# BezoutMatrix(R, UP, M, Row, Col)ΒΆ

BezoutMatrix contains functions for computing resultants and discriminants using Bezout matrices, and functions related with Sylvester matrix and subresultant.

bezoutDiscriminant: UP -> R if R has CommutativeRing

`bezoutDiscriminant(p)` computes the discriminant of a polynomial `p` by computing the determinant of a Bezout matrix.

bezoutMatrix: (UP, UP) -> M

`bezoutMatrix(p, q)` returns the Bezout matrix for the two polynomials `p` and `q`.

bezoutResultant: (UP, UP) -> R if R has CommutativeRing

`bezoutResultant(p, q)` computes the resultant of the two polynomials `p` and `q` by computing the determinant of a Bezout matrix.

subresultants: (UP, UP) -> IndexedVector(UP, Zero) if R has CommutativeRing

`subresultants(p, q)` returns a vector of subresultants of `p` and `q`, in ascending order, starting with index 0.

subSylvesterMatrix: (M, NonNegativeInteger) -> M

`subSylvesterMatrix(S, j)` returns the `j`th sub-Sylvester matrix `jS`.

subSylvesterMatrix: (M, NonNegativeInteger, NonNegativeInteger) -> M

`subSylvesterMatrix(S, j, i)` returns sub-Sylvester matrix jSi.

sylvesterMatrix: (UP, UP) -> M

`sylvesterMatrix(p, q)` returns the Sylvester matrix for the two nonzero polynomials `p` and `q`.