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Hi everyone

I am trying to work with finite rings. In Sagemath, I learned that we could create a finite quotient of a multivariate polynomial ring with the following syntax

S = PolynomialRing(GF(2), 'x, y')
x,y = S.gens()
I = S.ideal([x**2, y**2])
R = S.quotient(I, names=S.variable_names())
print(R)

This works fine. The problem is that I can't iterate through this ring (I guess Sagemath does not automatically know that the ring is finite). A similar question is posted here but only for quotients of univariate polynomial rings.

https://ask.sagemath.org/question/65155/iterate-over-elements-of-finite-quotient-of-a-polynomial-ring/

I tried to imitate the method there but have not been able to figure it out. I would love to hear your expertise on this. Additionally, I would love to hear if there is a built-in library in Sagemath for finite rings.

Thank you.

Tung

Hi everyone

I am trying to work with finite rings. In Sagemath, I learned that we could create a finite quotient of a multivariate polynomial ring with the following syntax

S = PolynomialRing(GF(2), 'x, y')
x,y = S.gens()
I = S.ideal([x**2, y**2])
R = S.quotient(I, names=S.variable_names())
print(R)

This works fine. The problem is that I can't iterate through this ring (I guess Sagemath does not automatically know that the ring is finite). A similar question is posted here but only for quotients of univariate polynomial rings.

https://ask.sagemath.org/question/65155/iterate-over-elements-of-finite-quotient-of-a-polynomial-ring/

I tried to imitate the method there but have not been able to figure it out. I would love to hear your expertise on this. Additionally, I would love to hear if there is a built-in library in Sagemath for finite rings.

Thank you.

Tung