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/*
 Copyright 2013 Edouard Griffiths <f4exb at free dot fr>

 This file is part of RSSoft. A Reed-Solomon Soft Decoding library

 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, Boston, MA  02110-1301  USA

 Bivariate polynomials with coefficients in GF(2^m) class

 */
#ifndef __GFQ_BIVARIATE_POLYNOMIAL_H__
#define __GFQ_BIVARIATE_POLYNOMIAL_H__

#include "GFq_BivariateMonomial.h"
#include "GFq_Polynomial.h"
#include <map>

namespace rssoft
{
namespace gf
{

class GFq_BivariatePolynomial
{
public:
        GFq_BivariatePolynomial(unsigned int w_x, unsigned int w_y);

        GFq_BivariatePolynomial(const std::pair<unsigned int, unsigned int>& _weights);

        GFq_BivariatePolynomial(const GFq_BivariatePolynomial& polynomial);

        ~GFq_BivariatePolynomial();

        void init(std::vector<GFq_BivariateMonomial>& _monomials);

        void init(const GFq_BivariatePolynomial& polynomial);

        void init(const std::map<GFq_BivariateMonomialExponents, GFq_Element, GFq_WeightedRevLex_BivariateMonomial>& monomials);
    
    void init_x_pow(const GFq& gf, unsigned int x_pow);

    void init_y_pow(const GFq& gf, unsigned int y_pow);

    void init_x_pow_series(const GFq& gf, unsigned int max_pow);

    void init_y_pow_series(const GFq& gf, unsigned int max_pow);

        const std::pair<unsigned int, unsigned int>& get_weights() const
        {
                return weights;
        }

        bool is_valid() const;

        bool is_const(GFq_Element& const_value) const;

        bool is_zero() const;

        bool is_one() const;

        const std::map<GFq_BivariateMonomialExponents, GFq_Element, GFq_WeightedRevLex_BivariateMonomial>& get_monomials() const
        {
                return monomials;
        }

        std::map<GFq_BivariateMonomialExponents, GFq_Element, GFq_WeightedRevLex_BivariateMonomial>& get_monomials_for_update() 
        {
                return monomials;
        }
    
        GFq_BivariateMonomial get_leading_monomial() const
        {
                return static_cast<GFq_BivariateMonomial>(*(monomials.rbegin()));
        }
    
    unsigned int lmX() const
    {
        return static_cast<GFq_BivariateMonomial>(*(monomials.rbegin())).eX();
    }
    
    unsigned int lmY() const
    {
        return static_cast<GFq_BivariateMonomial>(*(monomials.rbegin())).eY();
    }
    
    unsigned int wdeg() const;

        static void sum(std::vector<GFq_BivariateMonomial>& sum_monomials, const GFq_BivariatePolynomial& a, const GFq_BivariatePolynomial& b);

        static void product(std::map<GFq_BivariateMonomialExponents, GFq_Element, GFq_WeightedRevLex_BivariateMonomial>& prod_monomials,
                        const GFq_BivariatePolynomial& a,
                        const GFq_BivariatePolynomial& b);

        static void division(std::map<GFq_BivariateMonomialExponents, GFq_Element, GFq_WeightedRevLex_BivariateMonomial>& div_monomials,
                        const GFq_BivariatePolynomial& a,
                        const GFq_BivariateMonomial& b);

        static void pow(std::map<GFq_BivariateMonomialExponents, GFq_Element, GFq_WeightedRevLex_BivariateMonomial>& pow_monomials,
                        const GFq_BivariatePolynomial& a,
                        unsigned int n);

        static void simplify(std::map<GFq_BivariateMonomialExponents, GFq_Element, GFq_WeightedRevLex_BivariateMonomial>& monomials);

        GFq_BivariatePolynomial& operator =(const GFq_BivariatePolynomial& polynomial);
        GFq_BivariatePolynomial& operator+=(const GFq_BivariatePolynomial& polynomial);
        GFq_BivariatePolynomial& operator+=(const GFq_Element& gfe);
        GFq_BivariatePolynomial& operator-=(const GFq_BivariatePolynomial& polynomial);
        GFq_BivariatePolynomial& operator-=(const GFq_Element& gfe);
        GFq_BivariatePolynomial& operator*=(const GFq_BivariatePolynomial& polynomial);
        GFq_BivariatePolynomial& operator*=(const GFq_BivariateMonomial& monomial);
        GFq_BivariatePolynomial& operator*=(const GFq_Element& gfe);
        GFq_BivariatePolynomial& operator/=(const GFq_BivariateMonomial& monomial);
        GFq_BivariatePolynomial& operator/=(const GFq_Element& gfe);
        GFq_BivariatePolynomial& operator^=(unsigned int n);

        bool operator==(const GFq_BivariatePolynomial& polynomial) const;
        bool operator!=(const GFq_BivariatePolynomial& polynomial) const;

        GFq_Element operator()(const GFq_Element& x_value, const GFq_Element& y_value) const;

        GFq_BivariatePolynomial operator()(const GFq_BivariatePolynomial& P, const GFq_BivariatePolynomial& Q) const;

        GFq_Polynomial get_X_0() const;
        
        GFq_Polynomial get_0_Y() const;

    bool is_in_X() const;
    
    bool is_in_Y() const;
    
        GFq_BivariatePolynomial& make_star();

        GFq_BivariatePolynomial& make_dHasse(unsigned int mu, unsigned int nu);

        friend std::ostream& operator <<(std::ostream& os, const GFq_BivariatePolynomial& polynomial);

protected:

        GFq_Polynomial get_v_0(bool x_terms) const;
        bool is_in_v(bool x_terms) const;

        static void product(std::map<GFq_BivariateMonomialExponents, GFq_Element, GFq_WeightedRevLex_BivariateMonomial>& prod_monomials,
                        const std::map<GFq_BivariateMonomialExponents, GFq_Element, GFq_WeightedRevLex_BivariateMonomial>& a_monomials,
                        const std::map<GFq_BivariateMonomialExponents, GFq_Element, GFq_WeightedRevLex_BivariateMonomial>& b_monomials);

        static void product(std::map<GFq_BivariateMonomialExponents, GFq_Element, GFq_WeightedRevLex_BivariateMonomial>& prod_monomials,
                        const GFq_Element& v,
                        const std::map<GFq_BivariateMonomialExponents, GFq_Element, GFq_WeightedRevLex_BivariateMonomial>& a_monomials,
                        const std::map<GFq_BivariateMonomialExponents, GFq_Element, GFq_WeightedRevLex_BivariateMonomial>& b_monomials);

        static void add_monomial(std::map<GFq_BivariateMonomialExponents, GFq_Element, GFq_WeightedRevLex_BivariateMonomial>& monomials,
                        const GFq_BivariateMonomialKeyValueRepresentation& a);

        static void add_monomial(std::map<GFq_BivariateMonomialExponents, GFq_Element, GFq_WeightedRevLex_BivariateMonomial>& monomials,
                        const GFq_Element& coeff,
                        unsigned int x_pow,
                        unsigned int y_pow);

        std::pair<unsigned int, unsigned int> weights; //<! weights for weighted degree ordering
        std::map<GFq_BivariateMonomialExponents, GFq_Element, GFq_WeightedRevLex_BivariateMonomial> monomials; //<! set of monomials
};

void simplify(GFq_BivariatePolynomial& polynomial);

GFq_BivariatePolynomial operator +(const GFq_BivariatePolynomial& a, const GFq_BivariatePolynomial& b);
GFq_BivariatePolynomial operator +(const GFq_BivariatePolynomial& a, const GFq_Element& b);
GFq_BivariatePolynomial operator +(const GFq_Element& a, const GFq_BivariatePolynomial& b);
GFq_BivariatePolynomial operator -(const GFq_BivariatePolynomial& a, const GFq_BivariatePolynomial& b);
GFq_BivariatePolynomial operator -(const GFq_BivariatePolynomial& a, const GFq_Element& b);
GFq_BivariatePolynomial operator -(const GFq_Element& a, const GFq_BivariatePolynomial& b);
GFq_BivariatePolynomial operator *(const GFq_BivariatePolynomial& a, const GFq_BivariatePolynomial& b);
GFq_BivariatePolynomial operator *(const GFq_BivariatePolynomial& a, const GFq_BivariateMonomial& b);
GFq_BivariatePolynomial operator *(const GFq_BivariatePolynomial& a, const GFq_Element& b);
GFq_BivariatePolynomial operator *(const GFq_Element& a, const GFq_BivariatePolynomial& b);
GFq_BivariatePolynomial operator /(const GFq_BivariatePolynomial& a, const GFq_BivariateMonomial& b);
GFq_BivariatePolynomial operator /(const GFq_BivariatePolynomial& a, const GFq_Element& b);
GFq_BivariatePolynomial operator ^(const GFq_BivariatePolynomial& a, unsigned int n);

GFq_BivariatePolynomial star(const GFq_BivariatePolynomial& a);

GFq_BivariatePolynomial dHasse(unsigned int mu, unsigned int nu, const GFq_BivariatePolynomial& a);

} // namespace gf
} // namespace rssoft

#endif // __GFQ_BIVARIATE_POLYNOMIAL_H__