Question: Groebner

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.

Please, use this example and hopefully I will understand the explanation and able to follow the ideas of Help about this topic.

Thanks,   Sandor

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