polynomial_quotient.h

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/** @file
 *  @author Bram de Greve (bramz@users.sourceforge.net)
 *  @author Tom De Muer (tomdemuer@users.sourceforge.net)
 *
 *  *** BEGIN LICENSE INFORMATION ***
 *  
 *  The contents of this file are subject to the Common Public Attribution License 
 *  Version 1.0 (the "License"); you may not use this file except in compliance with 
 *  the License. You may obtain a copy of the License at 
 *  http://lass.sourceforge.net/cpal-license. The License is based on the 
 *  Mozilla Public License Version 1.1 but Sections 14 and 15 have been added to cover 
 *  use of software over a computer network and provide for limited attribution for 
 *  the Original Developer. In addition, Exhibit A has been modified to be consistent 
 *  with Exhibit B.
 *  
 *  Software distributed under the License is distributed on an "AS IS" basis, WITHOUT 
 *  WARRANTY OF ANY KIND, either express or implied. See the License for the specific 
 *  language governing rights and limitations under the License.
 *  
 *  The Original Code is LASS - Library of Assembled Shared Sources.
 *  
 *  The Initial Developer of the Original Code is Bram de Greve and Tom De Muer.
 *  The Original Developer is the Initial Developer.
 *  
 *  All portions of the code written by the Initial Developer are:
 *  Copyright (C) 2004-2007 the Initial Developer.
 *  All Rights Reserved.
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 *  GNU General Public License Version 2 or later (the GPL), in which case the 
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 *  *** END LICENSE INFORMATION ***
 */



/** @class lass::num::Polynomial
 *  @brief an univariate polynomial.
 *  @author Bram de Greve [BdG]
 *
 *  <i>A polynomial is a mathematical expression involving a sum of powers in one or more variables
 *  multiplied by coefficients.</i>,
 *  Eric W. Weisstein. "Polynomial." From MathWorld--A Wolfram Web Resource. 
 *  http://mathworld.wolfram.com/Polynomial.html
 */

#ifndef LASS_GUARDIAN_OF_INCLUSION_NUM_POLYNOMIAL_QUOTIENT_H
#define LASS_GUARDIAN_OF_INCLUSION_NUM_POLYNOMIAL_QUOTIENT_H

#include "num_common.h"
#include "polynomial.h"

namespace lass
{
namespace num
{

template <typename T>
class PolynomialQuotient
{
public:

    typedef PolynomialQuotient<T> TSelf;
    typedef Polynomial<T> TPolynomial;
    typedef NumTraits<T> TNumTraits;
    typedef typename util::CallTraits<T>::TValue TValue;
    typedef typename util::CallTraits<T>::TParam TParam;
    typedef typename util::CallTraits<T>::TReference TReference;
    typedef typename util::CallTraits<T>::TConstReference TConstReference;
    typedef std::vector<TValue> TCoefficients;
    typedef std::pair<TCoefficients, TCoefficients> TCoefficientsPair;

    PolynomialQuotient();
    explicit PolynomialQuotient(TParam scalar);
    explicit PolynomialQuotient(const TCoefficients& numerator);
    explicit PolynomialQuotient(const TPolynomial& numerator);
    explicit PolynomialQuotient(const TCoefficientsPair& numeratorDenominator);
    PolynomialQuotient(TParam scalar, const TCoefficients& denominator);
    PolynomialQuotient(TParam scalar, const TPolynomial& denominator);
    PolynomialQuotient(const TCoefficients& numerator, const TCoefficients& denominator);
    PolynomialQuotient(const TPolynomial& numerator, const TPolynomial& denominator);
    template <typename InputIterator> PolynomialQuotient(InputIterator numFirst, InputIterator numLast);
    template <typename InputIterator> PolynomialQuotient(InputIterator numFirst, InputIterator numLast,
        InputIterator denFirst, InputIterator denLast);

    const TPolynomial& numerator() const;
    const TPolynomial& denominator() const;

    const TValue operator()(TParam x) const;

    const TSelf& operator+() const;
    const TSelf operator-() const;

    TSelf& operator+=(const TSelf& other);
    TSelf& operator-=(const TSelf& other);
    TSelf& operator*=(const TSelf& other);
    TSelf& operator/=(const TSelf& other);

    TSelf& operator+=(const TPolynomial& other);
    TSelf& operator-=(const TPolynomial& other);
    TSelf& operator*=(const TPolynomial& other);
    TSelf& operator/=(const TPolynomial& other);

    TSelf& operator+=(TParam scalar);
    TSelf& operator-=(TParam scalar);
    TSelf& operator*=(TParam scalar);
    TSelf& operator/=(TParam scalar);

    TSelf derivative() const;
    TSelf pow(unsigned power) const;

    static TSelf one();
    static TSelf x();

private:

    TPolynomial numerator_;
    TPolynomial denominator_;
};

template <typename T> bool operator==(const PolynomialQuotient<T>& a, const PolynomialQuotient<T>& b);
template <typename T> bool operator!=(const PolynomialQuotient<T>& a, const PolynomialQuotient<T>& b);

template <typename T> PolynomialQuotient<T> operator+(const PolynomialQuotient<T>& a, const PolynomialQuotient<T>& b);
template <typename T> PolynomialQuotient<T> operator-(const PolynomialQuotient<T>& a, const PolynomialQuotient<T>& b);
template <typename T> PolynomialQuotient<T> operator*(const PolynomialQuotient<T>& a, const PolynomialQuotient<T>& b);
template <typename T> PolynomialQuotient<T> operator/(const PolynomialQuotient<T>& a, const PolynomialQuotient<T>& b);

template <typename T> PolynomialQuotient<T> operator+(const Polynomial<T>& a, const PolynomialQuotient<T>& b);
template <typename T> PolynomialQuotient<T> operator-(const Polynomial<T>& a, const PolynomialQuotient<T>& b);
template <typename T> PolynomialQuotient<T> operator*(const Polynomial<T>& a, const PolynomialQuotient<T>& b);
template <typename T> PolynomialQuotient<T> operator/(const Polynomial<T>& a, const PolynomialQuotient<T>& b);

template <typename T> PolynomialQuotient<T> operator+(const PolynomialQuotient<T>& a, const Polynomial<T>& b);
template <typename T> PolynomialQuotient<T> operator-(const PolynomialQuotient<T>& a, const Polynomial<T>& b);
template <typename T> PolynomialQuotient<T> operator*(const PolynomialQuotient<T>& a, const Polynomial<T>& b);
template <typename T> PolynomialQuotient<T> operator/(const PolynomialQuotient<T>& a, const Polynomial<T>& b);

template <typename T> PolynomialQuotient<T> operator+(const T& a, const PolynomialQuotient<T>& b);
template <typename T> PolynomialQuotient<T> operator-(const T& a, const PolynomialQuotient<T>& b);
template <typename T> PolynomialQuotient<T> operator*(const T& a, const PolynomialQuotient<T>& b);
template <typename T> PolynomialQuotient<T> operator/(const T& a, const PolynomialQuotient<T>& b);

template <typename T> PolynomialQuotient<T> operator+(const PolynomialQuotient<T>& a, const T& b);
template <typename T> PolynomialQuotient<T> operator-(const PolynomialQuotient<T>& a, const T& b);
template <typename T> PolynomialQuotient<T> operator*(const PolynomialQuotient<T>& a, const T& b);
template <typename T> PolynomialQuotient<T> operator/(const PolynomialQuotient<T>& a, const T& b);

template <typename T> PolynomialQuotient<T> operator/(const Polynomial<T>& a, const Polynomial<T>& b);

template <typename T, typename Char, typename Traits>
std::basic_ostream<Char, Traits>&
operator<<(std::basic_ostream<Char, Traits>& s, const PolynomialQuotient<T>& a);


}
}

#include "polynomial_quotient.inl"

#endif

// EOF