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// ---------------------------------------------------------------------------
//
// This file is part of PermLib.
//
// Copyright (c) 2009-2011 Thomas Rehn <thomas@carmen76.de>
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions
// are met:
// 1. Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
// 2. Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
// 3. The name of the author may not be used to endorse or promote products
// derived from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
// IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
// OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
// IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
// INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
// NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
// THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// ---------------------------------------------------------------------------
#include <permlib/common.h>
#include <permlib/permutation.h>
#include <permlib/bsgs.h>
#include <permlib/transversal/schreier_tree_transversal.h>
#include <permlib/construct/schreier_sims_construction.h>
#include <permlib/construct/random_schreier_sims_construction.h>
#include <permlib/generator/bsgs_random_generator.h>
#include <iostream>
int main(int argc, char *argv[]) {
using namespace permlib;
// we use elementary permutations
typedef Permutation PERM;
// and Schreier tree transversals
typedef SchreierTreeTransversal<PERM> TRANSVERSAL;
// our group will have degree 10
const unsigned long n = 10;
// group generators
std::list<PERM::ptr> groupGenerators;
PERM::ptr gen1(new PERM(n, std::string("1 3 5 7 9 10 2 4 6 8")));
groupGenerators.push_back(gen1);
PERM::ptr gen2(new PERM(n, std::string("1 5")));
groupGenerators.push_back(gen2);
PERM::ptr gen3(new PERM(n, std::string("2 6 5 9, 3 7 10 4 8")));
groupGenerators.push_back(gen3);
PERM::ptr gen4(new PERM(n, std::string("4 8 7 10")));
groupGenerators.push_back(gen4);
// BSGS construction
SchreierSimsConstruction<PERM, TRANSVERSAL> schreierSims(n);
BSGS<PERM, TRANSVERSAL> bsgs = schreierSims.construct(groupGenerators.begin(), groupGenerators.end());
std::cout << "Group " << bsgs << std::endl;
// In the following we try to find a small generating set for the group.
// Our goal is to find a set of two or three generators.
// In this case <$gen1, $gen2> already generate the group, but we may find
// other generators by the following randomized construction.
const boost::uint64_t groupOrder = bsgs.order();
bool haveSmallGeneratingSet = false;
std::list<PERM::ptr> subgroupGenerators;
for (unsigned int i = 2; i <= 3; ++i) {
for (unsigned int j = 0; j < 5; ++j) {
// Try #j times to build a subgroup from #i randomly chosen group elements.
// Then check the order of this subgroup.
// If it is the order of the original group, we found a small generating set.
subgroupGenerators.clear();
for (unsigned int c = 0; c < i; ++c) {
subgroupGenerators.push_back(PERM::ptr(new PERM(bsgs.random())));
}
RandomSchreierSimsConstruction<PERM, TRANSVERSAL> randomConstruction(n, new BSGSRandomGenerator<PERM,TRANSVERSAL>(bsgs), 0, 10, 100);
bool guaranteedBSGS = false;
BSGS<PERM, TRANSVERSAL> subgroupBSGS = randomConstruction.construct(subgroupGenerators.begin(), subgroupGenerators.end(), guaranteedBSGS);
if (subgroupBSGS.order() == groupOrder) {
haveSmallGeneratingSet = true;
break;
}
}
if (haveSmallGeneratingSet)
break;
}
if (haveSmallGeneratingSet) {
std::cout << "Group generated by:" << std::endl;
BOOST_FOREACH(const PERM::ptr& gen, subgroupGenerators) {
std::cout << *gen << std::endl;
}
} else {
std::cout << "Could not find small generating set." << std::endl;
}
return 0;
}
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