#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 jpflori):
To make things clear, I'm looking at PARI git version, though the version
in Sage is quite recent and should be similar as far as `hyperell.c` is
concerned.
Replying to [comment:3 kedlaya]:
> From a quick inspection of the PARI/GP implementation:
>
> The command hyperellpadicfrobenius appears to only work for prime
fields. There is an internal command nfhyperellpadicfrobenius which seems
to handle nonprime fields, which is called by hyperellcharpoly to get the
characteristic polynomial of Frobenius; but it does not appear to be
exposed.
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.
>
> 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?
For `p == 2` it indeed seems it only works for `F_2` using naive point
counting.
>
> In any case, it would be worth updating
HyperellipticCurve.frobenius_polynomial and related methods to include
calls to PARI as appropriate.
--
Ticket URL: <http://trac.sagemath.org/ticket/18916#comment:5>
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