#15115: correct set of points at infinity for hyperelliptic curve
-------------------------------------+-------------------------------------
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: | from ticket description to patch
| Commit:
| Stopgaps:
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Changes (by mstreng):
* work_issues: =>
doctest the rest of the sage library, check how documentation looks,
add example from ticket description to patch
Old description:
> 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.
New description:
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
Apply:
* [attachment:15115.patch]
--
Comment:
apply 15115.patch
--
Ticket URL: <http://trac.sagemath.org/ticket/15115#comment:1>
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