#20391: count_points breaks on even-degree hyperelliptic curves
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Reporter: kedlaya | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-7.2
Component: algebraic | Keywords: hyperelliptic curve, number
geometry | of points
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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The following is currently broken:
{{{
sage: x = polygen(GF(4099))
sage: H = HyperellipticCurve(x^6 + x + 1)
sage: H.count_points(1)
...
ValueError: Q must be a monic polynomial of odd degree >= 3
}}}
The problem is that ultimately this is trying to call hypellfrob, which is
only implemented for odd degree polynomials. One can patch around this
using either PARI's hyperellcharpoly or the naive point counting code.
In the longer term, some more intelligent switching needs to be
implemented for this method, as well as the related zeta_function and
zeta_series methods; these do not all optimize the same way. See #965,
#16931, #18916, #20309 for related discussions.
--
Ticket URL: <http://trac.sagemath.org/ticket/20391>
Sage <http://www.sagemath.org>
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