff in standard/oper.tst:868 # Input is: grt = DigraphTransitiveClosure(gr); # Expected output: true # But found: Error, Variable: 'grt' must have a value ######## ########> Diff in standard/oper.tst:872 # Input is: gr := CycleDigraph(1000); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/oper.tst:874 # Input is: gr2 := CompleteDigraph(100); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:876 # Input is: DigraphDisjointUnion(gr) = gr; # Expected output: true # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/oper.tst:878 # Input is: DigraphDisjointUnion([[]]); # Expected output: Error, the arguments must be digraphs by out-neighbours, or a single non-empty\ \ list of digraphs by out-neighbours, # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/oper.tst:881 # Input is: DigraphDisjointUnion([gr], [gr]); # Expected output: Error, the arguments must be digraphs by out-neighbours, or a single non-empty\ \ list of digraphs by out-neighbours, # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/oper.tst:884 # Input is: DigraphDisjointUnion(gr, Group(())); # Expected output: Error, the arguments must be digraphs by out-neighbours, or a single non-empty\ \ list of digraphs by out-neighbours, # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/oper.tst:887 # Input is: DigraphDisjointUnion(gr, gr); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/oper.tst:889 # Input is: DigraphDisjointUnion([gr2, gr2]); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/oper.tst:891 # Input is: DigraphDisjointUnion(gr, gr2); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/oper.tst:893 # Input is: gr := CycleDigraph(1000);; # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/oper.tst:894 # Input is: DigraphDisjointUnion(gr2, gr); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/oper.tst:896 # Input is: gr1 := Digraph([[2, 2, 3], [3], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:898 # Input is: gr2 := Digraph([[1, 2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:900 # Input is: gr3 := Digraph(rec(DigraphNrVertices := 2, DigraphSource := [1, 1, 2], DigraphRange := [2, 1, 1]));; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:902 # Input is: gr2 = gr3; # Expected output: true # But found: Error, Variable: 'gr2' must have a value ######## ########> Diff in standard/oper.tst:904 # Input is: u1 := DigraphDisjointUnion(gr1, gr2); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/oper.tst:906 # Input is: u2 := DigraphDisjointUnion(gr1, gr3); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/oper.tst:908 # Input is: u1 = u2; # Expected output: true # But found: Error, Variable: 'u1' must have a value ######## ########> Diff in standard/oper.tst:911 # Input is: DigraphDisjointUnion(List([1 .. n], x -> EmptyDigraph(x))) = EmptyDigraph(Int(n * (n + 1) / 2)); # Expected output: true # But found: Error, Variable: 'DigraphDisjointUnion' must have a value Syntax warning: Unbound global variable in stream:1 DigraphDisjointUnion(List([1 .. n], x -> EmptyDigraph(x))) = ^^^^^^^^^^^^ ######## ########> Diff in standard/oper.tst:914 # Input is: gr := DigraphDisjointUnion(List([2 .. 5], x -> ChainDigraph(x))); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value Syntax warning: Unbound global variable in stream:1 gr := DigraphDisjointUnion(List([2 .. 5], x -> ChainDigraph(x))); ^^^^^^^^^^^^ ######## ########> Diff in standard/oper.tst:916 # Input is: gr := DigraphAddEdges(gr, [[2, 3], [5, 6], [9, 10]]); # Expected output: # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/oper.tst:918 # Input is: gr = ChainDigraph(14); # Expected output: true # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/oper.tst:920 # Input is: D := CycleDigraph(IsMutableDigraph, 2); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/oper.tst:922 # Input is: DigraphVertexLabels(D); # Expected output: [ 1, 2 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:924 # Input is: DigraphDisjointUnion(D, D); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/oper.tst:926 # Input is: DigraphVertexLabels(D); # Expected output: [ 1 .. 4 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:930 # Input is: gr1 := DigraphFromDigraph6String("&I????@A_?AA???@d??"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/oper.tst:932 # Input is: gr2 := DigraphFromDiSparse6String(".H`OS?aEMC?bneOY`l_?QCJ"); # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/oper.tst:934 # Input is: DigraphEdgeUnion(gr1) = gr1; # Expected output: true # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/oper.tst:936 # Input is: DigraphEdgeUnion([[]]); # Expected output: Error, the arguments must be digraphs by out-neighbours, or a single list of d\ \ igraphs by out-neighbours, # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/oper.tst:939 # Input is: DigraphEdgeUnion([gr1], [gr1]); # Expected output: Error, the arguments must be digraphs by out-neighbours, or a single list of d\ \ igraphs by out-neighbours, # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/oper.tst:942 # Input is: DigraphEdgeUnion(gr1, Group(())); # Expected output: Error, the arguments must be digraphs by out-neighbours, or a single list of d\ \ igraphs by out-neighbours, # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/oper.tst:945 # Input is: m1 := DigraphEdgeUnion(gr1, gr2); # Expected output: # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/oper.tst:947 # Input is: m2 := DigraphEdgeUnion(gr2, gr1); # Expected output: # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/oper.tst:949 # Input is: gr1 := Digraph([[2], [], [4], [], [6], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:951 # Input is: gr2 := Digraph([[], [3], [], [5], [], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:953 # Input is: m := DigraphEdgeUnion(gr1, gr2); # Expected output: # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/oper.tst:955 # Input is: m = CycleDigraph(6); # Expected output: true # But found: Error, Variable: 'm' must have a value ######## ########> Diff in standard/oper.tst:957 # Input is: m = DigraphEdgeUnion(gr2, gr1); # Expected output: true # But found: Error, Variable: 'm' must have a value ######## ########> Diff in standard/oper.tst:959 # Input is: DigraphEdgeUnion(EmptyDigraph(0), EmptyDigraph(0)) = EmptyDigraph(0); # Expected output: true # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/oper.tst:961 # Input is: DigraphEdgeUnion(EmptyDigraph(5), EmptyDigraph(3)) = EmptyDigraph(5); # Expected output: true # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/oper.tst:963 # Input is: gr := DigraphNC([[6, 3, 3, 10, 6], [4], [5, 1], [5, 4, 6], [9], [8], [7, 6], [8, 10, 8, 1], [], [2]]);; # Expected output: # But found: Error, Variable: 'DigraphNC' must have a value ######## ########> Diff in standard/oper.tst:965 # Input is: gr := DigraphEdgeUnion(gr, gr); # Expected output: # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/oper.tst:967 # Input is: OutNeighbours(gr); # Expected output: [ [ 6, 3, 3, 10, 6, 6, 3, 3, 10, 6 ], [ 4, 4 ], [ 5, 1, 5, 1 ], [ 5, 4, 6, 5, 4, 6 ], [ 9, 9 ], [ 8, 8 ], [ 7, 6, 7, 6 ], [ 8, 10, 8, 1, 8, 10, 8, 1 ], [ ], [ 2, 2 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/oper.tst:971 # Input is: gr := DigraphEdgeUnion(ChainDigraph(2), ChainDigraph(3), ChainDigraph(4)); # Expected output: # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/oper.tst:973 # Input is: OutNeighbours(gr); # Expected output: [ [ 2, 2, 2 ], [ 3, 3 ], [ 4 ], [ ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/oper.tst:977 # Input is: gr := CompleteDigraph(20); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:979 # Input is: gr2 := EmptyDigraph(10); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/oper.tst:981 # Input is: DigraphJoin(gr) = gr; # Expected output: true # But found: Error, Variable: 'DigraphJoin' must have a value ######## ########> Diff in standard/oper.tst:983 # Input is: DigraphJoin([[]]); # Expected output: Error, the arguments must be digraphs by out-neighbours, or a single list of d\ \ igraphs by out-neighbours, # But found: Error, Variable: 'DigraphJoin' must have a value ######## ########> Diff in standard/oper.tst:986 # Input is: DigraphJoin([gr], [gr]); # Expected output: Error, the arguments must be digraphs by out-neighbours, or a single list of d\ \ igraphs by out-neighbours, # But found: Error, Variable: 'DigraphJoin' must have a value ######## ########> Diff in standard/oper.tst:989 # Input is: DigraphJoin([gr, Group(())]); # Expected output: Error, the arguments must be digraphs by out-neighbours, or a single list of d\ \ igraphs by out-neighbours, # But found: Error, Variable: 'DigraphJoin' must have a value ######## ########> Diff in standard/oper.tst:992 # Input is: DigraphJoin(gr, gr2); # Expected output: # But found: Error, Variable: 'DigraphJoin' must have a value ######## ########> Diff in standard/oper.tst:994 # Input is: DigraphJoin(gr, EmptyDigraph(0)); # Expected output: # But found: Error, Variable: 'DigraphJoin' must have a value ######## ########> Diff in standard/oper.tst:996 # Input is: DigraphJoin(EmptyDigraph(0), CycleDigraph(1000)); # Expected output: # But found: Error, Variable: 'DigraphJoin' must have a value ######## ########> Diff in standard/oper.tst:998 # Input is: DigraphJoin(EmptyDigraph(0), EmptyDigraph(0)); # Expected output: # But found: Error, Variable: 'DigraphJoin' must have a value ######## ########> Diff in standard/oper.tst:1000 # Input is: DigraphJoin(EmptyDigraph(5), EmptyDigraph(5)); # Expected output: # But found: Error, Variable: 'DigraphJoin' must have a value ######## ########> Diff in standard/oper.tst:1002 # Input is: gr1 := Digraph([[2, 2, 3], [3], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1004 # Input is: gr2 := Digraph([[1, 2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1006 # Input is: gr3 := Digraph(rec(DigraphNrVertices := 2, DigraphSource := [1, 1, 2], DigraphRange := [2, 1, 1]));; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1008 # Input is: gr2 = gr3; # Expected output: true # But found: Error, Variable: 'gr2' must have a value ######## ########> Diff in standard/oper.tst:1010 # Input is: j1 := DigraphJoin(gr1, gr2); # Expected output: # But found: Error, Variable: 'DigraphJoin' must have a value ######## ########> Diff in standard/oper.tst:1012 # Input is: j2 := DigraphJoin(gr1, gr3); # Expected output: # But found: Error, Variable: 'DigraphJoin' must have a value ######## ########> Diff in standard/oper.tst:1014 # Input is: u1 = u2; # Expected output: true # But found: Error, Variable: 'u1' must have a value ######## ########> Diff in standard/oper.tst:1016 # Input is: gr := DigraphJoin(ChainDigraph(2), CycleDigraph(4), EmptyDigraph(0)); # Expected output: # But found: Error, Variable: 'DigraphJoin' must have a value ######## ########> Diff in standard/oper.tst:1025 # Input is: AdjacencyMatrix(gr) = mat; # Expected output: true # But found: Error, Variable: 'AdjacencyMatrix' must have a value ######## ########> Diff in standard/oper.tst:1027 # Input is: DigraphJoin(List([1 .. 5], x -> EmptyDigraph(1))) = CompleteDigraph(5); # Expected output: true # But found: Error, Variable: 'DigraphJoin' must have a value Syntax warning: Unbound global variable in stream:1 DigraphJoin(List([1 .. 5], x -> EmptyDigraph(1))) = CompleteDigraph(5); ^^^^^^^^^^^^ ######## ########> Diff in standard/oper.tst:1029 # Input is: DigraphJoin(EmptyDigraph(3), EmptyDigraph(2)) = CompleteBipartiteDigraph(3, 2); # Expected output: true # But found: Error, Variable: 'DigraphJoin' must have a value ######## ########> Diff in standard/oper.tst:1034 # Input is: gr := Digraph([[3], [10], [6], [3], [10], [], [6], [3], [], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1036 # Input is: out1 := OutNeighbours(gr); # Expected output: [ [ 3 ], [ 10 ], [ 6 ], [ 3 ], [ 10 ], [ ], [ 6 ], [ 3 ], [ ], [ 3 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/oper.tst:1038 # Input is: IsMutable(out1); # Expected output: false # But found: Error, Variable: 'out1' must have a value ######## ########> Diff in standard/oper.tst:1040 # Input is: IsMutable(out1[1]); # Expected output: false # But found: Error, Variable: 'out1' must have a value ######## ########> Diff in standard/oper.tst:1042 # Input is: out2 := OutNeighboursMutableCopy(gr); # Expected output: [ [ 3 ], [ 10 ], [ 6 ], [ 3 ], [ 10 ], [ ], [ 6 ], [ 3 ], [ ], [ 3 ] ] # But found: Error, Variable: 'OutNeighboursMutableCopy' must have a value ######## ########> Diff in standard/oper.tst:1044 # Input is: IsMutable(out2); # Expected output: true # But found: Error, Variable: 'out2' must have a value ######## ########> Diff in standard/oper.tst:1046 # Input is: IsMutable(out2[1]); # Expected output: true # But found: Error, Variable: 'out2' must have a value ######## ########> Diff in standard/oper.tst:1048 # Input is: out3 := OutNeighborsMutableCopy(gr); # Expected output: [ [ 3 ], [ 10 ], [ 6 ], [ 3 ], [ 10 ], [ ], [ 6 ], [ 3 ], [ ], [ 3 ] ] # But found: Error, Variable: 'OutNeighborsMutableCopy' must have a value ######## ########> Diff in standard/oper.tst:1050 # Input is: IsMutable(out3); # Expected output: true # But found: Error, Variable: 'out3' must have a value ######## ########> Diff in standard/oper.tst:1052 # Input is: IsMutable(out3[1]); # Expected output: true # But found: Error, Variable: 'out3' must have a value ######## ########> Diff in standard/oper.tst:1056 # Input is: gr := Digraph([[3], [10], [6], [3], [10], [], [6], [3], [], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1058 # Input is: in1 := InNeighbours(gr); # Expected output: [ [ ], [ ], [ 1, 4, 8, 10 ], [ ], [ ], [ 3, 7 ], [ ], [ ], [ ], [ 2, 5 ] ] # But found: Error, Variable: 'InNeighbours' must have a value ######## ########> Diff in standard/oper.tst:1061 # Input is: IsMutable(in1); # Expected output: false # But found: Error, Variable: 'in1' must have a value ######## ########> Diff in standard/oper.tst:1063 # Input is: IsMutable(in1[1]); # Expected output: false # But found: Error, Variable: 'in1' must have a value ######## ########> Diff in standard/oper.tst:1065 # Input is: in2 := InNeighboursMutableCopy(gr); # Expected output: [ [ ], [ ], [ 1, 4, 8, 10 ], [ ], [ ], [ 3, 7 ], [ ], [ ], [ ], [ 2, 5 ] ] # But found: Error, Variable: 'InNeighboursMutableCopy' must have a value ######## ########> Diff in standard/oper.tst:1068 # Input is: IsMutable(in2); # Expected output: true # But found: Error, Variable: 'in2' must have a value ######## ########> Diff in standard/oper.tst:1070 # Input is: IsMutable(in2[1]); # Expected output: true # But found: Error, Variable: 'in2' must have a value ######## ########> Diff in standard/oper.tst:1072 # Input is: in3 := InNeighborsMutableCopy(gr); # Expected output: [ [ ], [ ], [ 1, 4, 8, 10 ], [ ], [ ], [ 3, 7 ], [ ], [ ], [ ], [ 2, 5 ] ] # But found: Error, Variable: 'InNeighborsMutableCopy' must have a value ######## ########> Diff in standard/oper.tst:1075 # Input is: IsMutable(in3); # Expected output: true # But found: Error, Variable: 'in3' must have a value ######## ########> Diff in standard/oper.tst:1077 # Input is: IsMutable(in3[1]); # Expected output: true # But found: Error, Variable: 'in3' must have a value ######## ########> Diff in standard/oper.tst:1081 # Input is: gr := CycleDigraph(3);; # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/oper.tst:1082 # Input is: adj := AdjacencyMatrixMutableCopy(gr);; # Expected output: # But found: Error, Variable: 'AdjacencyMatrixMutableCopy' must have a value ######## ########> Diff in standard/oper.tst:1083 # Input is: PrintArray(adj); # Expected output: [ [ 0, 1, 0 ], [ 0, 0, 1 ], [ 1, 0, 0 ] ] # But found: Error, must be a dense list ######## ########> Diff in standard/oper.tst:1087 # Input is: adj[3][2] := 1;; # Expected output: # But found: Error, List Element: must be a list (not a function) ######## ########> Diff in standard/oper.tst:1088 # Input is: PrintArray(adj); # Expected output: [ [ 0, 1, 0 ], [ 0, 0, 1 ], [ 1, 1, 0 ] ] # But found: Error, must be a dense list ######## ########> Diff in standard/oper.tst:1094 # Input is: gr := Digraph([[3], [2, 3], [3], [2, 4]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1095 # Input is: adj := BooleanAdjacencyMatrixMutableCopy(gr);; # Expected output: # But found: Error, Variable: 'BooleanAdjacencyMatrixMutableCopy' must have a value ######## ########> Diff in standard/oper.tst:1096 # Input is: PrintArray(adj); # Expected output: [ [ false, false, true, false ], [ false, true, true, false ], [ false, false, true, false ], [ false, true, false, true ] ] # But found: Error, must be a dense list ######## ########> Diff in standard/oper.tst:1101 # Input is: adj[3][1] := true;; # Expected output: # But found: Error, List Element: must be a list (not a function) ######## ########> Diff in standard/oper.tst:1102 # Input is: PrintArray(adj); # Expected output: [ [ false, false, true, false ], [ false, true, true, false ], [ true, false, true, false ], [ false, true, false, true ] ] # But found: Error, must be a dense list ######## ########> Diff in standard/oper.tst:1109 # Input is: gr1 := Digraph([[1, 1, 2, 1], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1111 # Input is: gr2 := DigraphRemoveAllMultipleEdges(gr1); # Expected output: # But found: Error, Variable: 'DigraphRemoveAllMultipleEdges' must have a value ######## ########> Diff in standard/oper.tst:1113 # Input is: OutNeighbours(gr2); # Expected output: [ [ 1, 2 ], [ 1 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/oper.tst:1115 # Input is: gr3 := DigraphEdgeUnion(gr1, gr1); # Expected output: # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/oper.tst:1117 # Input is: gr4 := DigraphRemoveAllMultipleEdges(gr3); # Expected output: # But found: Error, Variable: 'DigraphRemoveAllMultipleEdges' must have a value ######## ########> Diff in standard/oper.tst:1119 # Input is: gr2 = gr4; # Expected output: true # But found: Error, Variable: 'gr2' must have a value ######## ########> Diff in standard/oper.tst:1123 # Input is: gr1 := DigraphRemoveEdges(CycleDigraph(100), [[100, 1], [99, 100]]); # Expected output: # But found: Error, Variable: 'DigraphRemoveEdges' must have a value ######## ########> Diff in standard/oper.tst:1125 # Input is: IsReachable(gr1, 0, 1); # Expected output: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `IsReachable' on 3 arguments # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1128 # Input is: IsReachable(gr1, 101, 1); # Expected output: Error, the 2nd and 3rd arguments and must be vertices of the 1st argum\ \ ent , # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1131 # Input is: IsReachable(gr1, 1, 101); # Expected output: Error, the 2nd and 3rd arguments and must be vertices of the 1st argum\ \ ent , # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1134 # Input is: IsReachable(gr1, 1, 2); # Expected output: true # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1136 # Input is: gr1 := DigraphRemoveEdges(CycleDigraph(100), [[100, 1], [99, 100]]);; # Expected output: # But found: Error, Variable: 'DigraphRemoveEdges' must have a value ######## ########> Diff in standard/oper.tst:1137 # Input is: AdjacencyMatrix(gr1);; # Expected output: # But found: Error, Variable: 'AdjacencyMatrix' must have a value ######## ########> Diff in standard/oper.tst:1138 # Input is: IsReachable(gr1, 1, 2); # Expected output: true # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1140 # Input is: gr1 := DigraphRemoveEdges(CycleDigraph(100), [[100, 1], [99, 100]]);; # Expected output: # But found: Error, Variable: 'DigraphRemoveEdges' must have a value ######## ########> Diff in standard/oper.tst:1141 # Input is: IsReachable(gr1, 100, 1); # Expected output: false # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1143 # Input is: gr1 := DigraphRemoveEdges(CycleDigraph(100), [[100, 1], [99, 100]]);; # Expected output: # But found: Error, Variable: 'DigraphRemoveEdges' must have a value ######## ########> Diff in standard/oper.tst:1144 # Input is: DigraphConnectedComponents(gr1);; # Expected output: # But found: Error, Variable: 'DigraphConnectedComponents' must have a value ######## ########> Diff in standard/oper.tst:1145 # Input is: IsReachable(gr1, 100, 1); # Expected output: false # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1147 # Input is: gr1 := CycleDigraph(100); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/oper.tst:1149 # Input is: IsReachable(gr1, 1, 50); # Expected output: true # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1151 # Input is: IsReachable(gr1, 1, 1); # Expected output: true # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1153 # Input is: gr1 := CycleDigraph(100);; # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/oper.tst:1154 # Input is: DigraphStronglyConnectedComponents(gr1);; # Expected output: # But found: Error, Variable: 'DigraphStronglyConnectedComponents' must have a value ######## ########> Diff in standard/oper.tst:1155 # Input is: IsReachable(gr1, 1, 50); # Expected output: true # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1157 # Input is: IsReachable(gr1, 1, 1); # Expected output: true # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1159 # Input is: gr1 := Digraph([[2], [1], [3], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1161 # Input is: IsReachable(gr1, 1, 2); # Expected output: true # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1163 # Input is: IsReachable(gr1, 1, 1); # Expected output: true # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1165 # Input is: IsReachable(gr1, 3, 3); # Expected output: true # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1167 # Input is: IsReachable(gr1, 1, 3); # Expected output: false # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1169 # Input is: IsReachable(gr1, 4, 4); # Expected output: false # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1171 # Input is: gr1 := Digraph([[2], [1], [3], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1172 # Input is: DigraphStronglyConnectedComponents(gr1); # Expected output: rec( comps := [ [ 1, 2 ], [ 3 ], [ 4 ] ], id := [ 1, 1, 2, 3 ] ) # But found: Error, Variable: 'DigraphStronglyConnectedComponents' must have a value ######## ########> Diff in standard/oper.tst:1174 # Input is: IsReachable(gr1, 1, 2); # Expected output: true # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1176 # Input is: IsReachable(gr1, 1, 1); # Expected output: true # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1178 # Input is: IsReachable(gr1, 3, 3); # Expected output: true # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1180 # Input is: IsReachable(gr1, 1, 3); # Expected output: false # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1182 # Input is: IsReachable(gr1, 4, 4); # Expected output: false # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1184 # Input is: gr := DigraphFromSparse6String(":DA_IAMALN"); # Expected output: # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/oper.tst:1186 # Input is: IsReachable(gr, 1, 2); # Expected output: false # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1188 # Input is: IsReachable(gr, 1, 4); # Expected output: true # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1190 # Input is: gr := Digraph( [[1, 3, 4, 5], [], [1, 3, 4, 5], [1, 3, 4, 5], [1, 3, 4, 5]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1192 # Input is: IsTransitiveDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsTransitiveDigraph' must have a value ######## ########> Diff in standard/oper.tst:1194 # Input is: IsReachable(gr, 1, 2); # Expected output: false # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1196 # Input is: IsReachable(gr, 1, 4); # Expected output: true # But found: Error, Variable: 'IsReachable' must have a value ######## ########> Diff in standard/oper.tst:1200 # Input is: gr := ChainDigraph(10); # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/oper.tst:1202 # Input is: DigraphPath(gr, 1, 2); # Expected output: [ [ 1, 2 ], [ 1 ] ] # But found: Error, Variable: 'DigraphPath' must have a value ######## ########> Diff in standard/oper.tst:1204 # Input is: DigraphPath(gr, 1, 1); # Expected output: fail # But found: Error, Variable: 'DigraphPath' must have a value ######## ########> Diff in standard/oper.tst:1206 # Input is: DigraphPath(gr, 2, 1); # Expected output: fail # But found: Error, Variable: 'DigraphPath' must have a value ######## ########> Diff in standard/oper.tst:1208 # Input is: DigraphPath(gr, 3, 8); # Expected output: [ [ 3, 4, 5, 6, 7, 8 ], [ 1, 1, 1, 1, 1 ] ] # But found: Error, Variable: 'DigraphPath' must have a value ######## ########> Diff in standard/oper.tst:1210 # Input is: DigraphPath(gr, 11, 1); # Expected output: Error, the 2nd and 3rd arguments and must be vertices of the 1st argum\ \ ent , # But found: Error, Variable: 'DigraphPath' must have a value ######## ########> Diff in standard/oper.tst:1213 # Input is: DigraphPath(gr, 1, 11); # Expected output: Error, the 2nd and 3rd arguments and must be vertices of the 1st argum\ \ ent , # But found: Error, Variable: 'DigraphPath' must have a value ######## ########> Diff in standard/oper.tst:1216 # Input is: DigraphPath(gr, 11, 11); # Expected output: Error, the 2nd and 3rd arguments and must be vertices of the 1st argum\ \ ent , # But found: Error, Variable: 'DigraphPath' must have a value ######## ########> Diff in standard/oper.tst:1221 # Input is: gr := CompleteDigraph(5);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:1222 # Input is: iter := IteratorOfPaths(gr, 2, 6); # Expected output: Error, the 2nd and 3rd arguments and must be vertices of the 1st argum\ \ ent , # But found: Error, Variable: 'IteratorOfPaths' must have a value ######## ########> Diff in standard/oper.tst:1225 # Input is: iter := IteratorOfPaths(gr, 6, 6); # Expected output: Error, the 2nd and 3rd arguments and must be vertices of the 1st argum\ \ ent , # But found: Error, Variable: 'IteratorOfPaths' must have a value ######## ########> Diff in standard/oper.tst:1228 # Input is: iter := IteratorOfPaths(gr, 6, 2); # Expected output: Error, the 2nd and 3rd arguments and must be vertices of the 1st argum\ \ ent , # But found: Error, Variable: 'IteratorOfPaths' must have a value ######## ########> Diff in standard/oper.tst:1231 # Input is: iter := IteratorOfPaths(gr, 2, 5); # Expected output: # But found: Error, Variable: 'IteratorOfPaths' must have a value ######## ########> Diff in standard/oper.tst:1233 # Input is: for a in iter do Print(a, "\n"); od; # Expected output: [ [ 2, 1, 3, 4, 5 ], [ 1, 2, 3, 4 ] ] [ [ 2, 1, 3, 5 ], [ 1, 2, 4 ] ] [ [ 2, 1, 4, 3, 5 ], [ 1, 3, 3, 4 ] ] [ [ 2, 1, 4, 5 ], [ 1, 3, 4 ] ] [ [ 2, 1, 5 ], [ 1, 4 ] ] [ [ 2, 3, 1, 4, 5 ], [ 2, 1, 3, 4 ] ] [ [ 2, 3, 1, 5 ], [ 2, 1, 4 ] ] [ [ 2, 3, 4, 1, 5 ], [ 2, 3, 1, 4 ] ] [ [ 2, 3, 4, 5 ], [ 2, 3, 4 ] ] [ [ 2, 3, 5 ], [ 2, 4 ] ] [ [ 2, 4, 1, 3, 5 ], [ 3, 1, 2, 4 ] ] [ [ 2, 4, 1, 5 ], [ 3, 1, 4 ] ] [ [ 2, 4, 3, 1, 5 ], [ 3, 3, 1, 4 ] ] [ [ 2, 4, 3, 5 ], [ 3, 3, 4 ] ] [ [ 2, 4, 5 ], [ 3, 4 ] ] [ [ 2, 5 ], [ 4 ] ] # But found: Error, Variable: 'iter' must have an assigned value ######## ########> Diff in standard/oper.tst:1252 # Input is: iter := IteratorOfPaths(gr, 2, 5);; # Expected output: # But found: Error, Variable: 'IteratorOfPaths' must have a value ######## ########> Diff in standard/oper.tst:1253 # Input is: for a in iter do if not ForAll([1 .. Length(a[1]) - 1], x -> OutNeighboursOfVertex(gr, a[1][x])[a[2][x]] = a[1][x + 1]) then Print("fail\n"); fi; od; # Expected output: # But found: Syntax warning: Unbound global variable in stream:3 OutNeighboursOfVertex(gr, a[1][x])[a[2][x]] = a[1][x + 1]) then ^^^^^^^^^^^^^^^^^^^^^ Syntax warning: Unbound global variable in stream:3 OutNeighboursOfVertex(gr, a[1][x])[a[2][x]] = a[1][x + 1]) then ^^ Error, Variable: 'iter' must have an assigned value ######## ########> Diff in standard/oper.tst:1259 # Input is: iter := IteratorOfPaths(gr, 4, 3); # Expected output: # But found: Error, Variable: 'IteratorOfPaths' must have a value ######## ########> Diff in standard/oper.tst:1261 # Input is: NextIterator(iter); # Expected output: [ [ 4, 1, 2, 3 ], [ 1, 1, 2 ] ] # But found: Error, Variable: 'iter' must have a value ######## ########> Diff in standard/oper.tst:1263 # Input is: NextIterator(iter); # Expected output: [ [ 4, 1, 2, 5, 3 ], [ 1, 1, 4, 3 ] ] # But found: Error, Variable: 'iter' must have a value ######## ########> Diff in standard/oper.tst:1265 # Input is: copy := ShallowCopy(iter); # Expected output: # But found: Error, Variable: 'iter' must have a value ######## ########> Diff in standard/oper.tst:1267 # Input is: NextIterator(copy); # Expected output: [ [ 4, 1, 3 ], [ 1, 2 ] ] # But found: Error, Variable: 'copy' must have a value ######## ########> Diff in standard/oper.tst:1269 # Input is: NextIterator(iter); # Expected output: [ [ 4, 1, 3 ], [ 1, 2 ] ] # But found: Error, Variable: 'iter' must have a value ######## ########> Diff in standard/oper.tst:1272 # Input is: IteratorOfPaths(gr, 1, 1);; # Expected output: Error, the 2nd and 3rd arguments and must be vertices of the digraph d\ \ efined by the 1st argument , # But found: Error, Variable: 'IteratorOfPaths' must have a value ######## ########> Diff in standard/oper.tst:1276 # Input is: IteratorOfPaths(gr, 1, 1);; # Expected output: Error, the 1st argument must be a list of out-neighbours of a digraph, # But found: Error, Variable: 'IteratorOfPaths' must have a value ######## ########> Diff in standard/oper.tst:1279 # Input is: IteratorOfPaths(gr, 1, 1);; # Expected output: Error, the 1st argument must be a list of out-neighbours of a digraph, # But found: Error, Variable: 'IteratorOfPaths' must have a value ######## ########> Diff in standard/oper.tst:1282 # Input is: IteratorOfPaths(gr, 1, 1);; # Expected output: Error, the 1st argument must be a list of out-neighbours of a digraph, # But found: Error, Variable: 'IteratorOfPaths' must have a value ######## ########> Diff in standard/oper.tst:1285 # Input is: iter := IteratorOfPaths(gr, 1, 1); # Expected output: # But found: Error, Variable: 'IteratorOfPaths' must have a value ######## ########> Diff in standard/oper.tst:1287 # Input is: for a in iter do Print(a, "\n"); od; # Expected output: [ [ 1, 1 ], [ 1 ] ] # But found: Error, Variable: 'iter' must have an assigned value ######## ########> Diff in standard/oper.tst:1291 # Input is: gr := DigraphFromDigraph6String("+E?_OHCO"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/oper.tst:1293 # Input is: iter := IteratorOfPaths(gr, 1, 5); # Expected output: # But found: Error, Variable: 'IteratorOfPaths' must have a value ######## ########> Diff in standard/oper.tst:1295 # Input is: NextIterator(iter); # Expected output: [ [ 1, 2, 3, 4, 5 ], [ 1, 1, 1, 1 ] ] # But found: Error, Variable: 'iter' must have a value ######## ########> Diff in standard/oper.tst:1297 # Input is: NextIterator(iter); # Expected output: [ [ 1, 2, 6, 4, 5 ], [ 1, 2, 1, 1 ] ] # But found: Error, Variable: 'iter' must have a value ######## ########> Diff in standard/oper.tst:1299 # Input is: IsDoneIterator(iter); # Expected output: true # But found: Error, Variable: 'iter' must have a value ######## ########> Diff in standard/oper.tst:1305 # Input is: gr := Digraph(nbs); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1307 # Input is: DigraphHasLoops(gr); # Expected output: true # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/oper.tst:1309 # Input is: a := DigraphLongestDistanceFromVertex(gr, 1); # Expected output: 6 # But found: Error, Variable: 'DigraphLongestDistanceFromVertex' must have a value ######## ########> Diff in standard/oper.tst:1313 # Input is: b := DigraphLongestDistanceFromVertex(gr, 2); # Expected output: 3 # But found: Error, Variable: 'DigraphLongestDistanceFromVertex' must have a value ######## ########> Diff in standard/oper.tst:1315 # Input is: a >= b + 1; # Expected output: true # But found: Error, Variable: 'a' must have a value ######## ########> Diff in standard/oper.tst:1317 # Input is: DigraphLongestDistanceFromVertex(gr, 4); # Expected output: 0 # But found: Error, Variable: 'DigraphLongestDistanceFromVertex' must have a value ######## ########> Diff in standard/oper.tst:1319 # Input is: DigraphLongestDistanceFromVertex(gr, 15); # Expected output: infinity # But found: Error, Variable: 'DigraphLongestDistanceFromVertex' must have a value ######## ########> Diff in standard/oper.tst:1321 # Input is: DigraphLongestDistanceFromVertex(gr, 16); # Expected output: Error, the 2nd argument must be a vertex of the 1st argument , # But found: Error, Variable: 'DigraphLongestDistanceFromVertex' must have a value ######## ########> Diff in standard/oper.tst:1325 # Input is: gr := CompleteDigraph(4); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:1327 # Input is: DigraphLayers(gr, 1); # Expected output: [ [ 1 ], [ 2, 3, 4 ] ] # But found: Error, Variable: 'DigraphLayers' must have a value ######## ########> Diff in standard/oper.tst:1329 # Input is: DigraphLayers(gr, 2); # Expected output: [ [ 2 ], [ 3, 4, 1 ] ] # But found: Error, Variable: 'DigraphLayers' must have a value ######## ########> Diff in standard/oper.tst:1331 # Input is: DigraphLayers(gr, 3); # Expected output: [ [ 3 ], [ 4, 1, 2 ] ] # But found: Error, Variable: 'DigraphLayers' must have a value ######## ########> Diff in standard/oper.tst:1333 # Input is: DigraphLayers(gr, 4); # Expected output: [ [ 4 ], [ 1, 2, 3 ] ] # But found: Error, Variable: 'DigraphLayers' must have a value ######## ########> Diff in standard/oper.tst:1335 # Input is: gr := ChainDigraph(5);; # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/oper.tst:1336 # Input is: DigraphLayers(gr, 2); # Expected output: [ [ 2 ], [ 3 ], [ 4 ], [ 5 ] ] # But found: Error, Variable: 'DigraphLayers' must have a value ######## ########> Diff in standard/oper.tst:1338 # Input is: DigraphLayers(gr, 4); # Expected output: [ [ 4 ], [ 5 ] ] # But found: Error, Variable: 'DigraphLayers' must have a value ######## ########> Diff in standard/oper.tst:1340 # Input is: gr := Digraph([[2, 5], [3], [4], [5], [6], [7], [8], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1341 # Input is: DigraphLayers(gr, 1); # Expected output: [ [ 1 ], [ 2, 5 ], [ 3, 6 ], [ 4, 7 ], [ 8 ] ] # But found: Error, Variable: 'DigraphLayers' must have a value ######## ########> Diff in standard/oper.tst:1343 # Input is: DigraphLayers(gr, 3); # Expected output: [ [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8 ], [ 1 ], [ 2 ] ] # But found: Error, Variable: 'DigraphLayers' must have a value ######## ########> Diff in standard/oper.tst:1345 # Input is: DigraphLayers(gr, 6); # Expected output: [ [ 6 ], [ 7 ], [ 8 ], [ 1 ], [ 2, 5 ], [ 3 ], [ 4 ] ] # But found: Error, Variable: 'DigraphLayers' must have a value ######## ########> Diff in standard/oper.tst:1347 # Input is: DigraphLayers(gr, 7); # Expected output: [ [ 7 ], [ 8 ], [ 1 ], [ 2, 5 ], [ 3, 6 ], [ 4 ] ] # But found: Error, Variable: 'DigraphLayers' must have a value ######## ########> Diff in standard/oper.tst:1349 # Input is: gr := Digraph([[2, 5], [3], [4], [5], [6], [7], [8], [1], [9, 10, 11], [], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1351 # Input is: DigraphLayers(gr, 1); # Expected output: [ [ 1 ], [ 2, 5 ], [ 3, 6 ], [ 4, 7 ], [ 8 ] ] # But found: Error, Variable: 'DigraphLayers' must have a value ######## ########> Diff in standard/oper.tst:1353 # Input is: DigraphLayers(gr, 9); # Expected output: [ [ 9 ], [ 10, 11 ] ] # But found: Error, Variable: 'DigraphLayers' must have a value ######## ########> Diff in standard/oper.tst:1355 # Input is: DigraphLayers(gr, 10); # Expected output: [ [ 10 ] ] # But found: Error, Variable: 'DigraphLayers' must have a value ######## ########> Diff in standard/oper.tst:1357 # Input is: gr := DigraphFromDigraph6String("&GYHPQgWTIIPW");; # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/oper.tst:1358 # Input is: DigraphGroup(gr); # Expected output: Group([ (1,2)(3,4)(5,6)(7,8), (1,3,2,4)(5,7,6,8), (1,5)(2,6)(3,8)(4,7) ]) # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/oper.tst:1360 # Input is: DigraphOrbitReps(gr); # Expected output: [ 1 ] # But found: Error, Variable: 'DigraphOrbitReps' must have a value ######## ########> Diff in standard/oper.tst:1362 # Input is: DigraphLayers(gr, 1); # Expected output: [ [ 1 ], [ 2, 3, 5 ], [ 4, 6, 7, 8 ] ] # But found: Error, Variable: 'DigraphLayers' must have a value ######## ########> Diff in standard/oper.tst:1364 # Input is: DigraphLayers(gr, 2); # Expected output: [ [ 2 ], [ 1, 4, 6 ], [ 3, 5, 8, 7 ] ] # But found: Error, Variable: 'DigraphLayers' must have a value ######## ########> Diff in standard/oper.tst:1366 # Input is: DigraphLayers(gr, 3); # Expected output: [ [ 3 ], [ 4, 2, 7 ], [ 1, 8, 6, 5 ] ] # But found: Error, Variable: 'DigraphLayers' must have a value ######## ########> Diff in standard/oper.tst:1368 # Input is: DigraphLayers(gr, 4); # Expected output: [ [ 4 ], [ 3, 1, 8 ], [ 2, 7, 5, 6 ] ] # But found: Error, Variable: 'DigraphLayers' must have a value ######## ########> Diff in standard/oper.tst:1370 # Input is: DigraphLayers(gr, 10); # Expected output: Error, the 2nd argument must be a vertex of the 1st argument , # But found: Error, Variable: 'DigraphLayers' must have a value ######## ########> Diff in standard/oper.tst:1372 # Input is: DigraphShortestDistance(gr, [2, 5, 6], [3, 7]); # Expected output: 1 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1374 # Input is: DigraphShortestDistance(gr, [2], DigraphLayers(gr, 2)[3]); # Expected output: 2 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1376 # Input is: DigraphShortestDistance(gr, [2, 3], [3, 4]); # Expected output: 0 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1378 # Input is: gr := CompleteDigraph(64); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:1380 # Input is: DigraphShortestDistance(gr, [1 .. 10], [20 .. 23]); # Expected output: 1 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1382 # Input is: DigraphShortestDistance(gr, [1, 13], [20 .. 23]); # Expected output: 1 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1384 # Input is: DigraphShortestDistance(gr, [1, 13], [38, 41]); # Expected output: 1 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1386 # Input is: gr := ChainDigraph(72); # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/oper.tst:1388 # Input is: DigraphShortestDistance(gr, [1 .. 10], [20 .. 23]); # Expected output: 10 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1390 # Input is: DigraphShortestDistance(gr, [1, 13], [20 .. 23]); # Expected output: 7 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1392 # Input is: DigraphShortestDistance(gr, [1, 13], [38, 41]); # Expected output: 25 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1394 # Input is: gr := DigraphFromDigraph6String("+H^_HRR\P_FWEsio"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/oper.tst:1396 # Input is: DigraphShortestDistance(last, [1, 2], [7]); # Expected output: 2 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1398 # Input is: DigraphShortestDistance(gr, [1], DigraphLayers(gr, 1)[3]); # Expected output: 2 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1400 # Input is: DigraphShortestDistance(gr, [1, 2], DigraphLayers(gr, 1)[3]); # Expected output: 0 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1402 # Input is: DigraphShortestDistance(gr, [1, 3], DigraphLayers(gr, 1)[3]); # Expected output: 0 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1404 # Input is: DigraphShortestDistance(gr, [1, 6], DigraphLayers(gr, 1)[3]); # Expected output: 1 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1408 # Input is: gr := DigraphFromSparse6String( ":]n?AL`CB_EDbFE`IGaGHdJIeKGcLK_@MhDCiFLaBJmHFmKJ"); # Expected output: # But found: Error, Variable: 'DigraphFromSparse6String' must have a value ######## ########> Diff in standard/oper.tst:1411 # Input is: G1 := DigraphGroup(gr);; # Expected output: # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/oper.tst:1412 # Input is: IsPermGroup(G1) and Length(GeneratorsOfGroup(G1)) = 5; # Expected output: true # But found: Error, Variable: 'G1' must have a value ######## ########> Diff in standard/oper.tst:1414 # Input is: Size(G1); # Expected output: 1440 # But found: Error, Variable: 'G1' must have a value ######## ########> Diff in standard/oper.tst:1416 # Input is: DigraphShortestDistance(gr, 1, 16); # Expected output: 1 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1420 # Input is: gr := Digraph([[2], [3], [1, 4], [1, 3], [5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1422 # Input is: DigraphShortestDistance(gr, 1, 3); # Expected output: 2 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1424 # Input is: DigraphShortestDistance(gr, [3, 3]); # Expected output: 0 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1426 # Input is: DigraphShortestDistance(gr, 5, 2); # Expected output: fail # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1428 # Input is: DigraphShortestDistances(gr);; # Expected output: # But found: Error, Variable: 'DigraphShortestDistances' must have a value ######## ########> Diff in standard/oper.tst:1429 # Input is: DigraphShortestDistance(gr, [3, 4]); # Expected output: 1 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1433 # Input is: DigraphShortestDistance(gr, 1, 74); # Expected output: Error, the 2nd and 3rd arguments and must be vertices of the 1st argum\ \ ent , # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1436 # Input is: DigraphShortestDistance(gr, [1, 74]); # Expected output: Error, the 2nd argument must consist of vertices of the 1st argument , # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1439 # Input is: DigraphShortestDistance(gr, [1, 71, 3]); # Expected output: Error, the 2nd argument must be a list of length 2, # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:1443 # Input is: gr := ChainDigraph(10); # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/oper.tst:1445 # Input is: DigraphDistanceSet(gr, 5, 2); # Expected output: [ 7 ] # But found: Error, Variable: 'DigraphDistanceSet' must have a value ######## ########> Diff in standard/oper.tst:1447 # Input is: gr := DigraphSymmetricClosure(ChainDigraph(10)); # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/oper.tst:1449 # Input is: DigraphDistanceSet(gr, 5, 2); # Expected output: [ 3, 7 ] # But found: Error, Variable: 'DigraphDistanceSet' must have a value ######## ########> Diff in standard/oper.tst:1451 # Input is: gr := ChainDigraph(10);; # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/oper.tst:1452 # Input is: DigraphDistanceSet(gr, 20, 1); # Expected output: Error, the 2nd argument must be a vertex of the digraph, # But found: Error, Variable: 'DigraphDistanceSet' must have a value ######## ########> Diff in standard/oper.tst:1454 # Input is: DigraphDistanceSet(gr, 20, [1]); # Expected output: Error, the 2nd argument must be a vertex of the digraph, # But found: Error, Variable: 'DigraphDistanceSet' must have a value ######## ########> Diff in standard/oper.tst:1456 # Input is: DigraphDistanceSet(gr, 10, ["string", 1]); # Expected output: Error, the 3rd argument must be a list of non-negative integers, # But found: Error, Variable: 'DigraphDistanceSet' must have a value ######## ########> Diff in standard/oper.tst:1458 # Input is: gr := DigraphFromDigraph6String("&GYHPQgWTIIPW");; # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/oper.tst:1459 # Input is: DigraphDistanceSet(gr, 1, [3, 7]); # Expected output: [ ] # But found: Error, Variable: 'DigraphDistanceSet' must have a value ######## ########> Diff in standard/oper.tst:1461 # Input is: DigraphDistanceSet(gr, 1, [1]); # Expected output: [ 2, 3, 5 ] # But found: Error, Variable: 'DigraphDistanceSet' must have a value ######## ########> Diff in standard/oper.tst:1463 # Input is: DigraphDistanceSet(gr, 1, [1, 2]); # Expected output: [ 2, 3, 5, 4, 6, 7, 8 ] # But found: Error, Variable: 'DigraphDistanceSet' must have a value ######## ########> Diff in standard/oper.tst:1465 # Input is: DigraphDistanceSet(gr, 2, 2); # Expected output: [ 3, 5, 7, 8 ] # But found: Error, Variable: 'DigraphDistanceSet' must have a value ######## ########> Diff in standard/oper.tst:1467 # Input is: DigraphDistanceSet(gr, 2, -1); # Expected output: Error, the 3rd argument must be a non-negative integer, # But found: Error, Variable: 'DigraphDistanceSet' must have a value ######## ########> Diff in standard/oper.tst:1471 # Input is: gr1 := Digraph([[2], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1472 # Input is: gr2 := Digraph([[2, 2], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1473 # Input is: IsSubdigraph(gr1, gr2); # Expected output: false # But found: Error, Variable: 'IsSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:1475 # Input is: IsSubdigraph(gr2, gr1); # Expected output: true # But found: Error, Variable: 'IsSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:1477 # Input is: gr1 = gr2; # Expected output: false # But found: Error, Variable: 'gr1' must have a value ######## ########> Diff in standard/oper.tst:1481 # Input is: gr1 := CompleteDigraph(3);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:1482 # Input is: gr2 := CompleteDigraph(4);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:1483 # Input is: IsSubdigraph(gr1, gr2) or IsSubdigraph(gr1, gr2); # Expected output: false # But found: Error, Variable: 'IsSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:1485 # Input is: gr3 := CycleDigraph(3);; # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/oper.tst:1486 # Input is: IsSubdigraph(gr3, gr1); # Expected output: false # But found: Error, Variable: 'IsSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:1488 # Input is: IsSubdigraph(gr1, gr3); # Expected output: true # But found: Error, Variable: 'IsSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:1490 # Input is: gr4 := Digraph([[1, 1], [2, 2], [3, 3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1491 # Input is: IsSubdigraph(gr1, gr4) or IsSubdigraph(gr4, gr1); # Expected output: false # But found: Error, Variable: 'IsSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:1493 # Input is: gr1 := DigraphEdgeUnion(CompleteDigraph(3), CompleteDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/oper.tst:1495 # Input is: gr2 := DigraphEdgeUnion(CycleDigraph(3), CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/oper.tst:1497 # Input is: IsSubdigraph(gr1, gr2); # Expected output: true # But found: Error, Variable: 'IsSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:1499 # Input is: IsSubdigraph(gr2, gr1); # Expected output: false # But found: Error, Variable: 'IsSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:1501 # Input is: gr3 := Digraph([[2, 2, 3], [3], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1503 # Input is: gr4 := Digraph([[2, 3, 3], [3], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1505 # Input is: IsSubdigraph(gr3, gr4) or IsSubdigraph(gr4, gr3); # Expected output: false # But found: Error, Variable: 'IsSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:1507 # Input is: gr1 := Digraph([[1, 1], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1509 # Input is: gr2 := Digraph([[], [2, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1511 # Input is: IsSubdigraph(gr1, gr2) or IsSubdigraph(gr2, gr1); # Expected output: false # But found: Error, Variable: 'IsSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:1515 # Input is: gr1 := CompleteDigraph(10); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:1517 # Input is: gr2 := EmptyDigraph(9); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/oper.tst:1519 # Input is: IsUndirectedSpanningForest(gr1, gr2); # Expected output: false # But found: Error, Variable: 'IsUndirectedSpanningForest' must have a value ######## ########> Diff in standard/oper.tst:1521 # Input is: gr2 := DigraphAddEdge(EmptyDigraph(10), [1, 2]); # Expected output: # But found: Error, Variable: 'DigraphAddEdge' must have a value ######## ########> Diff in standard/oper.tst:1523 # Input is: IsUndirectedSpanningForest(gr1, gr2); # Expected output: false # But found: Error, Variable: 'IsUndirectedSpanningForest' must have a value ######## ########> Diff in standard/oper.tst:1525 # Input is: gr2 := DigraphAddEdge(gr2, [2, 1]); # Expected output: # But found: Error, Variable: 'DigraphAddEdge' must have a value ######## ########> Diff in standard/oper.tst:1527 # Input is: IsUndirectedSpanningForest(gr1, gr2); # Expected output: false # But found: Error, Variable: 'IsUndirectedSpanningForest' must have a value ######## ########> Diff in standard/oper.tst:1529 # Input is: IsUndirectedSpanningForest(gr1, DigraphFromSparse6String(":I`ESyTl^F")); # Expected output: true # But found: Error, Variable: 'IsUndirectedSpanningForest' must have a value ######## ########> Diff in standard/oper.tst:1531 # Input is: gr := DigraphFromDigraph6String("&I?PIMAQc@A?W?ADPP?"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/oper.tst:1533 # Input is: IsUndirectedSpanningForest(gr, DigraphByEdges([[2, 7], [7, 2]], 10)); # Expected output: true # But found: Error, Variable: 'IsUndirectedSpanningForest' must have a value ######## ########> Diff in standard/oper.tst:1537 # Input is: IsUndirectedSpanningTree(EmptyDigraph(1), EmptyDigraph(1)); # Expected output: true # But found: Error, Variable: 'IsUndirectedSpanningTree' must have a value ######## ########> Diff in standard/oper.tst:1539 # Input is: IsUndirectedSpanningTree(EmptyDigraph(2), EmptyDigraph(2)); # Expected output: false # But found: Error, Variable: 'IsUndirectedSpanningTree' must have a value ######## ########> Diff in standard/oper.tst:1541 # Input is: gr := DigraphFromDigraph6String("&I?PIMAQc@A?W?ADPP?"); # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/oper.tst:1543 # Input is: IsUndirectedSpanningTree(gr, EmptyDigraph(10)); # Expected output: false # But found: Error, Variable: 'IsUndirectedSpanningTree' must have a value ######## ########> Diff in standard/oper.tst:1545 # Input is: gr := DigraphFromGraph6String("INB`cZoQ_"); # Expected output: # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/oper.tst:1547 # Input is: IsUndirectedSpanningTree(gr, gr); # Expected output: false # But found: Error, Variable: 'IsUndirectedSpanningTree' must have a value ######## ########> Diff in standard/oper.tst:1549 # Input is: gr1 := DigraphEdgeUnion(CycleDigraph(5), DigraphReverse(CycleDigraph(5))); # Expected output: # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/oper.tst:1551 # Input is: gr2 := DigraphEdgeUnion(ChainDigraph(5), DigraphReverse(ChainDigraph(5))); # Expected output: # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/oper.tst:1553 # Input is: IsUndirectedSpanningTree(gr1, gr2); # Expected output: true # But found: Error, Variable: 'IsUndirectedSpanningTree' must have a value ######## ########> Diff in standard/oper.tst:1555 # Input is: IsUndirectedSpanningTree(gr2, gr2); # Expected output: true # But found: Error, Variable: 'IsUndirectedSpanningTree' must have a value ######## ########> Diff in standard/oper.tst:1559 # Input is: gr := CycleDigraph(5); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/oper.tst:1561 # Input is: PartialOrderDigraphJoinOfVertices(gr, 1, 4); # Expected output: Error, the 1st argument must satisfy IsPartialOrderDigraph, # But found: Error, Variable: 'PartialOrderDigraphJoinOfVertices' must have a value ######## ########> Diff in standard/oper.tst:1565 # Input is: gr := DigraphFromDiSparse6String(".HiR@AeNcC?oD?G`oAGXIoAGXAe_COqDK^F"); # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/oper.tst:1567 # Input is: PartialOrderDigraphMeetOfVertices(gr, 2, 3); # Expected output: 1 # But found: Error, Variable: 'PartialOrderDigraphMeetOfVertices' must have a value ######## ########> Diff in standard/oper.tst:1569 # Input is: PartialOrderDigraphJoinOfVertices(gr, 2, 3); # Expected output: 4 # But found: Error, Variable: 'PartialOrderDigraphJoinOfVertices' must have a value ######## ########> Diff in standard/oper.tst:1571 # Input is: PartialOrderDigraphJoinOfVertices(gr, 3, 9); # Expected output: 5 # But found: Error, Variable: 'PartialOrderDigraphJoinOfVertices' must have a value ######## ########> Diff in standard/oper.tst:1573 # Input is: PartialOrderDigraphMeetOfVertices(gr, 3, 9); # Expected output: fail # But found: Error, Variable: 'PartialOrderDigraphMeetOfVertices' must have a value ######## ########> Diff in standard/oper.tst:1575 # Input is: gr := DigraphReverse(gr); # Expected output: # But found: Error, Variable: 'DigraphReverse' must have a value ######## ########> Diff in standard/oper.tst:1577 # Input is: PartialOrderDigraphMeetOfVertices(gr, 2, 3); # Expected output: 4 # But found: Error, Variable: 'PartialOrderDigraphMeetOfVertices' must have a value ######## ########> Diff in standard/oper.tst:1579 # Input is: PartialOrderDigraphJoinOfVertices(gr, 2, 3); # Expected output: 1 # But found: Error, Variable: 'PartialOrderDigraphJoinOfVertices' must have a value ######## ########> Diff in standard/oper.tst:1581 # Input is: PartialOrderDigraphMeetOfVertices(gr, 3, 9); # Expected output: 5 # But found: Error, Variable: 'PartialOrderDigraphMeetOfVertices' must have a value ######## ########> Diff in standard/oper.tst:1585 # Input is: gr := Digraph([[1, 2, 3], [1, 2, 3], [1, 2, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1587 # Input is: PartialOrderDigraphMeetOfVertices(gr, 2, 3); # Expected output: Error, the 1st argument must satisfy IsPartialOrderDigraph, # But found: Error, Variable: 'PartialOrderDigraphMeetOfVertices' must have a value ######## ########> Diff in standard/oper.tst:1589 # Input is: PartialOrderDigraphJoinOfVertices(gr, 2, 3); # Expected output: Error, the 1st argument must satisfy IsPartialOrderDigraph, # But found: Error, Variable: 'PartialOrderDigraphJoinOfVertices' must have a value ######## ########> Diff in standard/oper.tst:1591 # Input is: gr1 := Digraph([[1], [2], [1, 2, 3], [1, 2, 4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1593 # Input is: gr2 := DigraphReverse(gr1); # Expected output: # But found: Error, Variable: 'DigraphReverse' must have a value ######## ########> Diff in standard/oper.tst:1597 # Input is: PartialOrderDigraphMeetOfVertices(gr1, 3, 4); # Expected output: fail # But found: Error, Variable: 'PartialOrderDigraphMeetOfVertices' must have a value ######## ########> Diff in standard/oper.tst:1599 # Input is: PartialOrderDigraphMeetOfVertices(gr2, 3, 4); # Expected output: fail # But found: Error, Variable: 'PartialOrderDigraphMeetOfVertices' must have a value ######## ########> Diff in standard/oper.tst:1603 # Input is: PartialOrderDigraphJoinOfVertices(gr2, 3, 4); # Expected output: fail # But found: Error, Variable: 'PartialOrderDigraphJoinOfVertices' must have a value ######## ########> Diff in standard/oper.tst:1605 # Input is: PartialOrderDigraphJoinOfVertices(gr1, 3, 4); # Expected output: fail # But found: Error, Variable: 'PartialOrderDigraphJoinOfVertices' must have a value ######## ########> Diff in standard/oper.tst:1609 # Input is: gr := Digraph([[4, 5, 6, 7, 9], [7, 3], [2, 6, 7, 9, 10], [5, 6, 7, 1, 9], [1, 4, 6, 7], [7, 1, 3, 4, 5], [1, 4, 9, 2, 3, 5, 6, 8], [7], [1, 4, 7, 3, 10], [9, 3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1612 # Input is: DigraphNrEdges(gr); # Expected output: 42 # But found: Error, Variable: 'DigraphNrEdges' must have a value ######## ########> Diff in standard/oper.tst:1614 # Input is: DigraphNrEdges(DigraphClosure(gr, 10)); # Expected output: 54 # But found: Error, Variable: 'DigraphNrEdges' must have a value ######## ########> Diff in standard/oper.tst:1616 # Input is: DigraphNrEdges(DigraphClosure(gr, 9)); # Expected output: 90 # But found: Error, Variable: 'DigraphNrEdges' must have a value ######## ########> Diff in standard/oper.tst:1618 # Input is: DigraphNrEdges(DigraphClosure(gr, 11)); # Expected output: 42 # But found: Error, Variable: 'DigraphNrEdges' must have a value ######## ########> Diff in standard/oper.tst:1620 # Input is: gr := Digraph([[1], [2], [3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1621 # Input is: DigraphClosure(gr, 2); # Expected output: Error, the 1st argument must be a symmetric digraph with no loops, and no \ \ multiple edges, # But found: Error, Variable: 'DigraphClosure' must have a value ######## ########> Diff in standard/oper.tst:1624 # Input is: gr := Digraph([[2], [3], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1625 # Input is: DigraphClosure(gr, 2); # Expected output: Error, the 1st argument must be a symmetric digraph with no loops, and no \ \ multiple edges, # But found: Error, Variable: 'DigraphClosure' must have a value ######## ########> Diff in standard/oper.tst:1630 # Input is: gr := Digraph([[2], [3], [4], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1632 # Input is: IsMatching(gr, edges); # Expected output: false # But found: Error, Variable: 'IsMatching' must have a value ######## ########> Diff in standard/oper.tst:1634 # Input is: gr := Digraph([[2], [3], [4], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1636 # Input is: IsMatching(gr, edges); # Expected output: false # But found: Error, Variable: 'IsMatching' must have a value ######## ########> Diff in standard/oper.tst:1639 # Input is: IsMatching(gr, edges); # Expected output: true # But found: Error, Variable: 'IsMatching' must have a value ######## ########> Diff in standard/oper.tst:1641 # Input is: gr := Digraph([[2], [3], [4], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1643 # Input is: IsMatching(gr, edges); # Expected output: false # But found: Error, Variable: 'IsMatching' must have a value ######## ########> Diff in standard/oper.tst:1645 # Input is: gr := Digraph([[2], [3], [4], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1647 # Input is: IsMatching(gr, edges); # Expected output: false # But found: Error, Variable: 'IsMatching' must have a value ######## ########> Diff in standard/oper.tst:1649 # Input is: gr := Digraph([[1, 2], [3], [4], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1651 # Input is: IsMatching(gr, edges); # Expected output: true # But found: Error, Variable: 'IsMatching' must have a value ######## ########> Diff in standard/oper.tst:1653 # Input is: gr := Digraph([[2], [3], [4], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1655 # Input is: IsMatching(gr, edges); # Expected output: true # But found: Error, Variable: 'IsMatching' must have a value ######## ########> Diff in standard/oper.tst:1657 # Input is: gr := Digraph([[2], [3], [4], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1659 # Input is: IsMatching(gr, edges); # Expected output: false # But found: Error, Variable: 'IsMatching' must have a value ######## ########> Diff in standard/oper.tst:1661 # Input is: gr := CompleteDigraph(999);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:1663 # Input is: IsMatching(gr, edges); # Expected output: true # But found: Error, Variable: 'IsMatching' must have a value ######## ########> Diff in standard/oper.tst:1665 # Input is: gr := CompleteDigraph(999);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:1668 # Input is: IsMatching(gr, edges); # Expected output: true # But found: Error, Variable: 'IsMatching' must have a value ######## ########> Diff in standard/oper.tst:1670 # Input is: gr := CompleteDigraph(999);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:1672 # Input is: IsMatching(gr, edges); # Expected output: false # But found: Error, Variable: 'IsMatching' must have a value ######## ########> Diff in standard/oper.tst:1676 # Input is: gr := Digraph([[2], [3], [4], [5], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1678 # Input is: IsPerfectMatching(gr, [[1, 3]]); # Expected output: false # But found: Error, Variable: 'IsPerfectMatching' must have a value ######## ########> Diff in standard/oper.tst:1681 # Input is: IsMatching(gr, edges); # Expected output: true # But found: Error, Variable: 'IsMatching' must have a value ######## ########> Diff in standard/oper.tst:1683 # Input is: IsPerfectMatching(gr, edges); # Expected output: false # But found: Error, Variable: 'IsPerfectMatching' must have a value ######## ########> Diff in standard/oper.tst:1685 # Input is: gr := CompleteDigraph(500); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:1691 # Input is: IsPerfectMatching(gr, edges); # Expected output: true # But found: Error, Variable: 'IsPerfectMatching' must have a value ######## ########> Diff in standard/oper.tst:1693 # Input is: gr := Digraph([[2], [3, 4], [], [5], [1, 6], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1696 # Input is: IsMatching(gr, edges); # Expected output: false # But found: Error, Variable: 'IsMatching' must have a value ######## ########> Diff in standard/oper.tst:1699 # Input is: IsPerfectMatching(gr, edges); # Expected output: true # But found: Error, Variable: 'IsPerfectMatching' must have a value ######## ########> Diff in standard/oper.tst:1701 # Input is: gr := Digraph([[2], [3], [4, 3], [5], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1704 # Input is: IsPerfectMatching(gr, edges); # Expected output: true # But found: Error, Variable: 'IsPerfectMatching' must have a value ######## ########> Diff in standard/oper.tst:1708 # Input is: gr := Digraph([[2], [3], [4], [5], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1711 # Input is: IsMatching(gr, edges); # Expected output: false # But found: Error, Variable: 'IsMatching' must have a value ######## ########> Diff in standard/oper.tst:1714 # Input is: IsMaximalMatching(gr, edges); # Expected output: true # But found: Error, Variable: 'IsMaximalMatching' must have a value ######## ########> Diff in standard/oper.tst:1716 # Input is: gr := Digraph([[2], [3], [4], [5], [1, 5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1719 # Input is: IsMaximalMatching(gr, edges); # Expected output: false # But found: Error, Variable: 'IsMaximalMatching' must have a value ######## ########> Diff in standard/oper.tst:1721 # Input is: gr := CompleteDigraph(5);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/oper.tst:1723 # Input is: IsMaximalMatching(gr, edges); # Expected output: false # But found: Error, Variable: 'IsMaximalMatching' must have a value ######## ########> Diff in standard/oper.tst:1725 # Input is: gr := Digraph([[2], [3], [4], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1727 # Input is: IsMatching(gr, edges); # Expected output: false # But found: Error, Variable: 'IsMatching' must have a value ######## ########> Diff in standard/oper.tst:1730 # Input is: IsMaximalMatching(gr, edges); # Expected output: true # But found: Error, Variable: 'IsMaximalMatching' must have a value ######## ########> Diff in standard/oper.tst:1732 # Input is: gr := Digraph([[2], [3], [1], [5], [6], [4]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1734 # Input is: IsMaximalMatching(gr, edges); # Expected output: true # But found: Error, Variable: 'IsMaximalMatching' must have a value ######## ########> Diff in standard/oper.tst:1736 # Input is: gr := Digraph([[1, 2], [3], [4], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1739 # Input is: IsMaximalMatching(gr, edges); # Expected output: true # But found: Error, Variable: 'IsMaximalMatching' must have a value ######## ########> Diff in standard/oper.tst:1743 # Input is: D := Digraph([[1, 2], [1, 2], [2, 3, 4], [3, 5], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1745 # Input is: IsMaximumMatching(D, [[1, 2], [3, 3], [4, 5]]); # Expected output: false # But found: Error, Variable: 'IsMaximumMatching' must have a value ######## ########> Diff in standard/oper.tst:1747 # Input is: IsMaximumMatching(D, [[1, 1], [2, 2], [3, 3], [4, 5]]); # Expected output: true # But found: Error, Variable: 'IsMaximumMatching' must have a value ######## ########> Diff in standard/oper.tst:1749 # Input is: IsMaximumMatching(D, [[1, 1], [1, 2], [2, 2], [3, 3], [4, 5]]); # Expected output: false # But found: Error, Variable: 'IsMaximumMatching' must have a value ######## ########> Diff in standard/oper.tst:1753 # Input is: gr := Digraph([[1], [3, 4], [5, 6], [4, 2, 3], [4, 5], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1754 # Input is: DigraphShortestPath(gr, 1, 6); # Expected output: fail # But found: Error, Variable: 'DigraphShortestPath' must have a value ######## ########> Diff in standard/oper.tst:1756 # Input is: DigraphShortestPath(gr, 2, 5); # Expected output: [ [ 2, 3, 5 ], [ 1, 1 ] ] # But found: Error, Variable: 'DigraphShortestPath' must have a value ######## ########> Diff in standard/oper.tst:1758 # Input is: DigraphShortestPath(gr, 3, 3); # Expected output: [ [ 3, 5, 4, 3 ], [ 1, 1, 3 ] ] # But found: Error, Variable: 'DigraphShortestPath' must have a value ######## ########> Diff in standard/oper.tst:1760 # Input is: DigraphShortestPath(gr, 6, 6); # Expected output: fail # But found: Error, Variable: 'DigraphShortestPath' must have a value ######## ########> Diff in standard/oper.tst:1762 # Input is: DigraphShortestPath(gr, 5, 5); # Expected output: [ [ 5, 5 ], [ 2 ] ] # But found: Error, Variable: 'DigraphShortestPath' must have a value ######## ########> Diff in standard/oper.tst:1764 # Input is: gr := Digraph([[]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1765 # Input is: DigraphShortestPath(gr, 1, 1); # Expected output: fail # But found: Error, Variable: 'DigraphShortestPath' must have a value ######## ########> Diff in standard/oper.tst:1767 # Input is: gr := Digraph([[], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1768 # Input is: DigraphShortestPath(gr, 2, 1); # Expected output: fail # But found: Error, Variable: 'DigraphShortestPath' must have a value ######## ########> Diff in standard/oper.tst:1770 # Input is: gr := Digraph([[2], [1], [3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1771 # Input is: DigraphShortestPath(gr, 1, 2); # Expected output: [ [ 1, 2 ], [ 1 ] ] # But found: Error, Variable: 'DigraphShortestPath' must have a value ######## ########> Diff in standard/oper.tst:1773 # Input is: gr := CayleyDigraph(SymmetricGroup(7));; # Expected output: # But found: Error, Variable: 'CayleyDigraph' must have a value ######## ########> Diff in standard/oper.tst:1774 # Input is: DigraphShortestPath(gr, 12, 5014); # Expected output: [ [ 12, 912, 1919, 3595, 4915, 3433, 4153, 3242, 2522, 2886, 23, 743, 238, 1558, 713, 5014 ], [ 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2 ] ] # But found: Error, Variable: 'DigraphShortestPath' must have a value ######## ########> Diff in standard/oper.tst:1779 # Input is: D := Digraph(IsMutableDigraph, [[1], [3, 4], [5, 6], [4, 2, 3], [4, 5], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1781 # Input is: DigraphAddAllLoops(D); # Expected output: # But found: Error, Variable: 'DigraphAddAllLoops' must have a value ######## ########> Diff in standard/oper.tst:1783 # Input is: IsIdenticalObj(last, D); # Expected output: true # But found: Error, Variable: 'D' must have a value ######## ########> Diff in standard/oper.tst:1785 # Input is: D := Digraph([[1], [3, 4], [5, 6], [4, 2, 3], [4, 5], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1787 # Input is: DigraphAddAllLoops(D); # Expected output: # But found: Error, Variable: 'DigraphAddAllLoops' must have a value ######## ########> Diff in standard/oper.tst:1789 # Input is: IsIdenticalObj(last, D); # Expected output: false # But found: Error, Variable: 'D' must have a value ######## ########> Diff in standard/oper.tst:1791 # Input is: D := Digraph([[1], [3, 4], [5, 6], [4, 2, 3], [4, 5], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1793 # Input is: D := DigraphAddEdge(D, 1, 3); # Expected output: # But found: Error, Variable: 'DigraphAddEdge' must have a value ######## ########> Diff in standard/oper.tst:1795 # Input is: D := DigraphAddEdge(D, 1, 3); # Expected output: # But found: Error, Variable: 'DigraphAddEdge' must have a value ######## ########> Diff in standard/oper.tst:1797 # Input is: D := DigraphRemoveEdge(D, 1, 3); # Expected output: Error, the 1st argument must be a digraph with no multiple edges, # But found: Error, Variable: 'DigraphRemoveEdge' must have a value ######## ########> Diff in standard/oper.tst:1799 # Input is: D := Digraph([[1], [3, 4], [5, 6], [4, 2, 3], [4, 5], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1801 # Input is: D := DigraphAddEdge(D, 1, 3); # Expected output: # But found: Error, Variable: 'DigraphAddEdge' must have a value ######## ########> Diff in standard/oper.tst:1803 # Input is: D := DigraphRemoveEdge(D, 1, 3); # Expected output: # But found: Error, Variable: 'DigraphRemoveEdge' must have a value ######## ########> Diff in standard/oper.tst:1805 # Input is: D := DigraphRemoveEdge(D, 1, 3); # Expected output: # But found: Error, Variable: 'DigraphRemoveEdge' must have a value ######## ########> Diff in standard/oper.tst:1809 # Input is: D := DigraphMutableCopy(CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphMutableCopy' must have a value ######## ########> Diff in standard/oper.tst:1811 # Input is: DigraphDisjointUnion(D, D, D, D, D, D, D, D, D, D); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/oper.tst:1813 # Input is: D := DigraphMutableCopy(CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphMutableCopy' must have a value ######## ########> Diff in standard/oper.tst:1815 # Input is: DigraphDisjointUnion(D, CycleDigraph(3), CycleDigraph(3), CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/oper.tst:1818 # Input is: D := DigraphMutableCopy(CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphMutableCopy' must have a value ######## ########> Diff in standard/oper.tst:1820 # Input is: DigraphJoin(D, D, D); # Expected output: # But found: Error, Variable: 'DigraphJoin' must have a value ######## ########> Diff in standard/oper.tst:1822 # Input is: D := CycleDigraph(IsMutableDigraph, 3); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/oper.tst:1824 # Input is: DigraphEdgeUnion(D, D, D); # Expected output: # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/oper.tst:1826 # Input is: D := DigraphMutableCopy(CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphMutableCopy' must have a value ######## ########> Diff in standard/oper.tst:1828 # Input is: DigraphJoin(D, CycleDigraph(3), CycleDigraph(3), CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphJoin' must have a value ######## ########> Diff in standard/oper.tst:1831 # Input is: D := CycleDigraph(3); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/oper.tst:1833 # Input is: DigraphJoin(D, D, D); # Expected output: # But found: Error, Variable: 'DigraphJoin' must have a value ######## ########> Diff in standard/oper.tst:1835 # Input is: DigraphJoin(D, CycleDigraph(3), CycleDigraph(3), CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphJoin' must have a value ######## ########> Diff in standard/oper.tst:1838 # Input is: D := DigraphMutableCopy(CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphMutableCopy' must have a value ######## ########> Diff in standard/oper.tst:1840 # Input is: DigraphEdgeUnion(D, CycleDigraph(3), CycleDigraph(3), CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/oper.tst:1843 # Input is: DD := CycleDigraph(3); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/oper.tst:1845 # Input is: DD := DigraphEdgeUnion(D, CycleDigraph(3), CycleDigraph(3), CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/oper.tst:1848 # Input is: D = DD; # Expected output: true # But found: Error, Variable: 'D' must have a value ######## ########> Diff in standard/oper.tst:1850 # Input is: D := Digraph(IsMutableDigraph, [[2, 3], [1, 3], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1852 # Input is: DigraphReverse(D) = Digraph(IsMutableDigraph, [[2, 3], [1, 3], [1, 2]]); # Expected output: true # But found: Error, Variable: 'DigraphReverse' must have a value ######## ########> Diff in standard/oper.tst:1854 # Input is: DigraphReverseEdge(D, 1, 2); # Expected output: # But found: Error, Variable: 'DigraphReverseEdge' must have a value ######## ########> Diff in standard/oper.tst:1856 # Input is: DigraphReverseEdge(D, 1, 1); # Expected output: Error, the 1st argument must be a digraph with no multiple edges, # But found: Error, Variable: 'DigraphReverseEdge' must have a value ######## ########> Diff in standard/oper.tst:1858 # Input is: DigraphAddEdge(D, 1, 1); # Expected output: # But found: Error, Variable: 'DigraphAddEdge' must have a value ######## ########> Diff in standard/oper.tst:1860 # Input is: DigraphReverseEdge(D, 1, 1); # Expected output: Error, the 1st argument must be a digraph with no multiple edges, # But found: Error, Variable: 'DigraphReverseEdge' must have a value ######## ########> Diff in standard/oper.tst:1862 # Input is: D := Digraph(IsMutableDigraph, [[2, 3], [1, 3], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1864 # Input is: DigraphAddEdge(D, 1, 1); # Expected output: # But found: Error, Variable: 'DigraphAddEdge' must have a value ######## ########> Diff in standard/oper.tst:1866 # Input is: DigraphReverseEdge(D, 1, 1); # Expected output: # But found: Error, Variable: 'DigraphReverseEdge' must have a value ######## ########> Diff in standard/oper.tst:1868 # Input is: DigraphReverseEdge(D, 1, 4); # Expected output: Error, there is no edge from 1 to 4 in the digraph that is the 1st argument, # But found: Error, Variable: 'DigraphReverseEdge' must have a value ######## ########> Diff in standard/oper.tst:1871 # Input is: D := MakeImmutable(D); # Expected output: # But found: Error, Variable: 'D' must have a value ######## ########> Diff in standard/oper.tst:1873 # Input is: D := DigraphReverseEdge(D, 1, 2); # Expected output: # But found: Error, Variable: 'DigraphReverseEdge' must have a value ######## ########> Diff in standard/oper.tst:1875 # Input is: D := CycleDigraph(3); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/oper.tst:1877 # Input is: DigraphReverseEdge(D, [1, 2]); # Expected output: # But found: Error, Variable: 'DigraphReverseEdge' must have a value ######## ########> Diff in standard/oper.tst:1879 # Input is: D := DigraphMutableCopy(CompleteDigraph(10)); # Expected output: # But found: Error, Variable: 'DigraphMutableCopy' must have a value ######## ########> Diff in standard/oper.tst:1881 # Input is: DD := InducedSubdigraph(D, [1, 2, 4, 6]); # Expected output: # But found: Error, Variable: 'InducedSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:1883 # Input is: D; # Expected output: # But found: Error, Variable: 'D' must have a value ######## ########> Diff in standard/oper.tst:1885 # Input is: D := DigraphMutableCopy(CompleteDigraph(10)); # Expected output: # But found: Error, Variable: 'DigraphMutableCopy' must have a value ######## ########> Diff in standard/oper.tst:1887 # Input is: DD := QuotientDigraph(D, [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10]]); # Expected output: # But found: Error, Variable: 'QuotientDigraph' must have a value ######## ########> Diff in standard/oper.tst:1889 # Input is: InNeighboursOfVertexNC(DD, 1); # Expected output: [ 1, 2, 3, 4 ] # But found: Error, Variable: 'InNeighboursOfVertexNC' must have a value ######## ########> Diff in standard/oper.tst:1891 # Input is: MakeImmutable(DD); # Expected output: # But found: Error, Variable: 'DD' must have a value ######## ########> Diff in standard/oper.tst:1893 # Input is: InNeighbours(DD);; # Expected output: # But found: Error, Variable: 'InNeighbours' must have a value ######## ########> Diff in standard/oper.tst:1894 # Input is: InNeighboursOfVertexNC(DD, 1); # Expected output: [ 1, 2, 3, 4 ] # But found: Error, Variable: 'InNeighboursOfVertexNC' must have a value ######## ########> Diff in standard/oper.tst:1896 # Input is: InDegreeOfVertexNC(DD, 1); # Expected output: 4 # But found: Error, Variable: 'InDegreeOfVertexNC' must have a value ######## ########> Diff in standard/oper.tst:1898 # Input is: DigraphShortestPath(DD, 1, 5); # Expected output: Error, the 2nd and 3rd arguments and must be vertices of the 1st argum\ \ ent , # But found: Error, Variable: 'DigraphShortestPath' must have a value ######## ########> Diff in standard/oper.tst:1901 # Input is: IsTransitiveDigraph(DD); # Expected output: false # But found: Error, Variable: 'IsTransitiveDigraph' must have a value ######## ########> Diff in standard/oper.tst:1903 # Input is: DD := DigraphTransitiveClosure(DigraphRemoveAllMultipleEdges(DD)); # Expected output: # But found: Error, Variable: 'DigraphTransitiveClosure' must have a value ######## ########> Diff in standard/oper.tst:1905 # Input is: IsTransitiveDigraph(DD); # Expected output: true # But found: Error, Variable: 'IsTransitiveDigraph' must have a value ######## ########> Diff in standard/oper.tst:1907 # Input is: DigraphShortestPath(DD, 1, 2); # Expected output: [ [ 1, 2 ], [ 2 ] ] # But found: Error, Variable: 'DigraphShortestPath' must have a value ######## ########> Diff in standard/oper.tst:1909 # Input is: D := ChainDigraph(4); # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/oper.tst:1911 # Input is: D := DigraphTransitiveClosure(D); # Expected output: # But found: Error, Variable: 'DigraphTransitiveClosure' must have a value ######## ########> Diff in standard/oper.tst:1913 # Input is: DigraphShortestPath(D, 2, 1); # Expected output: fail # But found: Error, Variable: 'DigraphShortestPath' must have a value ######## ########> Diff in standard/oper.tst:1915 # Input is: D := DigraphDisjointUnion(CycleDigraph(3), CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/oper.tst:1917 # Input is: DigraphConnectedComponents(D); # Expected output: rec( comps := [ [ 1, 2, 3 ], [ 4, 5, 6 ] ], id := [ 1, 1, 1, 2, 2, 2 ] ) # But found: Error, Variable: 'DigraphConnectedComponents' must have a value ######## ########> Diff in standard/oper.tst:1919 # Input is: DigraphShortestPath(D, 1, 4); # Expected output: fail # But found: Error, Variable: 'DigraphShortestPath' must have a value ######## ########> Diff in standard/oper.tst:1921 # Input is: D := Digraph([[1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1923 # Input is: PartialOrderDigraphMeetOfVertices(D, 1, 2); # Expected output: Error, the 3rd argument must be a vertex of the 1st argument , # But found: Error, Variable: 'PartialOrderDigraphMeetOfVertices' must have a value ######## ########> Diff in standard/oper.tst:1925 # Input is: PartialOrderDigraphMeetOfVertices(D, 2, 1); # Expected output: Error, the 2nd argument must be a vertex of the 1st argument , # But found: Error, Variable: 'PartialOrderDigraphMeetOfVertices' must have a value ######## ########> Diff in standard/oper.tst:1927 # Input is: PartialOrderDigraphJoinOfVertices(D, 1, 2); # Expected output: Error, the 3rd argument must be a vertex of the 1st argument , # But found: Error, Variable: 'PartialOrderDigraphJoinOfVertices' must have a value ######## ########> Diff in standard/oper.tst:1929 # Input is: PartialOrderDigraphJoinOfVertices(D, 2, 1); # Expected output: Error, the 2nd argument must be a vertex of the 1st argument , # But found: Error, Variable: 'PartialOrderDigraphJoinOfVertices' must have a value ######## ########> Diff in standard/oper.tst:1933 # Input is: D := DigraphMutableCopy(CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphMutableCopy' must have a value ######## ########> Diff in standard/oper.tst:1935 # Input is: DigraphCartesianProduct(D, D, D); # Expected output: # But found: Error, Variable: 'DigraphCartesianProduct' must have a value ######## ########> Diff in standard/oper.tst:1937 # Input is: D := DigraphMutableCopy(CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphMutableCopy' must have a value ######## ########> Diff in standard/oper.tst:1939 # Input is: DigraphCartesianProduct(D, CycleDigraph(3), CycleDigraph(3), CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphCartesianProduct' must have a value ######## ########> Diff in standard/oper.tst:1941 # Input is: D := DigraphCartesianProduct(ChainDigraph(3), CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphCartesianProduct' must have a value ######## ########> Diff in standard/oper.tst:1943 # Input is: IsIsomorphicDigraph(D, Digraph([[2, 4], [3, 5], [6], [5, 7], [6, 8], [9], [8, 1], [9, 2], [3]])); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/oper.tst:1946 # Input is: D := DigraphCartesianProduct(ChainDigraph(3), CycleDigraph(3), Digraph([[2], [2]])); # Expected output: # But found: Error, Variable: 'DigraphCartesianProduct' must have a value ######## ########> Diff in standard/oper.tst:1949 # Input is: HasDigraphCartesianProductProjections(D); # Expected output: true # But found: Error, Variable: 'HasDigraphCartesianProductProjections' must have a value ######## ########> Diff in standard/oper.tst:1951 # Input is: Length(DigraphCartesianProductProjections(D)); # Expected output: 3 # But found: Error, Variable: 'DigraphCartesianProductProjections' must have a value ######## ########> Diff in standard/oper.tst:1953 # Input is: G := DigraphFromDigraph6String( "&QSC?IA?@@?A__@OO?GG_OCOGAG?@?E_?BO?@G??s??Y??H?CE?AB?@@");; # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/oper.tst:1955 # Input is: IsIsomorphicDigraph(D, G); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/oper.tst:1957 # Input is: D := RandomDigraph(100);; IsIsomorphicDigraph(D, DigraphCartesianProduct(D, Digraph([[]]))); # Expected output: true # But found: Error, Variable: 'RandomDigraph' must have a value Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/oper.tst:1960 # Input is: DigraphCartesianProduct(Digraph([[1]]), Digraph([[1]])); # Expected output: # But found: Error, Variable: 'DigraphCartesianProduct' must have a value ######## ########> Diff in standard/oper.tst:1964 # Input is: D := DigraphMutableCopy(CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphMutableCopy' must have a value ######## ########> Diff in standard/oper.tst:1966 # Input is: DigraphDirectProduct(D, D, D); # Expected output: # But found: Error, Variable: 'DigraphDirectProduct' must have a value ######## ########> Diff in standard/oper.tst:1968 # Input is: D := DigraphMutableCopy(CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphMutableCopy' must have a value ######## ########> Diff in standard/oper.tst:1970 # Input is: DigraphDirectProduct(D, CycleDigraph(3), CycleDigraph(3), CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphDirectProduct' must have a value ######## ########> Diff in standard/oper.tst:1972 # Input is: D := DigraphDirectProduct(ChainDigraph(3), CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphDirectProduct' must have a value ######## ########> Diff in standard/oper.tst:1974 # Input is: IsIsomorphicDigraph(D, Digraph([[5], [6], [], [8], [9], [], [2], [3], []])); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/oper.tst:1977 # Input is: D := DigraphDirectProduct(ChainDigraph(3), CycleDigraph(3), Digraph([[2], [2]])); # Expected output: # But found: Error, Variable: 'DigraphDirectProduct' must have a value ######## ########> Diff in standard/oper.tst:1980 # Input is: HasDigraphDirectProductProjections(D); # Expected output: true # But found: Error, Variable: 'HasDigraphDirectProductProjections' must have a value ######## ########> Diff in standard/oper.tst:1982 # Input is: Length(DigraphDirectProductProjections(D)); # Expected output: 3 # But found: Error, Variable: 'DigraphDirectProductProjections' must have a value ######## ########> Diff in standard/oper.tst:1984 # Input is: G := DigraphFromDigraph6String( "&Q??O??G?????A??@????A??@??????O??G?????A??@????A??@????");; # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/oper.tst:1986 # Input is: IsIsomorphicDigraph(D, G); # Expected output: true # But found: Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/oper.tst:1988 # Input is: D := RandomDigraph(100);; IsIsomorphicDigraph(D, DigraphDirectProduct(D, Digraph([[1]]))); # Expected output: true # But found: Error, Variable: 'RandomDigraph' must have a value Error, Variable: 'IsIsomorphicDigraph' must have a value ######## ########> Diff in standard/oper.tst:1993 # Input is: D := Digraph(IsMutableDigraph, [[3, 4, 6, 8], [1, 3, 4, 6, 7, 8, 10], [1, 2, 6, 7, 8, 9], [3, 5, 7], [1, 2, 3, 6, 8, 9], [2, 6, 8, 10], [2, 7, 10], [1, 5, 8, 10], [1, 2, 6, 7, 8, 10], [1, 2, 6, 8, 9, 10]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:1997 # Input is: InducedSubdigraph(D, [4, 5]); # Expected output: # But found: Error, Variable: 'InducedSubdigraph' must have a value ######## ########> Diff in standard/oper.tst:1999 # Input is: DigraphVertexLabels(D); # Expected output: [ 4, 5 ] # But found: Error, Variable: 'DigraphVertexLabels' must have a value ######## ########> Diff in standard/oper.tst:2003 # Input is: D := Digraph([[6, 7, 8], [8], [8], [8], [8], [1, 7, 8], [1, 6, 8], [3, 2, 1, 7, 6, 5, 4]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/oper.tst:2005 # Input is: C := DigraphRemoveVertex(DigraphMutableCopy(D), 5);; # Expected output: # But found: Error, Variable: 'DigraphRemoveVertex' must have a value ######## ########> Diff in standard/oper.tst:2006 # Input is: DigraphEdgeLabels(C); # Expected output: [ [ 1, 1, 1 ], [ 1 ], [ 1 ], [ 1 ], [ 1, 1, 1 ], [ 1, 1, 1 ], [ 1, 1, 1, 1, 1, 1 ] ] # But found: Error, Variable: 'DigraphEdgeLabels' must have a value ######## ########> Diff in standard/oper.tst:2009 # Input is: OutNeighbours(C); # Expected output: [ [ 5, 6, 7 ], [ 7 ], [ 7 ], [ 7 ], [ 1, 6, 7 ], [ 1, 5, 7 ], [ 3, 2, 1, 6, 5, 4 ] ] # But found: Error, Variable: 'OutNeighbours' must have a value ######## ########> Diff in standard/oper.tst:2017 # Input is: gr := DigraphByAdjacencyMatrix(mat); # Expected output: # But found: Error, Variable: 'DigraphByAdjacencyMatrix' must have a value ######## ########> Diff in standard/oper.tst:2019 # Input is: DigraphShortestDistance(gr, 2, 3); # Expected output: 1 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:2021 # Input is: DigraphDijkstra(gr, 2, 3); # Expected output: [ [ infinity, 0, 1 ], [ -1, -1, 2 ] ] # But found: Error, Variable: 'DigraphDijkstra' must have a value ######## ########> Diff in standard/oper.tst:2023 # Input is: DigraphDijkstra(gr, 1, 3); # Expected output: [ [ 0, 1, 1 ], [ -1, 1, 1 ] ] # But found: Error, Variable: 'DigraphDijkstra' must have a value ######## ########> Diff in standard/oper.tst:2025 # Input is: DigraphDijkstra(gr, 1, 2); # Expected output: [ [ 0, 1, 1 ], [ -1, 1, 1 ] ] # But found: Error, Variable: 'DigraphDijkstra' must have a value ######## ########> Diff in standard/oper.tst:2027 # Input is: DigraphShortestDistance(gr, 1, 3); # Expected output: 1 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:2029 # Input is: DigraphShortestDistance(gr, 1, 2); # Expected output: 1 # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:2033 # Input is: gr := DigraphByAdjacencyMatrix(mat); # Expected output: # But found: Error, Variable: 'DigraphByAdjacencyMatrix' must have a value ######## ########> Diff in standard/oper.tst:2035 # Input is: DigraphShortestDistance(gr, 2, 3); # Expected output: fail # But found: Error, Variable: 'DigraphShortestDistance' must have a value ######## ########> Diff in standard/oper.tst:2037 # Input is: DigraphDijkstra(gr, 2, 3); # Expected output: [ [ infinity, 0, infinity ], [ -1, -1, -1 ] ] # But found: Error, Variable: 'DigraphDijkstra' must have a value ######## ########> Diff in standard/oper.tst:2041 # Input is: gr := DigraphByAdjacencyMatrix(mat); # Expected output: # But found: Error, Variable: 'DigraphByAdjacencyMatrix' must have a value ######## ########> Diff in standard/oper.tst:2043 # Input is: DigraphDijkstra(gr, 1, 4); # Expected output: [ [ 0, 1, 1, 1 ], [ -1, 1, 1, 1 ] ] # But found: Error, Variable: 'DigraphDijkstra' must have a value ######## ########> Diff in standard/oper.tst:2047 # Input is: gr := DigraphByAdjacencyMatrix(mat); # Expected output: # But found: Error, Variable: 'DigraphByAdjacencyMatrix' must have a value ######## ########> Diff in standard/oper.tst:2049 # Input is: DigraphDijkstra(gr, 1, 2); # Expected output: [ [ 0, 1, 1, 1 ], [ -1, 1, 1, 1 ] ] # But found: Error, Variable: 'DigraphDijkstra' must have a value ######## ########> Diff in standard/oper.tst:2051 # Input is: DigraphDijkstra(gr, 1, 3); # Expected output: [ [ 0, 1, 1, 1 ], [ -1, 1, 1, 1 ] ] # But found: Error, Variable: 'DigraphDijkstra' must have a value ######## ########> Diff in standard/oper.tst:2116 # Input is: DIGRAPHS_StopTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StopTest' must have a value ######## Digraphs package: standard/oper.tst msecs: 1077 false gap> ########> Diff in standard/orbits.tst:14 # Input is: DIGRAPHS_StartTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StartTest' must have a value ######## ########> Diff in standard/orbits.tst:17 # Input is: gr := NullDigraph(0); # Expected output: # But found: Error, Variable: 'NullDigraph' must have a value ######## ########> Diff in standard/orbits.tst:19 # Input is: DigraphStabilizer(gr, 1); # Expected output: Error, the 2nd argument must not exceed 0, the number of vertices of the digraph in the 1st argument , # But found: Error, Variable: 'DigraphStabilizer' must have a value ######## ########> Diff in standard/orbits.tst:24 # Input is: gr := CompleteDigraph(3); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/orbits.tst:26 # Input is: DigraphStabilizer(gr, 1); # Expected output: Group([ (2,3) ]) # But found: Error, Variable: 'DigraphStabilizer' must have a value ######## ########> Diff in standard/orbits.tst:28 # Input is: DigraphStabilizer(gr, 2); # Expected output: Group([ (1,3) ]) # But found: Error, Variable: 'DigraphStabilizer' must have a value ######## ########> Diff in standard/orbits.tst:30 # Input is: DigraphStabilizer(gr, 3); # Expected output: Group([ (1,2) ]) # But found: Error, Variable: 'DigraphStabilizer' must have a value ######## ########> Diff in standard/orbits.tst:34 # Input is: gr := Digraph([[2, 3], [1], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/orbits.tst:36 # Input is: DigraphGroup(gr); # Expected output: Group(()) # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/orbits.tst:38 # Input is: gr := Digraph([[3], [3], [1, 2, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/orbits.tst:40 # Input is: Size(AutomorphismGroup(gr)); # Expected output: 2 # But found: Error, Variable: 'gr' must have a value ######## ########> Diff in standard/orbits.tst:42 # Input is: gr := Digraph([[3, 2], [1], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/orbits.tst:44 # Input is: DigraphGroup(gr); # Expected output: Group([ (2,3) ]) # But found: Error, Variable: 'DigraphGroup' must have a value ######## ########> Diff in standard/orbits.tst:48 # Input is: gr := CycleDigraph(10); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/orbits.tst:50 # Input is: DigraphOrbits(gr); # Expected output: [ [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ] ] # But found: Error, Variable: 'DigraphOrbits' must have a value ######## ########> Diff in standard/orbits.tst:54 # Input is: gr := ChainDigraph(3); # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/orbits.tst:56 # Input is: RepresentativeOutNeighbours(gr); # Expected output: [ [ 2 ], [ 3 ], [ ] ] # But found: Error, Variable: 'RepresentativeOutNeighbours' must have a value ######## ########> Diff in standard/orbits.tst:58 # Input is: gr := CycleDigraph(12); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/orbits.tst:60 # Input is: RepresentativeOutNeighbours(gr); # Expected output: [ [ 2 ] ] # But found: Error, Variable: 'RepresentativeOutNeighbours' must have a value ######## ########> Diff in standard/orbits.tst:64 # Input is: DIGRAPHS_StopTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StopTest' must have a value ######## Digraphs package: standard/orbits.tst msecs: 26 false gap> ########> Diff in standard/planar.tst:14 # Input is: DIGRAPHS_StartTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StartTest' must have a value ######## ########> Diff in standard/planar.tst:17 # Input is: D := NullDigraph(0); # Expected output: # But found: Error, Variable: 'NullDigraph' must have a value ######## ########> Diff in standard/planar.tst:19 # Input is: IsPlanarDigraph(D); # Expected output: true # But found: Error, Variable: 'IsPlanarDigraph' must have a value ######## ########> Diff in standard/planar.tst:21 # Input is: D := CompleteDigraph(4); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/planar.tst:23 # Input is: IsPlanarDigraph(D); # Expected output: true # But found: Error, Variable: 'IsPlanarDigraph' must have a value ######## ########> Diff in standard/planar.tst:25 # Input is: D := CompleteDigraph(5); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/planar.tst:27 # Input is: IsPlanarDigraph(D); # Expected output: false # But found: Error, Variable: 'IsPlanarDigraph' must have a value ######## ########> Diff in standard/planar.tst:29 # Input is: D := Digraph([[2, 4, 7, 9, 10], [1, 3, 4, 6, 9, 10], [6, 10], [2, 5, 8, 9], [1, 2, 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10], [3, 4, 5, 6, 9, 10], [3, 4, 5, 7, 9], [2, 3, 5, 6, 7, 8], [3, 5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/planar.tst:33 # Input is: ChromaticNumber(D); # Expected output: 5 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/planar.tst:35 # Input is: IsPlanarDigraph(D); # Expected output: false # But found: Error, Variable: 'IsPlanarDigraph' must have a value ######## ########> Diff in standard/planar.tst:37 # Input is: D := CompleteBipartiteDigraph(3, 3); # Expected output: # But found: Error, Variable: 'CompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/planar.tst:39 # Input is: D := DigraphDisjointUnion(D, D); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/planar.tst:41 # Input is: IsPlanarDigraph(D); # Expected output: false # But found: Error, Variable: 'IsPlanarDigraph' must have a value ######## ########> Diff in standard/planar.tst:45 # Input is: D := Digraph([[2, 4, 7, 9, 10], [1, 3, 4, 6, 9, 10], [6, 10], [2, 5, 8, 9], [1, 2, 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10], [3, 4, 5, 6, 9, 10], [3, 4, 5, 7, 9], [2, 3, 5, 6, 7, 8], [3, 5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/planar.tst:49 # Input is: ChromaticNumber(D); # Expected output: 5 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/planar.tst:51 # Input is: IsPlanarDigraph(D); # Expected output: false # But found: Error, Variable: 'IsPlanarDigraph' must have a value ######## ########> Diff in standard/planar.tst:53 # Input is: IsOuterPlanarDigraph(D); # Expected output: false # But found: Error, Variable: 'IsOuterPlanarDigraph' must have a value ######## ########> Diff in standard/planar.tst:55 # Input is: D := NullDigraph(0); # Expected output: # But found: Error, Variable: 'NullDigraph' must have a value ######## ########> Diff in standard/planar.tst:57 # Input is: IsOuterPlanarDigraph(D); # Expected output: true # But found: Error, Variable: 'IsOuterPlanarDigraph' must have a value ######## ########> Diff in standard/planar.tst:59 # Input is: D := CompleteDigraph(4); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/planar.tst:61 # Input is: IsOuterPlanarDigraph(D); # Expected output: false # But found: Error, Variable: 'IsOuterPlanarDigraph' must have a value ######## ########> Diff in standard/planar.tst:63 # Input is: D := CompleteDigraph(4); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/planar.tst:65 # Input is: ChromaticNumber(D); # Expected output: 4 # But found: Error, Variable: 'ChromaticNumber' must have a value ######## ########> Diff in standard/planar.tst:67 # Input is: IsOuterPlanarDigraph(D); # Expected output: false # But found: Error, Variable: 'IsOuterPlanarDigraph' must have a value ######## ########> Diff in standard/planar.tst:69 # Input is: D := Digraph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], [1, 7, 11], [4, 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/planar.tst:72 # Input is: IsOuterPlanarDigraph(D); # Expected output: false # But found: Error, Variable: 'IsOuterPlanarDigraph' must have a value ######## ########> Diff in standard/planar.tst:74 # Input is: IsPlanarDigraph(D); # Expected output: true # But found: Error, Variable: 'IsPlanarDigraph' must have a value ######## ########> Diff in standard/planar.tst:78 # Input is: D := Digraph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], [1, 7, 11], [4, 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/planar.tst:81 # Input is: PlanarEmbedding(D); # Expected output: [ [ 3, 10, 5 ], [ 10, 8, 9 ], [ 4 ], [ 6 ], [ 11, 7 ], [ 7 ], [ 8 ], [ ], [ 11 ], [ ], [ ] ] # But found: Error, Variable: 'PlanarEmbedding' must have a value ######## ########> Diff in standard/planar.tst:84 # Input is: D := Digraph([[2, 4, 7, 9, 10], [1, 3, 4, 6, 9, 10], [6, 10], [2, 5, 8, 9], [1, 2, 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10], [3, 4, 5, 6, 9, 10], [3, 4, 5, 7, 9], [2, 3, 5, 6, 7, 8], [3, 5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/planar.tst:88 # Input is: IsPlanarDigraph(D); # Expected output: false # But found: Error, Variable: 'IsPlanarDigraph' must have a value ######## ########> Diff in standard/planar.tst:90 # Input is: PlanarEmbedding(D); # Expected output: fail # But found: Error, Variable: 'PlanarEmbedding' must have a value ######## ########> Diff in standard/planar.tst:92 # Input is: D := NullDigraph(0); # Expected output: # But found: Error, Variable: 'NullDigraph' must have a value ######## ########> Diff in standard/planar.tst:94 # Input is: PlanarEmbedding(D); # Expected output: [ ] # But found: Error, Variable: 'PlanarEmbedding' must have a value ######## ########> Diff in standard/planar.tst:96 # Input is: D := List(["D??", "D?_", "D?o", "D?w", "D?{", "DCO", "DCW", "DCc", "DCo", "DCs", "DCw", "DC{", "DEk", "DEo", "DEs", "DEw", "DE{", "DFw", "DF{", "DQg", "DQo", "DQw", "DQ{", "DTk", "DTw", "DT{", "DUW", "DUw", "DU{", "DV{", "D]w", "D]{", "D^{", "D~{"], DigraphFromGraph6String);; # Expected output: # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/planar.tst:100 # Input is: List(D, PlanarEmbedding); # Expected output: [ [ ], [ [ 5 ], [ ], [ ], [ ], [ ] ], [ [ 5 ], [ 5 ], [ ], [ ], [ ] ], [ [ 5 ], [ 5 ], [ 5 ], [ ], [ ] ], [ [ 5 ], [ 5 ], [ 5 ], [ 5 ], [ ] ], [ [ 4 ], [ 5 ], [ ], [ ], [ ] ], [ [ 4 ], [ 5 ], [ 5 ], [ ], [ ] ], [ [ 4, 5 ], [ ], [ ], [ 5 ], [ ] ], [ [ 4, 5 ], [ 5 ], [ ], [ ], [ ] ] , [ [ 4, 5 ], [ 5 ], [ ], [ 5 ], [ ] ], [ [ 4, 5 ], [ 5 ], [ 5 ], [ ], [ ] ], [ [ 4, 5 ], [ 5 ], [ 5 ], [ 5 ], [ ] ], [ [ 4, 5 ], [ 4 ], [ 5 ], [ 5 ], [ ] ], [ [ 4, 5 ], [ 5, 4 ], [ ], [ ], [ ] ], [ [ 4, 5 ], [ 5, 4 ], [ ], [ 5 ], [ ] ], [ [ 4, 5 ], [ 5, 4 ], [ 5 ], [ ], [ ] ], [ [ 4, 5 ], [ 5, 4 ], [ 5 ], [ 5 ], [ ] ], [ [ 4, 5 ], [ 5, 4 ], [ 4, 5 ], [ ], [ ] ], [ [ 4, 5 ], [ 5, 4 ], [ 4, 5 ], [ 5 ], [ ] ], [ [ 3, 5 ], [ 4 ], [ 5 ], [ ], [ ] ], [ [ 3, 5 ], [ 5, 4 ], [ ], [ ], [ ] ], [ [ 3, 5 ], [ 5, 4 ], [ 5 ], [ ], [ ] ], [ [ 3, 5 ], [ 4, 5 ], [ 5 ], [ 5 ], [ ] ], [ [ 3, 5, 4 ], [ ], [ 4, 5 ], [ 5 ], [ ] ], [ [ 3, 5, 4 ], [ 5 ], [ 4, 5 ], [ ], [ ] ], [ [ 3, 5, 4 ], [ 5 ], [ 4, 5 ], [ 5 ], [ ] ], [ [ 3, 4 ], [ 4, 5 ], [ 5 ], [ ], [ ] ], [ [ 3, 5, 4 ], [ 4, 5 ], [ 5 ], [ ], [ ] ], [ [ 3, 5, 4 ], [ 4, 5 ], [ 5 ], [ 5 ], [ ] ], [ [ 3, 5, 4 ], [ 5, 4 ], [ 4, 5 ], [ 5 ], [ ] ], [ [ 3, 5, 4 ], [ 4, 5, 3 ], [ 5 ], [ ], [ ] ], [ [ 3, 5, 4 ], [ 4, 5, 3 ], [ 5 ], [ 5 ], [ ] ], [ [ 3, 5, 4 ], [ 4, 5, 3 ], [ 4, 5 ], [ 5 ], [ ] ], fail ] # But found: Error, Variable: 'D' must have a value ######## ########> Diff in standard/planar.tst:131 # Input is: D := Digraph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], [1, 7, 11], [4, 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/planar.tst:134 # Input is: OuterPlanarEmbedding(D); # Expected output: fail # But found: Error, Variable: 'OuterPlanarEmbedding' must have a value ######## ########> Diff in standard/planar.tst:136 # Input is: D := Digraph([[2, 4, 7, 9, 10], [1, 3, 4, 6, 9, 10], [6, 10], [2, 5, 8, 9], [1, 2, 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10], [3, 4, 5, 6, 9, 10], [3, 4, 5, 7, 9], [2, 3, 5, 6, 7, 8], [3, 5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/planar.tst:140 # Input is: IsOuterPlanarDigraph(D); # Expected output: false # But found: Error, Variable: 'IsOuterPlanarDigraph' must have a value ######## ########> Diff in standard/planar.tst:142 # Input is: OuterPlanarEmbedding(D); # Expected output: fail # But found: Error, Variable: 'OuterPlanarEmbedding' must have a value ######## ########> Diff in standard/planar.tst:144 # Input is: D := NullDigraph(0); # Expected output: # But found: Error, Variable: 'NullDigraph' must have a value ######## ########> Diff in standard/planar.tst:146 # Input is: OuterPlanarEmbedding(D); # Expected output: [ ] # But found: Error, Variable: 'OuterPlanarEmbedding' must have a value ######## ########> Diff in standard/planar.tst:148 # Input is: D := CompleteDigraph(3); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/planar.tst:150 # Input is: OuterPlanarEmbedding(D); # Expected output: [ [ 2, 3 ], [ 3 ], [ ] ] # But found: Error, Variable: 'OuterPlanarEmbedding' must have a value ######## ########> Diff in standard/planar.tst:154 # Input is: D := Digraph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], [1, 7, 11], [4, 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/planar.tst:157 # Input is: SubdigraphHomeomorphicToK4(D); # Expected output: [ [ 3, 5, 10 ], [ 9, 8, 10 ], [ 4 ], [ 6 ], [ 7, 11 ], [ 7 ], [ 8 ], [ ], [ 11 ], [ ], [ ] ] # But found: Error, Variable: 'SubdigraphHomeomorphicToK4' must have a value ######## ########> Diff in standard/planar.tst:160 # Input is: SubdigraphHomeomorphicToK23(D); # Expected output: [ [ 3, 5, 10 ], [ 9, 8, 10 ], [ 4 ], [ 6 ], [ 11 ], [ 7 ], [ 8 ], [ ], [ 11 ], [ ], [ ] ] # But found: Error, Variable: 'SubdigraphHomeomorphicToK23' must have a value ######## ########> Diff in standard/planar.tst:163 # Input is: D := Digraph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], [1, 11], [4, 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/planar.tst:166 # Input is: SubdigraphHomeomorphicToK4(D); # Expected output: fail # But found: Error, Variable: 'SubdigraphHomeomorphicToK4' must have a value ######## ########> Diff in standard/planar.tst:168 # Input is: SubdigraphHomeomorphicToK23(D); # Expected output: [ [ 3, 10, 5 ], [ 10, 8, 9 ], [ 4 ], [ 6 ], [ 11 ], [ 7 ], [ 8 ], [ ], [ 11 ], [ ], [ ] ] # But found: Error, Variable: 'SubdigraphHomeomorphicToK23' must have a value ######## ########> Diff in standard/planar.tst:171 # Input is: SubdigraphHomeomorphicToK33(D); # Expected output: fail # But found: Error, Variable: 'SubdigraphHomeomorphicToK33' must have a value ######## ########> Diff in standard/planar.tst:173 # Input is: SubdigraphHomeomorphicToK23(NullDigraph(0)); # Expected output: fail # But found: Error, Variable: 'SubdigraphHomeomorphicToK23' must have a value ######## ########> Diff in standard/planar.tst:175 # Input is: SubdigraphHomeomorphicToK33(CompleteDigraph(5)); # Expected output: fail # But found: Error, Variable: 'SubdigraphHomeomorphicToK33' must have a value ######## ########> Diff in standard/planar.tst:177 # Input is: SubdigraphHomeomorphicToK33(CompleteBipartiteDigraph(3, 3)); # Expected output: [ [ 4, 6, 5 ], [ 4, 5, 6 ], [ 6, 5, 4 ], [ ], [ ], [ ] ] # But found: Error, Variable: 'SubdigraphHomeomorphicToK33' must have a value ######## ########> Diff in standard/planar.tst:179 # Input is: SubdigraphHomeomorphicToK4(CompleteDigraph(3)); # Expected output: fail # But found: Error, Variable: 'SubdigraphHomeomorphicToK4' must have a value ######## ########> Diff in standard/planar.tst:183 # Input is: D := Digraph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], [1, 7, 11], [4, 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/planar.tst:186 # Input is: KuratowskiPlanarSubdigraph(D); # Expected output: fail # But found: Error, Variable: 'KuratowskiPlanarSubdigraph' must have a value ######## ########> Diff in standard/planar.tst:188 # Input is: D := Digraph([[2, 4, 7, 9, 10], [1, 3, 4, 6, 9, 10], [6, 10], [2, 5, 8, 9], [1, 2, 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10], [3, 4, 5, 6, 9, 10], [3, 4, 5, 7, 9], [2, 3, 5, 6, 7, 8], [3, 5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/planar.tst:192 # Input is: IsPlanarDigraph(D); # Expected output: false # But found: Error, Variable: 'IsPlanarDigraph' must have a value ######## ########> Diff in standard/planar.tst:194 # Input is: KuratowskiPlanarSubdigraph(D); # Expected output: [ [ 2, 9, 7 ], [ 3 ], [ 6 ], [ 5, 9 ], [ 6 ], [ ], [ 4 ], [ 7, 9, 3 ], [ ], [ ] ] # But found: Error, Variable: 'KuratowskiPlanarSubdigraph' must have a value ######## ########> Diff in standard/planar.tst:197 # Input is: D := NullDigraph(0); # Expected output: # But found: Error, Variable: 'NullDigraph' must have a value ######## ########> Diff in standard/planar.tst:199 # Input is: KuratowskiPlanarSubdigraph(D); # Expected output: fail # But found: Error, Variable: 'KuratowskiPlanarSubdigraph' must have a value ######## ########> Diff in standard/planar.tst:203 # Input is: D := Digraph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], [1, 7, 11], [4, 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/planar.tst:206 # Input is: KuratowskiOuterPlanarSubdigraph(D); # Expected output: [ [ 3, 5, 10 ], [ 9, 8, 10 ], [ 4 ], [ 6 ], [ 11 ], [ 7 ], [ 8 ], [ ], [ 11 ], [ ], [ ] ] # But found: Error, Variable: 'KuratowskiOuterPlanarSubdigraph' must have a value ######## ########> Diff in standard/planar.tst:209 # Input is: D := Digraph([[2, 4, 7, 9, 10], [1, 3, 4, 6, 9, 10], [6, 10], [2, 5, 8, 9], [1, 2, 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10], [3, 4, 5, 6, 9, 10], [3, 4, 5, 7, 9], [2, 3, 5, 6, 7, 8], [3, 5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/planar.tst:213 # Input is: IsOuterPlanarDigraph(D); # Expected output: false # But found: Error, Variable: 'IsOuterPlanarDigraph' must have a value ######## ########> Diff in standard/planar.tst:215 # Input is: KuratowskiOuterPlanarSubdigraph(D); # Expected output: [ [ ], [ ], [ ], [ 8, 9 ], [ ], [ ], [ 9, 4 ], [ 7, 9 ], [ ], [ ] ] # But found: Error, Variable: 'KuratowskiOuterPlanarSubdigraph' must have a value ######## ########> Diff in standard/planar.tst:217 # Input is: D := NullDigraph(0); # Expected output: # But found: Error, Variable: 'NullDigraph' must have a value ######## ########> Diff in standard/planar.tst:219 # Input is: KuratowskiOuterPlanarSubdigraph(D); # Expected output: fail # But found: Error, Variable: 'KuratowskiOuterPlanarSubdigraph' must have a value ######## ########> Diff in standard/planar.tst:221 # Input is: D := CompleteDigraph(3); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/planar.tst:223 # Input is: KuratowskiOuterPlanarSubdigraph(D); # Expected output: fail # But found: Error, Variable: 'KuratowskiOuterPlanarSubdigraph' must have a value ######## ########> Diff in standard/planar.tst:227 # Input is: IS_PLANAR(2); # Expected output: Error, Digraphs: boyers_planarity_check (C): the 1st argument must be a digrap\ \ h, not integer # But found: Error, Variable: 'IS_PLANAR' must have a value ######## ########> Diff in standard/planar.tst:230 # Input is: IS_PLANAR(NullDigraph(0)); # Expected output: Error, Digraphs: boyers_planarity_check (C): invalid number of nodes! # But found: Error, Variable: 'IS_PLANAR' must have a value ######## ########> Diff in standard/planar.tst:232 # Input is: IS_PLANAR(NullDigraph(70000)); # Expected output: Error, Digraphs: boyers_planarity_check (C): invalid number of edges! # But found: Error, Variable: 'IS_PLANAR' must have a value ######## ########> Diff in standard/planar.tst:234 # Input is: IsPlanarDigraph(NullDigraph(70000)); # Expected output: true # But found: Error, Variable: 'IsPlanarDigraph' must have a value ######## ########> Diff in standard/planar.tst:236 # Input is: IS_PLANAR(CompleteDigraph(2)); # Expected output: Error, Digraphs: boyers_planarity_check (C): the 1st argument must be an antis\ \ ymmetric digraph # But found: Error, Variable: 'IS_PLANAR' must have a value ######## ########> Diff in standard/planar.tst:241 # Input is: DIGRAPHS_StopTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StopTest' must have a value ######## Digraphs package: standard/planar.tst msecs: 113 false gap> ########> Diff in standard/prop.tst:15 # Input is: DIGRAPHS_StartTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StartTest' must have a value ######## ########> Diff in standard/prop.tst:18 # Input is: IsChainDigraph(ChainDigraph(1)); # Expected output: true # But found: Error, Variable: 'IsChainDigraph' must have a value ######## ########> Diff in standard/prop.tst:20 # Input is: IsChainDigraph(ChainDigraph(7)); # Expected output: true # But found: Error, Variable: 'IsChainDigraph' must have a value ######## ########> Diff in standard/prop.tst:22 # Input is: IsChainDigraph(CycleDigraph(1)); # Expected output: false # But found: Error, Variable: 'IsChainDigraph' must have a value ######## ########> Diff in standard/prop.tst:24 # Input is: IsChainDigraph(CycleDigraph(7)); # Expected output: false # But found: Error, Variable: 'IsChainDigraph' must have a value ######## ########> Diff in standard/prop.tst:26 # Input is: IsChainDigraph(Digraph([[2], [3], [4], [5], [5]])); # Expected output: false # But found: Error, Variable: 'IsChainDigraph' must have a value ######## ########> Diff in standard/prop.tst:28 # Input is: IsChainDigraph(Digraph([[2, 3], [4], [5], [], []])); # Expected output: false # But found: Error, Variable: 'IsChainDigraph' must have a value ######## ########> Diff in standard/prop.tst:30 # Input is: IsChainDigraph(Digraph([[2], [3, 4], [], []])); # Expected output: false # But found: Error, Variable: 'IsChainDigraph' must have a value ######## ########> Diff in standard/prop.tst:34 # Input is: IsChainDigraph(CayleyDigraph(G)); # Expected output: false # But found: Error, Variable: 'IsChainDigraph' must have a value ######## ########> Diff in standard/prop.tst:36 # Input is: IsChainDigraph(DigraphReverse(ChainDigraph(21))); # Expected output: true # But found: Error, Variable: 'IsChainDigraph' must have a value ######## ########> Diff in standard/prop.tst:38 # Input is: IsChainDigraph(Digraph([[], [3], [4], []])); # Expected output: false # But found: Error, Variable: 'IsChainDigraph' must have a value ######## ########> Diff in standard/prop.tst:40 # Input is: IsChainDigraph(Digraph([[2], [3], [4], []])); # Expected output: true # But found: Error, Variable: 'IsChainDigraph' must have a value ######## ########> Diff in standard/prop.tst:44 # Input is: gr1 := Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:46 # Input is: IsMultiDigraph(gr1); # Expected output: false # But found: Error, Variable: 'IsMultiDigraph' must have a value ######## ########> Diff in standard/prop.tst:48 # Input is: gr2 := Digraph([[]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:50 # Input is: IsMultiDigraph(gr2); # Expected output: false # But found: Error, Variable: 'IsMultiDigraph' must have a value ######## ########> Diff in standard/prop.tst:55 # Input is: gr3 := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:57 # Input is: IsMultiDigraph(gr3); # Expected output: false # But found: Error, Variable: 'IsMultiDigraph' must have a value ######## ########> Diff in standard/prop.tst:62 # Input is: gr4 := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:64 # Input is: IsMultiDigraph(gr4); # Expected output: true # But found: Error, Variable: 'IsMultiDigraph' must have a value ######## ########> Diff in standard/prop.tst:68 # Input is: D := Digraph([[2], [1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:69 # Input is: IsStronglyConnectedDigraph(D);; # Expected output: # But found: Error, Variable: 'IsStronglyConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:70 # Input is: IsAcyclicDigraph(D); # Expected output: false # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:72 # Input is: loop := Digraph([[1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:74 # Input is: IsMultiDigraph(loop); # Expected output: false # But found: Error, Variable: 'IsMultiDigraph' must have a value ######## ########> Diff in standard/prop.tst:76 # Input is: IsAcyclicDigraph(loop); # Expected output: false # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:79 # Input is: multiple := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:81 # Input is: IsMultiDigraph(multiple); # Expected output: true # But found: Error, Variable: 'IsMultiDigraph' must have a value ######## ########> Diff in standard/prop.tst:83 # Input is: IsAcyclicDigraph(multiple); # Expected output: true # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:92 # Input is: complete100 := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:94 # Input is: IsMultiDigraph(complete100); # Expected output: false # But found: Error, Variable: 'IsMultiDigraph' must have a value ######## ########> Diff in standard/prop.tst:96 # Input is: IsAcyclicDigraph(complete100); # Expected output: false # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:113 # Input is: circuit := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:115 # Input is: IsMultiDigraph(circuit); # Expected output: false # But found: Error, Variable: 'IsMultiDigraph' must have a value ######## ########> Diff in standard/prop.tst:117 # Input is: IsAcyclicDigraph(circuit); # Expected output: true # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:122 # Input is: grid := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:124 # Input is: IsMultiDigraph(grid); # Expected output: true # But found: Error, Variable: 'IsMultiDigraph' must have a value ######## ########> Diff in standard/prop.tst:126 # Input is: IsAcyclicDigraph(grid); # Expected output: true # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:128 # Input is: gr := Digraph([[1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:129 # Input is: DigraphHasLoops(gr); # Expected output: true # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/prop.tst:131 # Input is: HasIsAcyclicDigraph(gr); # Expected output: false # But found: Error, Variable: 'HasIsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:133 # Input is: IsAcyclicDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:135 # Input is: gr := Digraph([[2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:137 # Input is: IsTournament(gr); # Expected output: true # But found: Error, Variable: 'IsTournament' must have a value ######## ########> Diff in standard/prop.tst:139 # Input is: IsTransitiveDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsTransitiveDigraph' must have a value ######## ########> Diff in standard/prop.tst:141 # Input is: HasIsAcyclicDigraph(gr); # Expected output: true # But found: Error, Variable: 'HasIsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:143 # Input is: IsAcyclicDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:145 # Input is: gr := Digraph([[2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:147 # Input is: DigraphStronglyConnectedComponents(gr); # Expected output: rec( comps := [ [ 2 ], [ 1 ] ], id := [ 2, 1 ] ) # But found: Error, Variable: 'DigraphStronglyConnectedComponents' must have a value ######## ########> Diff in standard/prop.tst:149 # Input is: IsAcyclicDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:151 # Input is: gr := Digraph([[1, 2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:153 # Input is: DigraphStronglyConnectedComponents(gr); # Expected output: rec( comps := [ [ 2 ], [ 1 ] ], id := [ 2, 1 ] ) # But found: Error, Variable: 'DigraphStronglyConnectedComponents' must have a value ######## ########> Diff in standard/prop.tst:155 # Input is: IsAcyclicDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:157 # Input is: gr := Digraph([[2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:159 # Input is: DigraphStronglyConnectedComponents(gr); # Expected output: rec( comps := [ [ 1, 2 ] ], id := [ 1, 1 ] ) # But found: Error, Variable: 'DigraphStronglyConnectedComponents' must have a value ######## ########> Diff in standard/prop.tst:161 # Input is: IsAcyclicDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:163 # Input is: gr := Digraph([ [9, 10], [8], [4], [1, 7, 8], [], [5], [], [6], [], [4, 8]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:166 # Input is: DigraphTopologicalSort(gr); # Expected output: fail # But found: Error, Variable: 'DigraphTopologicalSort' must have a value ######## ########> Diff in standard/prop.tst:168 # Input is: HasIsAcyclicDigraph(gr); # Expected output: false # But found: Error, Variable: 'HasIsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:170 # Input is: IsAcyclicDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:174 # Input is: IsFunctionalDigraph(multiple); # Expected output: false # But found: Error, Variable: 'IsFunctionalDigraph' must have a value ######## ########> Diff in standard/prop.tst:176 # Input is: IsFunctionalDigraph(grid); # Expected output: false # But found: Error, Variable: 'IsFunctionalDigraph' must have a value ######## ########> Diff in standard/prop.tst:178 # Input is: IsFunctionalDigraph(circuit); # Expected output: false # But found: Error, Variable: 'IsFunctionalDigraph' must have a value ######## ########> Diff in standard/prop.tst:180 # Input is: IsFunctionalDigraph(loop); # Expected output: true # But found: Error, Variable: 'IsFunctionalDigraph' must have a value ######## ########> Diff in standard/prop.tst:182 # Input is: gr := Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:184 # Input is: IsFunctionalDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsFunctionalDigraph' must have a value ######## ########> Diff in standard/prop.tst:195 # Input is: g1 := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:197 # Input is: IsFunctionalDigraph(g1); # Expected output: false # But found: Error, Variable: 'IsFunctionalDigraph' must have a value ######## ########> Diff in standard/prop.tst:199 # Input is: g2 := Digraph(OutNeighbours(g1)); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:201 # Input is: IsFunctionalDigraph(g2); # Expected output: false # But found: Error, Variable: 'IsFunctionalDigraph' must have a value ######## ########> Diff in standard/prop.tst:203 # Input is: g3 := Digraph([[1], [3], [2], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:205 # Input is: IsFunctionalDigraph(g3); # Expected output: true # But found: Error, Variable: 'IsFunctionalDigraph' must have a value ######## ########> Diff in standard/prop.tst:207 # Input is: g4 := Digraph(rec(DigraphVertices := [1 .. 3], DigraphSource := [3, 2, 1], DigraphRange := [2, 1, 3])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:210 # Input is: IsFunctionalDigraph(g4); # Expected output: true # But found: Error, Variable: 'IsFunctionalDigraph' must have a value ######## ########> Diff in standard/prop.tst:212 # Input is: g5 := Digraph(rec(DigraphVertices := [1 .. 3], DigraphSource := [3, 2, 2], DigraphRange := [2, 1, 3])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:215 # Input is: IsFunctionalDigraph(g5); # Expected output: false # But found: Error, Variable: 'IsFunctionalDigraph' must have a value ######## ########> Diff in standard/prop.tst:219 # Input is: IsSymmetricDigraph(g1); # Expected output: false # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/prop.tst:221 # Input is: IsSymmetricDigraph(g2); # Expected output: false # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/prop.tst:223 # Input is: IsSymmetricDigraph(g3); # Expected output: false # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/prop.tst:225 # Input is: IsSymmetricDigraph(g4); # Expected output: false # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/prop.tst:227 # Input is: IsSymmetricDigraph(g5); # Expected output: false # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/prop.tst:229 # Input is: IsSymmetricDigraph(loop); # Expected output: true # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/prop.tst:231 # Input is: IsSymmetricDigraph(multiple); # Expected output: false # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/prop.tst:233 # Input is: g6 := Digraph([[1, 2, 4], [1, 3], [2, 3, 4], [3, 1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:235 # Input is: IsSymmetricDigraph(g6); # Expected output: true # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/prop.tst:237 # Input is: gr := Digraph(rec(DigraphNrVertices := 3, DigraphSource := [1, 1, 2, 2, 2, 2, \ 3, 3], DigraphRange := [2, 2, 1, 1, 3, 3, 2, 2]));; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:239 # Input is: IsSymmetricDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsSymmetricDigraph' must have a value ######## ########> Diff in standard/prop.tst:243 # Input is: gr := Digraph(rec(DigraphNrVertices := 10, DigraphSource := [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, \ 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10], DigraphRange := [2, 4, 6, 10, 3, 5, 7, 4, 7, 1, 9, 10, 4, 6, 9, 8, 4, 3, 7, 1,\ 6, 8, 2, 3, 9, 7, 10, 9, 4, 1, 8, 9, 3, 1, 4, 2, 5, 2, 1, 10, 5, 6, 2, 4, 8])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:249 # Input is: IsAntisymmetricDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsAntisymmetricDigraph' must have a value ######## ########> Diff in standard/prop.tst:251 # Input is: gr := Digraph([[1, 1, 1, 2, 2], [2, 3], [3, 3, 4], [4, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:253 # Input is: IsAntisymmetricDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsAntisymmetricDigraph' must have a value ######## ########> Diff in standard/prop.tst:255 # Input is: gr := Digraph([[1, 1, 1, 2, 2], [2, 3], [3, 3, 4], [4, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:257 # Input is: IsAntisymmetricDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsAntisymmetricDigraph' must have a value ######## ########> Diff in standard/prop.tst:259 # Input is: gr := Digraph([[2, 3], [3], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:261 # Input is: IsAntisymmetricDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsAntisymmetricDigraph' must have a value ######## ########> Diff in standard/prop.tst:263 # Input is: gr := Digraph([[2], [3], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:265 # Input is: IsAntisymmetricDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsAntisymmetricDigraph' must have a value ######## ########> Diff in standard/prop.tst:267 # Input is: gr := Digraph([[1, 1, 1, 1, 2], [2, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:269 # Input is: IsAntisymmetricDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsAntisymmetricDigraph' must have a value ######## ########> Diff in standard/prop.tst:271 # Input is: gr := Digraph([[1, 1, 1, 1, 2], [2, 2, 2, 1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:273 # Input is: IsAntisymmetricDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsAntisymmetricDigraph' must have a value ######## ########> Diff in standard/prop.tst:277 # Input is: gr1 := Digraph(rec(DigraphNrVertices := 5, DigraphSource := [], DigraphRange :\ = []));; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:278 # Input is: IsEmptyDigraph(gr1); # Expected output: true # But found: Error, Variable: 'IsEmptyDigraph' must have a value ######## ########> Diff in standard/prop.tst:280 # Input is: gr2 := Digraph(rec(DigraphVertices := [1 .. 6], DigraphSource := [6], DigraphRange :=\ [1]));; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:282 # Input is: IsEmptyDigraph(gr2); # Expected output: false # But found: Error, Variable: 'IsEmptyDigraph' must have a value ######## ########> Diff in standard/prop.tst:284 # Input is: gr3 := DigraphNC([[], [], [], []]);; # Expected output: # But found: Error, Variable: 'DigraphNC' must have a value ######## ########> Diff in standard/prop.tst:285 # Input is: IsEmptyDigraph(gr3); # Expected output: true # But found: Error, Variable: 'IsEmptyDigraph' must have a value ######## ########> Diff in standard/prop.tst:287 # Input is: gr4 := DigraphNC([[], [3], [1]]);; # Expected output: # But found: Error, Variable: 'DigraphNC' must have a value ######## ########> Diff in standard/prop.tst:288 # Input is: IsEmptyDigraph(gr4); # Expected output: false # But found: Error, Variable: 'IsEmptyDigraph' must have a value ######## ########> Diff in standard/prop.tst:290 # Input is: gr5 := DigraphByAdjacencyMatrix([[0, 0], [0, 0]]); # Expected output: # But found: Error, Variable: 'DigraphByAdjacencyMatrix' must have a value ######## ########> Diff in standard/prop.tst:292 # Input is: IsEmptyDigraph(gr5); # Expected output: true # But found: Error, Variable: 'IsEmptyDigraph' must have a value ######## ########> Diff in standard/prop.tst:294 # Input is: gr6 := DigraphByEdges([[3, 5], [1, 1], [2, 3], [5, 4]]); # Expected output: # But found: Error, Variable: 'DigraphByEdges' must have a value ######## ########> Diff in standard/prop.tst:296 # Input is: IsEmptyDigraph(gr6); # Expected output: false # But found: Error, Variable: 'IsEmptyDigraph' must have a value ######## ########> Diff in standard/prop.tst:300 # Input is: gr := Digraph(rec( DigraphNrVertices := 2, DigraphSource := [1, 1], DigraphRange := [2, 2])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:303 # Input is: IsTournament(gr); # Expected output: false # But found: Error, Variable: 'IsTournament' must have a value ######## ########> Diff in standard/prop.tst:305 # Input is: gr := Digraph([[2], [1], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:307 # Input is: IsTournament(gr); # Expected output: false # But found: Error, Variable: 'IsTournament' must have a value ######## ########> Diff in standard/prop.tst:309 # Input is: gr := Digraph([[2, 3], [3], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:311 # Input is: IsAcyclicDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:313 # Input is: IsTournament(gr); # Expected output: true # But found: Error, Variable: 'IsTournament' must have a value ######## ########> Diff in standard/prop.tst:315 # Input is: gr := EmptyDigraph(0);; # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/prop.tst:316 # Input is: IsTournament(gr); # Expected output: true # But found: Error, Variable: 'IsTournament' must have a value ######## ########> Diff in standard/prop.tst:318 # Input is: gr := Digraph([[1], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:320 # Input is: IsTournament(gr); # Expected output: false # But found: Error, Variable: 'IsTournament' must have a value ######## ########> Diff in standard/prop.tst:322 # Input is: gr := EmptyDigraph(1); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/prop.tst:324 # Input is: HasIsTournament(gr); # Expected output: false # But found: Error, Variable: 'HasIsTournament' must have a value ######## ########> Diff in standard/prop.tst:326 # Input is: IsTournament(gr); # Expected output: true # But found: Error, Variable: 'IsTournament' must have a value ######## ########> Diff in standard/prop.tst:328 # Input is: gr := Digraph([[2], [3], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:330 # Input is: IsTournament(gr); # Expected output: true # But found: Error, Variable: 'IsTournament' must have a value ######## ########> Diff in standard/prop.tst:332 # Input is: gr := Digraph([[2], [1], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:334 # Input is: IsTournament(gr); # Expected output: false # But found: Error, Variable: 'IsTournament' must have a value ######## ########> Diff in standard/prop.tst:338 # Input is: gr := Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:340 # Input is: IsStronglyConnectedDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsStronglyConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:345 # Input is: gr := Digraph(adj); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:347 # Input is: IsStronglyConnectedDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsStronglyConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:349 # Input is: IsStronglyConnectedDigraph(multiple); # Expected output: false # But found: Error, Variable: 'IsStronglyConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:351 # Input is: IsStronglyConnectedDigraph(grid); # Expected output: false # But found: Error, Variable: 'IsStronglyConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:353 # Input is: IsStronglyConnectedDigraph(circuit); # Expected output: false # But found: Error, Variable: 'IsStronglyConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:355 # Input is: IsStronglyConnectedDigraph(loop); # Expected output: true # But found: Error, Variable: 'IsStronglyConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:360 # Input is: gr := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:362 # Input is: IsStronglyConnectedDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsStronglyConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:364 # Input is: gr := CycleDigraph(10000);; # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/prop.tst:365 # Input is: gr2 := DigraphRemoveEdge(gr, 10000, 1); # Expected output: # But found: Error, Variable: 'DigraphRemoveEdge' must have a value ######## ########> Diff in standard/prop.tst:367 # Input is: IsStronglyConnectedDigraph(gr2); # Expected output: false # But found: Error, Variable: 'IsStronglyConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:369 # Input is: gr2 := DigraphRemoveEdge(gr, 10000, 1); # Expected output: # But found: Error, Variable: 'DigraphRemoveEdge' must have a value ######## ########> Diff in standard/prop.tst:371 # Input is: IsAcyclicDigraph(gr2); # Expected output: true # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:373 # Input is: IsStronglyConnectedDigraph(gr2); # Expected output: false # But found: Error, Variable: 'IsStronglyConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:375 # Input is: gr := Digraph([[2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:377 # Input is: HasIsAcyclicDigraph(gr); # Expected output: false # But found: Error, Variable: 'HasIsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:379 # Input is: IsTournament(gr); # Expected output: true # But found: Error, Variable: 'IsTournament' must have a value ######## ########> Diff in standard/prop.tst:381 # Input is: HasIsAcyclicDigraph(gr); # Expected output: false # But found: Error, Variable: 'HasIsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:383 # Input is: IsTransitiveDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsTransitiveDigraph' must have a value ######## ########> Diff in standard/prop.tst:385 # Input is: HasIsAcyclicDigraph(gr); # Expected output: true # But found: Error, Variable: 'HasIsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:387 # Input is: IsAcyclicDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:389 # Input is: HasIsStronglyConnectedDigraph(gr); # Expected output: false # But found: Error, Variable: 'HasIsStronglyConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:391 # Input is: IsStronglyConnectedDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsStronglyConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:398 # Input is: gr := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:400 # Input is: IsReflexiveDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsReflexiveDigraph' must have a value ######## ########> Diff in standard/prop.tst:405 # Input is: gr := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:407 # Input is: IsReflexiveDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsReflexiveDigraph' must have a value ######## ########> Diff in standard/prop.tst:412 # Input is: gr := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:414 # Input is: IsReflexiveDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsReflexiveDigraph' must have a value ######## ########> Diff in standard/prop.tst:416 # Input is: gr := EmptyDigraph(0); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/prop.tst:418 # Input is: IsReflexiveDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsReflexiveDigraph' must have a value ######## ########> Diff in standard/prop.tst:420 # Input is: gr := Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:422 # Input is: HasIsAcyclicDigraph(gr) and IsAcyclicDigraph(gr); # Expected output: true # But found: Error, Variable: 'HasIsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:424 # Input is: IsReflexiveDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsReflexiveDigraph' must have a value ######## ########> Diff in standard/prop.tst:426 # Input is: HasIsAcyclicDigraph(gr); # Expected output: true # But found: Error, Variable: 'HasIsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:428 # Input is: IsAcyclicDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:430 # Input is: gr := Digraph([]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:431 # Input is: IsAcyclicDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsAcyclicDigraph' must have a value ######## ########> Diff in standard/prop.tst:434 # Input is: gr := Digraph(adj); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:436 # Input is: IsReflexiveDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsReflexiveDigraph' must have a value ######## ########> Diff in standard/prop.tst:439 # Input is: gr := Digraph(adj); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:441 # Input is: IsReflexiveDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsReflexiveDigraph' must have a value ######## ########> Diff in standard/prop.tst:444 # Input is: gr := DigraphByAdjacencyMatrix(mat); # Expected output: # But found: Error, Variable: 'DigraphByAdjacencyMatrix' must have a value ######## ########> Diff in standard/prop.tst:446 # Input is: IsReflexiveDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsReflexiveDigraph' must have a value ######## ########> Diff in standard/prop.tst:449 # Input is: gr := DigraphByAdjacencyMatrix(mat); # Expected output: # But found: Error, Variable: 'DigraphByAdjacencyMatrix' must have a value ######## ########> Diff in standard/prop.tst:451 # Input is: IsReflexiveDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsReflexiveDigraph' must have a value ######## ########> Diff in standard/prop.tst:455 # Input is: gr := Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:457 # Input is: IsCompleteDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsCompleteDigraph' must have a value ######## ########> Diff in standard/prop.tst:459 # Input is: gr := Digraph([[2, 2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:461 # Input is: IsCompleteDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsCompleteDigraph' must have a value ######## ########> Diff in standard/prop.tst:463 # Input is: gr := Digraph([[1, 2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:465 # Input is: IsCompleteDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsCompleteDigraph' must have a value ######## ########> Diff in standard/prop.tst:467 # Input is: gr := Digraph([[1, 2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:469 # Input is: IsCompleteDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsCompleteDigraph' must have a value ######## ########> Diff in standard/prop.tst:471 # Input is: gr := Digraph([[2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:473 # Input is: IsCompleteDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsCompleteDigraph' must have a value ######## ########> Diff in standard/prop.tst:477 # Input is: gr := Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:479 # Input is: IsConnectedDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:481 # Input is: gr := Digraph([[]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:483 # Input is: IsConnectedDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:485 # Input is: gr := Digraph([[1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:487 # Input is: IsConnectedDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:489 # Input is: gr := Digraph([[1, 1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:491 # Input is: IsConnectedDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:493 # Input is: gr := Digraph([[1], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:495 # Input is: IsStronglyConnectedDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsStronglyConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:497 # Input is: IsConnectedDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:499 # Input is: gr := Digraph([[2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:501 # Input is: IsStronglyConnectedDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsStronglyConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:503 # Input is: IsConnectedDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:505 # Input is: gr := Digraph([[2], [3], [], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:507 # Input is: IsConnectedDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:509 # Input is: gr := Digraph([[2], [3], [], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:511 # Input is: IsConnectedDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:515 # Input is: gr := Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:517 # Input is: DigraphHasLoops(gr); # Expected output: false # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/prop.tst:519 # Input is: gr := Digraph([[]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:521 # Input is: DigraphHasLoops(gr); # Expected output: false # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/prop.tst:523 # Input is: gr := Digraph([[1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:525 # Input is: DigraphHasLoops(gr); # Expected output: true # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/prop.tst:527 # Input is: gr := Digraph([[6, 7], [6, 9], [1, 2, 4, 5, 8, 9], [1, 2, 3, 4, 5, 6, 7, 10], [1, 5, 6, 7, 10], [2, 4, 5, 9, 10], [3, 4, 5, 6, 7, 8, 9, 10], [1, 3, 5, 7, 8, 9], [1, 2, 5], [1, 2, 4, 6, 7, 8]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:532 # Input is: DigraphHasLoops(gr); # Expected output: true # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/prop.tst:534 # Input is: gr := Digraph([[6, 7], [6, 9], [1, 2, 4, 5, 8, 9], [1, 2, 3, 7, 5, 6, 7, 10], [1, 2, 2, 6, 7, 10], [2, 4, 5, 9, 10], [3, 4, 5, 6, 8, 8, 9, 10], [1, 1, 3, 5, 7, 6, 9], [1, 1, 1, 2, 5], [1, 2, 4, 6, 7, 8]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:539 # Input is: DigraphHasLoops(gr); # Expected output: false # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/prop.tst:541 # Input is: gr := Digraph(rec(DigraphNrVertices := 0, DigraphSource := [], DigraphRange :=\ [])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:543 # Input is: DigraphHasLoops(gr); # Expected output: false # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/prop.tst:545 # Input is: gr := Digraph(rec(DigraphNrVertices := 1, DigraphSource := [], DigraphRange :=\ [])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:547 # Input is: DigraphHasLoops(gr); # Expected output: false # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/prop.tst:549 # Input is: gr := Digraph(rec(DigraphNrVertices := 1, DigraphSource := [1], DigraphRange :\ = [1])); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:551 # Input is: DigraphHasLoops(gr); # Expected output: true # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/prop.tst:561 # Input is: gr := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:563 # Input is: DigraphHasLoops(gr); # Expected output: true # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/prop.tst:565 # Input is: gr := Digraph(r);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:566 # Input is: AdjacencyMatrix(gr);; # Expected output: # But found: Error, Variable: 'AdjacencyMatrix' must have a value ######## ########> Diff in standard/prop.tst:567 # Input is: DigraphHasLoops(gr); # Expected output: true # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/prop.tst:578 # Input is: gr := Digraph(r); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:580 # Input is: DigraphHasLoops(gr); # Expected output: false # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/prop.tst:582 # Input is: gr := Digraph(r);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:583 # Input is: AdjacencyMatrix(gr);; # Expected output: # But found: Error, Variable: 'AdjacencyMatrix' must have a value ######## ########> Diff in standard/prop.tst:584 # Input is: DigraphHasLoops(gr); # Expected output: false # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/prop.tst:588 # Input is: gr := Digraph([[2], [3], [4], [5], [6], [1], [8], [7]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:590 # Input is: IsAperiodicDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsAperiodicDigraph' must have a value ######## ########> Diff in standard/prop.tst:592 # Input is: gr := Digraph([[1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:594 # Input is: IsAperiodicDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsAperiodicDigraph' must have a value ######## ########> Diff in standard/prop.tst:596 # Input is: gr := Digraph([[2, 2], [3, 3], [1], [5], [4, 4, 4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:598 # Input is: IsAperiodicDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsAperiodicDigraph' must have a value ######## ########> Diff in standard/prop.tst:600 # Input is: gr := Digraph([[2, 2], [3, 3], [4], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:602 # Input is: IsAperiodicDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsAperiodicDigraph' must have a value ######## ########> Diff in standard/prop.tst:606 # Input is: gr := Digraph([[2, 3, 4], [3, 4], [4], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:608 # Input is: IsTransitiveDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsTransitiveDigraph' must have a value ######## ########> Diff in standard/prop.tst:610 # Input is: gr := Digraph([[2, 3, 4], [3, 4, 1], [4], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:612 # Input is: IsTransitiveDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsTransitiveDigraph' must have a value ######## ########> Diff in standard/prop.tst:614 # Input is: gr := Digraph([[1, 1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:616 # Input is: IsTransitiveDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsTransitiveDigraph' must have a value ######## ########> Diff in standard/prop.tst:618 # Input is: gr := Digraph([[2, 2], [1, 1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:619 # Input is: IsTransitiveDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsTransitiveDigraph' must have a value ######## ########> Diff in standard/prop.tst:621 # Input is: gr := Digraph([[1, 2, 2], [1, 2]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:622 # Input is: IsTransitiveDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsTransitiveDigraph' must have a value ######## ########> Diff in standard/prop.tst:624 # Input is: gr := Digraph( [[2, 4, 5, 7], [4, 6, 9, 10, 12, 14], [2, 5, 6, 7, 8], [9], [2, 7, 10, 11, 12], [4, 9, 13, 16, 18, 19, 22, 23, 26, 28, 30], [2, 4, 6, 10], [2, 4, 11], [], [4, 9, 13, 15, 19, 21, 22, 24], [2, 4, 14], [4, 9, 15, 17, 20, 21, 24, 25, 27, 29, 31], [4, 9], [4, 9, 16, 17, 18, 20, 23, 25, 26, 27, 28, 29, 30, 31], [4, 9], [4], [4], [4], [4, 9], [4], [4, 9], [4, 9], [4], [4, 9], [4], [4], [4], [4], [4, 29], [4], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:633 # Input is: IsTransitiveDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsTransitiveDigraph' must have a value ######## ########> Diff in standard/prop.tst:635 # Input is: trans := Digraph([ [2, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [4, 6, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [9], [2, 4, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [4, 9, 13, 16, 18, 19, 22, 23, 26, 28, 30], [2, 4, 6, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [2, 4, 6, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [], [4, 9, 13, 15, 19, 21, 22, 24], [2, 4, 6, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [4, 9, 15, 17, 20, 21, 24, 25, 27, 29, 31], [4, 9], [4, 9, 16, 17, 18, 20, 23, 25, 26, 27, 28, 29, 30, 31], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:661 # Input is: IsTransitiveDigraph(trans); # Expected output: true # But found: Error, Variable: 'IsTransitiveDigraph' must have a value ######## ########> Diff in standard/prop.tst:663 # Input is: nottrans := Digraph([ [2, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [4, 6, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [9], [2, 4, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [4, 9, 13, 16, 18, 19, 22, 23, 26, 28, 30], [2, 4, 6, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [2, 4, 6, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [], [4, 9, 13, 15, 19, 21, 22, 24], [2, 4, 6, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [4, 9, 15, 17, 20, 21, 24, 25, 27, 29, 31], [4, 9], [4, 9, 16, 17, 18, 20, 23, 20, 25, 26, 27, 28, 29, 30, 31], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9], [4, 9]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:689 # Input is: IsTransitiveDigraph(nottrans); # Expected output: false # But found: Error, Variable: 'IsTransitiveDigraph' must have a value ######## ########> Diff in standard/prop.tst:691 # Input is: gr := Digraph([[2, 3, 3], [3, 3], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:692 # Input is: IsTransitiveDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsTransitiveDigraph' must have a value ######## ########> Diff in standard/prop.tst:694 # Input is: IS_TRANSITIVE_DIGRAPH(gr); # Expected output: true # But found: Error, Variable: 'IS_TRANSITIVE_DIGRAPH' must have a value ######## ########> Diff in standard/prop.tst:698 # Input is: gr := Digraph([[2, 4], [], [1], [1], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:700 # Input is: IsBipartiteDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:702 # Input is: gr := Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:704 # Input is: IsBipartiteDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:706 # Input is: gr := CycleDigraph(89); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/prop.tst:708 # Input is: IsBipartiteDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:710 # Input is: gr := CycleDigraph(314); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/prop.tst:712 # Input is: IsBipartiteDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:714 # Input is: gr := CompleteDigraph(4); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/prop.tst:716 # Input is: IsBipartiteDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:718 # Input is: gr := Digraph([[2, 4], [], [1], [1], [4], [7], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:720 # Input is: IsBipartiteDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:722 # Input is: gr := Digraph([[2], [3], [1], [6], [6], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:724 # Input is: IsBipartiteDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:726 # Input is: gr := Digraph([[1], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:728 # Input is: IsBipartiteDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:730 # Input is: gr := Digraph([[3], [2], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:732 # Input is: IsBipartiteDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:734 # Input is: gr := Digraph([[3], [3], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:736 # Input is: IsBipartiteDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:738 # Input is: gr := Digraph([[2, 3, 4], [5, 6], [], [7], [], [], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:740 # Input is: IsBipartiteDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:742 # Input is: gr := Digraph([[2, 3, 4], [5, 6], [], [7], [], [], [], [9], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:744 # Input is: IsBipartiteDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:746 # Input is: gr := Digraph([[1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:748 # Input is: DigraphHasLoops(gr); # Expected output: true # But found: Error, Variable: 'DigraphHasLoops' must have a value ######## ########> Diff in standard/prop.tst:750 # Input is: IsBipartiteDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:752 # Input is: D := Digraph([[4, 6, 8], [], [], [], [7], [2], [], [], [8], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:754 # Input is: IsBipartiteDigraph(D); # Expected output: true # But found: Error, Variable: 'IsBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:758 # Input is: gr := Digraph([[1, 2, 3, 4], [], [], []]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:759 # Input is: IsInRegularDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsInRegularDigraph' must have a value ######## ########> Diff in standard/prop.tst:761 # Input is: IsOutRegularDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsOutRegularDigraph' must have a value ######## ########> Diff in standard/prop.tst:763 # Input is: gr := CompleteDigraph(4);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/prop.tst:764 # Input is: IsInRegularDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsInRegularDigraph' must have a value ######## ########> Diff in standard/prop.tst:766 # Input is: IsOutRegularDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsOutRegularDigraph' must have a value ######## ########> Diff in standard/prop.tst:768 # Input is: gr := CompleteDigraph(4);; # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/prop.tst:769 # Input is: IsRegularDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsRegularDigraph' must have a value ######## ########> Diff in standard/prop.tst:773 # Input is: gr := DigraphSymmetricClosure(ChainDigraph(5));; # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/prop.tst:774 # Input is: IsDistanceRegularDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsDistanceRegularDigraph' must have a value ######## ########> Diff in standard/prop.tst:776 # Input is: gr := Digraph([[2, 3, 4], [1, 3, 4], [1, 2, 4], [1, 2, 3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:777 # Input is: IsDistanceRegularDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsDistanceRegularDigraph' must have a value ######## ########> Diff in standard/prop.tst:779 # Input is: gr := CompleteBipartiteDigraph(3, 3);; # Expected output: # But found: Error, Variable: 'CompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:780 # Input is: IsDistanceRegularDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsDistanceRegularDigraph' must have a value ######## ########> Diff in standard/prop.tst:782 # Input is: gr := DigraphFromGraph6String("MhEGHC@AI?_PC@_G_"); # Expected output: # But found: Error, Variable: 'DigraphFromGraph6String' must have a value ######## ########> Diff in standard/prop.tst:784 # Input is: IsDistanceRegularDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsDistanceRegularDigraph' must have a value ######## ########> Diff in standard/prop.tst:786 # Input is: IsDistanceRegularDigraph(ChainDigraph(5)); # Expected output: false # But found: Error, Variable: 'IsDistanceRegularDigraph' must have a value ######## ########> Diff in standard/prop.tst:788 # Input is: IsDistanceRegularDigraph(EmptyDigraph(2)); # Expected output: true # But found: Error, Variable: 'IsDistanceRegularDigraph' must have a value ######## ########> Diff in standard/prop.tst:790 # Input is: gr := Digraph([[2], [1], [4], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:792 # Input is: IsDistanceRegularDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsDistanceRegularDigraph' must have a value ######## ########> Diff in standard/prop.tst:794 # Input is: gr := Digraph([[2], [1, 3], [2, 4], [3, 5, 6], [4, 6], [4, 5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:796 # Input is: IsDistanceRegularDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsDistanceRegularDigraph' must have a value ######## ########> Diff in standard/prop.tst:798 # Input is: gr := CompleteBipartiteDigraph(3, 4); # Expected output: # But found: Error, Variable: 'CompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:800 # Input is: IsDistanceRegularDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsDistanceRegularDigraph' must have a value ######## ########> Diff in standard/prop.tst:802 # Input is: gr := Digraph([[], [3], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:804 # Input is: IsDistanceRegularDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsDistanceRegularDigraph' must have a value ######## ########> Diff in standard/prop.tst:808 # Input is: gr := CompleteBipartiteDigraph(4, 5); # Expected output: # But found: Error, Variable: 'CompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:810 # Input is: IsCompleteBipartiteDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsCompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:812 # Input is: gr := Digraph([[2, 2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:814 # Input is: IsCompleteBipartiteDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsCompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:816 # Input is: gr := CycleDigraph(3); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/prop.tst:818 # Input is: IsCompleteBipartiteDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsCompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:820 # Input is: gr := CycleDigraph(4); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/prop.tst:822 # Input is: IsCompleteBipartiteDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsCompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:824 # Input is: gr := Digraph([[2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:826 # Input is: IsCompleteBipartiteDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsCompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:830 # Input is: D := CompleteMultipartiteDigraph([5, 3, 3, 2, 7]); # Expected output: # But found: Error, Variable: 'CompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:832 # Input is: IsCompleteMultipartiteDigraph(D); # Expected output: true # But found: Error, Variable: 'IsCompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:834 # Input is: D := Digraph(OutNeighbours(D)); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:836 # Input is: IsCompleteMultipartiteDigraph(D); # Expected output: true # But found: Error, Variable: 'IsCompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:838 # Input is: IsCompleteMultipartiteDigraph(EmptyDigraph(5)); # empty # Expected output: false # But found: Error, Variable: 'IsCompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:840 # Input is: D := Digraph([[2, 2], [1]]); # multidigraph # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:842 # Input is: IsCompleteMultipartiteDigraph(D); # Expected output: false # But found: Error, Variable: 'IsCompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:844 # Input is: D := Digraph([[1, 2], [1]]); # has loops # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:846 # Input is: IsCompleteMultipartiteDigraph(D); # Expected output: false # But found: Error, Variable: 'IsCompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:848 # Input is: D := Digraph([[2], []]); # not symmetric # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:850 # Input is: IsCompleteMultipartiteDigraph(D); # Expected output: false # But found: Error, Variable: 'IsCompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:852 # Input is: D := Digraph(IsImmutableDigraph, [[2], [1]]); # complete bipartite digraph # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:854 # Input is: IsCompleteMultipartiteDigraph(D); # Expected output: true # But found: Error, Variable: 'IsCompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:856 # Input is: HasIsCompleteBipartiteDigraph(D) and IsCompleteBipartiteDigraph(D); # Expected output: true # But found: Error, Variable: 'HasIsCompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:858 # Input is: D := CompleteDigraph(5); # complete digraph # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/prop.tst:860 # Input is: IsCompleteMultipartiteDigraph(D); # Expected output: true # But found: Error, Variable: 'IsCompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:862 # Input is: D := Digraph(OutNeighbours(D));; # complete digraph created differently # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:863 # Input is: IsCompleteDigraph(D); # Expected output: true # But found: Error, Variable: 'IsCompleteDigraph' must have a value ######## ########> Diff in standard/prop.tst:865 # Input is: IsCompleteMultipartiteDigraph(D); # Expected output: true # But found: Error, Variable: 'IsCompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:867 # Input is: D := DigraphEdgeUnion(CycleDigraph(IsMutableDigraph, 4), DigraphReverse(CycleDigraph(IsMutableDigraph, 4))); # Expected output: # But found: Error, Variable: 'DigraphEdgeUnion' must have a value ######## ########> Diff in standard/prop.tst:870 # Input is: IsCompleteMultipartiteDigraph(D); # Expected output: true # But found: Error, Variable: 'IsCompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:872 # Input is: IsCompleteBipartiteDigraph(D); # Expected output: true # But found: Error, Variable: 'IsCompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:874 # Input is: DigraphRemoveEdges(D, [[1, 2], [2, 1]]); # Expected output: # But found: Error, Variable: 'DigraphRemoveEdges' must have a value ######## ########> Diff in standard/prop.tst:876 # Input is: IsCompleteMultipartiteDigraph(D); # Expected output: false # But found: Error, Variable: 'IsCompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:878 # Input is: D := Digraph(IsImmutableDigraph, [[2], [1, 3], [2, 4], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:880 # Input is: IsCompleteMultipartiteDigraph(D); # Expected output: false # But found: Error, Variable: 'IsCompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:884 # Input is: g := Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:886 # Input is: IsDirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsDirectedTree' must have a value ######## ########> Diff in standard/prop.tst:888 # Input is: g := Digraph([[]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:890 # Input is: IsDirectedTree(g); # Expected output: true # But found: Error, Variable: 'IsDirectedTree' must have a value ######## ########> Diff in standard/prop.tst:892 # Input is: g := Digraph([[], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:894 # Input is: IsDirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsDirectedTree' must have a value ######## ########> Diff in standard/prop.tst:896 # Input is: g := Digraph([[1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:898 # Input is: IsDirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsDirectedTree' must have a value ######## ########> Diff in standard/prop.tst:900 # Input is: g := Digraph([[2, 2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:902 # Input is: IsDirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsDirectedTree' must have a value ######## ########> Diff in standard/prop.tst:904 # Input is: g := Digraph([[], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:906 # Input is: IsDirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsDirectedTree' must have a value ######## ########> Diff in standard/prop.tst:908 # Input is: g := Digraph([[2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:910 # Input is: IsDirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsDirectedTree' must have a value ######## ########> Diff in standard/prop.tst:912 # Input is: g := Digraph([[3], [3], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:914 # Input is: IsDirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsDirectedTree' must have a value ######## ########> Diff in standard/prop.tst:916 # Input is: g := Digraph([[2], [3], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:918 # Input is: IsDirectedTree(g); # Expected output: true # But found: Error, Variable: 'IsDirectedTree' must have a value ######## ########> Diff in standard/prop.tst:920 # Input is: g := Digraph([[2], [3], [], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:922 # Input is: IsDirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsDirectedTree' must have a value ######## ########> Diff in standard/prop.tst:924 # Input is: g := Digraph([[2, 3], [6], [4, 5], [], [], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:926 # Input is: IsDirectedTree(g); # Expected output: true # But found: Error, Variable: 'IsDirectedTree' must have a value ######## ########> Diff in standard/prop.tst:928 # Input is: g := Digraph([[2, 3], [6], [4, 5], [], [], [], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:930 # Input is: IsDirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsDirectedTree' must have a value ######## ########> Diff in standard/prop.tst:932 # Input is: g := Digraph([[2, 3], [6], [4, 5], [7], [], [7], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:934 # Input is: IsDirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsDirectedTree' must have a value ######## ########> Diff in standard/prop.tst:936 # Input is: g := Digraph([[2, 3], [1, 3], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:938 # Input is: IsDirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsDirectedTree' must have a value ######## ########> Diff in standard/prop.tst:940 # Input is: g := Digraph([[2, 3, 4], [1, 3, 4], [1, 2, 4], [1, 2, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:942 # Input is: IsDirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsDirectedTree' must have a value ######## ########> Diff in standard/prop.tst:946 # Input is: g := Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:948 # Input is: IsUndirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsUndirectedTree' must have a value ######## ########> Diff in standard/prop.tst:950 # Input is: g := Digraph([[]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:952 # Input is: IsUndirectedTree(g); # Expected output: true # But found: Error, Variable: 'IsUndirectedTree' must have a value ######## ########> Diff in standard/prop.tst:954 # Input is: g := Digraph([[], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:956 # Input is: IsUndirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsUndirectedTree' must have a value ######## ########> Diff in standard/prop.tst:958 # Input is: g := Digraph([[1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:960 # Input is: IsUndirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsUndirectedTree' must have a value ######## ########> Diff in standard/prop.tst:962 # Input is: g := Digraph([[2, 2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:964 # Input is: IsUndirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsUndirectedTree' must have a value ######## ########> Diff in standard/prop.tst:966 # Input is: g := Digraph([[], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:968 # Input is: IsUndirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsUndirectedTree' must have a value ######## ########> Diff in standard/prop.tst:970 # Input is: g := Digraph([[2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:972 # Input is: IsUndirectedTree(g); # Expected output: true # But found: Error, Variable: 'IsUndirectedTree' must have a value ######## ########> Diff in standard/prop.tst:974 # Input is: g := Digraph([[3], [3], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:976 # Input is: IsUndirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsUndirectedTree' must have a value ######## ########> Diff in standard/prop.tst:978 # Input is: g := Digraph([[3], [3], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:980 # Input is: IsUndirectedTree(g); # Expected output: true # But found: Error, Variable: 'IsUndirectedTree' must have a value ######## ########> Diff in standard/prop.tst:982 # Input is: g := Digraph([[3], [3], [1, 2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:984 # Input is: IsUndirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsUndirectedTree' must have a value ######## ########> Diff in standard/prop.tst:986 # Input is: g := Digraph([[2, 3], [6], [4, 5], [], [], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:988 # Input is: IsUndirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsUndirectedTree' must have a value ######## ########> Diff in standard/prop.tst:990 # Input is: g := Digraph([[2, 3], [6, 1], [4, 5, 1], [3], [3], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:992 # Input is: IsUndirectedTree(g); # Expected output: true # But found: Error, Variable: 'IsUndirectedTree' must have a value ######## ########> Diff in standard/prop.tst:994 # Input is: g := Digraph([[2, 3], [1, 3], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:996 # Input is: IsUndirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsUndirectedTree' must have a value ######## ########> Diff in standard/prop.tst:998 # Input is: g := Digraph([[2, 3, 4], [1, 3, 4], [1, 2, 4], [1, 2, 3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1000 # Input is: IsUndirectedTree(g); # Expected output: false # But found: Error, Variable: 'IsUndirectedTree' must have a value ######## ########> Diff in standard/prop.tst:1002 # Input is: g := Digraph([[1], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1004 # Input is: IsConnectedDigraph(g); # Expected output: false # But found: Error, Variable: 'IsConnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:1008 # Input is: gr := ChainDigraph(10); # Expected output: # But found: Error, Variable: 'ChainDigraph' must have a value ######## ########> Diff in standard/prop.tst:1010 # Input is: IsUndirectedForest(gr); # Expected output: false # But found: Error, Variable: 'IsUndirectedForest' must have a value ######## ########> Diff in standard/prop.tst:1012 # Input is: gr := EmptyDigraph(0); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/prop.tst:1014 # Input is: IsUndirectedForest(gr); # Expected output: false # But found: Error, Variable: 'IsUndirectedForest' must have a value ######## ########> Diff in standard/prop.tst:1016 # Input is: gr := EmptyDigraph(1); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/prop.tst:1018 # Input is: IsUndirectedForest(gr); # Expected output: true # But found: Error, Variable: 'IsUndirectedForest' must have a value ######## ########> Diff in standard/prop.tst:1020 # Input is: gr := Digraph([[1, 1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1022 # Input is: IsUndirectedForest(gr); # Expected output: false # But found: Error, Variable: 'IsUndirectedForest' must have a value ######## ########> Diff in standard/prop.tst:1024 # Input is: gr := Digraph([[1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1026 # Input is: IsUndirectedForest(gr); # Expected output: false # But found: Error, Variable: 'IsUndirectedForest' must have a value ######## ########> Diff in standard/prop.tst:1028 # Input is: gr := DigraphSymmetricClosure(ChainDigraph(4)); # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/prop.tst:1030 # Input is: HasIsUndirectedTree(gr) or HasIsUndirectedForest(gr); # Expected output: false # But found: Error, Variable: 'HasIsUndirectedTree' must have a value ######## ########> Diff in standard/prop.tst:1032 # Input is: IsUndirectedTree(gr); # Expected output: true # But found: Error, Variable: 'IsUndirectedTree' must have a value ######## ########> Diff in standard/prop.tst:1034 # Input is: HasIsUndirectedForest(gr); # Expected output: true # But found: Error, Variable: 'HasIsUndirectedForest' must have a value ######## ########> Diff in standard/prop.tst:1036 # Input is: IsUndirectedForest(gr); # Expected output: true # But found: Error, Variable: 'IsUndirectedForest' must have a value ######## ########> Diff in standard/prop.tst:1038 # Input is: gr := DigraphDisjointUnion(gr, gr, gr); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/prop.tst:1040 # Input is: IsUndirectedTree(gr); # Expected output: false # But found: Error, Variable: 'IsUndirectedTree' must have a value ######## ########> Diff in standard/prop.tst:1042 # Input is: IsUndirectedForest(gr); # Expected output: true # But found: Error, Variable: 'IsUndirectedForest' must have a value ######## ########> Diff in standard/prop.tst:1044 # Input is: gr := DigraphDisjointUnion(CompleteDigraph(2), CycleDigraph(3)); # Expected output: # But found: Error, Variable: 'DigraphDisjointUnion' must have a value ######## ########> Diff in standard/prop.tst:1046 # Input is: IsUndirectedForest(gr); # Expected output: false # But found: Error, Variable: 'IsUndirectedForest' must have a value ######## ########> Diff in standard/prop.tst:1048 # Input is: gr := Digraph(IsMutableDigraph, [[2], [1, 3], [2], [5], [4, 6], [5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1050 # Input is: IsUndirectedForest(gr); # Expected output: true # But found: Error, Variable: 'IsUndirectedForest' must have a value ######## ########> Diff in standard/prop.tst:1054 # Input is: g := Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1056 # Input is: IsEulerianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsEulerianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1058 # Input is: g := Digraph([[]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1060 # Input is: IsEulerianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsEulerianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1062 # Input is: g := Digraph([[], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1064 # Input is: IsEulerianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsEulerianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1066 # Input is: g := Digraph([[1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1068 # Input is: IsEulerianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsEulerianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1070 # Input is: g := Digraph([[2, 2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1072 # Input is: IsEulerianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsEulerianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1074 # Input is: g := Digraph([[2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1076 # Input is: IsEulerianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsEulerianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1078 # Input is: g := Digraph([[3], [3], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1080 # Input is: IsEulerianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsEulerianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1082 # Input is: g := Digraph([[3], [3], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1084 # Input is: IsEulerianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsEulerianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1086 # Input is: g := Digraph([[3], [], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1088 # Input is: IsEulerianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsEulerianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1090 # Input is: g := Digraph([[2], [3], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1092 # Input is: IsEulerianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsEulerianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1094 # Input is: g := Digraph([[2], [3], [1], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1096 # Input is: IsEulerianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsEulerianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1098 # Input is: g := Digraph([[2], [3], [1, 4], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1100 # Input is: IsEulerianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsEulerianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1102 # Input is: g := Digraph([[3, 6], [4], [2, 1], [5, 1], [3], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1104 # Input is: IsEulerianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsEulerianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1106 # Input is: g := Digraph([[3, 6], [4], [2, 1], [5, 1], [3], [4], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1108 # Input is: IsEulerianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsEulerianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1110 # Input is: g := Digraph([[3, 6], [4], [2, 1], [5, 1], [3], [4, 7], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1112 # Input is: IsEulerianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsEulerianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1114 # Input is: g := Digraph([[3, 6], [4], [2, 1], [5, 1], [3], [4, 7], [6]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1116 # Input is: IsEulerianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsEulerianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1118 # Input is: g := Digraph([[2, 3], [3], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1120 # Input is: IsEulerianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsEulerianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1122 # Input is: g := EmptyDigraph(IsMutableDigraph, 10); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/prop.tst:1124 # Input is: IsEulerianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsEulerianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1126 # Input is: g; # Expected output: # But found: Error, Variable: 'g' must have a value ######## ########> Diff in standard/prop.tst:1130 # Input is: gr := Digraph([[1, 2], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1132 # Input is: IsMeetSemilatticeDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsMeetSemilatticeDigraph' must have a value ######## ########> Diff in standard/prop.tst:1134 # Input is: IsJoinSemilatticeDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsJoinSemilatticeDigraph' must have a value ######## ########> Diff in standard/prop.tst:1136 # Input is: IsLatticeDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsLatticeDigraph' must have a value ######## ########> Diff in standard/prop.tst:1138 # Input is: gr := CycleDigraph(5); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/prop.tst:1140 # Input is: IsMeetSemilatticeDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsMeetSemilatticeDigraph' must have a value ######## ########> Diff in standard/prop.tst:1142 # Input is: IsJoinSemilatticeDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsJoinSemilatticeDigraph' must have a value ######## ########> Diff in standard/prop.tst:1146 # Input is: gr := DigraphFromDiSparse6String(".HiR@AeNcC?oD?G`oAGXIoAGXAe_COqDK^F"); # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/prop.tst:1148 # Input is: IsMeetSemilatticeDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsMeetSemilatticeDigraph' must have a value ######## ########> Diff in standard/prop.tst:1150 # Input is: IsJoinSemilatticeDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsJoinSemilatticeDigraph' must have a value ######## ########> Diff in standard/prop.tst:1152 # Input is: IsLatticeDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsLatticeDigraph' must have a value ######## ########> Diff in standard/prop.tst:1154 # Input is: gr := DigraphReverse(gr); # Expected output: # But found: Error, Variable: 'DigraphReverse' must have a value ######## ########> Diff in standard/prop.tst:1156 # Input is: IsMeetSemilatticeDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsMeetSemilatticeDigraph' must have a value ######## ########> Diff in standard/prop.tst:1158 # Input is: IsJoinSemilatticeDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsJoinSemilatticeDigraph' must have a value ######## ########> Diff in standard/prop.tst:1160 # Input is: IsLatticeDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsLatticeDigraph' must have a value ######## ########> Diff in standard/prop.tst:1164 # Input is: gr := NullDigraph(5); # Expected output: # But found: Error, Variable: 'NullDigraph' must have a value ######## ########> Diff in standard/prop.tst:1166 # Input is: IsPartialOrderDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsPartialOrderDigraph' must have a value ######## ########> Diff in standard/prop.tst:1168 # Input is: gr := Digraph([[1], [2], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1170 # Input is: IsPartialOrderDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsPartialOrderDigraph' must have a value ######## ########> Diff in standard/prop.tst:1174 # Input is: gr := DigraphFromDiSparse6String(Concatenation( ".~?CI_A?WA_M@G@_G@gB?]@?G_SAWA?Y@oJ__BGH?uA_M_IAoO_oCWL@IB_R_{DGB?mB?U_sDwM@"\ , "aBoX_KCGP@WEwQ@[FGR@_FWS@cFgT@gFwB@A?oO_KCGZACGwZAGGw[AUFOcAYF_f`{IG_Ae@?U`["\ , "IwWAqEOl`gJgC@mF?jBAFOkBEF_lBIFomBMG?nBQ@?ZAE@?ZAI@?ZAMH?oBWMGdB?LowaWKOya[K"\ , "_xBmI?rBqIOsBuI_tBy@?`AMH?uCA@?aaOHOuB[OgCAIHOvCQ@?baOM@?CYMP@C]HOwCYMOyCKPp"\ , "HbgPPHbkQw{CgRG|C_RW}CyNpN_SIwkDEJPQawSwnDQ@OobCSPUbGS`VbKSpWbOT@XbSTPY_SK?u"\ , "_SK?v_SK?wbcT`[DyM`UDsVgzD[WG{D_Vp`bsUPabwU`bb{Upc_SL`?bcOP[EY@OvCIMOyCKV@\\"\ , "Ea@OvCQM`DDsYgDB_PgxC[V`kc_VpfEuM`HDwZHID{W@hEsZxJE?YpncoWPpcsW`oFIR`bEw[xNE"\ , "O\\HOES\\WDC?Ph@C[X`vc_Xpw_SOhBEWY@yc_Q`fEc]wDCQH@DE_Y`|cgQphEk^gDCQPPiGAQpj"\ , "GE@PEc[Z@vGMQ@lF_`HmFc`XHEo_xIEsZqCG]Z`oFo`QGckZqFf?[P~G_ahpGGahqGq[qJGu\\AH"\ , "Gy\\QEG}\\aO_G@gF@?cgGAKcwHCWdGIGKdWA_KCAV`CeGQACeWRAOegSC[ewTGOfG`AGeGBH]Ga"\ , "WH}@?bHaH?dC?Oa]IEHQ_IEHaba[gaca_OQdacQAeag`QfcCOqa_OeA^aCO`CI?ihBCSgabIm@A^"\ , "cOgAlcSgqm_SPa`c[QPvFggaoc_Q`wFkiQpccgqocgQqkJCkxJI{kxKJURQsJYRaqJ]RpxJaSAEJ"\ , "e?qQaGcqzaSdA{ccdQ|g[da}hcigQCGoHBHkoXIHooiGHsoy^i?ialKU@Q`IiH@yFsgqjK]grEK]"\ , "hBHa[oRGKiI@zISobJfohrKgciBL_OmxCJorxDJssHJJwsYIJ{sgDIgjZ?LQC`|LU^aZKCth~KKt"\ , "yJKOuGDK}_BOLi_RPLm_bQLqbBRLu@gPHKvweJswHKLGwYLLwwgDIuCaVMAHqZH{wRdcsjRBMGxi"\ , "MLcwrcM]GP|G?jbELQ_AmMQjRDkWtBcMmxBja_fa_KSxhMI[iqmKWxrjMybrMM_yRiMozRncC]p}"\ , "IoqH}GCganMeOamKYOqnK_qRhNMjbEMmO`|MgzBtmgzRti{qRkNUyzkMs|Rxms}XNIcjAnM{{rtN"\ , "e_QnMg|YOJg{BpNG|BuN[}ByNk~B|fc^Aqfo^qqJO{XzNG|H~GGlAtNG|H}K_|bwNu^RvNi_atN_"\ , "~ZvN_}b|n[}bznmcR}N|?C@OH?sCOT@cFObAiQ@ECgR`QDWaaSOgea]IGhaiOxCcUQPycg]xJcqR"\ , "XMc}SH{fsgx}f}_I@gI`yGgeaiJgqbYMg}cIPheeiZhqfYciUhifiajinjMlItjYlywjemj?kEoj"\ , "BkQqZIkmrJLkytZUl]uJXmkyjrNI}Rv")); # Expected output: # But found: Error, Variable: 'DigraphFromDiSparse6String' must have a value ######## ########> Diff in standard/prop.tst:1197 # Input is: gr := DigraphReflexiveTransitiveClosure(gr); # Expected output: # But found: Error, Variable: 'DigraphReflexiveTransitiveClosure' must have a value ######## ########> Diff in standard/prop.tst:1199 # Input is: IsPartialOrderDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsPartialOrderDigraph' must have a value ######## ########> Diff in standard/prop.tst:1201 # Input is: IsMeetSemilatticeDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsMeetSemilatticeDigraph' must have a value ######## ########> Diff in standard/prop.tst:1203 # Input is: IsJoinSemilatticeDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsJoinSemilatticeDigraph' must have a value ######## ########> Diff in standard/prop.tst:1205 # Input is: IsLatticeDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsLatticeDigraph' must have a value ######## ########> Diff in standard/prop.tst:1209 # Input is: IsCycleDigraph(NullDigraph(10)); # Expected output: false # But found: Error, Variable: 'IsCycleDigraph' must have a value ######## ########> Diff in standard/prop.tst:1211 # Input is: IsCycleDigraph(CycleDigraph(10)); # Expected output: true # But found: Error, Variable: 'IsCycleDigraph' must have a value ######## ########> Diff in standard/prop.tst:1213 # Input is: IsCycleDigraph(NullDigraph(0)); # Expected output: false # But found: Error, Variable: 'IsCycleDigraph' must have a value ######## ########> Diff in standard/prop.tst:1215 # Input is: IsCycleDigraph(NullDigraph(1)); # Expected output: false # But found: Error, Variable: 'IsCycleDigraph' must have a value ######## ########> Diff in standard/prop.tst:1217 # Input is: IsCycleDigraph(CycleDigraph(1)); # Expected output: true # But found: Error, Variable: 'IsCycleDigraph' must have a value ######## ########> Diff in standard/prop.tst:1221 # Input is: gr := Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1223 # Input is: IsBiconnectedDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsBiconnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:1225 # Input is: gr := Digraph([[]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1227 # Input is: IsBiconnectedDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsBiconnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:1229 # Input is: gr := Digraph([[1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1231 # Input is: IsBiconnectedDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsBiconnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:1233 # Input is: gr := Digraph([[1, 1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1235 # Input is: IsBiconnectedDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsBiconnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:1237 # Input is: gr := Digraph([[1], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1239 # Input is: IsBiconnectedDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsBiconnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:1241 # Input is: gr := Digraph([[2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1243 # Input is: IsBiconnectedDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsBiconnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:1245 # Input is: gr := Digraph([[2], [3], [], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1247 # Input is: IsBiconnectedDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsBiconnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:1249 # Input is: gr := Digraph([[2], [3], [], [3]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1251 # Input is: IsBiconnectedDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsBiconnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:1253 # Input is: IsBiconnectedDigraph(DigraphFromGraph6String("FlCX?")); # Expected output: false # But found: Error, Variable: 'IsBiconnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:1255 # Input is: IsBiconnectedDigraph(Digraph([[2, 4, 5], [1, 4], [4, 7], [1, 2, 3, 5, 6, 7], [1, 4], [4, 7], [3, 4, 6]])); # Expected output: false # But found: Error, Variable: 'IsBiconnectedDigraph' must have a value ######## ########> Diff in standard/prop.tst:1260 # Input is: g := Digraph([]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1262 # Input is: IsHamiltonianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1264 # Input is: g := Digraph([[]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1266 # Input is: IsHamiltonianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1268 # Input is: g := Digraph([[], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1270 # Input is: IsHamiltonianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1272 # Input is: g := Digraph([[1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1274 # Input is: IsHamiltonianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1276 # Input is: g := Digraph([[2, 2], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1278 # Input is: IsHamiltonianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1280 # Input is: g := Digraph([[2], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1282 # Input is: IsHamiltonianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1284 # Input is: g := Digraph([[3], [3], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1286 # Input is: IsHamiltonianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1288 # Input is: g := Digraph([[3], [3], [1, 2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1290 # Input is: IsHamiltonianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1292 # Input is: g := Digraph([[3], [], [2]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1294 # Input is: IsHamiltonianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1296 # Input is: g := Digraph([[2], [3], [1]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1298 # Input is: IsHamiltonianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1300 # Input is: g := Digraph([[2], [3], [1], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1302 # Input is: IsHamiltonianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1304 # Input is: g := Digraph([[2], [3], [1, 4], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1306 # Input is: IsHamiltonianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1308 # Input is: g := Digraph([[3, 6], [4], [2, 1], [5, 1], [3], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1310 # Input is: IsHamiltonianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1312 # Input is: g := Digraph([[3, 6], [4, 1], [2, 1], [5, 1], [3], [4]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1314 # Input is: IsHamiltonianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1316 # Input is: g := Digraph([[3, 6], [4], [2, 1], [5, 1], [3], [4, 7], []]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1318 # Input is: IsHamiltonianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1320 # Input is: g := Digraph([[3, 6, 7], [4, 1], [2, 1], [5, 1], [3], [4, 7], [6]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1322 # Input is: IsHamiltonianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1324 # Input is: g := Digraph([[3, 6], [4], [2, 1], [5, 1], [3], [4, 7], [6]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1326 # Input is: IsHamiltonianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1328 # Input is: g := Digraph([[5, 6, 10], [2, 9], [3, 7], [2, 3], [9, 10], [2, 9], [1], [2, 3, 4, 7, 9], [3, 10], [4, 5, 6, 8]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1331 # Input is: IsHamiltonianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1333 # Input is: g := Digraph([[2, 4, 6, 10], [1, 3, 4, 5, 6, 7, 9, 10], [1, 5, 7, 8], [6, 10], [1, 7], [3, 4, 6, 7, 9], [2, 3, 4, 7], [2, 4, 5, 6], [2, 3, 5, 6, 7, 9, 10], [2, 3, 5]]); # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1337 # Input is: IsHamiltonianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1339 # Input is: g := CompleteMultipartiteDigraph([1, 30]); # Expected output: # But found: Error, Variable: 'CompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:1341 # Input is: IsHamiltonianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1343 # Input is: g := CompleteMultipartiteDigraph([16, 15]); # Expected output: # But found: Error, Variable: 'CompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:1345 # Input is: IsHamiltonianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1347 # Input is: g := CompleteMultipartiteDigraph([1, 1, 2, 3, 5, 8, 13, 21]); # Expected output: # But found: Error, Variable: 'CompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:1349 # Input is: IsHamiltonianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1351 # Input is: g := CompleteMultipartiteDigraph([1, 1, 2, 3, 5, 8, 13, 21, 34]); # Expected output: # But found: Error, Variable: 'CompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:1353 # Input is: IsHamiltonianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1355 # Input is: g := CompleteBipartiteDigraph(50, 50); # Expected output: # But found: Error, Variable: 'CompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:1357 # Input is: IsHamiltonianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1359 # Input is: g := CompleteMultipartiteDigraph([1, 15, 1, 1, 1, 1, 1, 1]); # Expected output: # But found: Error, Variable: 'CompleteMultipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:1361 # Input is: IsHamiltonianDigraph(g); # Expected output: false # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1363 # Input is: g := CompleteDigraph(50); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/prop.tst:1365 # Input is: IsHamiltonianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1367 # Input is: g := CycleDigraph(1000000); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/prop.tst:1369 # Input is: IsHamiltonianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1371 # Input is: g := CompleteDigraph(100); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/prop.tst:1373 # Input is: IsHamiltonianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1375 # Input is: g := CycleDigraph(513); # Expected output: # But found: Error, Variable: 'CycleDigraph' must have a value ######## ########> Diff in standard/prop.tst:1377 # Input is: g := DigraphAddEdges(g, [[6, 8], [8, 7], [7, 9]]); # Expected output: # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/prop.tst:1379 # Input is: g := DigraphRemoveEdge(g, [6, 7]); # Expected output: # But found: Error, Variable: 'DigraphRemoveEdge' must have a value ######## ########> Diff in standard/prop.tst:1381 # Input is: IsHamiltonianDigraph(g); # Expected output: true # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1383 # Input is: gr := DigraphAddEdges(DigraphAddVertex(CycleDigraph(600)), [[600, 601], [601, 600]]); # Expected output: # But found: Error, Variable: 'DigraphAddEdges' must have a value ######## ########> Diff in standard/prop.tst:1386 # Input is: HamiltonianPath(gr); # Expected output: fail # But found: Error, Variable: 'HamiltonianPath' must have a value ######## ########> Diff in standard/prop.tst:1388 # Input is: IsHamiltonianDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsHamiltonianDigraph' must have a value ######## ########> Diff in standard/prop.tst:1390 # Input is: gr := Digraph([[2, 2], [1, 1]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1391 # Input is: IsMultiDigraph(gr) and IsHamiltonianDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsMultiDigraph' must have a value ######## ########> Diff in standard/prop.tst:1395 # Input is: D := CompleteDigraph(10); # Expected output: # But found: Error, Variable: 'CompleteDigraph' must have a value ######## ########> Diff in standard/prop.tst:1397 # Input is: IsDigraphCore(D); # Expected output: true # But found: Error, Variable: 'IsDigraphCore' must have a value ######## ########> Diff in standard/prop.tst:1399 # Input is: D := JohnsonDigraph(8, 3); # Expected output: # But found: Error, Variable: 'JohnsonDigraph' must have a value ######## ########> Diff in standard/prop.tst:1401 # Input is: IsDigraphCore(D); # Expected output: true # But found: Error, Variable: 'IsDigraphCore' must have a value ######## ########> Diff in standard/prop.tst:1403 # Input is: D := CompleteBipartiteDigraph(500, 500); # Expected output: # But found: Error, Variable: 'CompleteBipartiteDigraph' must have a value ######## ########> Diff in standard/prop.tst:1405 # Input is: IsDigraphCore(D); # Expected output: false # But found: Error, Variable: 'IsDigraphCore' must have a value ######## ########> Diff in standard/prop.tst:1407 # Input is: D := PetersenGraph(); # Expected output: # But found: Error, Variable: 'PetersenGraph' must have a value ######## ########> Diff in standard/prop.tst:1409 # Input is: IsDigraphCore(D); # Expected output: true # But found: Error, Variable: 'IsDigraphCore' must have a value ######## ########> Diff in standard/prop.tst:1411 # Input is: D := DigraphSymmetricClosure(CycleDigraph(IsMutableDigraph, 40)); # Expected output: # But found: Error, Variable: 'DigraphSymmetricClosure' must have a value ######## ########> Diff in standard/prop.tst:1413 # Input is: IsDigraphCore(D); # Expected output: false # But found: Error, Variable: 'IsDigraphCore' must have a value ######## ########> Diff in standard/prop.tst:1415 # Input is: D; # Expected output: # But found: Error, Variable: 'D' must have a value ######## ########> Diff in standard/prop.tst:1417 # Input is: D := EmptyDigraph(100000); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/prop.tst:1419 # Input is: IsDigraphCore(D); # Expected output: false # But found: Error, Variable: 'IsDigraphCore' must have a value ######## ########> Diff in standard/prop.tst:1421 # Input is: D := EmptyDigraph(0); # Expected output: # But found: Error, Variable: 'EmptyDigraph' must have a value ######## ########> Diff in standard/prop.tst:1423 # Input is: IsDigraphCore(D); # Expected output: true # But found: Error, Variable: 'IsDigraphCore' must have a value ######## ########> Diff in standard/prop.tst:1427 # Input is: gr := Digraph([[1], [1, 2], [1, 3], [1, 4], [1 .. 5], [1 .. 6], [1, 2, 3, 4, 5, 7], [1, 8]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1429 # Input is: IsPreorderDigraph(gr) and IsQuasiorderDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsPreorderDigraph' must have a value ######## ########> Diff in standard/prop.tst:1433 # Input is: gr := DigraphFromDigraph6String(gr);; # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/prop.tst:1434 # Input is: IsPreorderDigraph(gr) and IsQuasiorderDigraph(gr); # Expected output: true # But found: Error, Variable: 'IsPreorderDigraph' must have a value ######## ########> Diff in standard/prop.tst:1439 # Input is: gr := DigraphFromDigraph6String(gr);; # Expected output: # But found: Error, Variable: 'DigraphFromDigraph6String' must have a value ######## ########> Diff in standard/prop.tst:1440 # Input is: IsPreorderDigraph(gr) or IsQuasiorderDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsPreorderDigraph' must have a value ######## ########> Diff in standard/prop.tst:1442 # Input is: gr := Digraph([[], [2], [1, 2, 3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1443 # Input is: IsPreorderDigraph(gr) or IsQuasiorderDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsPreorderDigraph' must have a value ######## ########> Diff in standard/prop.tst:1445 # Input is: gr := Digraph([[1], [1, 2], [2, 3]]);; # Expected output: # But found: Error, Variable: 'Digraph' must have a value ######## ########> Diff in standard/prop.tst:1446 # Input is: IsPreorderDigraph(gr) or IsQuasiorderDigraph(gr); # Expected output: false # But found: Error, Variable: 'IsPreorderDigraph' must have a value ######## ########> Diff in standard/prop.tst:1450 # Input is: D := DigraphCopy(NullDigraph(4)); # Expected output: # But found: Error, Variable: 'DigraphCopy' must have a value ######## ########> Diff in standard/prop.tst:1452 # Input is: HasIsNullDigraph(D) and IsNullDigraph(D); # Expected output: true # But found: Error, Variable: 'HasIsNullDigraph' must have a value ######## ########> Diff in standard/prop.tst:1454 # Input is: HasIsEmptyDigraph(D) and IsEmptyDigraph(D); # Expected output: true # But found: Error, Variable: 'HasIsEmptyDigraph' must have a value ######## ########> Diff in standard/prop.tst:1456 # Input is: HasDigraphNrEdges(D); # Expected output: true # But found: Error, Variable: 'HasDigraphNrEdges' must have a value ######## ########> Diff in standard/prop.tst:1458 # Input is: IsEmptyDigraph(D); # Expected output: true # But found: Error, Variable: 'IsEmptyDigraph' must have a value ######## ########> Diff in standard/prop.tst:1462 # Input is: IsVertexTransitive(Digraph([])); # Expected output: true # But found: Error, Variable: 'IsVertexTransitive' must have a value ######## ########> Diff in standard/prop.tst:1464 # Input is: IsVertexTransitive(Digraph([[1], [2]])); # Expected output: true # But found: Error, Variable: 'IsVertexTransitive' must have a value ######## ########> Diff in standard/prop.tst:1466 # Input is: IsVertexTransitive(Digraph([[2], [3], []])); # Expected output: false # But found: Error, Variable: 'IsVertexTransitive' must have a value ######## ########> Diff in standard/prop.tst:1468 # Input is: IsVertexTransitive(CompleteDigraph(20)); # Expected output: true # But found: Error, Variable: 'IsVertexTransitive' must have a value ######## ########> Diff in standard/prop.tst:1472 # Input is: IsEdgeTransitive(Digraph([])); # Expected output: true # But found: Error, Variable: 'IsEdgeTransitive' must have a value ######## ########> Diff in standard/prop.tst:1474 # Input is: IsEdgeTransitive(Digraph([[1], [2]])); # Expected output: true # But found: Error, Variable: 'IsEdgeTransitive' must have a value ######## ########> Diff in standard/prop.tst:1476 # Input is: IsEdgeTransitive(Digraph([[2], [3], []])); # Expected output: false # But found: Error, Variable: 'IsEdgeTransitive' must have a value ######## ########> Diff in standard/prop.tst:1478 # Input is: IsEdgeTransitive(CompleteDigraph(20)); # Expected output: true # But found: Error, Variable: 'IsEdgeTransitive' must have a value ######## ########> Diff in standard/prop.tst:1480 # Input is: IsEdgeTransitive(Digraph([[2], [3, 3, 3], []])); # Expected output: Error, the argument must be a digraph with no multiple edges, # But found: Error, Variable: 'IsEdgeTransitive' must have a value ######## ########> Diff in standard/prop.tst:1514 # Input is: DIGRAPHS_StopTest(); # Expected output: # But found: Error, Variable: 'DIGRAPHS_StopTest' must have a value ######## Digraphs package: standard/prop.tst msecs: 1067 false gap> gap> RPM build errors: error: Bad exit status from /var/tmp/rpm-tmp.saif8L (%check) Bad exit status from /var/tmp/rpm-tmp.saif8L (%check) Child return code was: 1 EXCEPTION: [Error()] Traceback (most recent call last): File "/usr/lib/python3.8/site-packages/mockbuild/trace_decorator.py", line 95, in trace result = func(*args, **kw) File "/usr/lib/python3.8/site-packages/mockbuild/util.py", line 746, in do_with_status raise exception.Error("Command failed: \n # %s\n%s" % (command, output), child.returncode) mockbuild.exception.Error: Command failed: # bash --login -c /usr/bin/rpmbuild -bb --target riscv64 --nodeps /builddir/build/SPECS/gap-pkg-digraphs.spec