MathTL::MultivariateLaurentPolynomial< R, DIMENSION > Class Template Reference

#include <multi_laurent_polynomial.h>

Inheritance diagram for MathTL::MultivariateLaurentPolynomial< R, DIMENSION >:

List of all members.

Public Types
typedef InfiniteVector< R, MultiIndex< int, DIMENSION > >::const_iterator	const_iterator
typedef InfiniteVector< R, MultiIndex< int, DIMENSION > >::const_reverse_iterator	const_reverse_iterator
Public Member Functions
	MultivariateLaurentPolynomial ()
	MultivariateLaurentPolynomial (const MultivariateLaurentPolynomial< R, DIMENSION > &p)
	MultivariateLaurentPolynomial (const R c)
	MultivariateLaurentPolynomial (const LaurentPolynomial< R > &p, const unsigned int n=0)
virtual	~MultivariateLaurentPolynomial ()
MultivariateLaurentPolynomial < R, DIMENSION > &	operator= (const MultivariateLaurentPolynomial< R, DIMENSION > &p)
MultivariateLaurentPolynomial < R, DIMENSION > &	operator= (const R c)
R	get_coefficient (const MultiIndex< int, DIMENSION > &k) const
void	set_coefficient (const MultiIndex< int, DIMENSION > &k, const R coeff)
const_iterator	begin () const
const_iterator	end () const
const_reverse_iterator	rbegin () const
const_reverse_iterator	rend () const
R	value (const Point< DIMENSION > &p, const unsigned int component=0) const
void	vector_value (const Point< DIMENSION > &p, Vector< R > &values) const
void	add (const MultivariateLaurentPolynomial< R, DIMENSION > &p)
void	add (const R s, const MultivariateLaurentPolynomial< R, DIMENSION > &p)
void	sadd (const R s, const MultivariateLaurentPolynomial< R, DIMENSION > &p)
MultivariateLaurentPolynomial < R, DIMENSION > &	operator+= (const MultivariateLaurentPolynomial< R, DIMENSION > &p)
MultivariateLaurentPolynomial < R, DIMENSION >	operator+ (const MultivariateLaurentPolynomial< R, DIMENSION > &p) const
void	subtract (const MultivariateLaurentPolynomial< R, DIMENSION > &p)
MultivariateLaurentPolynomial < R, DIMENSION > &	operator-= (const MultivariateLaurentPolynomial< R, DIMENSION > &p)
MultivariateLaurentPolynomial < R, DIMENSION >	operator- () const
MultivariateLaurentPolynomial < R, DIMENSION >	operator- (const MultivariateLaurentPolynomial< R, DIMENSION > &p) const
MultivariateLaurentPolynomial < R, DIMENSION > &	operator*= (const R c)
void	multiply (const MultivariateLaurentPolynomial< R, DIMENSION > &p)
MultivariateLaurentPolynomial < R, DIMENSION > &	operator*= (const MultivariateLaurentPolynomial< R, DIMENSION > &p)
void	dump () const

---

Detailed Description

template<class R, unsigned int DIMENSION>
class MathTL::MultivariateLaurentPolynomial< R, DIMENSION >

A template class for general multivariate Laurent polynomials, i.e., expressions of the form a(z)={k Z^d} a_k z^k The a_k are elements of a (number) ring R, z is from R^d.

Examples: R= R or C

---

Member Typedef Documentation

template<class R, unsigned int DIMENSION>

typedef InfiniteVector<R, MultiIndex<int, DIMENSION> >::const_iterator MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::const_iterator

const_iterator scanning the nontrivial coefficients

template<class R, unsigned int DIMENSION>

typedef InfiniteVector<R, MultiIndex<int, DIMENSION> >::const_reverse_iterator MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::const_reverse_iterator

const_reverse_iterator scanning the nontrivial coefficients

---

Constructor & Destructor Documentation

template<class R , unsigned int DIMENSION>

MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::MultivariateLaurentPolynomial

(

)

default constructor, yields zero (Laurent) polynomial

template<class R, unsigned int DIMENSION>

MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::MultivariateLaurentPolynomial

(

const MultivariateLaurentPolynomial< R, DIMENSION > &

p

)

copy constructor

template<class R, unsigned int DIMENSION>

MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::MultivariateLaurentPolynomial

(

const R

c

)

[explicit]

constructor from a constant

template<class R, unsigned int DIMENSION>

MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::MultivariateLaurentPolynomial	(	const LaurentPolynomial< R > &	p,
		const unsigned int	n = 0
	)

constructor from a univariate Laurent polynomial, embedding via z -> z_{n+1}

template<class R , unsigned int DIMENSION>

MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::~MultivariateLaurentPolynomial

(

)

[virtual]

virtual destructor

---

Member Function Documentation

template<class R, unsigned int DIMENSION>

void MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::add

(

const MultivariateLaurentPolynomial< R, DIMENSION > &

p

)

[inline]

pointwise sum of two Laurent polynomials *this += p

template<class R, unsigned int DIMENSION>

void MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::add	(	const R	s,
		const MultivariateLaurentPolynomial< R, DIMENSION > &	p
	)		[inline]

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

template<class R , unsigned int DIMENSION>

MultivariateLaurentPolynomial< R, DIMENSION >::const_iterator MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::begin

(

)

const [inline]

const_iterator pointing to the first nontrivial coefficient

Reimplemented from MathTL::InfiniteVector< R, MultiIndex< int, DIMENSION > >.

template<class R , unsigned int DIMENSION>

void MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::dump

(

)

const

just for testing

template<class R , unsigned int DIMENSION>

MultivariateLaurentPolynomial< R, DIMENSION >::const_iterator MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::end

(

)

const [inline]

const_iterator pointing to one behind the last nontrivial coefficient

Reimplemented from MathTL::InfiniteVector< R, MultiIndex< int, DIMENSION > >.

template<class R , unsigned int DIMENSION>

R MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::get_coefficient

(

const MultiIndex< int, DIMENSION > &

k

)

const [inline]

(Polynomial-like) read-only access to single coefficients

Reimplemented from MathTL::InfiniteVector< R, MultiIndex< int, DIMENSION > >.

template<class R, unsigned int DIMENSION>

void MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::multiply

(

const MultivariateLaurentPolynomial< R, DIMENSION > &

p

)

pointwise multiplication with another Laurent polynomial

template<class R, unsigned int DIMENSION>

MultivariateLaurentPolynomial< R, DIMENSION > & MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::operator*=

(

const R

c

)

[inline]

multiplication with a real number

Reimplemented from MathTL::InfiniteVector< R, MultiIndex< int, DIMENSION > >.

template<class R, unsigned int DIMENSION>

MultivariateLaurentPolynomial< R, DIMENSION > & MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::operator*=

(

const MultivariateLaurentPolynomial< R, DIMENSION > &

p

)

[inline]

pointwise multiplication with another Laurent polynomial

template<class R, unsigned int DIMENSION>

MultivariateLaurentPolynomial< R, DIMENSION > MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::operator+

(

const MultivariateLaurentPolynomial< R, DIMENSION > &

p

)

const [inline]

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

template<class R, unsigned int DIMENSION>

MultivariateLaurentPolynomial< R, DIMENSION > & MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::operator+=

(

const MultivariateLaurentPolynomial< R, DIMENSION > &

p

)

[inline]

pointwise sum of two Laurent polynomials

template<class R , unsigned int DIMENSION>

MultivariateLaurentPolynomial< R, DIMENSION > MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::operator-

(

)

const [inline]

sign (makes a copy of *this)

template<class R, unsigned int DIMENSION>

MultivariateLaurentPolynomial< R, DIMENSION > MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::operator-

(

const MultivariateLaurentPolynomial< R, DIMENSION > &

p

)

const [inline]

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

template<class R, unsigned int DIMENSION>

MultivariateLaurentPolynomial< R, DIMENSION > & MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::operator-=

(

const MultivariateLaurentPolynomial< R, DIMENSION > &

p

)

[inline]

pointwise difference of two Laurent polynomials

template<class R, unsigned int DIMENSION>

MultivariateLaurentPolynomial< R, DIMENSION > & MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::operator=

(

const MultivariateLaurentPolynomial< R, DIMENSION > &

p

)

assignment of another Laurent polynomial

template<class R, unsigned int DIMENSION>

MultivariateLaurentPolynomial< R, DIMENSION > & MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::operator=

(

const R

c

)

assignment of a constant

template<class R , unsigned int DIMENSION>

MultivariateLaurentPolynomial< R, DIMENSION >::const_reverse_iterator MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::rbegin

(

)

const [inline]

const_reverse_iterator pointing to the last nontrivial coefficient

Reimplemented from MathTL::InfiniteVector< R, MultiIndex< int, DIMENSION > >.

template<class R , unsigned int DIMENSION>

MultivariateLaurentPolynomial< R, DIMENSION >::const_reverse_iterator MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::rend

(

)

const [inline]

const_reverse_iterator pointing to one before the first nontrivial coefficient

Reimplemented from MathTL::InfiniteVector< R, MultiIndex< int, DIMENSION > >.

template<class R, unsigned int DIMENSION>

void MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::sadd	(	const R	s,
		const MultivariateLaurentPolynomial< R, DIMENSION > &	p
	)		[inline]

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

template<class R, unsigned int DIMENSION>

void MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::set_coefficient	(	const MultiIndex< int, DIMENSION > &	k,
		const R	coeff
	)		[inline]

(Polynomial-like) write access to single coefficients

Reimplemented from MathTL::InfiniteVector< R, MultiIndex< int, DIMENSION > >.

template<class R, unsigned int DIMENSION>

void MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::subtract

(

const MultivariateLaurentPolynomial< R, DIMENSION > &

p

)

[inline]

pointwise difference of two Laurent polynomials *this -= p

template<class R , unsigned int DIMENSION>

R MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::value	(	const Point< DIMENSION > &	p,
		const unsigned int	component = 0
	)		const

evaluate the Laurent polynomial

template<class R, unsigned int DIMENSION>

void MathTL::MultivariateLaurentPolynomial< R, DIMENSION >::vector_value	(	const Point< DIMENSION > &	p,
		Vector< R > &	values
	)		const [inline]

evaluate the Laurent polynomial

---

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

• algebra/multi_laurent_polynomial.h
• algebra/multi_laurent_polynomial.cpp