#11800: Problem with points at infinity in hyperelliptic curves
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Reporter: gaudry | Owner: AlexGhitza
Type: defect | Status: needs_info
Priority: minor | Milestone: sage-4.8
Component: algebraic geometry | Keywords: ecc2011, sd35,
hyperelliptic curve, conic
Work_issues: | Upstream: N/A
Reviewer: | Author: David Eklund
Merged: | Dependencies: #11930
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Changes (by mstreng):
* status: needs_review => needs_info
Comment:
Actually, I don't see any reason to ban conics from being hyperelliptic
curves in Sage. Mathematically, I would say that a hyperelliptic curve has
genus >= 2, but I don't want to forbid people to use the
HyperelllipticCurve classes for lower-genus curves. For example, a user
may have some loop going on where curves sometimes have genus 0, but
sometimes higher.
The point {{{(0:1:0)}}} is not a reason to change things: for genus >=2 it
is a singular point that you are not really interested in anyway! Indeed,
the 0, 1, or 2 rational points that you get when you resolve that
singularity are much more interesting.
Rather than disallowing conics, we could make a separate case in the
{{{points}}} function instead.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11800#comment:10>
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