RationalUnivariatePolynomial.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_RATIONALUNIVARIATEPOLYNOMIAL_H
#define GINACRA_RATIONALUNIVARIATEPOLYNOMIAL_H

#include "UnivariatePolynomial.h"
#include "OpenInterval.h"

using GiNaC::ex_to;

namespace GiNaCRA
{
    class RationalUnivariatePolynomial:
        public UnivariatePolynomial
    {
        public:

            // Con- and destructors //

            RationalUnivariatePolynomial():
                UnivariatePolynomial()
            {}

            RationalUnivariatePolynomial( const ex& p, const symbol& s ) throw ( invalid_argument );

            RationalUnivariatePolynomial( const UnivariatePolynomial& p ) throw ( invalid_argument );

            // Operations //

            numeric coeff( int i ) const
            {
                return ex_to<numeric>( ex::coeff( mVariable, i ));    // cast safe because of the constructor
            }

            numeric lcoeff() const
            {
                return ex_to<numeric>( ex::lcoeff( mVariable ));
            }

            numeric tcoeff() const
            {
                return ex_to<numeric>( ex::tcoeff( mVariable ));
            }

            GiNaC::sign sgn( const numeric& a ) const;

            numeric evaluateAt( const numeric& a ) const;

            numeric oneNorm() const;

            numeric twoNorm() const;

            numeric maximumNorm() const;

            numeric cauchyBound() const;

            unsigned countRealRoots() const;

            numeric approximateRealRoot( const numeric start, const OpenInterval& i, unsigned steps = 3 ) const;

            // Static Methods //

            static list<RationalUnivariatePolynomial> standardSturmSequence( const RationalUnivariatePolynomial& a,
                                                                             const RationalUnivariatePolynomial& b );

            static unsigned signVariations( const list<RationalUnivariatePolynomial>& seq, const numeric& a );

            static int calculateSturmCauchyIndex( const RationalUnivariatePolynomial& p, const RationalUnivariatePolynomial& q );

            static unsigned countRealRoots( const list<RationalUnivariatePolynomial>& seq, const OpenInterval& i )
            {
                // number of real roots in i, due to Sturm's theorem
                return signVariations( seq, i.left() ) - signVariations( seq, i.right() );
            }

            static unsigned countRealRoots( const RationalUnivariatePolynomial& p, const OpenInterval& i )
            {
                list<RationalUnivariatePolynomial> seq = standardSturmSequence( p, p.diff() );
                return signVariations( seq, i.left() ) - signVariations( seq, i.right() );
            }

            static int calculateRemainderTarskiQuery( const RationalUnivariatePolynomial& p, const RationalUnivariatePolynomial& q );

            //template<class BidirectionalIterator>
            //static std::set<std::vector<Sign> > calculateSignDetermination(const RationalUnivariatePolynomial& z, const std::vector<RationalUnivariatePolynomial>& polynomials);
    };

}    // namespace GiNaC

#endif // GINACRA_RATIONALUNIVARIATEPOLYNOMIAL_H