2019-03-12 06:23:14 -0600 commented answer How to compute the sums of squares of elements of a quotient ring? Thank you, that is very helpful. 2019-03-12 06:22:44 -0600 received badge ● Scholar (source) 2019-03-12 04:04:16 -0600 asked a question How to compute the sums of squares of elements of a quotient ring? Hi, I'm new to Sage, and I would like to be able to test, given some $q$, whether $$\sum_{p(t) \in \mathbb{F}_{q}[t]/(f)}^{}{p^2(t)}=k \bmod (f)$$ for some fixed $f \in \mathbb{F}_q [t]$ and $k \in \mathbb{F}_q$. I can get as far as (for $q=3$ and $f=x^2+1$): sage: R = PolynomialRing(GF(3),'x'); x = R.gen() sage: S = R.quotient(x^2 + 1)  But I'm not sure how to sum over all the elements of the quotient ring, let alone their squares. Any hints?