I want to solve a system of multivariate polynomials with parameters. Mathematically, the ground field is F = Q(a, b, c, …), the field of rational functions. The polynomials are in F[x,y,z,…]. I want, say, the resultant in x; i.e., eliminate the other variables y,z,… .
Example: I've been told to do this, and it works on simple examples but not real problems of interest:
Q := RationalField();
A1<x, y, z, a, b, c> := AffineSpace(Q,6);
X := Scheme(A1,[ a*x^2*y + b*z*y - x, ... fill in 3 equations... ]);
I:=Ideal(X);
time J := EliminationIdeal(I,{x,a,b,c});
On real problems, it goes on "forever". Any help would be much appreciated. Does the order I list the variable names matter?