#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 | Keywords: hyperelliptic curve points at
Merged in: | infinity
Reviewers: | Authors: Marco Streng
Work issues: | Report Upstream: N/A
Commit: | Branch:
Stopgaps: | Dependencies:
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Here are two isomorphic hyperelliptic curves:
{{{
sage: HyperellipticCurve(x^6+x-1).points()
[(0 : 1 : 0),
(1 : 6 : 1),
(1 : 1 : 1),
(2 : 4 : 1),
(2 : 3 : 1),
(4 : 5 : 1),
(4 : 2 : 1)]
sage: HyperellipticCurve(-x^6+x^5+1).points()
[(0 : 1 : 0),
(0 : 6 : 1),
(0 : 1 : 1),
(1 : 6 : 1),
(1 : 1 : 1),
(2 : 5 : 1),
(2 : 2 : 1),
(4 : 4 : 1),
(4 : 3 : 1)]
}}}
The isomorphism is {{{(x,y) |-> (1/x,y/x^3)}}}. They don't have the same
number of points because of singularities at infinity. But by
"hyperelliptic curve", one really means the desingularized curve. So the
function "points" should return points on the desingularized curve.
See also #11800 and #11980
I'm writing a patch now.
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Ticket URL: <http://trac.sagemath.org/ticket/15115>
Sage <http://www.sagemath.org>
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