/* Copyright (c) 1997-2020
   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.
--------------------------------------------------------------------------------
*/

#include "polymake/Rational.h"
#include "polymake/client.h"
#include "polymake/Array.h"
#include "polymake/Set.h"
#include "polymake/Matrix.h"
#include "polymake/Vector.h"
#include "polymake/linalg.h"

namespace polymake { namespace topaz {

Rational volume(BigObject p)
{
  const Int dim = p.give("DIM");
  const Array<Set<Int>> F = p.give("FACETS");
  Matrix<Rational> GR = p.give("COORDINATES");
  Vector<Rational> homogenization(GR.rows(),Rational(1));
  GR = homogenization | GR;
  
  Rational volume(0);
  for (auto f=entire(F); !f.at_end(); ++f) {
    const Rational vol = abs(det( GR.minor(*f,All) ));
    if (vol == 0)
      cerr << "volume: WARNING simplex of volume 0." << endl;
    volume += vol;
  }
  volume /= Integer::fac(dim);
  
  return volume;
}

Function4perl(&volume,"volume");

} }

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