SpecialQuotientRingMultiplicationTable.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_QUOTIENTRINGMULTIPLICATIONTABLE_H
#define GINACRA_QUOTIENTRINGMULTIPLICATIONTABLE_H

#include "MultivariatePolynomialFactory.h"
#include "operators.h"

namespace GiNaCRA
{
    template<class monomialOrdering>
    class SpecialQuotientRingMultiplicationTable
    {
        public:

            // Con- and destructors //

            SpecialQuotientRingMultiplicationTable<monomialOrdering>( list<MultivariatePolynomial<monomialOrdering> > gb ) throw ( invalid_argument );

            SpecialQuotientRingMultiplicationTable<monomialOrdering>( MultivariatePolynomial<monomialOrdering> p );

            // Selectors //

            const list<MultivariatePolynomial<monomialOrdering> > GroebnerBasis() const;

            const vector<MultivariateTerm<monomialOrdering> > TermsUnderTheStaircase() const;

            inline const int dim() const;

            const list<symbol> Variables() const;

            // Operators //

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

            // Operations //

            const MultivariatePolynomial<monomialOrdering> product( const MultivariateTerm<monomialOrdering> m1,
                                                                    const MultivariateTerm<monomialOrdering> m2 ) const
                    throw ( invalid_argument );

            inline const MultivariatePolynomial<monomialOrdering> product( const int i, const int j ) const throw ( invalid_argument );

            void realRoots() const;

            std::ostream& print( std::ostream& os ) const;

        protected:

            // Operations //

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

            inline const MultivariatePolynomial<monomialOrdering> trace( const MultivariatePolynomial<monomialOrdering> p ) const
                    throw ( invalid_argument );

            inline const MultivariatePolynomial<monomialOrdering> generalPositionTemplatePowerTrace( const numeric& i,
                                                                                                     const unsigned e ) const
                    throw ( invalid_argument );

        private:

            // Attributes //

            symbol                                          mInfinitesimal;
            list<MultivariatePolynomial<monomialOrdering> > mGroebnerBasis;
            MultivariateCoefficient<monomialOrdering>       coefficientLcm;
            vector<MultivariateTerm<monomialOrdering> >     mTermsUnderTheStaircase;
            list<symbol>                                    mVariables;
            // If m_1, ..., m_l are the monomials under the staircase, then m_i * m_j = mMultiplicationTable[ (i,j), 1 ] * m_1 + ... + mMultiplicationTable[ (i,j), l ] * m_l.
            map<pair<pair<int, int>, int>, set<ex, ex_is_less>::iterator> mMultiplicationTable;
            set<ex, ex_is_less>                                           mProductCoeffs;

            // Auxiliary methods //

            inline void initializeMultiplicationTable();

            inline void initializeBasis();

    };
    // class SpecialQuotientRingMultiplicationTable

#include "SpecialQuotientRingMultiplicationTable.tpp"

}    // namespace GiNaC

#endif // GINACRA_QUOTIENTRINGMULTIPLICATIONTABLE_H