#  Copyright (c) 1997-2004
#  Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Berlin, Germany)
#  http://www.math.tu-berlin.de/polymake,  mailto:polymake@math.tu-berlin.de
#
#  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.
#-----------------------------------------------------------------------------
#  $Project: polymake $$Id: polytope_completeness 5639 2004-12-17 21:36:25Z gawrilow $

sub complete($) {
  my ($pq)=@_;    # maybe only a partial polytope
  my $d=$pq->DIM; # impossible to detect completeness without the dimension
  my $crosscut=new Apps::topaz::SimplicialComplex();
  Modules::client("crosscut_complex", $crosscut, $pq, "-noc"); # reads VERTICES_IN_FACETS
  return ${$crosscut->HOMOLOGY}[$d-1] eq "({} 1)\n";
}

sub verify_poly($) {
  my ($pq)=@_;
  eval { Modules::client("check_inc", $pq, "VERTICES", "FACETS", "0+", "-q") };
  return $@==0 ? complete($pq) : undef;
}

sub main($$) {
  my ($p,$q)=@_;
  die "only works if first polytope is full-dimensional" if ($p->AMBIENT_DIM!=$p->DIM);
  my $same=($p->AMBIENT_DIM == $q->AMBIENT_DIM);
  if ($same) {
    # what follows is a severe abuse of polymake semantics
    my $pq=new Apps::polytope::RationalPolytope(VERTICES => $p->VERTICES, FACETS => $q->FACETS, DIM => $p->DIM);
    $same=verify_poly($pq);
  }
  if ($same) {
    print "the two polytopes agree\n";
  } else {
    print "the two polytopes do not agree\n";
  }
}

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