[GAP Forum] Polynomial ring of indeterminates

[Stefan Kohl]

On Mon, April 20, 2015 5:04 pm, Nagy Gabor wrote:
>
> 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?

Not from one of the indeterminates -- but from both x and y,
together with the coefficient field:

gap> PolynomialRing(GF(q^2),[x,y]) = R;
true

The coefficient field is needed since for every characteristic,
there is only one indeterminate -- i.e.

gap> Indeterminate(GF(q)) = Indeterminate(GF(q^2));
true

Hope this helps,

    Stefan