algebra/polynomial.h

// -*- c++ -*-

// +--------------------------------------------------------------------+
// | This file is part of MathTL - the Mathematical Template Library    |
// |                                                                    |
// | Copyright (c) 2002-2009                                            |
// | Thorsten Raasch, Manuel Werner                                     |
// +--------------------------------------------------------------------+

#ifndef _MATHTL_POLYNOMIAL_H
#define _MATHTL_POLYNOMIAL_H

#include <iostream>
#include <algebra/vector.h>
#include <utils/function.h>

namespace MathTL
{
  template <class C>
  class Polynomial
    : protected Vector<C>, public Function<1, C>
  {
  public:
    Polynomial();

    Polynomial(const Polynomial<C>& p);

    Polynomial(const Vector<C>& coeffs);

    explicit Polynomial(const C c);

    virtual ~Polynomial();

    unsigned int degree() const;

    C get_coefficient(const unsigned int k) const;

    void get_coefficients(Vector<C>& coeffs) const;

    void set_coefficient(const unsigned int k, const C coeff);

    void set_coefficients(const Vector<C>& coeffs);

    C value(const C x) const;

    C value(const C x, const unsigned int derivative) const;

    C value(const Point<1>& p,
            const unsigned int component = 0) const;

    void vector_value(const Point<1> &p,
                      Vector<C>& values) const;

    void scale(const C s);

    void shift(const C s);

    void chain(const Polynomial<C>& p);

    Polynomial<C> substitute_into(const Polynomial<C>& p) const;

    Polynomial<C>& operator = (const Polynomial<C>& p);

    Polynomial<C>& operator = (const C c);

    void add(const Polynomial<C>& p);

    void add(const C s, const Polynomial<C>& p);

    void sadd(const C s, const Polynomial<C>& p);

    Polynomial<C>& operator += (const Polynomial<C>& p);

    Polynomial<C> operator + (const Polynomial<C>& p) const;

    void subtract(const Polynomial<C> &p);

    Polynomial<C>& operator -= (const Polynomial<C> &p);

    Polynomial<C> operator - () const;
    
    Polynomial<C> operator - (const Polynomial<C> &p) const;

    Polynomial<C>& operator *= (const C c);

    Polynomial<C> operator * (const C c) const;

    void multiply(const Polynomial<C>& p);

    Polynomial<C>& operator *= (const Polynomial<C>& p);

    Polynomial<C> operator * (const Polynomial<C>& p);

    Polynomial<C> power(const unsigned int k) const;

    void divide(const Polynomial<C>& q, Polynomial<C>& p) const;

    void divide(const Polynomial<C>& q, Polynomial<C>& p, Polynomial<C>& r) const;

    Polynomial differentiate() const;

    Polynomial integrate() const;

    double integrate(const double a,
                     const double b,
                     const bool quadrature = false) const;

    double inner_product(Polynomial<C> p2, double a, double b);

  protected:
    void trim();
  };
  
  template <class C>
  Polynomial<C> operator * (const C c, const Polynomial<C>& p);
  
  template <class C>
  std::ostream& operator << (std::ostream &s, const Polynomial<C> &p);
}

// implementation of inline functions
#include <algebra/polynomial.cpp>

#endif