#  Copyright (c) 1997-2021
#  Ewgenij Gawrilow, Michael Joswig, and the polymake team
#  Technische Universität Berlin, Germany
#  https://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.
#-------------------------------------------------------------------------------

# @category Symmetry
# Compute the combinatorial symmetries (i.e., automorphisms of the face lattice) of
# a given simplicial complex. They are stored in terms of a GROUP.RAYS_ACTION and a GROUP.FACETS_ACTION
# property, and the GROUP.RAYS_ACTION is also returned.
# @param SimplicialComplex sigma
# @return group::PermutationAction the action of the combinatorial symmetry group on the vertices
# @example To get the vertex symmetry group of the square and print its generators, type the following:
# > $sigma = new SimplicialComplex(FACETS=>[[0,1],[1,2],[2,3],[0,3]]);
# > print combinatorial_symmetries($sigma)->GENERATORS;
# | 3 2 1 0
# | 0 3 2 1
# > print $sigma->GROUP->RAYS_ACTION->GENERATORS;
# | 0 3 2 1
# | 1 0 3 2
# > print $sigma->GROUP->FACETS_ACTION->GENERATORS;
# | 3 2 1 0
# | 0 3 2 1
user_function combinatorial_symmetries(SimplicialComplex) {
    my ($p) = @_;
    return group::combinatorial_symmetries_impl($p, new IncidenceMatrix($p->FACETS), "FACETS_ACTION", "RAYS_ACTION");
}
   
# Local Variables:
# mode: perl
# cperl-indent-level:3
# indent-tabs-mode:nil
# End:
