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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/change/conjugating_base_change.h>
#include <permlib/search/classic/set_stabilizer_search.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);
// BSGS construction
SchreierSimsConstruction<PERM, TRANSVERSAL> schreierSims(n);
BSGS<PERM, TRANSVERSAL> bsgs = schreierSims.construct(groupGenerators.begin(),
groupGenerators.end());
std::cout << "Group " << bsgs << std::endl;
// we want to stabilize a set
const unsigned long DeltaSize = 4;
// represents the set {1,5,8,9}, translated by -1 as the elements of the domain are 0-based
const unsigned long Delta[DeltaSize] = {0, 4, 7, 8};
// change the base so that is prefixed by the set
ConjugatingBaseChange<PERM,TRANSVERSAL,
RandomBaseTranspose<PERM,TRANSVERSAL> > baseChange(bsgs);
baseChange.change(bsgs, Delta, Delta+DeltaSize);
// prepare search without DCM pruning
classic::SetStabilizerSearch<BSGS<PERM,TRANSVERSAL>, TRANSVERSAL> backtrackSearch(bsgs, 0);
backtrackSearch.construct(Delta, Delta+DeltaSize);
// start the search
BSGS<PERM,TRANSVERSAL> stabilizer(n);
backtrackSearch.search(stabilizer);
std::cout << "Stabilizer of {1,5,8,9}: " << stabilizer << std::endl;
return 0;
}
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