permlib  0.2.9
Library for permutation computations
base_transpose.h
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31 
32 
33 #ifndef BASETRANSPOSE_H_
34 #define BASETRANSPOSE_H_
35 
36 #include <permlib/predicate/pointwise_stabilizer_predicate.h>
37 #include <permlib/generator/generator.h>
38 
39 #include <boost/scoped_ptr.hpp>
40 #include <boost/iterator/indirect_iterator.hpp>
41 #include <boost/next_prior.hpp>
42 
43 namespace permlib {
44 
46 
49 template<class PERM, class TRANS>
51 public:
53  BaseTranspose();
55  virtual ~BaseTranspose() {}
56 
58 
62  void transpose(BSGS<PERM,TRANS> &bsgs, unsigned int i) const;
63 
65  mutable unsigned int m_statScheierGeneratorsConsidered;
67  mutable unsigned int m_statNewGenerators;
68 protected:
69  typedef std::list<typename PERM::ptr> PERMlist;
70 
72 
78  virtual Generator<PERM>* setupGenerator(BSGS<PERM,TRANS> &bsgs, unsigned int i, const PERMlist &S_i, const TRANS &U_i) const = 0;
79 };
80 
81 //
82 // ---- IMPLEMENTATION
83 //
84 
85 template<class PERM, class TRANS>
87  : m_statScheierGeneratorsConsidered(0), m_statNewGenerators(0)
88 { }
89 
90 template<class PERM, class TRANS>
91 void BaseTranspose<PERM,TRANS>::transpose(BSGS<PERM,TRANS> &bsgs, unsigned int i) const {
92  std::vector<dom_int> &B = bsgs.B;
93  std::vector<TRANS> &U = bsgs.U;
94 
95  if (i+1 >= B.size())
96  // illegal transpose index
97  return;
98 
99  PERMlist S_i;
100  std::copy_if(bsgs.S.begin(), bsgs.S.end(), std::back_inserter(S_i), PointwiseStabilizerPredicate<PERM>(B.begin(), B.begin() + i));
101 
102  std::swap(B[i], B[i+1]);
103 
104  PERMlist S_i1;
105  std::copy_if(bsgs.S.begin(), bsgs.S.end(), std::back_inserter(S_i1), PointwiseStabilizerPredicate<PERM>(B.begin(), B.begin() + (i+1)));
106 
107  unsigned int targetTransversalSize = U[i+1].size() * U[i].size();
108 
109  // new transversal
110  TRANS U_i(U[i].n());
111  U_i.orbit(B[i], S_i);
112  targetTransversalSize /= U_i.size();
113 
114  m_statScheierGeneratorsConsidered = 0;
115  m_statNewGenerators = 0;
116  TRANS U_i1(U[i+1].n());
117  U_i1.orbit(B[i+1], S_i1);
118  boost::scoped_ptr<Generator<PERM> > generator(setupGenerator(bsgs, i, S_i, U_i));
119  BOOST_ASSERT(generator != 0);
120 
121  while (U_i1.size() < targetTransversalSize) {
122  bool newGeneratorFound = false;
123  while (generator->hasNext()) {
124  PERM g = generator->next();
125  ++m_statScheierGeneratorsConsidered;
126  boost::indirect_iterator<typename PERMlist::iterator> sBegin(S_i1.begin()), sEnd(S_i1.end());
127  if (!U_i1.contains(g / B[i+1]) && std::find(sBegin, sEnd, g) == sEnd) {
128  g.flush();
129  boost::shared_ptr<PERM> gen(new PERM(g));
130  S_i1.push_front(gen);
131  ++m_statNewGenerators;
132  U_i1.orbitUpdate(B[i+1], S_i1, gen);
133  newGeneratorFound = true;
134  break;
135  }
136  }
137  if (!newGeneratorFound)
138  // we have exhausted all available generators, and we won't find any new ones in the loop
139  break;
140  }
141  BOOST_ASSERT(U_i1.size() >= targetTransversalSize);
142 
143  bsgs.S.insert(bsgs.S.end(), S_i1.begin(), boost::next(S_i1.begin(), m_statNewGenerators));
144  U[i] = U_i;
145  U[i+1] = U_i1;
146 }
147 
148 }
149 
150 #endif // -- BASETRANSPOSE_H_
virtual Generator< PERM > * setupGenerator(BSGS< PERM, TRANS > &bsgs, unsigned int i, const PERMlist &S_i, const TRANS &U_i) const =0
initializes the specific Schreier Generator that is used for the BaseTranpose implementation
BaseTranspose()
constructor
Definition: base_transpose.h:86
unsigned int m_statScheierGeneratorsConsidered
number of Schreier generators that have been considered during the last transpose call
Definition: base_transpose.h:65
void transpose(BSGS< PERM, TRANS > &bsgs, unsigned int i) const
performs a base transposition on bsgs between bsgs.B[i] and bsgs.B[i+1]
Definition: base_transpose.h:91
interface for group element generators
Definition: generator.h:40
predicate matching a permutation if it stabilizes a given list of points pointwise
Definition: pointwise_stabilizer_predicate.h:42
std::vector< dom_int > B
base
Definition: bsgs_core.h:55
unsigned int m_statNewGenerators
number of new strong generators that have been added during the last transpose call
Definition: base_transpose.h:67
abstract base class for base transposition
Definition: base_transpose.h:50
Represents a base and strong generating set (BSGS)
Definition: bsgs.h:59
std::vector< TRANS > U
transversals along the stabilizer chain
Definition: bsgs_core.h:59
virtual ~BaseTranspose()
virtual destructor
Definition: base_transpose.h:55
PERMlist S
strong generating set
Definition: bsgs_core.h:57