/* Copyright (c) 1997-2018
   Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Berlin, Germany)
   http://www.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/PowerSet.h"
#include "polymake/TropicalNumber.h"

namespace polymake { namespace tropical {

        template<typename Addition>
                perl::Object hypersimplex(int d, int k)
                {
                        if (d < 1)
                                throw std::runtime_error("hypersimplex: dimension >= 2 required");
                        if (k < 1 || k > d)
                                throw std::runtime_error("hypersimplex: 1 <= k <= d required");

                        perl::Object p(perl::ObjectType::construct<Addition>("Polytope"));
                        p.set_description() << "tropical (" << k << "," << d << ")-hypersimplex" << endl;

                        // number of vertices
                        const int n(Integer::binom(d+1,k));

                        Matrix<TropicalNumber<Addition> > Vertices(n,d+1);
                                Vertices.fill( TropicalNumber<Addition>::one());
                        typename Rows< Matrix<TropicalNumber<Addition> > >::iterator v=rows(Vertices).begin();
                        Subsets_of_k<sequence> enumerator(range(0,d), k);
                        for (Subsets_of_k<sequence>::iterator s=entire(enumerator); !s.at_end(); ++s, ++v) {
                                v->slice(*s).fill(TropicalNumber<Addition>(-Addition::orientation()));
                        }
                        p.take("POINTS") << Vertices;

                        return p;
                }

        UserFunctionTemplate4perl("# @category Producing a tropical polytope"
                        "# Produce the tropical hypersimplex &Delta;(//k//,//d//)."
                        "# Cf." 
                        "# \t M. Joswig math/0312068v3, Ex. 2.10."
                        "# The value of //k// defaults to 1, yielding a tropical standard simplex."
                        "# @param Int d the dimension"
                        "# @param Int k the number of +/-1 entries"
                        "# @tparam Addition Max or Min"
                        "# @return Polytope<Addition>"
                        "# @example"
                        "# > $h = hypersimplex<Min>(2,1);"
                        "# > print $h->VERTICES;"
                        "# | 0 1 1"
                        "# | 0 -1 0"
                        "# | 0 0 -1",
                        "hypersimplex<Addition>($;$=1)");
} }

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