 | 1 | initial version |
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?
| | 2 | retagged |
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?
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