Definition in file resultant.h.
Go to the source code of this file.
Functions | |
| template<class MATR, class R> | |
| MATR | bezout (const UPolDse< R > &P, const UPolDse< R > &Q) |
The Bezout matrix of P and Q. | |
| template<class R> | |
| MatrStr< linalg::hankel< typename R::value_type > > | bezout (const R &P) |
The Bezout matrix of P and 1. The result is a Hankel matrix. | |
| template<class MATR, class R> | |
| MATR | sylvester (const UPolDse< R > &P, const UPolDse< R > &Q) |
The Sylvester matrix of P and Q. | |
| template<class C, class R, class MATR> | |
| MATR | sylvester (const UPolDse< C, R > &P, const UPolDse< C, R > &Q, char c) |
| The Sylvester matrix, with the maximum degree coefficient at the beginning. | |
| template<class UPOL, class MPOL> | |
| MatrDse< UPOL > | u_sylvester (const MPOL &p1, const MPOL &p2, typename MPOL::monom_t::index_t i=1) |
| template<class MATR, class R> | |
| MATR | companion (const UPolDse< R > &P) |
The companion matrix of a polynomial P. | |
| template<class MPOL> | |
| MatrDse< MPOL > | u_sylvester (const MPOL &p1, const MPOL &p2, int I) |
| template<class MPOL> | |
| MPOL | Resultant (const MPOL &p1, const MPOL &p2, int I) |
| Compute the resultant of p1 and p2, hiding the I first vars. | |
| template<class C, class O, class R> | |
| C | Subresultant (const MPol< C, O, R > &p1, const MPol< C, O, R > &p2, int I, int Ord, int Deg, C x, C y) |
| MatrStr<linalg::hankel<typename R::value_type> > bezout | ( | const R & | P | ) |
The Bezout matrix of P and 1. The result is a Hankel matrix.
Definition at line 54 of file resultant.h.
References degree().
The Bezout matrix of P and Q.
The type of the the matrix result is specified by the parameter MATR.
bezout<MatrDse<double> >(P,Q);
Definition at line 26 of file resultant.h.
References degree().
Referenced by quotient::ModUPol< C, R >::horner_to_monomial().
| MATR companion | ( | const UPolDse< R > & | P | ) |
The companion matrix of a polynomial P.
Definition at line 169 of file resultant.h.
References degree().
| MPOL Resultant | ( | const MPOL & | p1, | |
| const MPOL & | p2, | |||
| int | I | |||
| ) |
Compute the resultant of p1 and p2, hiding the I first vars.
Definition at line 272 of file resultant.h.
References u_sylvester().
Referenced by Solve_with_subres().
| C Subresultant | ( | const MPol< C, O, R > & | p1, | |
| const MPol< C, O, R > & | p2, | |||
| int | I, | |||
| int | Ord, | |||
| int | Deg, | |||
| C | x, | |||
| C | y | |||
| ) |
Compute the subresultant coefficient of degree Deg of order Ord hidding the I first var and evaluate it in (x,y)
Definition at line 285 of file resultant.h.
References MPol< C, O, R >::begin(), degree(), and MPol< C, O, R >::end().
| MATR sylvester | ( | const UPolDse< C, R > & | P, | |
| const UPolDse< C, R > & | Q, | |||
| char | c | |||
| ) |
The Sylvester matrix, with the maximum degree coefficient at the beginning.
Definition at line 91 of file resultant.h.
References degree().
The Sylvester matrix of P and Q.
The type of the matrix result is specified by the parameter MATR.
sylvester<MatrDse<double> >(P,Q);
Definition at line 73 of file resultant.h.
References degree().
| MatrDse<MPOL> u_sylvester | ( | const MPOL & | p1, | |
| const MPOL & | p2, | |||
| int | I | |||
| ) |
Computes the Sylvester matrix of p1 and p2,hidding the I fist variables. If d is the number of variables,the result is a matrix of polynomials in "x0,x1,...,xd-I",
Definition at line 188 of file resultant.h.
References degree().
| MatrDse<UPOL> u_sylvester | ( | const MPOL & | p1, | |
| const MPOL & | p2, | |||
| typename MPOL::monom_t::index_t | i = 1 | |||
| ) |
Computes the Sylvester matrix 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:
sylvester<MyUPoly>(p1,p2);
Definition at line 139 of file resultant.h.
References degree().
Referenced by Resultant().
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