iterating over quotient ring and polynomial ring

Hello

I have been studied some finite algebraic structure as follows:

P.<v> = PolynomialRing(GF(2))
R.<v> = P.quotient((v^2-v))
T.<x> = PolynomialRing(R)

R is a quotient ring with elements : 0,1,v,1+v. I want to list all of the polynomials with degree 2. So I write:

for r in T.polynomials(of_degree=2): r

but the error is "object does not support iteration".

And also the same problem arises when I want to list the elements of R.

Is there any solution to this problem? How can I iterate over this structure?

thank you

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This is something that is indeed missing in Sage. Thanks for your report! I proposed a fixed on ticket #23467. If this ticket is positively reviewed, then the changes will be incorporated into later versions of Sage. And then you will be able to use the exact command you wrote.

In the mean time you can use the following to make the list of nonzero elements in R

sage: P.<v> = PolynomialRing(GF(2))
sage: R.<v> = P.quotient((v^2-v))
sage: T.<x> = PolynomialRing(R)
sage: R_nonzero = [R(p) for i in range(3) for p in P.polynomials(of_degree=i)]

from there it is not hard to build polynomials with coefficients in R.

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