#21093: Unhandled case in EllipticCurve_from_cubic()
---------------------------------+-------------------------------
Reporter: cremona | Type: defect
Status: new | Priority: major
Milestone: sage-7.3 | Component: elliptic curves
Keywords: | Merged in:
Authors: Robin Houston | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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''I ran into an unexpected error in `EllipticCurve_from_cubic`, with the
following cubic and rational point:''
{{{
#!python
R.<x,y,z> = QQ[]
cubic = -3*x^2*y + 3*x*y^2 + 4*x^2*z + 4*y^2*z - 3*x*z^2 + 3*y*z^2 - 8*z^3
EllipticCurve_from_cubic(cubic, (-4/5, 4/5, 3/5))
}}}
''Note that it works as expected using instead the different rational
point `(1, 1, 0)`.''
''On investigation, I found there is a case that isn’t handled correctly.
The code computes''
{{{
#!python
P2 = chord_and_tangent(F, P)
}}}
''and if `P2` is projectively equivalent to `P` then it uses a different
algorithm. If they’re different, it then computes''
{{{
#!python
P3 = chord_and_tangent(F, P2)
}}}
''and uses an algorithm that fails if `P3` is equivalent to `P2`.''
''I think the attached patch fixes this problem. At least, with this patch
it now works for my examples.''
----
(From [http://permalink.gmane.org/gmane.comp.mathematics.sage.devel/87847
sage-devel].)
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Ticket URL: <https://trac.sagemath.org/ticket/21093>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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