#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
Work_issues: | Upstream: N/A
Reviewer: | Author: David Eklund
Merged: | Dependencies:
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Changes (by newvalueoldvalue):
* status: new => needs_review
* author: => David Eklund
Comment:
The problem arises exactly when {{{F=y^2+h*y-f}}} has degree 2. But then F
defines a conic! Even though the definition of hyperelliptic curve seems
to vary (sometimes requiring genus > 1 and sometimes including the genus 1
case) I think that the case where {{{y^2+h*y-f}}} has degree 2 should
raise an error since it is rather confusing to call a rational curve
hyperelliptic. Banning this case also seems to get rid of some additional
weirdness such as for example the TypeError when {{{h=0}}} and
{{{f=x+1}}}.
As far as I can tell, it is not checked at the moment whether the curve
defined by {{{y^2+h*y-f}}} has any singularities away from infinity, or
whether it is irreducible or reduced.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11800#comment:5>
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