#11800: Problem with points at infinity in hyperelliptic curves
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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
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Changes (by davideklund):
* status: needs_info => needs_review
Old description:
> The function that lists the points on a hyperelliptic curve assumes that
> the point [0, 1, 0] is always valid. This is wrong and creates the
> following bug:
> {{{
> sage: R.<x> = GF(67)[]
> sage: H = HyperellipticCurve(24*x^2 + 33*x + 43)
> sage: H.points()
> ...
> TypeError: Coordinates [0, 1, 0] do not define a point on Hyperelliptic
> Curve over Finite Field of size 67 defined by y^2 = 24*x^2 + 33*x + 43
> }}}
>
> Apply [attachment:11800.patch]
New description:
The function that lists the points on a hyperelliptic curve assumes that
the point [0, 1, 0] is always valid. This is wrong and creates the
following bug:
{{{
sage: R.<x> = GF(7)[]
sage: H = HyperellipticCurve(3*x^2 + 5*x + 1)
sage: H.points()
...
TypeError: Coordinates [0, 1, 0] do not define a point on Hyperelliptic
Curve over Finite Field of size 7 defined by y^2 = 3*x^2 + 5*x + 1
}}}
Apply [attachment:trac_11800_allow_conics.patch]
--
Comment:
I changed the description to a simpler example (to include in the
documentation) which illustrates the same issue.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11800#comment:12>
Sage <http://www.sagemath.org>
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