#11800: Problem with points at infinity in hyperelliptic curves
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Reporter: gaudry | Owner: AlexGhitza
Type: defect | Status: needs_work
Priority: minor | Milestone: sage-5.0
Component: algebraic geometry | Keywords: ecc2011, sd35,
hyperelliptic curve, conic
Work_issues: | Upstream: N/A
Reviewer: Marco Streng | Author: David Eklund
Merged: | Dependencies: #11930
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Comment(by mstreng):
I see that the new patch isn't set to "needs review" yet, but I'll comment
on it anyway: I think some explanation of the situation at infinity is in
order in the documentation. How about the following?
"This method currently lists points in the plane projective model, which
means that one point (0:1:0) at infinity is returned if the degree of the
curve is at least 4. Later implementations may consider the more
mathematically correct desingularisation at infinity, replacing (0:1:0) by
0 or 2 smooth rational points if the degree is even." + EXAMPLE of degree
6.
Also, your method of finding points at infinity is linear in the field
order, this can be improved by taking (1:y:0) and solving for y (i.e.,
extracting 1 square root), exactly as currently the affine points are
found by taking (x:y:1) for each x and solving for y.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11800#comment:18>
Sage <http://www.sagemath.org>
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