#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 mstreng):
Replying to [comment:16 davideklund]:
> 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).
Yes, this is a standard textbook approach to hyperelliptic curves. It is
requested in the documentation of
[http://www.sagemath.org/doc/reference/sage/schemes/generic/algebraic_scheme.html#sage.schemes.generic.algebraic_scheme.AlgebraicScheme_subscheme.rational_points
rational_points] as a way of representing two points at infinity. I don't
think weighted projective spaces exist in Sage, so a minimal
implementation of weighted projective spaces (like Magma's
{{{WeightedProjectiveSpace}}}) would be a first step.
Anyway, your patch looks good. I'll test it now.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11800#comment:17>
Sage <http://www.sagemath.org>
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