/* 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/tropical/double_description.h"
#include "polymake/polytope/hasse_diagram.h"


namespace polymake { namespace tropical {

    template<typename Scalar>
    BigObject monomial_cone_lattice(const Matrix<Scalar>& m)
    {
      BigObject H("Lattice<BasicDecoration, Nonsequential>");
      H = polytope::hasse_diagram(tropical::monomial_dual_description(m).second,m.cols());
      return H;
    }

    template <typename Addition, typename Scalar>
    Matrix<TropicalNumber<Addition, Scalar> > V_trop_input(BigObject p) {
         const std::pair<Matrix<TropicalNumber<Addition,Scalar>>,Matrix<TropicalNumber<Addition,Scalar>>> Ineq = p.lookup("INEQUALITIES");
	 Matrix<TropicalNumber<Addition, Scalar> > extremals(extremals_from_halfspaces(Ineq.first,Ineq.second));
	 if (extremals.rows() == 0)
	   throw std::runtime_error("the inequalities form an infeasible system");
	 return extremals;
    }

    FunctionTemplate4perl("V_trop_input<Addition,Scalar>(Polytope<Addition,Scalar>)");
    
    UserFunctionTemplate4perl("# @category Tropical operations"
			      "# computes the VIF of a monomial tropical cone "
			      "# given by generators "
			      "# @param Matrix M the exponent vectors of the generators. "
			      "# @return Lattice<BasicDecoration, Nonsequential>",
			      "monomial_cone_lattice(Matrix)");
    
    FunctionTemplate4perl("monoextremals(Matrix, Matrix, Vector)");

    FunctionTemplate4perl("extremals_from_generators(Matrix)");

    FunctionTemplate4perl("extremals_from_halfspaces(Matrix,Matrix)");

    FunctionTemplate4perl("matrixPair2splitApices(Matrix,Matrix)");

    UserFunctionTemplate4perl("# @category Tropical operations"
			      "# This computes the __extremal generators__ of a tropical cone "
			      "# given by generators //G// intersected with one inequality //a//x ~ //b//x."
			      "# Here, ~ is <= for min and >= for max."
			      "# @param Matrix<TropicalNumber> G"
			      "# @param Vector<TropicalNumber> a"
			      "# @param Vector<TropicalNumber> b"
			      "# @return Matrix<TropicalNumber> extrls"
			      "# @example"
			      "# > $G = new Matrix<TropicalNumber<Min>>([[0,0,2],[0,4,0],[0,3,1]]);"
			      "# > $a = new Vector<TropicalNumber<Min>>(['inf','inf',-2]);"
			      "# > $b = new Vector<TropicalNumber<Min>>([0,-1,'inf']);"
			      "# > print intersection_extremals($G,$a,$b);"
			      "# | 0 0 1"
			      "# | 0 4 0"
			      "# | 0 3 1",
			      "intersection_extremals(Matrix, Vector, Vector)");

    UserFunctionTemplate4perl("# @category Tropical operations"
			      "# compute the dual description of "
			      "# a monomial tropical cone. "
			      "# @param Matrix monomial_generators"
			      "# @return Pair<Matrix, IncidenceMatrix<>>",
			      "monomial_dual_description(Matrix)");


    UserFunctionTemplate4perl("# @category Tropical operations"
			      "# Reformulate the description of an "
			      "# inequality system given by two matrices"
			      "# to the description by apices and infeasible sectors " 
			      "# @param Matrix<TropicalNumber> G"
			      "# @param Matrix<TropicalNumber> A"
			      "# @return Pair<Matrix<TropicalNumber>, Array<Set<Int>>> signed_apices",
			      "matrixPair2apexSet(Matrix, Matrix)");

    UserFunctionTemplate4perl("# @category Tropical operations"
			      "# Check if a point is contained in "
			      "# all tropical halfspaces given by "
			      "# their apices and the infeasible sectors " 
			      "# @param Matrix<TropicalNumber> apices"
			      "# @param Array<Set<Int>> sectors"
			      "# @return Bool",
			      "is_contained(Vector, Matrix, Array)");

    
}}
