/*
	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
	of the License, or (at your option) any later version.

	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.

	You should have received a copy of the GNU General Public License
	along with this program; if not, write to the Free Software
	Foundation, Inc., 51 Franklin Street, Fifth Floor,
	Boston, MA  02110-1301, USA.

	---
	Copyright (C) 2011 - 2015, Simon Hampe <simon.hampe@googlemail.com>

	---
	Copyright (c) 2016-2021
	Ewgenij Gawrilow, Michael Joswig, and the polymake team
	Technische Universität Berlin, Germany
	https://polymake.org

	Implements the pullback of RationalFunction via a Morphism
	*/

#pragma once

#include "polymake/client.h"
#include "polymake/Matrix.h"
#include "polymake/Rational.h"
#include "polymake/Vector.h"
#include "polymake/Set.h"
#include "polymake/TropicalNumber.h"
#include "polymake/Polynomial.h"
#include "polymake/IncidenceMatrix.h"
#include "polymake/tropical/morphism_composition.h"

namespace polymake { namespace tropical {

/*
 * @brief Computes the pull-back form of a rational function given by numerator and denominator via
 * a morphism given by a matrix and translate.
 * @return A pair of (numerator, denominator).
 */
template <typename Addition>
std::pair<Polynomial<TropicalNumber<Addition>>, Polynomial<TropicalNumber<Addition>>>
polynomialPullback(const Matrix<Rational>& matrix, const Vector<Rational>& translate,
                   const Polynomial<TropicalNumber<Addition>>& numerator, 
                   const Polynomial<TropicalNumber<Addition>>& denominator)
{
  Matrix<Rational> numerator_monoms( numerator.monomials_as_matrix());
  Vector<Rational> numerator_coeffs(numerator.coefficients_as_vector());
  Matrix<Rational> denominator_monoms( denominator.monomials_as_matrix());
  Vector<Rational> denominator_coeffs(denominator.coefficients_as_vector());

  Matrix<Rational> newnum_monoms = numerator_monoms*matrix;
  Matrix<Rational> newden_monoms = denominator_monoms*matrix;

  Vector<Rational> newnum_coeffs_rational = numerator_monoms*translate + numerator_coeffs;
  Vector<Rational> newden_coeffs_rational = denominator_monoms*translate + denominator_coeffs;

  Vector<TropicalNumber<Addition>> newnum_coeffs( newnum_coeffs_rational.dim(), newnum_coeffs_rational.begin());
  Vector<TropicalNumber<Addition>> newden_coeffs( newden_coeffs_rational.dim(), newden_coeffs_rational.begin());
						
  Polynomial<TropicalNumber<Addition>> newnum(newnum_coeffs, Matrix<Int>(newnum_monoms));
  Polynomial<TropicalNumber<Addition>> newden(newden_coeffs, Matrix<Int>(newden_monoms));
  return std::make_pair(newnum, newden);
}

template <typename Addition>
BigObject pullback(BigObject morphism, BigObject function)
{
  // Convert the rational function to a morphism object
  BigObject fmorphism("Morphism", mlist<Addition>());
  BigObject function_domain = function.give("DOMAIN");

  const bool is_function_global = function.give("IS_GLOBALLY_DEFINED");
  const bool is_morphism_global = morphism.give("IS_GLOBALLY_AFFINE_LINEAR");
  // If both are global, we're quickly done
  if (is_function_global && is_morphism_global) {
    const Matrix<Rational>& matrix = morphism.give("MATRIX");
    const Vector<Rational>& translate = morphism.give("TRANSLATE");
    const Polynomial<TropicalNumber<Addition>>& numerator = function.give("NUMERATOR");
    const Polynomial<TropicalNumber<Addition>>& denominator = function.give("DENOMINATOR");
    std::pair<Polynomial<TropicalNumber<Addition>>, Polynomial<TropicalNumber<Addition>>> newpair =
      polynomialPullback(matrix, translate, numerator, denominator);
    return BigObject("TropicalRationalFunction", mlist<Addition>(),
                     "NUMERATOR", newpair.first,
                     "DENOMINATOR", newpair.second);
  }

  const Vector<Rational>& function_vvalues = function.give("VERTEX_VALUES");
  const Vector<Rational>& function_lvalues = function.give("LINEALITY_VALUES");
  Matrix<Rational> fmorph_vvalues(function_vvalues.dim(),0);
  Matrix<Rational> fmorph_lvalues(function_lvalues.dim(),0);
  fmorph_vvalues |= function_vvalues;
  fmorph_lvalues |= function_lvalues;
  fmorphism.take("DOMAIN") << function_domain;
  fmorphism.take("VERTEX_VALUES") << thomog(fmorph_vvalues,0,false);
  fmorphism.take("LINEALITY_VALUES") << thomog(fmorph_lvalues,0,false);

  // Compute the composition
  BigObject comp = morphism_composition<Addition>(morphism,fmorphism);

  // Now convert back to rational function
  BigObject resultDomain = comp.give("DOMAIN");
  const Matrix<Rational>& result_vvalues = comp.give("VERTEX_VALUES");
  const Matrix<Rational>& result_lvalues = comp.give("LINEALITY_VALUES");

  BigObject result("TropicalRationalFunction", mlist<Addition>());
  result.take("DOMAIN") << resultDomain;
  result.take("VERTEX_VALUES") << tdehomog(result_vvalues,0,false).col(0);
  result.take("LINEALITY_VALUES") << (result_lvalues.rows() > 0 ? tdehomog(result_lvalues,0,false).col(0) : Vector<Rational>());
  if ((function.exists("NUMERATOR") || function.exists("DENOMINATOR")) &&
      (morphism.exists("MATRIX") || morphism.exists("TRANSLATE")) ) {
    const Matrix<Rational>& matrix = morphism.give("MATRIX");
    const Vector<Rational>& translate = morphism.give("TRANSLATE");
    const Polynomial<TropicalNumber<Addition>>& numerator = function.give("NUMERATOR");
    const Polynomial<TropicalNumber<Addition>>& denominator= function.give("DENOMINATOR");
    BigObject newfunction("TropicalRationalFunction", mlist<Addition>());
    std::pair<Polynomial<TropicalNumber<Addition> >, Polynomial<TropicalNumber<Addition>>> newpair =
      polynomialPullback(matrix, translate, numerator, denominator);
    result.take("NUMERATOR") << newpair.first;
    result.take("DENOMINATOR") << newpair.second;
  }
  return result;
}

} }

