#11800: Problem with points at infinity in hyperelliptic curves
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Reporter: gaudry | Owner: AlexGhitza
Type: defect | Status: needs_work
Priority: minor | Milestone: sage-5.0
Component: algebraic geometry | Keywords: ecc2011, sd35,
hyperelliptic curve, conic
Work_issues: | Upstream: N/A
Reviewer: Marco Streng | Author: David Eklund
Merged: | Dependencies: #11930
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Comment(by davideklund):
In the present patch, the points() method returns all the rational points
on the plane projective model, including those on the line at infinity.
I agree that when the projective plane model is singular (the typical
case) we really want the points() method to spit out points on a smooth
model. Maybe the issue should be raised in a separate ticket. A comment on
the matter by David Kohel:
The approach of Magma is to use weighted projective space which allows one
to represent two points at infinity (when the degree of {{{f + h^2/4}}} is
even). In this case one gets two points at infinity rather than one
(singular when g > 0).
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11800#comment:16>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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