polynomial.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.
 *  
 *  Contributor(s):
 *
 *  Alternatively, the contents of this file may be used under the terms of the 
 *  GNU General Public License Version 2 or later (the GPL), in which case the 
 *  provisions of GPL are applicable instead of those above.  If you wish to allow use
 *  of your version of this file only under the terms of the GPL and not to allow 
 *  others to use your version of this file under the CPAL, indicate your decision by 
 *  deleting the provisions above and replace them with the notice and other 
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 *  a recipient may use your version of this file under either the CPAL or the GPL.
 *  
 *  *** 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_H
#define LASS_GUARDIAN_OF_INCLUSION_NUM_POLYNOMIAL_H

#include "num_common.h"
#include "num_traits.h"

namespace lass
{
namespace num
{

template <typename T>
class Polynomial
{
public:

    typedef Polynomial<T> TSelf;
    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 typename TCoefficients::size_type size_type;
    typedef typename TCoefficients::const_iterator const_iterator;

    Polynomial();
    explicit Polynomial(TParam iScalar);
    explicit Polynomial(const TCoefficients& iCoefficients);
    template <typename InputIterator> Polynomial(InputIterator iBegin, InputIterator iEnd);

    const TCoefficients& coefficients() const;
    const TValue operator[](size_t iIndex) const;
    const TValue at(size_t iIndex) const;

    const TValue operator()(TParam iX) const;

    const Polynomial<T>& operator+() const;
    const Polynomial<T> operator-() const;

    Polynomial<T>& operator+=(const Polynomial<T>& iOther);
    Polynomial<T>& operator-=(const Polynomial<T>& iOther);
    Polynomial<T>& operator*=(const Polynomial<T>& iOther);

    Polynomial<T>& operator+=(TParam iScalar);
    Polynomial<T>& operator-=(TParam iScalar);
    Polynomial<T>& operator*=(TParam iScalar);
    Polynomial<T>& operator/=(TParam iScalar);

    Polynomial<T> derivative() const;
    Polynomial<T> integral() const;
    Polynomial<T> pow(unsigned iPower) const;

    const size_type size() const;
    const const_iterator begin() const;
    const const_iterator end() const;

    static Polynomial<T> one();
    static Polynomial<T> x();

private:

    TCoefficients a_;
};

template <typename T> bool operator==(const Polynomial<T>& iA, const Polynomial<T>& iB);
template <typename T> bool operator!=(const Polynomial<T>& iA, const Polynomial<T>& iB);

template <typename T> Polynomial<T> operator+(const Polynomial<T>& iA, const Polynomial<T>& iB);
template <typename T> Polynomial<T> operator-(const Polynomial<T>& iA, const Polynomial<T>& iB);
template <typename T> Polynomial<T> operator*(const Polynomial<T>& iA, const Polynomial<T>& iB);

template <typename T> Polynomial<T> operator+(const T& iA, const Polynomial<T>& iB);
template <typename T> Polynomial<T> operator-(const T& iA, const Polynomial<T>& iB);
template <typename T> Polynomial<T> operator*(const T& iA, const Polynomial<T>& iB);

template <typename T> Polynomial<T> operator+(const Polynomial<T>& iA, const T& iB);
template <typename T> Polynomial<T> operator-(const Polynomial<T>& iA, const T& iB);
template <typename T> Polynomial<T> operator*(const Polynomial<T>& iA, const T& iB);
template <typename T> Polynomial<T> operator/(const Polynomial<T>& iA, const T& iB);

template <typename T, typename Char, typename Traits>
std::basic_ostream<Char, Traits>&
operator<<(std::basic_ostream<Char, Traits>& iS, const Polynomial<T>& iA);


}
}

#include "polynomial.inl"

#endif

// EOF