/* Copyright (c) 1997-2015
   Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Berlin, Germany)
   http://www.polymake.org

   This program is free software; you can redistribute it and/or modify it
   under the terms of the GNU General Public License as published by the
   Free Software Foundation; either version 2, or (at your option) any
   later version: http://www.gnu.org/licenses/gpl.txt.

   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.
--------------------------------------------------------------------------------
*/

#ifndef POLYMAKE_POLYTOPE_QUOTIENT_SPACE_TOOLS_H
#define POLYMAKE_POLYTOPE_QUOTIENT_SPACE_TOOLS_H

#include "polymake/graph/HasseDiagram.h"
#include "polymake/hash_set"
#include "polymake/Set.h"
#include "polymake/Array.h"
#include "polymake/group/permlib_tools.h"

namespace polymake { namespace polytope {

Array<Array<int> > induced_symmetry_group_generators(int n, const Array<Array<int> >& sym_group_generators, const Array<Set<Set<Set<int> > > >& face_orbits)
{
   typedef permlib::Permutation PERM;
   typedef permlib::SchreierTreeTransversal<PERM> TRANSVERSAL;
   typedef permlib::BSGS<PERM, TRANSVERSAL> BSGSType;

   // construct BSGS of symmetry group
   permlib::SchreierSimsConstruction<PERM, TRANSVERSAL> schreierSims(n);
   std::list<PERM::ptr> gen_list;
   for (Entire<Array<Array<int> > >::const_iterator perm = entire(sym_group_generators); !perm.at_end(); ++perm){
      PERM::ptr gen(new PERM((*perm).begin(), (*perm).end()));
      gen_list.push_back(gen);
   }

   BSGSType sym_bsgs = schreierSims.construct(gen_list.begin(), gen_list.end());


   // prepare search without DCM pruning
   typedef Set<Set<int> > Container;
   typedef Array<Set<Container> > ArrayType;
   typedef permlib::LayeredSetSystemStabilizerPredicate<PERM, Container, ArrayType> PredType;

   permlib::classic::SetSystemStabilizerSearch<BSGSType, TRANSVERSAL, PredType> backtrackSearch(sym_bsgs, 0);
   backtrackSearch.construct(n, face_orbits);
        
   // start the search
   BSGSType stabilizer(n);
   backtrackSearch.search(stabilizer);

   // extract a strong generating set
   Array< Array<int> > new_bsgs(stabilizer.S.size());
   Entire<Array<Array<int> > >::iterator pit = entire(new_bsgs);
   for(std::list<boost::shared_ptr<PERM> >::const_iterator perm = stabilizer.S.begin(); perm!=stabilizer.S.end(); ++perm)
      *pit++ = group::PermlibGroup::perm2Array(*perm);
   return new_bsgs;
}
      
} } // end namespaces

#endif // POLYMAKE_POLYTOPE_QUOTIENT_SPACE_TOOLS_H

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