/* 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/client.h"
#include "polymake/Rational.h"
#include "polymake/Matrix.h"
#include "polymake/polytope/transform.h"

namespace polymake { namespace polytope {

template <typename Scalar>
BigObject facet_to_infinity(BigObject p_in, const Int inf_facet)
{
   BigObject p_out("Polytope", mlist<Scalar>());

   const Matrix<Scalar> facets=p_in.give("FACETS");

   const Vector<Scalar> inf_f= facets.row(inf_facet);
   const Matrix<Scalar> tau=null_space(inf_f);
   transform_section(p_out, p_in, "FACETS | INEQUALITIES", T(inf_f/tau));
   transform_section(p_out, p_in, "AFFINE_HULL | EQUATIONS", T(inf_f/tau));
   transform_section(p_out, p_in, "VERTICES", inv(inf_f/tau));
   transform_section(p_out, p_in, "LINEALITY_SPACE", inv(inf_f/tau));
  
   p_out.take("BOUNDED") << false;

   return p_out;
}

  UserFunctionTemplate4perl("# @category Producing a polytope from polytopes"
                            "# Make an affine transformation such that the i-th facet is transformed to infinity"
                            "# @param Polytope P"
                            "# @param Int i the facet index"
                            "# @return Polytope"
                            "# @author Sven Herrmann"
                            "# @example [prefer cdd] This generates the polytope that is the positive quadrant in 2-space:"
                            "# > $q = new Polytope(VERTICES=>[[1,-1,-1],[1,0,1],[1,1,0]]);"
                            "# > $pf = facet_to_infinity($q,2);"
                            "# > print $pf->VERTICES;"
                            "# | 0 -1 -1"
                            "# | 0 0 1"
                            "# | 1 0 1",
                            "facet_to_infinity<Scalar>(Polytope<Scalar> $)");
} }

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