synaps/mpol/bezoutian.h File Reference


Detailed Description

Multivariate Bezoutian.

See also:
UniReslt.h matrix_of.h Macaulay.h

Definition in file bezoutian.h.

Go to the source code of this file.

Functions

template<class T>
T::value_type Theta (const T &l, typename T::value_type::monom_t::index_t c=0)
template<class UPOL, class MPOL>
MatrDse< UPOL > UBezout (const MPOL &PP, const MPOL QQ)
template<class T, class I>
void add_from_iterator (T &v, const I &it, unsigned l0)
template<class C, class R, class I>
void add_from_iterator (UPolDse< C, R > &v, const I &it, unsigned l0)
template<class C, class R, class O>
void add_from_iterator (MPol< C, R, O > &v, const typename MPol< C, R, O >::const_iterator &it, int l0)
template<class MAT, class POL>
MAT DeltaOf (const POL &P, int l0, int l1, int l2)
template<class MAT, class T>
MAT mbezout (const T &l, typename T::value_type::monom_t::index_t c=0)


Function Documentation

template<class MAT, class POL>
MAT DeltaOf ( const POL &  P,
int  l0,
int  l1,
int  l2 
)

Compute the matrix associated with the polynomial p, assuming the variables up to l0 are hidden, the first block of variables is of size l1 and the second one of size l2. The monomials in the first block of variables are indexing the rows, the monomials in the second block of variables are indexing the columns. The entries of this matrix are polynomials in the variables $x_{0},..x_{l_{0}}$. The type MAT specifies the the type of the output matrix. In order to construct the matrix, the function void add_from_iterator(T & v, const I & it, unsigned l0) is used.

Definition at line 163 of file bezoutian.h.

References add_from_iterator().

template<class MAT, class T>
MAT mbezout ( const T &  l,
typename T::value_type::monom_t::index_t  c = 0 
)

Compute the bezoutian matrix of the list of polynomials l, and hiding the c first variables. Its type MAT is let as follows:

    mbezout<MAT>(L);
If c=0, the matrix type can be a scalar matrix. If the c>0, the coefficients of the matrix should be polynomials.

Definition at line 229 of file bezoutian.h.

References Theta().

template<class T>
T::value_type Theta ( const T &  l,
typename T::value_type::monom_t::index_t  c = 0 
)

Compute the polynomial in the two set variables, which is the determinant associated with the list of polynomials l. The c first variables are considered as parameters. The n next variables (where n is the length of l-1) are the variables $\x$ and the next n variables are the $\y$.

Definition at line 30 of file bezoutian.h.

References degree(), and MPOLDST::div_rem_x().

Referenced by mbezout(), and UBezout().

template<class UPOL, class MPOL>
MatrDse<UPOL> UBezout ( const MPOL &  PP,
const MPOL  QQ 
)

Computes the variante of Bezout matrix (see report) of p1(x0,x1), p2(x0,x1), as polynomials in x1. The result is a matrix of univariate polynomials ""in x0", of type UPOL. Example: UBezout<MyUPoly>(p1,p2).

Definition at line 97 of file bezoutian.h.

References degree(), and Theta().


SYNAPS DOCUMENTATION
logo