How does this generic code interact with the existing code for elliptic curves?
John
2008/4/15 Kiran Kedlaya <[EMAIL PROTECTED]>:
>
> There is an old ticket #793 about implementing a zeta_function method
> for hyperelliptic curves. Such a method would have to have a default
> behavior in case none of the special-purpose methods we have already
> implemented are appropriate.
>
> So I thought I'd try writing a generic method for schemes over finite
> fields. Unfortunately, it's limited right now to schemes over prime
> fields because it requires at least a random coercion from F_q to
> F_{q^n}, which we don't yet support for q composite. (Maybe soon...)
>
> It's also a bit stupid because it counts rational points over F_q by
> actually constructing the list of them. Better would be to construct a
> scheme consisting of these points and then compute the length of this
> over the field. For example, if your scheme were the affine scheme
> V(I) for I an ideal in F_q[x_1, ..., x_n], you could form the ideal J
> = I + (x_1^q - x_1, ..., x_n^q-x_n) and then call
> J.vector_space_dimension().
>
> But in any case, see
> http://math.mit.edu/~kedlaya/Zeta_functions.sws
> for a notebook containing what I have so far. Comments and
> improvements welcome...
>
> Kiran
>
> >
>
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to [email protected]
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at http://groups.google.com/group/sage-devel
URLs: http://www.sagemath.org
-~----------~----~----~----~------~----~------~--~---
