#11800: Problem with points at infinity in hyperelliptic curves
----------------------------------+-----------------------------------------
Reporter: gaudry | Owner: AlexGhitza
Type: defect | Status: needs_review
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
----------------------------------+-----------------------------------------
Comment(by mstreng):
Not related to the example in the ticket description or to the patch, but
very much related to the title of this ticket and the first line of the
description: what is "points" supposed to mean? I assume it means points
over the base field, but of which model?
* The affine model in {{{_repr_}}} means no points at infinity.
* The plane projective model (currently underlying the implementation) is
not the natural thing to look at at infinity, it always has one point
{{{(0:1:0)}}} at infinity, which is singular (assuming genus > 1).
* The smooth projective model (the actual hyperelliptic curve) is what
you get when you desingularize {{{(0:1:0)}}}. It has 0, 1 or 2 points at
infinity defined over the base field. Is there a framework in Sage that
would make it possible to have 2 point objects representing the different
points at infinity?
See #11980
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11800#comment:14>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
