[GAP Forum] Polynomial ring of indeterminates
Nagy Gabor
nagyg at math.u-szeged.hu
Mon Apr 20 17:04:23 BST 2015
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
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