#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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Changes (by kedlaya):
* keywords: => hyperelliptic curves, matrix of Frobenius
Comment:
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.
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.
In any case, it would be worth updating
HyperellipticCurve.frobenius_polynomial and related methods to include
calls to PARI as appropriate.
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Ticket URL: <http://trac.sagemath.org/ticket/18916#comment:3>
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