BezoutMatrix(R, UP, M, Row, Col)ΒΆ

bezout.spad line 1

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.
subResultant: (UP, UP, NonNegativeInteger) -> UP if R has CommutativeRing
subResultant(p, q, j) returns the jth subresultant Sj, computed by its definition method (using determinant of subSylvesterMatrix). subResultant(p, q, 0) = resultant(p, q).
subResultantList: (UP, UP) -> List UP if R has CommutativeRing
subResultantList(p, q) returns the subresultants of p and q, in descending order, the last element is resultant(p, q).
subSylvesterMatrix: (M, NonNegativeInteger) -> M
subSylvesterMatrix(S, j) returns the jth 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 polynomials p and q.