BezoutMatrix(R, UP, M, Row, Col)

bezout.spad line 1 [edit on github]

• R: Ring

• UP: UnivariatePolynomialCategory R

• M: MatrixCategory(R, Row, Col)

• Row: FiniteLinearAggregate R

• Col: FiniteLinearAggregate R

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 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 nonzero polynomials p and q.