/* Copyright (c) 1997-2022
   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/Polynomial.h"
#include "polymake/Matrix.h"

namespace polymake { namespace polytope {

template <typename Coefficient, typename Exponent>
BigObject newton(const Polynomial<Coefficient,Exponent>& p)
{
   const Matrix<Exponent> exps(p.template monomials_as_matrix< Matrix<Exponent> >());
   const Int n = exps.rows();
   const Int d = exps.cols();

   BigObject np("Polytope<Rational>",
                "POINTS", same_element_vector(1, n) | exps,
                "CONE_AMBIENT_DIM", d+1,
                "LATTICE", true,
                "BOUNDED", true);
   np.set_description() << "Newton polytope of " << p << endl;
   return np;
}

UserFunctionTemplate4perl("# @category Producing a polytope from scratch"
                          "# Produce the Newton polytope of a polynomial //p//."
                          "# @param Polynomial p"
                          "# @return Polytope<Rational>"
                          "# @example [nocompare] Create the newton polytope of 1+x^2+y like so:"
                          "# > local_var_names<Polynomial>(qw(x y));  $p=new Polynomial('1+x^2+y');"
                          "# > $n = newton($p);"
                          "# > print $n->VERTICES;"
                          "# | 1 0 0"
                          "# | 1 0 1"
                          "# | 1 2 0",
                          "newton(Polynomial)");
} }

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