I'm at the very beginning of Goebner bases, so sorry if my question is too elementary or I don't use the correct terminology.

I have polynomials, p1(x1,...,x9), ..., p8(x1,...,x9), and q(x1,...,x9).

I need an algebraic representation of q by p1,.... . Since the answer can be long, it would be useful to obtain the "coefficients" separately also. One (a bit stupid) example is:

p1(x1,x2):= x1 + x2, p2:= x1^2 + x2^2, q(x1,x2):= x1^3 + x2^3.