synaps/mpol/approximate.h File Reference


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)


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().


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