permlib 0.2.9
Library for permutation computations
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schreier_sims_construction.h
1// ---------------------------------------------------------------------------
2//
3// This file is part of PermLib.
4//
5// Copyright (c) 2009-2011 Thomas Rehn <thomas@carmen76.de>
6// All rights reserved.
7//
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9// modification, are permitted provided that the following conditions
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31
32
33#ifndef SCHREIERSIMSCONSTRUCTION_H_
34#define SCHREIERSIMSCONSTRUCTION_H_
35
36#include <permlib/construct/base_construction.h>
37#include <permlib/bsgs.h>
38#include <permlib/generator/schreier_generator.h>
39
40#include <boost/foreach.hpp>
41
42namespace permlib {
43
45template <class PERM, class TRANS>
46class SchreierSimsConstruction : public BaseConstruction<PERM, TRANS> {
47public:
49
52 explicit SchreierSimsConstruction(unsigned int n);
53
55
57 template <class ForwardIterator>
58 BSGS<PERM, TRANS> construct(ForwardIterator generatorsBegin, ForwardIterator generatorsEnd) const;
59
61
67 template <class ForwardIterator, class InputIterator>
68 BSGS<PERM, TRANS> construct(ForwardIterator generatorsBegin, ForwardIterator generatorsEnd, InputIterator prescribedBaseBegin, InputIterator prescribedBaseEnd) const;
69
72};
73
74//
75// ---- IMPLEMENTATION
76//
77
78template <class PERM, class TRANS>
80 : BaseConstruction<PERM, TRANS>(n), m_statScheierGeneratorsConsidered(0)
81{ }
82
83template <class PERM, class TRANS>
84template <class ForwardIterator>
85inline BSGS<PERM, TRANS> SchreierSimsConstruction<PERM,TRANS>::construct(ForwardIterator generatorsBegin, ForwardIterator generatorsEnd) const {
86 return construct(generatorsBegin, generatorsEnd, BaseConstruction<PERM,TRANS>::empty, BaseConstruction<PERM,TRANS>::empty);
87}
88
89template <class PERM, class TRANS>
90template <class ForwardIterator, class InputIterator>
92 ::construct(ForwardIterator generatorsBegin, ForwardIterator generatorsEnd, InputIterator prescribedBaseBegin, InputIterator prescribedBaseEnd) const
93{
94 const dom_int &n = this->m_n;
95 BSGS<PERM, TRANS> ret(n);
96 std::vector<dom_int> &B = ret.B;
97 std::vector<TRANS> &U = ret.U;
98 std::vector<std::list<typename PERM::ptr> > S;
99 this->setup(generatorsBegin, generatorsEnd, prescribedBaseBegin, prescribedBaseEnd, ret, S);
100
101 std::vector<boost::shared_ptr<SchreierGenerator<PERM, TRANS> > > SchreierGens;
102 for (unsigned int i = 0; i < B.size(); ++i) {
103 BOOST_ASSERT( i < U.size() );
104 BOOST_ASSERT( i < S.size() );
105 SchreierGens.push_back(boost::shared_ptr<SchreierGenerator<PERM, TRANS> >(new SchreierGenerator<PERM, TRANS>(&U[i], S[i].begin(), S[i].end())));
106 }
107
108 unsigned int j = B.size();
109 bool breakUp = false;
110 while (j >= 1) {
111 breakUp = false;
112 SchreierGenerator<PERM, TRANS> &sg = *SchreierGens[j-1];
113 sg.update(&U[j-1], S[j-1].begin(), S[j-1].end());
114
115 while (sg.hasNext()) {
116 ++m_statScheierGeneratorsConsidered;
117 PERMLIB_DEBUG(for(unsigned int jjj=0; jjj<j; ++jjj) std::cout << " ";)
118 PERMLIB_DEBUG(std::cout << "schreier j = " << (j-1) << " [" << S[j-1].size() << "," << U[j-1].size() << "]: ";)
119 PERM g = sg.next();
120 PERM h(n);
121 // sift for S_{j+1}, so use index j here
122 unsigned int k = ret.sift(g, h, j);
123 if (k < B.size() - j || !h.isIdentity()) {
124 // flush it, because we add it as a generator
125 h.flush();
126
127 if (j == B.size()) {
128 dom_int gamma = n+1;
129 if (ret.chooseBaseElement(h, gamma)) {
130 B.push_back(gamma);
131 }
132 BOOST_ASSERT(j < B.size());
133 S.push_back(std::list<typename PERM::ptr>());
134 U.push_back(TRANS(n));
135 }
136 boost::shared_ptr<PERM> hPtr(new PERM(h));
137 S[j].insert(S[j].end(), hPtr);
138
139 ret.orbitUpdate(j, S[j], hPtr);
140 if (j >= SchreierGens.size()) {
141 boost::shared_ptr<SchreierGenerator<PERM, TRANS> > localVar(new SchreierGenerator<PERM, TRANS>(&U[j], S[j].begin(), S[j].end()));
142 SchreierGens.push_back(localVar);
143 } else {
144 SchreierGens[j]->update(S[j].size() - 1);
145 }
146
147 breakUp = true;
148 ++j;
149 break;
150 }
151 }
152 if (!breakUp)
153 --j;
154 }
155
156 this->mergeGenerators(S, ret);
157
158 return ret;
159}
160
161}
162
163#endif // -- SCHREIERSIMSCONSTRUCTION_H_
base class for BSGS construction algorithms
Definition base_construction.h:46
stateful generator of Schreier generators
Definition schreier_generator.h:55
PERM next()
generates an element
Definition schreier_generator.h:185
bool hasNext()
true, iff more elements can be generated
Definition schreier_generator.h:142
void update(TRANS *U, PERMlistIt S_begin, PERMlistIt S_end)
updates transversal and group generators that the Schreier generators are constructed from
Definition schreier_generator.h:216
BSGS construction with classic Schreier-Sims algorithm.
Definition schreier_sims_construction.h:46
unsigned int m_statScheierGeneratorsConsidered
number of Schreier generators examined during the last construct call
Definition schreier_sims_construction.h:71
BSGS< PERM, TRANS > construct(ForwardIterator generatorsBegin, ForwardIterator generatorsEnd) const
constructs a BSGS for group given by generators with no base prescribed
Definition schreier_sims_construction.h:85
SchreierSimsConstruction(unsigned int n)
constructor
Definition schreier_sims_construction.h:79
std::vector< TRANS > U
transversals along the stabilizer chain
Definition bsgs_core.h:59
std::vector< dom_int > B
base
Definition bsgs_core.h:55
Represents a base and strong generating set (BSGS)
Definition redundant_base_point_insertion_strategy.h:39
void orbitUpdate(unsigned int j, const PERMlist &generators, const typename PERM::ptr &g)
updates the j-th fundamental orbit with the given orbit generators and a new generator g
Definition bsgs.h:306
unsigned int sift(const PERM &g, PERM &siftee, unsigned int j=0) const
sifts an element through the specified transversal range
Definition bsgs.h:273
bool chooseBaseElement(const PERM &h, dom_int &beta) const
tries to find a new base element
Definition bsgs.h:290