MathTL::Polynomial< C > Class Template Reference

#include <polynomial.h>

Inheritance diagram for MathTL::Polynomial< C >:

List of all members.

Public Member Functions
	Polynomial ()
	Polynomial (const Polynomial< C > &p)
	Polynomial (const Vector< C > &coeffs)
	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 Member Functions
void	trim ()

---

Detailed Description

template<class C>
class MathTL::Polynomial< C >

A template class for univariate polynomials of the form p(x)={k=0}^n a_k*x^k with coefficients from a class C.

You can perform

• point evaluation (via Horner scheme)
• summation (coeffientwise)
• multiplication with constants
• multiplication with other polynomials
• division with remainder
• raising a polynomial to some power
• substitution into another polynomial, special version for scale and shift
• symbolic differentiation and integration
• exact integration over an interval (with or without quadrature formulae)

We derive Polynomial<C> from the class Function<1>, as it is indeed one. Since polynomials are completely determined by their coefficients, we derive the class also from Vector<C>, but protected to hide the Vector signature.

---

Constructor & Destructor Documentation

template<class C >

MathTL::Polynomial< C >::Polynomial

(

)

default constructor: yields the zero polynomial of degree zero

template<class C >

MathTL::Polynomial< C >::Polynomial

(

const Polynomial< C > &

p

)

copy constructor

template<class C >

MathTL::Polynomial< C >::Polynomial

(

const Vector< C > &

coeffs

)

constructor from a coefficient vector

template<class C >

MathTL::Polynomial< C >::Polynomial

(

const C

c

)

[explicit]

constructor from a constant

template<class C >

MathTL::Polynomial< C >::~Polynomial

(

)

[virtual]

virtual destructor

---

Member Function Documentation

template<class C >

void MathTL::Polynomial< C >::add

(

const Polynomial< C > &

p

)

pointwise sum of two polynomials *this += p

template<class C >

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

pointwise weighted sum of two polynomials *this += s*p

template<class C >

void MathTL::Polynomial< C >::chain

(

const Polynomial< C > &

p

)

substitute another polynomial into this one *this <- *this p

template<class C >

unsigned int MathTL::Polynomial< C >::degree

(

)

const [inline]

degree of the polynomial

template<class C >

Polynomial< C > MathTL::Polynomial< C >::differentiate

(

)

const

(symbolic) differentiation

template<class C >

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

divide the polynomial by another one with remainder: *this = p * q + r

template<class C >

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

divide the polynomial by another one with remainder: *this = p * q + r

template<class C >

C MathTL::Polynomial< C >::get_coefficient

(

const unsigned int

k

)

const [inline]

read-only access to single coefficients

template<class C >

void MathTL::Polynomial< C >::get_coefficients

(

Vector< C > &

coeffs

)

const [inline]

get all coefficients at once

template<class C >

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

inner product

template<class C >

Polynomial< C > MathTL::Polynomial< C >::integrate

(

)

const

(symbolic) integration

template<class C >

double MathTL::Polynomial< C >::integrate	(	const double	a,
		const double	b,
		const bool	quadrature = false
	)		const

integration over [a,b], optional use of (Gauss) quadrature formulae

template<class C >

void MathTL::Polynomial< C >::multiply

(

const Polynomial< C > &

p

)

pointwise multiplication with another polynomial *this *= p

template<class C >

Polynomial< C > MathTL::Polynomial< C >::operator*

(

const C

c

)

const [inline]

multiplication with a real number (don't use this extensively, since one copy has to be made!)

template<class C >

Polynomial< C > MathTL::Polynomial< C >::operator*

(

const Polynomial< C > &

p

)

[inline]

pointwise multiplication with another polynomial (don't use this extensively, since one copy has to be made!)

template<class C >

Polynomial< C > & MathTL::Polynomial< C >::operator*=

(

const C

c

)

multiplication with a real number

Reimplemented from MathTL::Vector< C >.

template<class C >

Polynomial< C > & MathTL::Polynomial< C >::operator*=

(

const Polynomial< C > &

p

)

[inline]

pointwise multiplication with another polynomial

template<class C >

Polynomial< C > MathTL::Polynomial< C >::operator+

(

const Polynomial< C > &

p

)

const [inline]

pointwise sum of two polynomials (don't use this extensively, since one copy has to be made!)

template<class C >

Polynomial< C > & MathTL::Polynomial< C >::operator+=

(

const Polynomial< C > &

p

)

[inline]

pointwise sum of two polynomials

template<class C >

Polynomial< C > MathTL::Polynomial< C >::operator-

(

)

const [inline]

sign (makes a copy of *this)

template<class C >

Polynomial< C > MathTL::Polynomial< C >::operator-

(

const Polynomial< C > &

p

)

const [inline]

pointwise difference of two polynomials (don't use this extensively, since one copy has to be made!)

template<class C >

Polynomial< C > & MathTL::Polynomial< C >::operator-=

(

const Polynomial< C > &

p

)

[inline]

pointwise difference of two polynomials

template<class C >

Polynomial< C > & MathTL::Polynomial< C >::operator=

(

const Polynomial< C > &

p

)

assignment of another polynomial

template<class C >

Polynomial< C > & MathTL::Polynomial< C >::operator=

(

const C

c

)

assignment of a constant polynomial (implicit conversion)

Reimplemented from MathTL::Vector< C >.

template<class C >

Polynomial< C > MathTL::Polynomial< C >::power

(

const unsigned int

k

)

const

raise the polynomial to some power

template<class C >

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

pointwise weighted sum of two polynomials *this = s*(*this) + v

template<class C >

void MathTL::Polynomial< C >::scale

(

const C

s

)

in place scaling p(x) -> p(s*x)

Reimplemented from MathTL::Vector< C >.

template<class C >

void MathTL::Polynomial< C >::set_coefficient	(	const unsigned int	k,
		const C	coeff
	)

write access to single coefficients

template<class C >

void MathTL::Polynomial< C >::set_coefficients

(

const Vector< C > &

coeffs

)

set all coefficients at once

template<class C >

void MathTL::Polynomial< C >::shift

(

const C

s

)

in place shift p(x) -> p(x+s)

template<class C >

Polynomial< C > MathTL::Polynomial< C >::substitute_into

(

const Polynomial< C > &

p

)

const

substitute another polynomial into this one without changing this object ( return *this p )

template<class C >

void MathTL::Polynomial< C >::subtract

(

const Polynomial< C > &

p

)

pointwise difference of two polynomials *this -= p

template<class C >

void MathTL::Polynomial< C >::trim

(

)

[protected]

trim leading zero coefficients in the polynomial

template<class C >

C MathTL::Polynomial< C >::value

(

const C

x

)

const

evaluate the polynomial (Horner scheme)

template<class C >

C MathTL::Polynomial< C >::value	(	const C	x,
		const unsigned int	derivative
	)		const

evaluate n-th derivative of the polynomial (full Horner scheme)

template<class C >

C MathTL::Polynomial< C >::value	(	const Point< 1 > &	p,
		const unsigned int	component = 0
	)		const [inline]

evaluate the polynomial (Horner scheme) (calls the above value(const C))

template<class C >

void MathTL::Polynomial< C >::vector_value	(	const Point< 1 > &	p,
		Vector< C > &	values
	)		const [inline]

evaluate the polynomial (Horner scheme) (calls the above value(const C))

---

The documentation for this class was generated from the following files:

• algebra/polynomial.h
• algebra/polynomial.cpp