Floating-point nu\ mbers

\n\n" ), chaptitle := rec( 1 := "Licensing", 2 := "Float package", 3 := "Polynomials", 4 := "Implemented packages" ), content := [ rec( content := "xml version=\"1.0\" encoding=\"UTF-8\"", count := [ 0, 0, 0, 1 ], name := "XMLPI", root := ~ ), rec( content := "Book SYSTEM \"gapdoc.dtd\" [\n $\\to$--&tgt;'>\n \n\n\n]", count := [ 0, 0, 0, 1 ], name := "XMLDOCTYPE", root := ~ ), rec( attributes := rec( Name := "FLOAT" ), content := [ rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Floating-point numbers", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], name := "Title", next := 286, root := ~, start := 249, stop := 285 ), rec( attributes := rec( ), content := [ rec( content := "Version 0.9.1", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], name := "Version", next := 325, root := ~, start := 289, stop := 324 ), rec( attributes := rec( ), content := [ rec( content := "\n MPFR- and CXSC-based librar\ y for GAP\n ", count := [ 0, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 2 ], name := "TitleComment", next := 401, root := ~, start := 328, stop := 400 ), rec( attributes := rec( ), content := [ rec( content := "Laurent Bartholdi\n ", count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Only := "HTML" ), content := [ rec( HTML := true, content := "laurent.barthold\ i@gmail.com", count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "Alt", next := 497, root := ~, start := 447, stop := 496 ), rec( content := "\n\t\t ", count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "HTML" ), content := [ rec( content := "laurent.bartholdi\ @gmail.com", count := [ 0, 0, 0, 3 ], name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "Alt", next := 550, root := ~, start := 501, stop := 549 ) ], count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "Email", next := 558, root := ~, start := 440, stop := 557 ), rec( content := " \n\t ", count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "http://www.uni-math.gwdg.\ de/laurent/", count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "Homepage", next := 620, root := ~, start := 563, stop := 619 ), rec( content := "\n ", count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 3 ], name := "Author", next := 632, root := ~, start := 404, stop := 631 ), rec( attributes := rec( ), content := [ rec( content := "14/06/2018", count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 3 ], name := "Date", next := 654, root := ~, start := 635, stop := 653 ), rec( attributes := rec( ), content := [ rec( content := "\n Mathematisches Institut", count := [ 0, 0, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 0, 0, 0, 4 ], mathmode := "Text", name := "Br", next := 697, root := ~, start := 692, stop := 696 ), rec( content := "Bunsenstraße 3-5", count := [ 0, 0, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 0, 0, 0, 4 ], mathmode := "Text", name := "Br", next := 719, root := ~, start := 714, stop := 718 ), rec( content := "D-37073 Göttingen", count := [ 0, 0, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 0, 0, 0, 4 ], mathmode := "Text", name := "Br", next := 742, root := ~, start := 737, stop := 741 ), rec( content := "Germany\n ", count := [ 0, 0, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 4 ], name := "Address", next := 762, root := ~, start := 657, stop := 761 ), rec( attributes := rec( ), content := [ rec( content := "\n This document describes the\ package ", count := [ 0, 0, 1, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Float", count := [ 0, 0, 1, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 1 ], mathmode := "Text", name := "Package", next := 840, root := ~, start := 816, stop := 839 ), rec( content := ", which\n implements in ", count := [ 0, 0, 1, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "GAP", count := [ 0, 0, 1, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 1 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " arbitrary-precision floating-po\ int numbers.\n ", count := [ 0, 0, 1, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Only := "HTML" ), content := [ rec( HTML := true, content := "\n ", 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 := 942, root := ~, start := 938, stop := 941 ), rec( HTML := true, content := "\n The computer algebra\ system ", count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( HTML := true, content := "GAP", count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( HTML := true, content := " is available at\n ", count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( HTML := true, content := "http://gap-syste\ m.org", count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "URL", next := 1029, root := ~, start := 997, stop := 1028 ), rec( HTML := true, content := ".\n ", count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "P", next := 1037, root := ~, start := 1033, stop := 1036 ), rec( HTML := true, content := "\n This documentation f\ or ", count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( HTML := true, content := "Float", count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "Package", next := 1087, root := ~, start := 1063, stop := 1086 ), rec( HTML := true, content := " is available at\n ", count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( HTML := true, content := "http://www.gap-s\ ystem.org/Manuals/pkg/float-0.9.1/doc/manual.pdf", count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "URL", next := 1185, root := ~, start := 1106, stop := 1184 ), rec( HTML := true, content := " in PDF format, and may \ be\n accessed online at ", count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( HTML := true, content := "http://gap-packa\ ges.github.io/float/", count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "URL", next := 1280, root := ~, start := 1233, stop := 1279 ), rec( HTML := true, content := ".\n ", count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "P", next := 1288, root := ~, start := 1284, stop := 1287 ), rec( HTML := true, content := "\n The latest release o\ f the package may be downloaded as\n ", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( HTML := true, content := "https://github.c\ om/gap-packages/float/releases/download/v0.9.1/float-0.9.1.tar.gz", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "URL", next := 1448, root := ~, start := 1348, stop := 1447 ), rec( HTML := true, content := " (tar, gzipped).\n The \ latest repository version (possibly unstable) may be downloaded as\n ", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( HTML := true, content := "https://github.c\ om/gap-packages/float/tarball/master", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "URL", next := 1603, root := ~, start := 1540, stop := 1602 ), rec( HTML := true, content := " (tar, gzipped),\n ", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( HTML := true, content := "https://github.c\ om/gap-packages/float.git", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "URL", next := 1674, root := ~, start := 1622, stop := 1673 ), rec( HTML := true, content := " (git repository),\n ", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( HTML := true, content := "https://packages\ .debian.org/search?keywords=gap-float&searchon=names&suite=all§ion=all", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "URL", next := 1808, root := ~, start := 1695, stop := 1807 ), rec( HTML := true, content := " (debian package), or\n \ explored at ", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( HTML := true, content := "https://github.c\ om/gap-packages/float/tree/master/", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "URL", next := 1905, root := ~, start := 1844, stop := 1904 ), rec( HTML := true, content := ".\n ", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 1 ], name := "Alt", next := 1915, root := ~, start := 918, stop := 1914 ), rec( content := "\n ", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 0, 0, 1, 5 ], mathmode := "Text", name := "P", next := 1922, root := ~, start := 1918, stop := 1921 ), rec( content := "\n For comments or questions \ on ", count := [ 0, 0, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Float", count := [ 0, 0, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 5 ], mathmode := "Text", name := "Package", next := 1980, root := ~, start := 1956, stop := 1979 ), rec( content := " please contact\n the author.\ \n ", count := [ 0, 0, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 1 ], name := "Abstract", next := 2025, root := ~, start := 765, stop := 2024 ), rec( attributes := rec( ), content := [ rec( content := "© 2011-2016 by Laurent Bartholdi\ \n ", count := [ 0, 0, 2, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 2, 1 ], name := "Copyright", next := 2096, root := ~, start := 2028, stop := 2095 ), rec( attributes := rec( ), content := [ rec( content := "Part of this work is supported by\ the \"Swiss\n National Fund for Scientific Research (SNF)\", the \"German Na\ tional Science Foundation (DFG)\",\n and the Courant Research Centre \"Higher\ Order Structures\" of the University of Göttingen.\n ", count := [ 0, 0, 3, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 3, 1 ], name := "Acknowledgements", next := 2372, root := ~, start := 2099, stop := 2371 ) ], count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "TitlePage", next := 2386, root := ~, start := 235, stop := 2385 ), rec( attributes := rec( ), content := 0, count := [ 0, 0, 4, 1 ], mathmode := "Text", name := "TableOfContents", next := 2406, root := ~, start := 2388, stop := 2405 ), rec( attributes := rec( ), content := [ rec( content := "\n\n", count := [ 0, 0, 4, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Licensing", count := [ 1, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 0, 0, 2 ], mathmode := "Text", name := "Heading", next := 2453, root := ~, start := 2425, stop := 2452 ), rec( content := "\n\nThis program is free softwar\ e; you can redistribute it and/or modify\nit under the terms of the GNU Genera\ l Public License as published by\nthe Free Software Foundation; either version\ 2 of the License, or any\nlater version.\n\n", count := [ 1, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 1, 0, 0, 4 ], mathmode := "Text", name := "P", next := 2683, root := ~, start := 2679, stop := 2682 ), rec( content := " This program is distributed in \ the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; without even the i\ mplied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See \ the GNU\nGeneral Public License for more details.\n\n", count := [ 1, 0, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 1, 0, 0, 5 ], mathmode := "Text", name := "P", next := 2923, root := ~, start := 2919, stop := 2922 ), rec( content := " You should have received a copy\ of the GNU General Public\nLicense along with this program, in the file COPYI\ NG. If not, see\n", count := [ 1, 0, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "http://www.gnu.org/licens\ es/", count := [ 1, 0, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 0, 0, 5 ], mathmode := "Text", name := "URL", next := 3088, root := ~, start := 3049, stop := 3087 ), rec( content := ".\n\n", count := [ 1, 0, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 0, 0, 1 ], mathmode := "Text", name := "Chapter", next := 3101, root := ~, start := 2416, stop := 3100 ), rec( content := "\n\n", count := [ 1, 0, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "floatpackage" ), content := [ rec( attributes := rec( ), content := [ rec( content := "Float package", count := [ 2, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 0, 0, 2 ], mathmode := "Text", name := "Heading", next := 3165, root := ~, start := 3133, stop := 3164 ), rec( content := "\n\n", count := [ 2, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "sample" ), content := [ rec( attributes := rec( ), content := [ rec( content := "A sample run", count := [ 2, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 2 ], mathmode := "Text", name := "Heading", next := 3222, root := ~, start := 3191, stop := 3221 ), rec( content := "\n\nThe extended floatin\ g-point capabilities of ", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "GAP", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " are installed by loadin\ g the package\nvia ", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "LoadPackage(\"flo\ at\");", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "C", next := 3343, root := ~, start := 3315, stop := 3342 ), rec( content := " and selecting new float\ ing-point handlers via\n", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "SetFloats(MPFR)", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "C", next := 3412, root := ~, start := 3390, stop := 3411 ), rec( content := ", ", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "SetFloats(MPFI)", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "C", next := 3436, root := ~, start := 3414, stop := 3435 ), rec( content := ", ", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "SetFloats(MPC)", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "C", next := 3459, root := ~, start := 3438, stop := 3458 ), rec( content := " or", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "SetFloats(CXSC)", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "C", next := 3484, root := ~, start := 3462, stop := 3483 ), rec( content := ",\ndepending on whether \ high-precision real, interval or complex arithmetic are desired, or\nwhether a\ fast package containing all four real/complex element/interval arithmetic is \ desired:\n", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\ngap> LoadPackag\ e(\"float\");\nLoading FLOAT 0.7.0 ...\ntrue\ngap> SetFloats(MPFR); # floating\ -point\ngap> x := 4*Atan(1.0);\n.314159e1\ngap> Sin(x);\n.169569e-30\ngap> Set\ Floats(MPFR,1000); # 1000 bits\ngap> x := 4*Atan(1.0);\n.314159e1\ngap> Sin(x)\ ;\n.125154e-300\ngap> String(x,300);\n\".3141592653589793238462643383279502884\ 197169399375105820974944592307816406286\\\n20899862803482534211706798214808651\ 3282306647093844609550582231725359408128481\\\n1174502841027019385211055596446\ 22948954930381964428810975665933446128475648233\\\n786783165271201909145648566\ 92346034861045432664821339360726024914127e1\"\ngap>\ngap> SetFloats(MPFI); # i\ ntervals\ngap> x := 4*Atan(1.0);\n.314159e1(99)\ngap> AbsoluteDiameter(x); Sup\ (x); Inf(x);\n.100441e-29\n.314159e1\n.314159e1\ngap> Sin(x);\n-.140815e-29(97\ )\ngap> 0.0 in last;\ntrue\ngap> 1.0; # exact representation\n.1e1(∞)\ngap> \ IncreaseInterval(last,0.001); # now only 8 significant bits\n.1e1(8)\ngap> Inc\ reaseInterval(last,-0.002); # now becomes empty\n∅\ngap> MinimalPolynomial(R\ ationals,Sqrt(2.0));\n-2*x_1^2+1\ngap> Cyc(last);\nE(8)-E(8)^3\ngap>\ngap> Set\ Floats(MPC); # complex numbers\ngap> z := 5.0-1.0i;\n.5e1-.1e1i\ngap> (1+1.0i)\ *last^4*(239+1.0i);\n.228488e6\ngap> Exp(6.2835i);\n.1e1+.314693e-3i\n", count := [ 2, 1, 0, 4 ], name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 4 ], mathmode := "Text", name := "Example", next := 4903, root := ~, start := 3671, stop := 4902 ), rec( content := "\n\n", count := [ 2, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 1 ], mathmode := "Text", name := "Section", next := 4915, root := ~, start := 3167, stop := 4914 ), rec( content := "\n\n", count := [ 2, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 0, 0, 1 ], mathmode := "Text", name := "Chapter", next := 4927, root := ~, start := 3103, stop := 4926 ), rec( content := "\n\n", count := [ 2, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "poly" ), content := [ rec( attributes := rec( ), content := [ rec( content := "Polynomials", count := [ 3, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 0, 0, 2 ], mathmode := "Text", name := "Heading", next := 4981, root := ~, start := 4951, stop := 4980 ), rec( content := "\n\n", count := [ 3, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "The Floats pseudo\ -field", count := [ 3, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 0, 2 ], mathmode := "Text", name := "Heading", next := 5034, root := ~, start := 4992, stop := 5033 ), rec( content := "\n\nPolynomials with flo\ ating-point coefficients may be manipulated in\n", count := [ 3, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "GAP", count := [ 3, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 0, 3 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := "; though they behave, in\ subtle ways, quite differently than\npolynomials over rings.\n", count := [ 3, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 0, 4 ], mathmode := "Text", name := "P", next := 5197, root := ~, start := 5193, stop := 5196 ), rec( content := "\n\nThe \"pseudo-field\"\ of floating-point numbers is an object in ", count := [ 3, 1, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "GAP", count := [ 3, 1, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 0, 4 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := ",\ncalled ", count := [ 3, 1, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "FLOAT_PSEUDOFIELD\ ", count := [ 3, 1, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 0, 4 ], mathmode := "Text", name := "C", next := 5298, root := ~, start := 5274, stop := 5297 ), rec( content := ". (It is not really a fi\ eld,\ne.g. because addition of floating-point numbers in not\nassociative). It\ may be used to create indeterminates, for example as\n", count := [ 3, 1, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\ngap> x := Indet\ erminate(FLOAT_PSEUDOFIELD,\"x\");\nx\ngap> 2*x^2+3;\n2.0*x^2+3.0\ngap> Value(\ last,10);\n203.0\n", count := [ 3, 1, 0, 5 ], name := "PCDATA", root := ~ ) ], count := [ 3, 1, 0, 5 ], mathmode := "Text", name := "Example", next := 5587, root := ~, start := 5452, stop := 5586 ), rec( content := "\n\n", count := [ 3, 1, 0, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 0, 1 ], mathmode := "Text", name := "Section", next := 5599, root := ~, start := 4983, stop := 5598 ), rec( content := "\n\n", count := [ 3, 1, 0, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Roots of polynomi\ als", count := [ 3, 2, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 0, 2 ], mathmode := "Text", name := "Heading", next := 5649, root := ~, start := 5610, stop := 5648 ), rec( content := "\n\nThe Jenkins-Traub al\ gorithm has been implemented, in arbitrary\nprecision for MPFR and MPC.\n", count := [ 3, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 2, 0, 4 ], mathmode := "Text", name := "P", next := 5746, root := ~, start := 5742, stop := 5745 ), rec( content := "\nFurthermore, CXSC can \ provide complex enclosures for the roots of a\ncomplex polynomial.\n\n", count := [ 3, 2, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 0, 1 ], mathmode := "Text", name := "Section", next := 5846, root := ~, start := 5601, stop := 5845 ), rec( content := "\n\n", count := [ 3, 2, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Finding integer r\ elations", count := [ 3, 3, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 0, 2 ], mathmode := "Text", name := "Heading", next := 5901, root := ~, start := 5857, stop := 5900 ), rec( content := "\nThe PSLQ algorithm has\ been implemented by Steve A. Linton, as an external\r\ncontribution to ", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Float", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "Package", next := 6018, root := ~, start := 5994, stop := 6017 ), rec( content := ". This algorithm receive\ s as\r\ninput a vector of floats ", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "M", next := 6081, root := ~, start := 6073, stop := 6080 ), rec( content := " and a required precisio\ n ", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\epsilon", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "M", next := 6122, root := ~, start := 6107, stop := 6121 ), rec( content := ",\r\nand seeks an intege\ r vector ", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "M", next := 6161, root := ~, start := 6153, stop := 6160 ), rec( content := " such that\r\n", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "|x\\cdot v|<\\eps\ ilon", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "M", next := 6202, root := ~, start := 6173, stop := 6201 ), rec( content := ". The implementation fol\ lows quite closely the\r\noriginal article ", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "MR1836930" ), content := 0, count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "Cite", next := 6290, root := ~, start := 6267, stop := 6289 ), rec( content := ".\r\n\r\n", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "x, epsilon[, gam\ ma]", Name := "PSLQ" ), content := 0, count := [ 3, 3, 1, 2 ], mathmode := "Text", name := "Func", next := 6356, root := ~, start := 6311, stop := 6355 ), rec( attributes := rec( Arg := "x, epsilon[, gam\ ma [,beta]]", Name := "PSLQ_MP" ), content := 0, count := [ 3, 3, 1, 4 ], mathmode := "Text", name := "Func", next := 6416, root := ~, start := 6360, stop := 6415 ), rec( attributes := rec( ), content := [ rec( content := "An intege\ r vector ", count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "M", next := 6455, root := ~, start := 6447, stop := 6454 ), rec( content := " with ", count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "|\ x\\cdot v|<\\epsilon", count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "M", next := 6490, root := ~, start := 6461, stop := 6489 ), rec( content := ".", count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "Returns", next := 6501, root := ~, start := 6420, stop := 6500 ), rec( attributes := rec( ), content := [ rec( content := "\r\n T\ he PSLQ algorithm by Bailey and Broadhurst (see ", count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "MR183693\ 0" ), content := 0, count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "Cite", next := 6596, root := ~, start := 6573, stop := 6595 ), rec( content := ")\r\n \ searches for an integer relation between the entries in ", count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ", count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "M", next := 6667, root := ~, start := 6659, stop := 6666 ), rec( content := ".\r\n\r\\ n ", count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "P", next := 6680, root := ~, start := 6676, stop := 6679 ), rec( attributes := rec( ), content := [ rec( content := "\\ \beta", count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "M", next := 6692, root := ~, start := 6680, stop := 6691 ), rec( content := " and ", count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ \gamma", count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "M", next := 6710, root := ~, start := 6697, stop := 6709 ), rec( content := " are alg\ orithm tuning parameters, and\r\n default to ", count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "4\ /10", count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "M", next := 6775, root := ~, start := 6764, stop := 6774 ), rec( content := " and ", count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "2\ /\\sqrt(3)", count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "M", next := 6797, root := ~, start := 6780, stop := 6796 ), rec( content := " respect\ ively.\r\n\r\n ", count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 1, 7 ], mathmode := "Text", name := "P", next := 6823, root := ~, start := 6819, stop := 6822 ), rec( content := "The seco\ nd form implements the \"Multi-pair\" variant of the algorithm, which is\r\n \ better suited to parallelization.\r\n", count := [ 3, 3, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ r\ngap> PSLQ([1.0,(1+Sqrt(5.0))/2],1.e-2);\r\n[ 55, -34 ] # Fibonacci numbers\ \r\ngap> RootsFloat([1,-4,2]*1.0);\r\n[ 0.292893, 1.70711 ] # roots of 2x^2-4x\ +1\r\ngap> PSLQ(List([0..2],i->last[1]^i),1.e-7);\r\n[ 1, -4, 2 ] # a degree-2\ polynomial fitting well\r\n", count := [ 3, 3, 1, 8 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 8 ], mathmode := "Text", name := "Example", next := 7221, root := ~, start := 6942, stop := 7220 ), rec( content := "\r\n ", count := [ 3, 3, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "Description", next := 7239, root := ~, start := 6505, stop := 7238 ) ], count := [ 3, 3, 1, 1 ], mathmode := "Text", name := "ManSection", next := 7254, root := ~, start := 6295, stop := 7253 ), rec( content := "\r\n\n", count := [ 3, 3, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 0, 1 ], mathmode := "Text", name := "Section", next := 7267, root := ~, start := 5848, stop := 7266 ), rec( content := "\n\n", count := [ 3, 3, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "LLL lattice reduc\ tion", count := [ 3, 4, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 0, 2 ], mathmode := "Text", name := "Heading", next := 7318, root := ~, start := 7278, stop := 7317 ), rec( content := "\n\nA faster implementat\ ion of the LLL lattice reduction algorithm has\nalso been implemented. It is a\ ccessible via the commands\n", count := [ 3, 4, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "FPLLLReducedBasis\ (m)", count := [ 3, 4, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 0, 3 ], mathmode := "Text", name := "C", next := 7471, root := ~, start := 7444, stop := 7470 ), rec( content := " and \n", count := [ 3, 4, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "FPLLLShortestVect\ or(m)", count := [ 3, 4, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 0, 3 ], mathmode := "Text", name := "C", next := 7506, root := ~, start := 7477, stop := 7505 ), rec( content := ".\n", count := [ 3, 4, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 4, 0, 4 ], mathmode := "Text", name := "P", next := 7512, root := ~, start := 7508, stop := 7511 ), rec( content := "\n\n", count := [ 3, 4, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 0, 1 ], mathmode := "Text", name := "Section", next := 7524, root := ~, start := 7269, stop := 7523 ), rec( content := "\n\n", count := [ 3, 4, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 0, 0, 1 ], mathmode := "Text", name := "Chapter", next := 7536, root := ~, start := 4929, stop := 7535 ), rec( content := "\n\n", count := [ 3, 4, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "impl" ), content := [ rec( attributes := rec( ), content := [ rec( content := "Implemented packages", count := [ 4, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 0, 0, 2 ], mathmode := "Text", name := "Heading", next := 7599, root := ~, start := 7560, stop := 7598 ), rec( content := "\n\n", count := [ 4, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "MPFR", count := [ 4, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 2 ], mathmode := "Text", name := "Heading", next := 7633, root := ~, start := 7610, stop := 7632 ), rec( content := "\n", count := [ 4, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Name := "IsMPFRFloat" ), content := 0, count := [ 4, 1, 1, 2 ], mathmode := "Text", name := "Filt", next := 7675, root := ~, start := 7649, stop := 7674 ), rec( attributes := rec( Name := "TYPE_MPFR" ) , content := 0, count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "Var", next := 7701, root := ~, start := 7678, stop := 7700 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ category of floating-point numbers.\n\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 := 7771, root := ~, start := 7767, stop := 7770 ), rec( content := " Note th\ at they are treated as commutative and scalar, but are\n not necessarily as\ sociative.\n ", count := [ 4, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "Description", next := 7883, root := ~, start := 7704, stop := 7882 ) ], count := [ 4, 1, 1, 1 ], mathmode := "Text", name := "ManSection", next := 7897, root := ~, start := 7634, stop := 7896 ), rec( content := "\n\n", count := [ 4, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 1 ], mathmode := "Text", name := "Section", next := 7909, root := ~, start := 7601, stop := 7908 ), rec( content := "\n\n", count := [ 4, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "MPFI", count := [ 4, 2, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 2, 0, 2 ], mathmode := "Text", name := "Heading", next := 7943, root := ~, start := 7920, stop := 7942 ), rec( content := "\n", count := [ 4, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Name := "IsMPFIFloat" ), content := 0, count := [ 4, 2, 1, 2 ], mathmode := "Text", name := "Filt", next := 7985, root := ~, start := 7959, stop := 7984 ), rec( attributes := rec( Name := "TYPE_MPFI" ) , content := 0, count := [ 4, 2, 1, 4 ], mathmode := "Text", name := "Var", next := 8011, root := ~, start := 7988, stop := 8010 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ category of intervals of floating-point numbers.\n\n ", count := [ 4, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 4, 2, 1, 6 ], mathmode := "Text", name := "P", next := 8094, root := ~, start := 8090, stop := 8093 ), rec( content := " Note th\ at they are treated as commutative and scalar, but are\n not necessarily as\ sociative.\n ", count := [ 4, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 2, 1, 5 ], mathmode := "Text", name := "Description", next := 8206, root := ~, start := 8014, stop := 8205 ) ], count := [ 4, 2, 1, 1 ], mathmode := "Text", name := "ManSection", next := 8220, root := ~, start := 7944, stop := 8219 ), rec( content := "\n\n", count := [ 4, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 2, 0, 1 ], mathmode := "Text", name := "Section", next := 8232, root := ~, start := 7911, stop := 8231 ), rec( content := "\n\n", count := [ 4, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "MPC", count := [ 4, 3, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 3, 0, 2 ], mathmode := "Text", name := "Heading", next := 8265, root := ~, start := 8243, stop := 8264 ), rec( content := "\n", count := [ 4, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Name := "IsMPCFloat" ), content := 0, count := [ 4, 3, 1, 2 ], mathmode := "Text", name := "Filt", next := 8306, root := ~, start := 8281, stop := 8305 ), rec( attributes := rec( Name := "TYPE_MPC" ), content := 0, count := [ 4, 3, 1, 4 ], mathmode := "Text", name := "Var", next := 8331, root := ~, start := 8309, stop := 8330 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ category of intervals of floating-point numbers.\n\n ", count := [ 4, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 4, 3, 1, 6 ], mathmode := "Text", name := "P", next := 8414, root := ~, start := 8410, stop := 8413 ), rec( content := " Note th\ at they are treated as commutative and scalar, but are\n not necessarily as\ sociative.\n ", count := [ 4, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 3, 1, 5 ], mathmode := "Text", name := "Description", next := 8526, root := ~, start := 8334, stop := 8525 ) ], count := [ 4, 3, 1, 1 ], mathmode := "Text", name := "ManSection", next := 8540, root := ~, start := 8266, stop := 8539 ), rec( content := "\n\n", count := [ 4, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 3, 0, 1 ], mathmode := "Text", name := "Section", next := 8552, root := ~, start := 8234, stop := 8551 ), rec( content := "\n\n", count := [ 4, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "CXSC", count := [ 4, 4, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 4, 0, 2 ], mathmode := "Text", name := "Heading", next := 8586, root := ~, start := 8563, stop := 8585 ), rec( content := "\n", count := [ 4, 4, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Name := "IsCXSCReal" ), content := 0, count := [ 4, 4, 1, 2 ], mathmode := "Text", name := "Filt", next := 8627, root := ~, start := 8602, stop := 8626 ), rec( attributes := rec( Name := "IsCXSCComplex" ), content := 0, count := [ 4, 4, 1, 4 ], mathmode := "Text", name := "Filt", next := 8658, root := ~, start := 8630, stop := 8657 ), rec( attributes := rec( Name := "IsCXSCInterval"\ ), content := 0, count := [ 4, 4, 1, 6 ], mathmode := "Text", name := "Filt", next := 8690, root := ~, start := 8661, stop := 8689 ), rec( attributes := rec( Name := "IsCXSCBox" ) , content := 0, count := [ 4, 4, 1, 8 ], mathmode := "Text", name := "Filt", next := 8717, root := ~, start := 8693, stop := 8716 ), rec( attributes := rec( Name := "TYPE_CXSC_RP" ) , content := 0, count := [ 4, 4, 1, 10 ], mathmode := "Text", name := "Var", next := 8746, root := ~, start := 8720, stop := 8745 ), rec( attributes := rec( Name := "TYPE_CXSC_CP" ) , content := 0, count := [ 4, 4, 1, 12 ], mathmode := "Text", name := "Var", next := 8775, root := ~, start := 8749, stop := 8774 ), rec( attributes := rec( Name := "TYPE_CXSC_RI" ) , content := 0, count := [ 4, 4, 1, 14 ], mathmode := "Text", name := "Var", next := 8804, root := ~, start := 8778, stop := 8803 ), rec( attributes := rec( Name := "TYPE_CXSC_CI" ) , content := 0, count := [ 4, 4, 1, 16 ], mathmode := "Text", name := "Var", next := 8833, root := ~, start := 8807, stop := 8832 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ category of floating-point numbers.\n\n ", count := [ 4, 4, 1, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 4, 4, 1, 18 ], mathmode := "Text", name := "P", next := 8903, root := ~, start := 8899, stop := 8902 ), rec( content := " Note th\ at they are treated as commutative and scalar, but are\n not necessarily as\ sociative.\n ", count := [ 4, 4, 1, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 4, 1, 17 ], mathmode := "Text", name := "Description", next := 9015, root := ~, start := 8836, stop := 9014 ) ], count := [ 4, 4, 1, 1 ], mathmode := "Text", name := "ManSection", next := 9029, root := ~, start := 8587, stop := 9028 ), rec( content := "\n\n", count := [ 4, 4, 1, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 4, 0, 1 ], mathmode := "Text", name := "Section", next := 9041, root := ~, start := 8554, stop := 9040 ), rec( content := "\n\n", count := [ 4, 4, 1, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "FPLLL", count := [ 4, 5, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 5, 0, 2 ], mathmode := "Text", name := "Heading", next := 9076, root := ~, start := 9052, stop := 9075 ), rec( content := "\n", count := [ 4, 5, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "m", Name := "FPLLLReducedBas\ is" ), content := 0, count := [ 4, 5, 1, 2 ], mathmode := "Text", name := "Oper", next := 9132, root := ~, start := 9092, stop := 9131 ), rec( attributes := rec( ), content := [ rec( content := "A matrix \ spanning the same lattice as ", count := [ 4, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 4, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 5, 1, 3 ], mathmode := "Text", name := "A", next := 9190, root := ~, start := 9182, stop := 9189 ), rec( content := ".", count := [ 4, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 5, 1, 3 ], mathmode := "Text", name := "Returns", next := 9201, root := ~, start := 9135, stop := 9200 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function implements the LLL (Lenstra-Lenstra-Lovász) lattice\n reduction\ algorithm via the external library ", count := [ 4, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ plll", count := [ 4, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 5, 1, 3 ], mathmode := "Text", name := "Package", next := 9362, root := ~, start := 9338, stop := 9361 ), rec( content := ".\n\n \ ", count := [ 4, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) , rec( attributes := rec( ), content := 0, count := [ 4, 5, 1, 4 ], mathmode := "Text", name := "P", next := 9373, root := ~, start := 9369, stop := 9372 ), rec( content := " The res\ ult is guaranteed to be optimal up to 1%.\n ", count := [ 4, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 5, 1, 3 ], mathmode := "Text", name := "Description", next := 9439, root := ~, start := 9204, stop := 9438 ) ], count := [ 4, 5, 1, 1 ], mathmode := "Text", name := "ManSection", next := 9453, root := ~, start := 9077, stop := 9452 ), rec( content := "\n\n", count := [ 4, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "m", Name := "FPLLLShortestVe\ ctor" ), content := 0, count := [ 4, 5, 2, 2 ], mathmode := "Text", name := "Oper", next := 9512, root := ~, start := 9470, stop := 9511 ), rec( attributes := rec( ), content := [ rec( content := "A short v\ ector in the lattice spanned by ", count := [ 4, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "m\ ", count := [ 4, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 5, 2, 3 ], mathmode := "Text", name := "A", next := 9573, root := ~, start := 9565, stop := 9572 ), rec( content := ".", count := [ 4, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 5, 2, 3 ], mathmode := "Text", name := "Returns", next := 9584, root := ~, start := 9515, stop := 9583 ), rec( attributes := rec( ), content := [ rec( content := "\n Thi\ s function implements the LLL (Lenstra-Lenstra-Lovász) lattice\n reduction\ algorithm via the external library ", count := [ 4, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "f\ plll", count := [ 4, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 5, 2, 3 ], mathmode := "Text", name := "Package", next := 9745, root := ~, start := 9721, stop := 9744 ), rec( content := ",\n a\ nd then computes a short vector in this lattice.\n\n ", count := [ 4, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 4, 5, 2, 4 ], mathmode := "Text", name := "P", next := 9810, root := ~, start := 9806, stop := 9809 ), rec( content := " The res\ ult is guaranteed to be optimal up to 1%.\n ", count := [ 4, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 5, 2, 3 ], mathmode := "Text", name := "Description", next := 9876, root := ~, start := 9587, stop := 9875 ) ], count := [ 4, 5, 2, 1 ], mathmode := "Text", name := "ManSection", next := 9890, root := ~, start := 9455, stop := 9889 ), rec( content := "\n\n", count := [ 4, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 5, 0, 1 ], mathmode := "Text", name := "Section", next := 9902, root := ~, start := 9043, stop := 9901 ), rec( content := "\n\n", count := [ 4, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 0, 0, 1 ], mathmode := "Text", name := "Chapter", next := 9914, root := ~, start := 7538, stop := 9913 ), rec( content := "\n\n", count := [ 4, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 4, 1 ], mathmode := "Text", name := "Body", next := 9923, root := ~, start := 2408, stop := 9922 ), rec( attributes := rec( Databases := "floatbib.xml" ), content := 0, count := [ "Bib", 0, 0, 1 ], mathmode := "Text", name := "Bibliography", next := 9965, root := ~, start := 9925, stop := 9964 ), rec( attributes := rec( ), content := 0, count := [ "Ind", 0, 0, 1 ], mathmode := "Text", name := "TheIndex", next := 9977, root := ~, start := 9966, stop := 9976 ) ], count := [ 0, 0, 0, 1 ], name := "Book", next := 9986, root := ~, start := 214, stop := 9985 ) ], count := [ 0, 0, 0, 1 ], indent := "", indextext := "FPLLLReducedBasis 4.5-1
\n

FPLLLShortes\
tVector

4.5-2
\nIsCXSCBox \ 4.4-1
\nIsCXSCComplex 4.4-1
\n

IsCXSCInterva\
l

4.4-1
\nIsCXSCReal 4.4-1\
\nIsMPCFloat 4.3-1
\nIsMPFIFloat <\ a href=\"chap4.html#X842290DB8034BF90\">4.2-1
\nIsMPFRFloat 4.1-1 \nPSLQ 3.3-1
\nPSLQ_MP 3.3-1
\n

TYPE_CXSC_CI  4.4-1  
\nTYPE_CXSC_CP  4.4-1  
\nTYPE_CXSC_RI  4.4-1  
\nTYPE_CXSC_RP  \
4.4-1  
\nTYPE_MPC  4.3-1  
\
\nTYPE_MPFI  4.2-1  
\nTYPE_MPFR  4.1-1  
\n", 
  input := "\n\n$\\to$--&tgt;'>\n \n\n\n]>\n\n\n\n  Floating-point nu\
mbers\n  Version &Version;\n  \n    M\
PFR- and CXSC-based library for GAP\n  \n  Laurent Bart\
holdi\n          laurent.bartholdi@gmail.com\n\
\t\t laurent.bartholdi@gmail.com \n\t  http://www.uni-math.gwdg.de/laurent/\n  \n  &Date\
;\n  \n  Mathematisches Institut
Bunsenstraße 3-5
D-3\
7073 Göttingen
Germany\n  
\n  \n    This document des\
cribes the package Float, which\n    implements in &GAP; ar\
bitrary-precision floating-point numbers.\n  \n  \n  Th\
e computer algebra system &GAP; is available at\n  http://gap-system.org<\
/URL>.\n  
\n  This documentation for Float is available\
 at\n  http://www.gap-system.org/Manuals/pkg/float-&Version;/doc/manual.p\
df in PDF format, and may be\n  accessed online at http://gap-packa\
ges.github.io/float/.\n  
\n  The latest release of the package may b\
e downloaded as\n  https://github.com/gap-packages/float/releases/downloa\
d/v&Version;/float-&Version;.tar.gz (tar, gzipped).\n  The latest reposi\
tory version (possibly unstable) may be downloaded as\n  https://github.c\
om/gap-packages/float/tarball/master (tar, gzipped),\n  https://git\
hub.com/gap-packages/float.git (git repository),\n  https://package\
s.debian.org/search?keywords=gap-float&searchon=names&suite=all&se\
ction=all (debian package), or\n  explored at https://github.com/ga\
p-packages/float/tree/master/.\n  \n  
\n    For comments or qu\
estions on Float please contact\n    the author.\n  \n  ©right; 2011-2016 by Laurent Bartholdi\n  \
\n  Part of this work is supported by the \"Swiss\n  Nationa\
l Fund for Scientific Research (SNF)\", the \"German National Science Foundati\
on (DFG)\",\n  and the Courant Research Centre \"Higher Order Structures\" of \
the University of Göttingen.\n  \n\n\n\n\n\n\n\nLicensing\n\nThis progra\
m is free software; you can redistribute it and/or modify\nit under the terms \
of the GNU General Public License as published by\nthe Free Software Foundatio\
n; either version 2 of the License, or any\nlater version.\n\n
 This progra\
m is distributed in the hope that it will be useful,\nbut WITHOUT ANY WARRANTY\
; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTI\
CULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\n
 \
You should have received a copy of the GNU General Public\nLicense along with \
this program, in the file COPYING.  If not, see\nhttp://www.gnu.org/licen\
ses/.\n\n\n\nFloat pa\
ckage\n\n
A sample run\n\
\nThe extended floating-point capabilities of &GAP; are installed by loading t\
he package\nvia LoadPackage(\"float\"); and selecting new floating-poin\
t handlers via\nSetFloats(MPFR), SetFloats(MPFI), SetFloats(M\
PC) orSetFloats(CXSC),\ndepending on whether high-precision real, i\
nterval or complex arithmetic are desired, or\nwhether a fast package containi\
ng all four real/complex element/interval arithmetic is desired:\n LoadPackage(\"float\");\nLoading FLOAT 0.7.0 ...\ntrue\ngap> SetF\
loats(MPFR); # floating-point\ngap> x := 4*Atan(1.0);\n.314159e1\ngap> Sin(x);\
\n.169569e-30\ngap> SetFloats(MPFR,1000); # 1000 bits\ngap> x := 4*Atan(1.0);\
\n.314159e1\ngap> Sin(x);\n.125154e-300\ngap> String(x,300);\n\".3141592653589\
793238462643383279502884197169399375105820974944592307816406286\\\n20899862803\
4825342117067982148086513282306647093844609550582231725359408128481\\\n1174502\
84102701938521105559644622948954930381964428810975665933446128475648233\\\n786\
78316527120190914564856692346034861045432664821339360726024914127e1\"\ngap>\ng\
ap> SetFloats(MPFI); # intervals\ngap> x := 4*Atan(1.0);\n.314159e1(99)\ngap> \
AbsoluteDiameter(x); Sup(x); Inf(x);\n.100441e-29\n.314159e1\n.314159e1\ngap> \
Sin(x);\n-.140815e-29(97)\ngap> 0.0 in last;\ntrue\ngap> 1.0; # exact represen\
tation\n.1e1(∞)\ngap> IncreaseInterval(last,0.001); # now only 8 significant\
 bits\n.1e1(8)\ngap> IncreaseInterval(last,-0.002); # now becomes empty\n∅\n\
gap> MinimalPolynomial(Rationals,Sqrt(2.0));\n-2*x_1^2+1\ngap> Cyc(last);\nE(8\
)-E(8)^3\ngap>\ngap> SetFloats(MPC); # complex numbers\ngap> z := 5.0-1.0i;\n.\
5e1-.1e1i\ngap> (1+1.0i)*last^4*(239+1.0i);\n.228488e6\ngap> Exp(6.2835i);\n.1\
e1+.314693e-3i\n]]>\n\n
\n\n\n\nPolynomials\n\nThe Floats pseudo-f\
ield\n\nPolynomials with floating-point coefficients may be manipula\
ted in\n&GAP;; though they behave, in subtle ways, quite differently than\npol\
ynomials over rings.\n\n\nThe \"pseudo-field\" of floating-point numbers i\
s an object in &GAP;,\ncalled FLOAT_PSEUDOFIELD. (It is not really a fi\
eld,\ne.g. because addition of floating-point numbers in not\nassociative). It\
 may be used to create indeterminates, for example as\n x := Indeterminate(FLOAT_PSEUDOFIELD,\"x\");\nx\ngap> 2*x^2+3;\n2.0*x^2+3.0\
\ngap> Value(last,10);\n203.0\n]]>\n\n
\n\nRoots of polynomials\n\nThe Jenkins-Traub algorithm has been imple\
mented, in arbitrary\nprecision for MPFR and MPC.\n\nFurthermore, CXSC can\
 provide complex enclosures for the roots of a\ncomplex polynomial.\n\n\n\n
Finding integer relations\nThe PSLQ algorit\
hm has been implemented by Steve A. Linton, as an external\r\ncontribution to \
Float. This algorithm receives as\r\ninput a vector of floa\
ts x and a required precision \\epsilon,\r\nand seeks an integer\
 vector v such that\r\n|x\\cdot v|<\\epsilon. The implementat\
ion follows quite closely the\r\noriginal article .\r\
\n\r\n\r\n  \r\n \
 \r\n  An\
 integer vector v with |x\\cdot v|<\\epsilon.\r\n  \
\r\n    The PSLQ algorithm by Bailey and Broadhurst (see )\r\n    searches for an integer relation between the entries\
 in x.\r\n\r\n    \\beta and \\gamma are algorithm tu\
ning parameters, and\r\n    default to 4/10 and 2/\\sqrt(3) resp\
ectively.\r\n\r\n    
The second form implements the \"Multi-pair\" variant\
 of the algorithm, which is\r\n    better suited to parallelization.\r\n PSLQ([1.0,(1+Sqrt(5.0))/2],1.e-2);\r\n[ 55, -34 ] # Fibon\
acci numbers\r\ngap> RootsFloat([1,-4,2]*1.0);\r\n[ 0.292893, 1.70711 ] # root\
s of 2x^2-4x+1\r\ngap> PSLQ(List([0..2],i->last[1]^i),1.e-7);\r\n[ 1, -4, 2 ] \
# a degree-2 polynomial fitting well\r\n]]>\r\n  \r\n<\
/ManSection>\r\n\n
\n\nLLL lattice reduction\n\nA faster implementation of the LLL lattice reduction algorithm has\nals\
o been implemented. It is accessible via the commands\nFPLLLReducedBasis(m)\
 and \nFPLLLShortestVector(m).\n\n\n\n\n\n\
\nImplemented packages\n\n\
MPFR\n\n  \n  \n  \n    The category of floating-point numb\
ers.\n\n     Note that they are treated as commutative and scalar, but are\
\n    not necessarily associative.\n  \n\n\n\n\n
MPFI\n\n  \n  \n  \n    The category of int\
ervals of floating-point numbers.\n\n     Note that they are treated as co\
mmutative and scalar, but are\n    not necessarily associative.\n  \n\n\n
\n\nMPC\n\n  \n  \n  \n    The category of intervals of floating-point numbers.\n\n     Note t\
hat they are treated as commutative and scalar, but are\n    not necessarily a\
ssociative.\n  \n\n\n
\n\nCXSC\n\n  \n  \n  \n  \n  \n  \n  \n  \n  \n    T\
he category of floating-point numbers.\n\n     Note that they are treated \
as commutative and scalar, but are\n    not necessarily associative.\n  \n\n\n
\n\nFPLLL\n\n  \n  A matri\
x spanning the same lattice as m.\n  \n    This \
function implements the LLL (Lenstra-Lenstra-Lovász) lattice\n    reduction a\
lgorithm via the external library fplll.\n\n     The re\
sult is guaranteed to be optimal up to 1%.\n  \n\n\
\n\n  \n  A\
 short vector in the lattice spanned by m.\n  \n\
    This function implements the LLL (Lenstra-Lenstra-Lovász) lattice\n    re\
duction algorithm via the external library fplll,\n    and \
then computes a short vector in this lattice.\n\n    
 The result is guaran\
teed to be optimal up to 1%.\n  \n\n\n\n\
\n\n\n\n\n\n\n\n\n", 
  inputorigins := [ [ 1, "doc/float.xml", 1 ], [ 40, "doc/float.xml", 2 ], 
      [ 41, "doc/float.xml", 3 ], [ 78, "doc/float.xml", 4 ], 
      [ 155, "doc/float.xml", 5 ], [ 156, "doc/../PackageInfo.g", 11 ], 
      [ 182, "doc/../PackageInfo.g", 12 ], [ 210, "doc/float.xml", 5 ], 
      [ 211, "doc/float.xml", 6 ], [ 214, "doc/float.xml", 7 ], 
      [ 234, "doc/float.xml", 8 ], [ 235, "doc/float.xml", 9 ], 
      [ 247, "doc/float.xml", 10 ], [ 287, "doc/float.xml", 11 ], 
      [ 326, "doc/float.xml", 12 ], [ 343, "doc/float.xml", 13 ], 
      [ 384, "doc/float.xml", 14 ], [ 402, "doc/float.xml", 15 ], 
      [ 430, "doc/float.xml", 16 ], [ 498, "doc/float.xml", 17 ], 
      [ 560, "doc/float.xml", 18 ], [ 621, "doc/float.xml", 19 ], 
      [ 633, "doc/float.xml", 20 ], [ 655, "doc/float.xml", 21 ], 
      [ 667, "doc/float.xml", 22 ], [ 750, "doc/float.xml", 23 ], 
      [ 763, "doc/float.xml", 24 ], [ 776, "doc/float.xml", 25 ], 
      [ 848, "doc/float.xml", 26 ], [ 916, "doc/float.xml", 27 ], 
      [ 936, "doc/float.xml", 28 ], [ 943, "doc/float.xml", 29 ], 
      [ 995, "doc/float.xml", 30 ], [ 1031, "doc/float.xml", 31 ], 
      [ 1038, "doc/float.xml", 32 ], [ 1104, "doc/float.xml", 33 ], 
      [ 1212, "doc/float.xml", 34 ], [ 1282, "doc/float.xml", 35 ], 
      [ 1289, "doc/float.xml", 36 ], [ 1346, "doc/float.xml", 37 ], 
      [ 1465, "doc/float.xml", 38 ], [ 1538, "doc/float.xml", 39 ], 
      [ 1620, "doc/float.xml", 40 ], [ 1693, "doc/float.xml", 41 ], 
      [ 1830, "doc/float.xml", 42 ], [ 1907, "doc/float.xml", 43 ], 
      [ 1916, "doc/float.xml", 44 ], [ 1923, "doc/float.xml", 45 ], 
      [ 1996, "doc/float.xml", 46 ], [ 2012, "doc/float.xml", 47 ], 
      [ 2026, "doc/float.xml", 48 ], [ 2082, "doc/float.xml", 49 ], 
      [ 2097, "doc/float.xml", 50 ], [ 2162, "doc/float.xml", 51 ], 
      [ 2258, "doc/float.xml", 52 ], [ 2351, "doc/float.xml", 53 ], 
      [ 2373, "doc/float.xml", 54 ], [ 2374, "doc/float.xml", 55 ], 
      [ 2387, "doc/float.xml", 56 ], [ 2388, "doc/float.xml", 57 ], 
      [ 2407, "doc/float.xml", 58 ], [ 2408, "doc/float.xml", 59 ], 
      [ 2415, "doc/float.xml", 60 ], [ 2416, "doc/float.xml", 61 ], 
      [ 2454, "doc/float.xml", 62 ], [ 2455, "doc/float.xml", 63 ], 
      [ 2524, "doc/float.xml", 64 ], [ 2593, "doc/float.xml", 65 ], 
      [ 2663, "doc/float.xml", 66 ], [ 2678, "doc/float.xml", 67 ], 
      [ 2679, "doc/float.xml", 68 ], [ 2748, "doc/float.xml", 69 ], 
      [ 2811, "doc/float.xml", 70 ], [ 2877, "doc/float.xml", 71 ], 
      [ 2918, "doc/float.xml", 72 ], [ 2919, "doc/float.xml", 73 ], 
      [ 2982, "doc/float.xml", 74 ], [ 3049, "doc/float.xml", 75 ], 
      [ 3090, "doc/float.xml", 76 ], [ 3091, "doc/float.xml", 77 ], 
      [ 3102, "doc/float.xml", 78 ], [ 3103, "doc/float.xml", 79 ], 
      [ 3166, "doc/float.xml", 80 ], [ 3167, "doc/float.xml", 81 ], 
      [ 3223, "doc/float.xml", 82 ], [ 3224, "doc/float.xml", 83 ], 
      [ 3311, "doc/float.xml", 84 ], [ 3390, "doc/float.xml", 85 ], 
      [ 3486, "doc/float.xml", 86 ], [ 3575, "doc/float.xml", 87 ], 
      [ 3671, "doc/float.xml", 88 ], [ 3690, "doc/float.xml", 89 ], 
      [ 3717, "doc/float.xml", 90 ], [ 3741, "doc/float.xml", 91 ], 
      [ 3746, "doc/float.xml", 92 ], [ 3785, "doc/float.xml", 93 ], 
      [ 3808, "doc/float.xml", 94 ], [ 3818, "doc/float.xml", 95 ], 
      [ 3831, "doc/float.xml", 96 ], [ 3843, "doc/float.xml", 97 ], 
      [ 3882, "doc/float.xml", 98 ], [ 3905, "doc/float.xml", 99 ], 
      [ 3915, "doc/float.xml", 100 ], [ 3928, "doc/float.xml", 101 ], 
      [ 3941, "doc/float.xml", 102 ], [ 3961, "doc/float.xml", 103 ], 
      [ 4041, "doc/float.xml", 104 ], [ 4121, "doc/float.xml", 105 ], 
      [ 4201, "doc/float.xml", 106 ], [ 4273, "doc/float.xml", 107 ], 
      [ 4278, "doc/float.xml", 108 ], [ 4312, "doc/float.xml", 109 ], 
      [ 4335, "doc/float.xml", 110 ], [ 4349, "doc/float.xml", 111 ], 
      [ 4391, "doc/float.xml", 112 ], [ 4403, "doc/float.xml", 113 ], 
      [ 4413, "doc/float.xml", 114 ], [ 4423, "doc/float.xml", 115 ], 
      [ 4436, "doc/float.xml", 116 ], [ 4453, "doc/float.xml", 117 ], 
      [ 4471, "doc/float.xml", 118 ], [ 4476, "doc/float.xml", 119 ], 
      [ 4509, "doc/float.xml", 120 ], [ 4519, "doc/float.xml", 121 ], 
      [ 4584, "doc/float.xml", 122 ], [ 4592, "doc/float.xml", 123 ], 
      [ 4648, "doc/float.xml", 124 ], [ 4652, "doc/float.xml", 125 ], 
      [ 4697, "doc/float.xml", 126 ], [ 4708, "doc/float.xml", 127 ], 
      [ 4724, "doc/float.xml", 128 ], [ 4736, "doc/float.xml", 129 ], 
      [ 4741, "doc/float.xml", 130 ], [ 4780, "doc/float.xml", 131 ], 
      [ 4800, "doc/float.xml", 132 ], [ 4811, "doc/float.xml", 133 ], 
      [ 4844, "doc/float.xml", 134 ], [ 4854, "doc/float.xml", 135 ], 
      [ 4873, "doc/float.xml", 136 ], [ 4890, "doc/float.xml", 137 ], 
      [ 4904, "doc/float.xml", 138 ], [ 4905, "doc/float.xml", 139 ], 
      [ 4916, "doc/float.xml", 140 ], [ 4917, "doc/float.xml", 141 ], 
      [ 4928, "doc/float.xml", 142 ], [ 4929, "doc/float.xml", 143 ], 
      [ 4982, "doc/float.xml", 144 ], [ 4983, "doc/float.xml", 145 ], 
      [ 5035, "doc/float.xml", 146 ], [ 5036, "doc/float.xml", 147 ], 
      [ 5103, "doc/float.xml", 148 ], [ 5169, "doc/float.xml", 149 ], 
      [ 5193, "doc/float.xml", 150 ], [ 5198, "doc/float.xml", 151 ], 
      [ 5199, "doc/float.xml", 152 ], [ 5267, "doc/float.xml", 153 ], 
      [ 5327, "doc/float.xml", 154 ], [ 5382, "doc/float.xml", 155 ], 
      [ 5452, "doc/float.xml", 156 ], [ 5471, "doc/float.xml", 157 ], 
      [ 5519, "doc/float.xml", 158 ], [ 5521, "doc/float.xml", 159 ], 
      [ 5535, "doc/float.xml", 160 ], [ 5547, "doc/float.xml", 161 ], 
      [ 5568, "doc/float.xml", 162 ], [ 5574, "doc/float.xml", 163 ], 
      [ 5588, "doc/float.xml", 164 ], [ 5589, "doc/float.xml", 165 ], 
      [ 5600, "doc/float.xml", 166 ], [ 5601, "doc/float.xml", 167 ], 
      [ 5650, "doc/float.xml", 168 ], [ 5651, "doc/float.xml", 169 ], 
      [ 5714, "doc/float.xml", 170 ], [ 5742, "doc/float.xml", 171 ], 
      [ 5747, "doc/float.xml", 172 ], [ 5815, "doc/float.xml", 173 ], 
      [ 5835, "doc/float.xml", 174 ], [ 5836, "doc/float.xml", 175 ], 
      [ 5847, "doc/float.xml", 176 ], [ 5848, "doc/float.xml", 177 ], 
      [ 5902, "doc/../lib/pslq.gi", 25 ], [ 5978, "doc/../lib/pslq.gi", 26 ], 
      [ 6048, "doc/../lib/pslq.gi", 27 ], [ 6125, "doc/../lib/pslq.gi", 28 ], 
      [ 6173, "doc/../lib/pslq.gi", 29 ], [ 6250, "doc/../lib/pslq.gi", 30 ], 
      [ 6293, "doc/../lib/pslq.gi", 31 ], [ 6295, "doc/../lib/pslq.gi", 32 ], 
      [ 6309, "doc/../lib/pslq.gi", 33 ], [ 6358, "doc/../lib/pslq.gi", 34 ], 
      [ 6418, "doc/../lib/pslq.gi", 35 ], [ 6503, "doc/../lib/pslq.gi", 36 ], 
      [ 6520, "doc/../lib/pslq.gi", 37 ], [ 6599, "doc/../lib/pslq.gi", 38 ], 
      [ 6670, "doc/../lib/pslq.gi", 39 ], [ 6672, "doc/../lib/pslq.gi", 40 ], 
      [ 6749, "doc/../lib/pslq.gi", 41 ], [ 6813, "doc/../lib/pslq.gi", 42 ], 
      [ 6815, "doc/../lib/pslq.gi", 43 ], [ 6903, "doc/../lib/pslq.gi", 44 ], 
      [ 6942, "doc/../lib/pslq.gi", 45 ], [ 6962, "doc/../lib/pslq.gi", 46 ], 
      [ 7003, "doc/../lib/pslq.gi", 47 ], [ 7036, "doc/../lib/pslq.gi", 48 ], 
      [ 7068, "doc/../lib/pslq.gi", 49 ], [ 7112, "doc/../lib/pslq.gi", 50 ], 
      [ 7157, "doc/../lib/pslq.gi", 51 ], [ 7208, "doc/../lib/pslq.gi", 52 ], 
      [ 7223, "doc/../lib/pslq.gi", 53 ], [ 7241, "doc/../lib/pslq.gi", 54 ], 
      [ 7256, "doc/float.xml", 178 ], [ 7257, "doc/float.xml", 179 ], 
      [ 7268, "doc/float.xml", 180 ], [ 7269, "doc/float.xml", 181 ], 
      [ 7319, "doc/float.xml", 182 ], [ 7320, "doc/float.xml", 183 ], 
      [ 7387, "doc/float.xml", 184 ], [ 7444, "doc/float.xml", 185 ], 
      [ 7477, "doc/float.xml", 186 ], [ 7508, "doc/float.xml", 187 ], 
      [ 7513, "doc/float.xml", 188 ], [ 7514, "doc/float.xml", 189 ], 
      [ 7525, "doc/float.xml", 190 ], [ 7526, "doc/float.xml", 191 ], 
      [ 7537, "doc/float.xml", 192 ], [ 7538, "doc/float.xml", 193 ], 
      [ 7600, "doc/float.xml", 194 ], [ 7601, "doc/float.xml", 195 ], 
      [ 7634, "doc/../lib/float.gd", 19 ], [ 7647, "doc/../lib/float.gd", 20 ]
        , [ 7676, "doc/../lib/float.gd", 21 ], 
      [ 7702, "doc/../lib/float.gd", 22 ], [ 7718, "doc/../lib/float.gd", 23 ]
        , [ 7762, "doc/../lib/float.gd", 24 ], 
      [ 7763, "doc/../lib/float.gd", 25 ], [ 7834, "doc/../lib/float.gd", 26 ]
        , [ 7867, "doc/../lib/float.gd", 27 ], 
      [ 7884, "doc/../lib/float.gd", 28 ], [ 7898, "doc/float.xml", 196 ], 
      [ 7899, "doc/float.xml", 197 ], [ 7910, "doc/float.xml", 198 ], 
      [ 7911, "doc/float.xml", 199 ], [ 7944, "doc/../lib/float.gd", 46 ], 
      [ 7957, "doc/../lib/float.gd", 47 ], [ 7986, "doc/../lib/float.gd", 48 ]
        , [ 8012, "doc/../lib/float.gd", 49 ], 
      [ 8028, "doc/../lib/float.gd", 50 ], [ 8085, "doc/../lib/float.gd", 51 ]
        , [ 8086, "doc/../lib/float.gd", 52 ], 
      [ 8157, "doc/../lib/float.gd", 53 ], [ 8190, "doc/../lib/float.gd", 54 ]
        , [ 8207, "doc/../lib/float.gd", 55 ], [ 8221, "doc/float.xml", 200 ],
      [ 8222, "doc/float.xml", 201 ], [ 8233, "doc/float.xml", 202 ], 
      [ 8234, "doc/float.xml", 203 ], [ 8266, "doc/../lib/float.gd", 73 ], 
      [ 8279, "doc/../lib/float.gd", 74 ], [ 8307, "doc/../lib/float.gd", 75 ]
        , [ 8332, "doc/../lib/float.gd", 76 ], 
      [ 8348, "doc/../lib/float.gd", 77 ], [ 8405, "doc/../lib/float.gd", 78 ]
        , [ 8406, "doc/../lib/float.gd", 79 ], 
      [ 8477, "doc/../lib/float.gd", 80 ], [ 8510, "doc/../lib/float.gd", 81 ]
        , [ 8527, "doc/../lib/float.gd", 82 ], [ 8541, "doc/float.xml", 204 ],
      [ 8542, "doc/float.xml", 205 ], [ 8553, "doc/float.xml", 206 ], 
      [ 8554, "doc/float.xml", 207 ], [ 8587, "doc/../lib/float.gd", 102 ], 
      [ 8600, "doc/../lib/float.gd", 103 ], 
      [ 8628, "doc/../lib/float.gd", 104 ], 
      [ 8659, "doc/../lib/float.gd", 105 ], 
      [ 8691, "doc/../lib/float.gd", 106 ], 
      [ 8718, "doc/../lib/float.gd", 107 ], 
      [ 8747, "doc/../lib/float.gd", 108 ], 
      [ 8776, "doc/../lib/float.gd", 109 ], 
      [ 8805, "doc/../lib/float.gd", 110 ], 
      [ 8834, "doc/../lib/float.gd", 111 ], 
      [ 8850, "doc/../lib/float.gd", 112 ], 
      [ 8894, "doc/../lib/float.gd", 113 ], 
      [ 8895, "doc/../lib/float.gd", 114 ], 
      [ 8966, "doc/../lib/float.gd", 115 ], 
      [ 8999, "doc/../lib/float.gd", 116 ], 
      [ 9016, "doc/../lib/float.gd", 117 ], [ 9030, "doc/float.xml", 208 ], 
      [ 9031, "doc/float.xml", 209 ], [ 9042, "doc/float.xml", 210 ], 
      [ 9043, "doc/float.xml", 211 ], [ 9077, "doc/../lib/float.gd", 156 ], 
      [ 9090, "doc/../lib/float.gd", 157 ], 
      [ 9133, "doc/../lib/float.gd", 158 ], 
      [ 9202, "doc/../lib/float.gd", 159 ], 
      [ 9218, "doc/../lib/float.gd", 160 ], 
      [ 9289, "doc/../lib/float.gd", 161 ], 
      [ 9364, "doc/../lib/float.gd", 162 ], 
      [ 9365, "doc/../lib/float.gd", 163 ], 
      [ 9423, "doc/../lib/float.gd", 164 ], 
      [ 9440, "doc/../lib/float.gd", 165 ], 
      [ 9454, "doc/../lib/float.gd", 166 ], 
      [ 9455, "doc/../lib/float.gd", 167 ], 
      [ 9468, "doc/../lib/float.gd", 168 ], 
      [ 9513, "doc/../lib/float.gd", 169 ], 
      [ 9585, "doc/../lib/float.gd", 170 ], 
      [ 9601, "doc/../lib/float.gd", 171 ], 
      [ 9672, "doc/../lib/float.gd", 172 ], 
      [ 9747, "doc/../lib/float.gd", 173 ], 
      [ 9801, "doc/../lib/float.gd", 174 ], 
      [ 9802, "doc/../lib/float.gd", 175 ], 
      [ 9860, "doc/../lib/float.gd", 176 ], 
      [ 9877, "doc/../lib/float.gd", 177 ], [ 9891, "doc/float.xml", 212 ], 
      [ 9892, "doc/float.xml", 213 ], [ 9903, "doc/float.xml", 214 ], 
      [ 9904, "doc/float.xml", 215 ], [ 9915, "doc/float.xml", 216 ], 
      [ 9916, "doc/float.xml", 217 ], [ 9924, "doc/float.xml", 218 ], 
      [ 9925, "doc/float.xml", 219 ], [ 9966, "doc/float.xml", 220 ], 
      [ 9978, "doc/float.xml", 221 ], [ 9979, "doc/float.xml", 222 ] ], 
  labels := 
    rec( FPLLLReducedBasis := [ "4.5-1", "chap4.html#X832DFC257C5C4D32" ], 
      FPLLLShortestVector := [ "4.5-2", "chap4.html#X7C759DED84B77805" ], 
      IsCXSCBox := [ "4.4-1", "chap4.html#X794C3A0F7925BDA1" ], 
      IsCXSCComplex := [ "4.4-1", "chap4.html#X794C3A0F7925BDA1" ], 
      IsCXSCInterval := [ "4.4-1", "chap4.html#X794C3A0F7925BDA1" ], 
      IsCXSCReal := [ "4.4-1", "chap4.html#X794C3A0F7925BDA1" ], 
      IsMPCFloat := [ "4.3-1", "chap4.html#X7D7AD4C67FF04E38" ], 
      IsMPFIFloat := [ "4.2-1", "chap4.html#X842290DB8034BF90" ], 
      IsMPFRFloat := [ "4.1-1", "chap4.html#X82B38FFE86A5A0B5" ], 
      PSLQ := [ "3.3-1", "chap3.html#X85DEB4B584870F67" ], 
      PSLQ_MP := [ "3.3-1", "chap3.html#X85DEB4B584870F67" ], 
      TYPE_CXSC_CI := [ "4.4-1", "chap4.html#X794C3A0F7925BDA1" ], 
      TYPE_CXSC_CP := [ "4.4-1", "chap4.html#X794C3A0F7925BDA1" ], 
      TYPE_CXSC_RI := [ "4.4-1", "chap4.html#X794C3A0F7925BDA1" ], 
      TYPE_CXSC_RP := [ "4.4-1", "chap4.html#X794C3A0F7925BDA1" ], 
      TYPE_MPC := [ "4.3-1", "chap4.html#X7D7AD4C67FF04E38" ], 
      TYPE_MPFI := [ "4.2-1", "chap4.html#X842290DB8034BF90" ], 
      TYPE_MPFR := [ "4.1-1", "chap4.html#X82B38FFE86A5A0B5" ], 
      floatpackage := [ "2", "chap2.html#X7E12358984CA3111" ], 
      impl := [ "4", "chap4.html#X82DC33E982C4D157" ], 
      poly := [ "3", "chap3.html#X826D8334845549EC" ], 
      sample := [ "2.1", "chap2.html#X7B4092CA7ABB93B0" ] ), 
  labeltexts := 
    rec( floatpackage := "Float package", 
      impl := "Implemented packages", 
      poly := "Polynomials", 
      sample := "A sample run" ), 
  linelength := 76, mathmode := "Text", name := "WHOLEDOCUMENT", 
  next := 10003, root := ~, 
  six := 
    [ 
      [ "Title page", ".", [ 0, 0, 0 ], 1, 1, "title page", 
          "X7D2C85EC87DD46E5" ], 
      [ "Abstract", ".-1", [ 0, 0, 1 ], 32, 2, "abstract", 
          "X7AA6C5737B711C89" ], 
      [ "Copyright", ".-2", [ 0, 0, 2 ], 40, 2, "copyright", 
          "X81488B807F2A1CF1" ], 
      [ "Acknowledgements", ".-3", [ 0, 0, 3 ], 45, 2, "acknowledgements", 
          "X82A988D47DFAFCFA" ], 
      [ "Table of Contents", ".-4", [ 0, 0, 4 ], 53, 3, "table of contents", 
          "X8537FEB07AF2BEC8" ], 
      [ "\033[1X\033[33X\033[0;-2YLicensing\033[133X\033[101X", "1", 
          [ 1, 0, 0 ], 1, 4, "licensing", "X86DB23CC834ABD71" ], 
      [ "\033[1X\033[33X\033[0;-2YFloat package\033[133X\033[101X", "2", 
          [ 2, 0, 0 ], 1, 5, "float package", "X7E12358984CA3111" ], 
      [ "\033[1X\033[33X\033[0;-2YA sample run\033[133X\033[101X", "2.1", 
          [ 2, 1, 0 ], 4, 5, "a sample run", "X7B4092CA7ABB93B0" ], 
      [ "\033[1X\033[33X\033[0;-2YPolynomials\033[133X\033[101X", "3", 
          [ 3, 0, 0 ], 1, 7, "polynomials", "X826D8334845549EC" ], 
      [ "\033[1X\033[33X\033[0;-2YThe Floats pseudo-field\033[133X\033[101X", 
          "3.1", [ 3, 1, 0 ], 4, 7, "the floats pseudo-field", 
          "X7BDA2E7C85ECC18C" ], 
      [ "\033[1X\033[33X\033[0;-2YRoots of polynomials\033[133X\033[101X", 
          "3.2", [ 3, 2, 0 ], 25, 7, "roots of polynomials", 
          "X788CDC24834012D7" ], 
      [ "\033[1X\033[33X\033[0;-2YFinding integer relations\033[133X\033[101X"
            , "3.3", [ 3, 3, 0 ], 34, 7, "finding integer relations", 
          "X7C9EF7E27EFA3288" ], 
      [ "\033[1X\033[33X\033[0;-2YLLL lattice reduction\033[133X\033[101X", 
          "3.4", [ 3, 4, 0 ], 66, 8, "lll lattice reduction", 
          "X83445BFB7901B88F" ], 
      [ "\033[1X\033[33X\033[0;-2YImplemented packages\033[133X\033[101X", 
          "4", [ 4, 0, 0 ], 1, 9, "implemented packages", "X82DC33E982C4D157" 
         ], 
      [ "\033[1X\033[33X\033[0;-2YMPFR\033[133X\033[101X", "4.1", 
          [ 4, 1, 0 ], 4, 9, "mpfr", "X79E38C3781F79E35" ], 
      [ "\033[1X\033[33X\033[0;-2YMPFI\033[133X\033[101X", "4.2", 
          [ 4, 2, 0 ], 17, 9, "mpfi", "X8145D0A97986133C" ], 
      [ "\033[1X\033[33X\033[0;-2YMPC\033[133X\033[101X", "4.3", [ 4, 3, 0 ], 
          30, 9, "mpc", "X82C3C26F7C11A26F" ], 
      [ "\033[1X\033[33X\033[0;-2YCXSC\033[133X\033[101X", "4.4", 
          [ 4, 4, 0 ], 43, 10, "cxsc", "X82DF12317C250153" ], 
      [ "\033[1X\033[33X\033[0;-2YFPLLL\033[133X\033[101X", "4.5", 
          [ 4, 5, 0 ], 62, 10, "fplll", "X7CD9EDF079B439BC" ], 
      [ "Bibliography", "Bib", [ "Bib", 0, 0 ], 1, 11, "bibliography", 
          "X7A6F98FD85F02BFE" ], 
      [ "References", "Bib", [ "Bib", 0, 0 ], 1, 11, "references", 
          "X7A6F98FD85F02BFE" ], 
      [ "Index", "Ind", [ "Ind", 0, 0 ], 1, 12, "index", "X83A0356F839C696F" ]
        , 
      [ "\033[2XPSLQ\033[102X", "3.3-1", [ 3, 3, 1 ], 42, 7, "pslq", 
          "X85DEB4B584870F67" ], 
      [ "\033[2XPSLQ_MP\033[102X", "3.3-1", [ 3, 3, 1 ], 42, 7, "pslq_mp", 
          "X85DEB4B584870F67" ], 
      [ "\033[2XIsMPFRFloat\033[102X", "4.1-1", [ 4, 1, 1 ], 7, 9, 
          "ismpfrfloat", "X82B38FFE86A5A0B5" ], 
      [ "\033[2XTYPE_MPFR\033[102X", "4.1-1", [ 4, 1, 1 ], 7, 9, "type_mpfr", 
          "X82B38FFE86A5A0B5" ], 
      [ "\033[2XIsMPFIFloat\033[102X", "4.2-1", [ 4, 2, 1 ], 20, 9, 
          "ismpfifloat", "X842290DB8034BF90" ], 
      [ "\033[2XTYPE_MPFI\033[102X", "4.2-1", [ 4, 2, 1 ], 20, 9, 
          "type_mpfi", "X842290DB8034BF90" ], 
      [ "\033[2XIsMPCFloat\033[102X", "4.3-1", [ 4, 3, 1 ], 33, 9, 
          "ismpcfloat", "X7D7AD4C67FF04E38" ], 
      [ "\033[2XTYPE_MPC\033[102X", "4.3-1", [ 4, 3, 1 ], 33, 9, "type_mpc", 
          "X7D7AD4C67FF04E38" ], 
      [ "\033[2XIsCXSCReal\033[102X", "4.4-1", [ 4, 4, 1 ], 46, 10, 
          "iscxscreal", "X794C3A0F7925BDA1" ], 
      [ "\033[2XIsCXSCComplex\033[102X", "4.4-1", [ 4, 4, 1 ], 46, 10, 
          "iscxsccomplex", "X794C3A0F7925BDA1" ], 
      [ "\033[2XIsCXSCInterval\033[102X", "4.4-1", [ 4, 4, 1 ], 46, 10, 
          "iscxscinterval", "X794C3A0F7925BDA1" ], 
      [ "\033[2XIsCXSCBox\033[102X", "4.4-1", [ 4, 4, 1 ], 46, 10, 
          "iscxscbox", "X794C3A0F7925BDA1" ], 
      [ "\033[2XTYPE_CXSC_RP\033[102X", "4.4-1", [ 4, 4, 1 ], 46, 10, 
          "type_cxsc_rp", "X794C3A0F7925BDA1" ], 
      [ "\033[2XTYPE_CXSC_CP\033[102X", "4.4-1", [ 4, 4, 1 ], 46, 10, 
          "type_cxsc_cp", "X794C3A0F7925BDA1" ], 
      [ "\033[2XTYPE_CXSC_RI\033[102X", "4.4-1", [ 4, 4, 1 ], 46, 10, 
          "type_cxsc_ri", "X794C3A0F7925BDA1" ], 
      [ "\033[2XTYPE_CXSC_CI\033[102X", "4.4-1", [ 4, 4, 1 ], 46, 10, 
          "type_cxsc_ci", "X794C3A0F7925BDA1" ], 
      [ "\033[2XFPLLLReducedBasis\033[102X", "4.5-1", [ 4, 5, 1 ], 65, 10, 
          "fplllreducedbasis", "X832DFC257C5C4D32" ], 
      [ "\033[2XFPLLLShortestVector\033[102X", "4.5-2", [ 4, 5, 2 ], 75, 10, 
          "fplllshortestvector", "X7C759DED84B77805" ] ], 
  sixcount := [ [ 0, 0, 0 ], [ 0, 0, 1 ], [ 0, 0, 2 ], [ 0, 0, 3 ], 
      [ 0, 0, 4 ], [ 1, 0, 0 ], [ 2, 0, 0 ], [ 2, 1, 0 ], [ 3, 0, 0 ], 
      [ 3, 1, 0 ], [ 3, 2, 0 ], [ 3, 3, 0 ], [ 3, 3, 1 ], [ 3, 3, 1 ], 
      [ 3, 4, 0 ], [ 4, 0, 0 ], [ 4, 1, 0 ], [ 4, 1, 1 ], [ 4, 1, 1 ], 
      [ 4, 2, 0 ], [ 4, 2, 1 ], [ 4, 2, 1 ], [ 4, 3, 0 ], [ 4, 3, 1 ], 
      [ 4, 3, 1 ], [ 4, 4, 0 ], [ 4, 4, 1 ], [ 4, 4, 1 ], [ 4, 4, 1 ], 
      [ 4, 4, 1 ], [ 4, 4, 1 ], [ 4, 4, 1 ], [ 4, 4, 1 ], [ 4, 4, 1 ], 
      [ 4, 5, 0 ], [ 4, 5, 1 ], [ 4, 5, 2 ], [ "Bib", 0, 0 ], [ "Bib", 0, 0 ],
      [ "Ind", 0, 0 ] ], 
  sixindex := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 24, 23, 13, 14, 15, 
      26, 25, 16, 27, 28, 17, 29, 30, 18, 38, 37, 31, 32, 33, 34, 35, 36, 19, 
      39, 40, 21, 20, 22 ], start := 0, stop := 10002, 
  toctext := "1 Licensing\n
\n2 Float pa\
ckage\n 2.1 A sample run\n\n
\n
\n3 P\
olynomials\n 3.1 The Floats pseudo-field\n\n
\n <\
a href=\"chap3.html#X788CDC24834012D7\">3.2 Roots of p\
olynomials\n\n
\n 3.3 Finding integer relations\n\n\n
  3.3-1 PSLQ<\
/a>\n
\n 3.4 LLL lattice reduction\n\n
\n\n4 Implemented packages\n 4.1 MPFR\n\n\n
 \
; 4.1-1 IsMPFRFloat\n
\n 4.2 MPFI\n\n\n
  4.2-1 IsMPFIFloat\n
\n 4.3 MPC<\
/a>\n\n\n
  4.\
3-1 IsMPCFloat\n
\n 4.4 CXSC\n\n\n
  \
4.4-1 IsCXSCReal\n<\
/div>
\n 4.5 FPLLL\n\n\n
  4.5-1 FPLLLReducedBasis\n
  4.5-2 FPLLLShortestVector\n
\n
\nReferences\
\nIndex
\n1 Licensing\n\n2 Float package\n 2.1 A sample run\n\n\
\n
\n3 <\
span class=\"Heading\">Polynomials\n 3.1 The Floats pseudo-field\
\n\n
\n 3.2 Roots of polynomials\n\n
\n 3.3 Finding integer r\
elations\n\n\n
  3.3-1 PSLQ\n
\n 3.4 LLL lattice reduction\n\n
\n
\n4 Implemented packages\n 4.1 MPFR\n\n\n
  4.1-1 IsMPFRFloat\n
\n 4.2 MPFI\n\n\n
 &\
nbsp;4.2-1 IsMPFIFloat\n
\n 4.3 MPC\n\n\n
  4.3-1 IsMPCFloat\n
\n 4.4 CXSC\
\n\n\n
  4.4-1\
 IsCXSCReal\n
\n 4.5 FPLLL\n\n\n
  4.5-1 FPLLLReducedBasis\n
  4.5-2 FPLLLShortestVector\n
\n
\nReferences
\nIndex\n" )
gap> gap> Loading modules [mpfr, mpfi, mpc, fplll, cxsc] for float 0.9.1 ...
#I  File: /builddir/build/BUILD/float-0.9.1/../pkg/float-0.9.1/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.6uENPO
+ umask 022
+ cd /builddir/build/BUILD
+ '[' /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64 '!=' / ']'
+ rm -rf /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64
++ dirname /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64
+ mkdir -p /builddir/build/BUILDROOT
+ mkdir /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64
+ cd float-0.9.1
+ /usr/bin/make install DESTDIR=/builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64 'INSTALL=/usr/bin/install -p'
Making install in src
make[1]: Entering directory '/builddir/build/BUILD/float-0.9.1/src'
make[2]: Entering directory '/builddir/build/BUILD/float-0.9.1/src'
 /usr/bin/mkdir -p '/builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/lib/gap/pkg/float/bin/riscv64-redhat-linux-gnu-default64-kv3'
 /bin/sh ../libtool   --mode=install /usr/bin/install -p   float.la '/builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/lib/gap/pkg/float/bin/riscv64-redhat-linux-gnu-default64-kv3'
libtool: install: /usr/bin/install -p .libs/float.so /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/lib/gap/pkg/float/bin/riscv64-redhat-linux-gnu-default64-kv3/float.so
libtool: install: /usr/bin/install -p .libs/float.lai /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/lib/gap/pkg/float/bin/riscv64-redhat-linux-gnu-default64-kv3/float.la
libtool: warning: remember to run 'libtool --finish /usr/lib/gap/pkg/float/bin/riscv64-redhat-linux-gnu-default64-kv3'
make[2]: Nothing to be done for 'install-data-am'.
make[2]: Leaving directory '/builddir/build/BUILD/float-0.9.1/src'
make[1]: Leaving directory '/builddir/build/BUILD/float-0.9.1/src'
make[1]: Entering directory '/builddir/build/BUILD/float-0.9.1'
make[2]: Entering directory '/builddir/build/BUILD/float-0.9.1'
make[2]: Nothing to be done for 'install-exec-am'.
make[2]: Nothing to be done for 'install-data-am'.
make[2]: Leaving directory '/builddir/build/BUILD/float-0.9.1'
make[1]: Leaving directory '/builddir/build/BUILD/float-0.9.1'
+ mv /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/lib/gap/pkg/float /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/lib/gap/pkg/float-0.9.1
+ rm -f /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/lib/gap/pkg/float-0.9.1/bin/riscv64-redhat-linux-gnu-default64-kv3/float.la
+ cp -a PackageInfo.g init.g makedoc.g read.g lib tst /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/lib/gap/pkg/float-0.9.1
+ rm -f /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/lib/gap/pkg/float-0.9.1/lib/Makefile.am /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/lib/gap/pkg/float-0.9.1/tst/Makefile.am
+ mkdir -p /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/lib/gap/pkg/float-0.9.1/doc
+ cp -p doc/floatbib.xml.bib doc/lefttoc.css doc/manual.css doc/nocolorprompt.css doc/ragged.css doc/times.css doc/toggless.css doc/chap0.html doc/chap1.html doc/chap2.html doc/chap3.html doc/chap4.html doc/chapBib.html doc/chapInd.html doc/chooser.html doc/manual.js doc/rainbow.js doc/toggless.js doc/manual.lab doc/manual.pdf doc/manual.six doc/float.toc doc/chap0.txt doc/chap1.txt doc/chap2.txt doc/chap3.txt doc/chap4.txt doc/chapBib.txt doc/chapInd.txt doc/float.xml doc/floatbib.xml /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/lib/gap/pkg/float-0.9.1/doc
+ /usr/lib/rpm/find-debuginfo.sh -j4 --strict-build-id -m -i --build-id-seed 0.9.1-8.fc33 --unique-debug-suffix -0.9.1-8.fc33.riscv64 --unique-debug-src-base gap-pkg-float-0.9.1-8.fc33.riscv64 --run-dwz --dwz-low-mem-die-limit 10000000 --dwz-max-die-limit 50000000 -S debugsourcefiles.list /builddir/build/BUILD/float-0.9.1
explicitly decompress any DWARF compressed ELF sections in /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/lib/gap/pkg/float-0.9.1/bin/riscv64-redhat-linux-gnu-default64-kv3/float.so
extracting debug info from /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/lib/gap/pkg/float-0.9.1/bin/riscv64-redhat-linux-gnu-default64-kv3/float.so
original debug info size: 2528kB, size after compression: 2380kB
/usr/lib/rpm/sepdebugcrcfix: Updated 1 CRC32s, 0 CRC32s did match.
280 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
Executing(%check): /bin/sh -e /var/tmp/rpm-tmp.KgUipO
+ umask 022
+ cd /builddir/build/BUILD
+ cd float-0.9.1
+ gap -l '/builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/lib/gap;/usr/lib/gap'
 *********   GAP 4.10.2 of 19-Jun-2019
 *  GAP  *   https://www.gap-system.org
 *********   Architecture: riscv64-redhat-linux-gnu-default64-kv3
 Configuration:  gmp 6.2.0, 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 3.4.0, SmallGrp 1.4.1, TransGrp 2.0.5
 Try '??help' for help. See also '?copyright', '?cite' and '?authors'
gap> Loading modules [mpfr, mpfi, mpc, fplll, cxsc] for float 0.9.1 ...
true
gap> gap> [ dir("/builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/lib/ga\
p/pkg/float-0.9.1/tst/") ]
gap> gap> true
gap> gap> gap> gap> arithmetic
msecs: 18
true
gap> gap> > #I  testing MPFR...
> > arithmetic
msecs: 31
> > > gap> gap> > #I  testing MPFI...
> > arithmetic
msecs: 33
> > > gap> gap> > #I  testing MPC...
> > arithmetic
msecs: 11
> > > polynomials
msecs: 94
> > > gap> gap> > #I  testing CXSC...
> > arithmetic
msecs: 24
> > > polynomials
msecs: 50
> > > gap> gap> > #I  testing FPLLL...
> fplll
msecs: 24
> > > gap> gap> gap> > #I  No errors detected while testing package float
> > > > > + RPM_EC=0
++ jobs -p
+ exit 0
Processing files: gap-pkg-float-0.9.1-8.fc33.riscv64
Executing(%doc): /bin/sh -e /var/tmp/rpm-tmp.rQONcN
+ umask 022
+ cd /builddir/build/BUILD
+ cd float-0.9.1
+ DOCDIR=/builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/share/doc/gap-pkg-float
+ export LC_ALL=C
+ LC_ALL=C
+ export DOCDIR
+ /usr/bin/mkdir -p /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/share/doc/gap-pkg-float
+ cp -pr README /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/share/doc/gap-pkg-float
+ cp -pr THANKS /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/share/doc/gap-pkg-float
+ RPM_EC=0
++ jobs -p
+ exit 0
Executing(%license): /bin/sh -e /var/tmp/rpm-tmp.JO2U8N
+ umask 022
+ cd /builddir/build/BUILD
+ cd float-0.9.1
+ LICENSEDIR=/builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/share/licenses/gap-pkg-float
+ export LC_ALL=C
+ LC_ALL=C
+ export LICENSEDIR
+ /usr/bin/mkdir -p /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/share/licenses/gap-pkg-float
+ cp -pr COPYING /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64/usr/share/licenses/gap-pkg-float
+ RPM_EC=0
++ jobs -p
+ exit 0
Provides: gap-pkg-float = 0.9.1-8.fc33 gap-pkg-float(riscv-64) = 0.9.1-8.fc33
Requires(rpmlib): rpmlib(CompressedFileNames) <= 3.0.4-1 rpmlib(FileDigests) <= 4.6.0-1 rpmlib(PayloadFilesHavePrefix) <= 4.0-1
Requires: ld-linux-riscv64-lp64d.so.1()(64bit) ld-linux-riscv64-lp64d.so.1(GLIBC_2.27)(64bit) libc.so.6()(64bit) libc.so.6(GLIBC_2.27)(64bit) libcxsc.so.2()(64bit) libfplll.so.6()(64bit) libgcc_s.so.1()(64bit) libgcc_s.so.1(GCC_3.0)(64bit) libm.so.6()(64bit) libm.so.6(GLIBC_2.27)(64bit) libmpc.so.3()(64bit) libmpfi.so.0()(64bit) libmpfr.so.6()(64bit) libstdc++.so.6()(64bit) libstdc++.so.6(CXXABI_1.3)(64bit) libstdc++.so.6(CXXABI_1.3.8)(64bit) libstdc++.so.6(CXXABI_1.3.9)(64bit) libstdc++.so.6(GLIBCXX_3.4)(64bit) libstdc++.so.6(GLIBCXX_3.4.11)(64bit) libstdc++.so.6(GLIBCXX_3.4.9)(64bit) rtld(GNU_HASH)
Processing files: gap-pkg-float-doc-0.9.1-8.fc33.noarch
Provides: gap-pkg-float-doc = 0.9.1-8.fc33
Requires(rpmlib): rpmlib(CompressedFileNames) <= 3.0.4-1 rpmlib(FileDigests) <= 4.6.0-1 rpmlib(PayloadFilesHavePrefix) <= 4.0-1
Processing files: gap-pkg-float-debugsource-0.9.1-8.fc33.riscv64
Provides: gap-pkg-float-debugsource = 0.9.1-8.fc33 gap-pkg-float-debugsource(riscv-64) = 0.9.1-8.fc33
Requires(rpmlib): rpmlib(CompressedFileNames) <= 3.0.4-1 rpmlib(FileDigests) <= 4.6.0-1 rpmlib(PayloadFilesHavePrefix) <= 4.0-1
Processing files: gap-pkg-float-debuginfo-0.9.1-8.fc33.riscv64
Provides: debuginfo(build-id) = 697c0bf3caf3e70fb7fea78cae36e58376c5f1f4 gap-pkg-float-debuginfo = 0.9.1-8.fc33 gap-pkg-float-debuginfo(riscv-64) = 0.9.1-8.fc33
Requires(rpmlib): rpmlib(CompressedFileNames) <= 3.0.4-1 rpmlib(FileDigests) <= 4.6.0-1 rpmlib(PayloadFilesHavePrefix) <= 4.0-1
Recommends: gap-pkg-float-debugsource(riscv-64) = 0.9.1-8.fc33
Checking for unpackaged file(s): /usr/lib/rpm/check-files /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64
Wrote: /builddir/build/RPMS/gap-pkg-float-debugsource-0.9.1-8.fc33.riscv64.rpm
Wrote: /builddir/build/RPMS/gap-pkg-float-doc-0.9.1-8.fc33.noarch.rpm
Wrote: /builddir/build/RPMS/gap-pkg-float-0.9.1-8.fc33.riscv64.rpm
Wrote: /builddir/build/RPMS/gap-pkg-float-debuginfo-0.9.1-8.fc33.riscv64.rpm
Executing(%clean): /bin/sh -e /var/tmp/rpm-tmp.l2q47N
+ umask 022
+ cd /builddir/build/BUILD
+ cd float-0.9.1
+ /usr/bin/rm -rf /builddir/build/BUILDROOT/gap-pkg-float-0.9.1-8.fc33.riscv64
+ RPM_EC=0
++ jobs -p
+ exit 0
Child return code was: 0