#18916: Use Kedlaya algorithm to count points on hyperelliptic curves
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Reporter: jpflori | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.8
Component: number fields | Resolution:
Keywords: hyperelliptic curves, matrix | Merged in:
of Frobenius | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Comment (by kedlaya):
Replying to [comment:5 jpflori]:
> I confirm that `hyperellpadicfrobenius` only works for prime fields
whereas the `nf...` one handles extensions.
> Though both of them are not marked `static` and use `gerepile` magic to
leave a clean stack so I guess they are possible and safe to use from
outside the PARI library.
>
Bill Allombert confirmed this. The `nf...` command is not (currently)
available in GP, but we can call it from the library.
> >
> > Also, the Frobenius matrix commands have a similar restriction on p as
in Harvey's code. The charpoly command seems to be doing a naive point
count for smaller p.
> Do you mean those in the PARI library?
> I don't see at first glance such restriction.
> There is some naive point counting involved in `hyperellcharpoly` but
that is when the curve is of (very) low genus and the characteristic is
small.
> Did I miss something else?
>
Oh, maybe that is just an optimization for cases where naive point
counting is actually faster?
--
Ticket URL: <http://trac.sagemath.org/ticket/18916#comment:6>
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