Help on polynomial coefficients

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!

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