With http://trac.sagemath.org/ticket/16953 (hint: needs review) you can do:
sage: F.<q> = GF(13^2)
sage: P2.<x,y,z> = toric_varieties.P2(base_ring=F)
sage: C = P2.subscheme(x^8 + y^8 + z^8)
sage: C.cardinality()
512
Thats of course a generic count, you could be much smarter just for Fermat
curves. Though getting an answer can be nice, too...
On Tuesday, March 3, 2015 at 6:04:36 PM UTC+1, David Joyner wrote:
>
> Hi Sage-support: At his request, the question below is posted for Norm
> Hurt, who is not on this list. - David
>
>
> I was reading a recent paper of Arakelian and Borges on Frobenius
> nonclassicality of Fermat curves with respect to cubics, in which at
> some point they state that the curve C: X^8 + Y^8 + Z^8 = 0 over F_q =
> F_{13^2} has N_q(C) F_q-rational points equal to 512. I thought
> this is something someone must have worked out in SAGE. However, I
> could not find anything on a quick search of SAGE literature. There is
> the work on hyper-elliptic curves but has anyone treated just the case
> of Fermat curves over a finite field?
>
> Sincerely,
> Norm Hurt
>
--
You received this message because you are subscribed to the Google Groups
"sage-support" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-support.
For more options, visit https://groups.google.com/d/optout.
