Hi I'm new to sage. Can you tell me how to construct finite fields
using quotient of poly ring? For instance suppose I want to construct
GF(5^2) using a GF(5) poly ring mod out by x^2 + x + 1 how do I do
that? I can construct the quotient like this:

p = 5
F = GF(p)
R.<x> = F['x']
f = x * x + x + 1
S = R.quotient(f, 'a')

How do I force S to a field so that I can use it with elliptic curves?
I know that I can simply do GF(5^2) but I want to be able to specify
the modulus explicitly.

Thanks.


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