Resultants and Discriminants

Resultant(f, g, i) : RngMPolElt, RngMPolElt, RngIntElt -> RngMPolElt

Resultant(f, g, v) : RngMPolElt, RngMPolElt, RngMPolElt -> RngMPolElt

The resultant of multivariate polynomials f and g in P=R[x_1, ..., x_n] with respect to the variable v=x_i, which is by definition the determinant of the Sylvester matrix for f and g when considered as polynomials in the single variable x_i. The result will be an element of P again. The coefficient ring R must be a domain. There are two ways to indicate with respect to which variable the integral is to be taken: either one specifies i, the integer 1 <= i <= n that is the number of the variable (upon creation of P, corresponding to P.i) or the variable v itself (as an element of P).

The algorithm used is the modular interpolation method, as given in [GCL92, pp. 412--413].

Discriminant(f, i) : RngMPolElt, RngIntElt -> RngMPolElt

Discriminant(f, v) : RngMPolElt, RngMPolElt -> RngMPolElt

The discriminant D of f in R[x_1, ..., x_n] is returned, where f is considered as a polynomial in v=x_i. The result will be an element of P again. The coefficient ring R must be a domain. There are two ways to indicate with respect to which variable the integral is to be taken: either one specifies i, the integer 1 <= i <= n that is the number of the variable (upon creation of P, corresponding to P.i) or the variable v itself (as an element of P).