[Axiom-mail] Help on polynomial coefficients

[Rodrigo Canaan]

I am making a program to find a polynomial P(x,y) that is the solution to a given system. The degree of P is given. I need one variable to represent each coefficient P, so I can find all coefficients, determining the polinomial.
Problem is, I don't know how to assign one variable to each coefficient, as I don't know in advance the degree of P, thus don't even know in advance how many coefficients I am going to use

What I wish I could do is, given the degree P, build P as a sum of terms where each coefficient is a variable.
If my degree was 1, for example, I want to build P as
P:=A*x+B*y+C
If my degree was 2, I would have:
P:=A*x^2 + B*y^2 +C*x*y +D*x +E*y +F
I have no idea how to do it for a general degree, on axiom

Thanks for the help!