MultivariatePolynomial.h

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/*
 * GiNaCRA - GiNaC Real Algebra package
 * Copyright (C) 2010-2012  Ulrich Loup, Joachim Redies, Sebastian Junges
 *
 * This file is part of GiNaCRA.
 *
 * GiNaCRA 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 3 of the License, or
 * (at your option) any later version.
 *
 * GiNaCRA 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 GiNaCRA.  If not, see <http://www.gnu.org/licenses/>.
 *
 */


#ifndef GINACRA_MULTIVARIATEPOLYNOMIAL_H
#define GINACRA_MULTIVARIATEPOLYNOMIAL_H

// #define GINACRA_MULTIVARIATEPOLYNOMIAL_DEBUG

#include <ginac/ginac.h>
#include <stdexcept>

#include "Polynomial.h"
#include "utilities.h"

namespace GiNaCRA
{
    template<class monomialOrdering>
    class MultivariatePolynomial:
        public Polynomial
    {
        template<typename monomialOrdering1>
        friend class MultivariateTerm;
        template<typename monomialOrdering2>
        friend class MultivariateMonomial;
        template<typename monomialOrdering3>
        friend class MultivariateCoefficient;

        public:

            // Con- and destructors //

            MultivariatePolynomial<monomialOrdering>();

            MultivariatePolynomial<monomialOrdering>( const MultivariatePolynomial<monomialOrdering>& p );

            MultivariatePolynomial<monomialOrdering>( const ex& p, const vector<symbol>& l ) throw ( invalid_argument );

            // Selectors //

            const vector<symbol> Variables() const;

            const symbol Variable() const;

            const list<ex> CoefficientExs() const;

            const list<ex> MonomialExs() const;

            // Operators //

            // binary arithmetic operators, see: operators.h
            // const MultivariatePolynomial<monomialOrdering> operator+(const MultivariatePolynomial<monomialOrdering>&);
            // const MultivariatePolynomial<monomialOrdering> operator-(const MultivariatePolynomial<monomialOrdering>&);
            // const MultivariatePolynomial<monomialOrdering> operator*(const MultivariatePolynomial<monomialOrdering>&);

            // unary arithmetic operators, see: operators.h
            // const MultivariatePolynomial<monomialOrdering> operator-();

            // relational operators
            const bool operator ==( const MultivariatePolynomial<monomialOrdering>& ) const;
            const bool operator !=( const MultivariatePolynomial<monomialOrdering>& ) const;

            // assignment operators
            const MultivariatePolynomial<monomialOrdering>& operator = ( const MultivariatePolynomial<monomialOrdering>& );
            const MultivariatePolynomial<monomialOrdering>& operator = ( const ex& );

            // Operations //

            MultivariatePolynomial<monomialOrdering> diff( const symbol& s, unsigned nth = 1 ) const;

            MultivariatePolynomial<monomialOrdering> diff( const vector<symbol>::const_iterator i, unsigned nth = 1 ) const;

            MultivariatePolynomial<monomialOrdering> trunc( const symbol& s ) const;

            MultivariatePolynomial<monomialOrdering> trunc() const;

            const MultivariatePolynomial<monomialOrdering> divideByLcoeff() const;

            int degree( const symbol& s ) const;

            int degree() const;

            int ldegree( const symbol& s ) const;

            int ldegree() const;

            int tdegree() const;

            int tdegree( const symbol& s ) const;

            const ex lterm() const;

            const ex lcoeff() const;

            const ex coeff( const symbol& s, const unsigned int& n ) const;

            const ex lcoeff( const symbol& s ) const;

            const ex coeff( const ex& monomial ) const throw ( invalid_argument );

            const ex lmon() const;

            bool isZero() const;

            bool isConstant() const;

            const MultivariatePolynomial<monomialOrdering> reduction( const MultivariatePolynomial<monomialOrdering>& g,
                                                                      const ex& m ) const
                    throw ( invalid_argument );

            const MultivariatePolynomial<monomialOrdering> normalForm( const list<MultivariatePolynomial<monomialOrdering> >& gb ) const
                    throw ( invalid_argument );

            // Arithmetic Operations //

            const MultivariatePolynomial<monomialOrdering> add( const MultivariatePolynomial<monomialOrdering>& o ) const throw ( invalid_argument );

            const MultivariatePolynomial<monomialOrdering> minus() const;

            const MultivariatePolynomial<monomialOrdering> mul( const MultivariatePolynomial<monomialOrdering>& o ) const throw ( invalid_argument );

            const MultivariatePolynomial<monomialOrdering> pow( const unsigned e ) const throw ( invalid_argument );

            // Methods from ex //

            void print( const print_context& c, unsigned level = 0 ) const;

            // Auxiliary methods//

            const vector<symbol> mergeVariables( vector<symbol> l ) const;

        protected:

            // Relational Operations //

            inline const bool isEqual( const MultivariatePolynomial<monomialOrdering>& o ) const;

        private:

            // Attributes //

            // Caution: order of declaration == order of initialization
            vector<symbol>                     mVariables;    // ordered lexicographicly
            symbol                             mVariable;    // the symbol with the maximal degree (not necessarily unique)
            std::map<ex, ex, monomialOrdering> mTermExs;    // std::map assigning monomials to their respective coefficients of this polynomial in order given by constructor. mTermExs.first are the monomials, mTermExs.second the coefficients

            // Auxiliary methods//

            const symbol determineVariable() const;

            const std::map<ex, ex, monomialOrdering> determineTermExs() const;

    };    // class MultivariatePolynomial

    // IMPLEMENTATION (in header file because of template parameter) //

#include "MultivariatePolynomial.tpp"

}    // namespace GiNaC

#endif