synaps/mpol/approximate.h File Reference

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Detailed Description

Definition in file approximate.h.

Go to the source code of this file.

Functions
template<class POL>
POL	MonomV (const int v, const int n)
template<class LP>
LP	baseLocal (const LP &f, const std::vector< int > &d, const int nv)
template<class MAT, class LL>
MAT	evaluation (const LL &f, const std::vector< int > &d, const std::vector< double > &u, const int cas=1)
template<class LL>
LL::value_type	Elim_Approximate (const LL &f, const std::vector< int > &d, const std::vector< double > &u, const int cas=1)

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Function Documentation

template<class LP>

LP baseLocal	(	const LP &	f,
		const std::vector< int > &	d,
		const int	nv
	)

Create the list of base local for Sylvester-like matrix

Definition at line 61 of file approximate.h.

References MPOLDST::swap().

template<class LL>

LL::value_type Elim_Approximate	(	const LL &	f,
		const std::vector< int > &	d,
		const std::vector< double > &	u,
		const int	cas = 1
	)

Eliminate the f.size()-1 last variables, by using approximative method with evaluation (see report).

Parameters:

	f	list of polynomials,
	d	degree of the munomial multiplicators for each polynomial
	u	list of coordinates of the points of evaluation. It size should be greater that the sume of the number of monomials of degrees d.

Returns:

a multivariate polynomial in the first variables.

Definition at line 155 of file approximate.h.

template<class MAT, class LL>

MAT evaluation	(	const LL &	f,
		const std::vector< int > &	d,
		const std::vector< double > &	u,
		const int	cas = 1
	)

Evaluation with the Sylvester-like matrix

Parameters:

	f	list of polynomials,
	d	multiplied degree for each polynomial
	u	list of real values

Returns:

Evaluation matrix This procedure thus calls another function of evaluation

Definition at line 86 of file approximate.h.

References matrixof::assigncoeff(), MPOLDST::diff(), matrixof::reserve(), and MPOLDST::subs().

template<class POL>

POL MonomV	(	const int	v,
		const int	n
	)

Create the list of monomials of total degree d<=V in n variables

Parameters:

	v	maximum degree
	n	number of variables

Definition at line 25 of file approximate.h.

References MPOLDST::degree().