The resultant of multivariate polynomials f and g in P=R[x1, ..., xn] with respect to the variable v=xi, which is by definition the determinant of the Sylvester matrix for f and g when considered as polynomials in the single variable xi. 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].
The discriminant D of f∈R[x1, ..., xn] is returned, where f is considered as a polynomial in v=xi. 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).