I have taken a look at the code. Some tweaking will be needed to make
it sensibly compatible with the existing code for point counting of
elliptic curves. There, the function cardinality() takes a parameter
extension_degree with default 1, while you do a base change to get the
cardinality over extensions. Secondly, I think having a cardinality()
method is better than calling a rational_points() functioI have taken
a look at the code. Some tweaking will be needed to make it sensibly
compatible with the existing code for point counting of elliptic
curves. There, the function cardinality() takes a n and then taking
the len() of the result, since there is little point in creating a
list of all the rational points at all if what one needs is their
number.
I'm adding these remaqrks to the ticket (#3031) although it has been
merged already.
John
2008/4/27 Kiran Kedlaya <[EMAIL PROTECTED]>:
>
> For the record, a version of my generic code (with a bit of help from
> craigcitro) has been merged into 3.0.1alpha1, as ticket #3031. Anyone
> now interested in tackling #793 should let me know.
>
> Kiran
>
>
>
> On Apr 15, 1:56 pm, Kiran Kedlaya <[EMAIL PROTECTED]> wrote:
> > 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
> >
>
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