[GAP Forum] Polynomial ring of indeterminates

[Nagy Gabor]

Dear Forum,

Assume that the indetermines x,y are defined using the command 
<PolynomialRing> as follows:

q:=7;
R:=PolynomialRing(GF(q^2),["x","y"]);
x:=R.1; y:=R.2;

Is it then possible to get back the base ring R from x or y?

In need this for the following reason.

Let H(u,v) be a fixed polynomial in two variables, say H(u,v)=u^2-v^3+v.

I need a function rho which maps the polynomial f(u,v) to the univariate 
polynomial

h(u)=Resultant(H,f,v).

Now, I need this WHITOUT knowing the names of the indeterminates of f.

So, my program should look like this:

rho:=function(f)
     local indets, basering;
     basering:=BaseRingOrWhateverCommand(f);
     indets:=IndeterminatesOfPolynomialRing(basering);
     return Resultant(f,indets[1]^2-indets[2]^3+indets[2],indets[2]);
end;

The solution should work also when f depends only on 1 variable, or when 
f is a constant polynomial.

Thanks for your help in advance!

Bye,

Gabor