#15115: correct set of points at infinity for hyperelliptic curve
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Reporter: mstreng | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-5.12
Component: geometry | Resolution:
Keywords: hyperelliptic | Merged in:
curve points at infinity | Reviewers:
Authors: Marco Streng | Work issues: doctest the rest of
Report Upstream: N/A | the sage library, check how
Branch: | documentation looks, add example
Dependencies: #15108 | from ticket description to patch
| Commit:
| Stopgaps:
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Comment (by mstreng):
Replying to [comment:3 nbruin]
I looked at polynomial rings and projective spaces for a while, then found
that there is a long way to go before we have weighted projective spaces
in Sage. But I did not see that `is_homogeneous()` and `degree` are
already working, so maybe I was pessimistic.
One more pessimistic remark though: elliptic curves over the p-adics
inherit from hyperelliptic curves, so switching to weighed projective
space with weights (1, g+1, 1) for all hyperelliptic curves will lead to
trouble.
Anyway, note that many changes in the patch must happen also with weighted
projective spaces, this patch just does it now, rather than waiting.
Of course the fake points at infinity in this patch are an ugly hack, but
using a singular model gives mathematically incorrect answers (as in
#11980), and doing the whole weighted projective spaces thing takes time.
So which is the lesser of three evils?
--
Ticket URL: <http://trac.sagemath.org/ticket/15115#comment:4>
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