#8820: elliptic_exponential broken for curves over number fields
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Reporter: robertwb | Owner: cremona
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.6
Component: elliptic curves | Keywords:
Author: John Cremona | Upstream: N/A
Reviewer: Chris Wuthrich, Jeroen Demeyer | Merged:
Work_issues: |
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Changes (by cremona):
* status: needs_work => needs_review
Comment:
8820_rebase_after_9931-new.patch adresses the doctest failures in
heegner.py. I did this quite carefully (even refining a little the code
which does the modular parametrization). I took account where sensible of
Chris's remark that it is better in approximate doctests not to have
numbers which are approximately zero; but when the output is an
approximate integral Heegner point one cannot easily change the point. I
hope reviewer(s) do not object to the various ways I found around this --
with very little use of ... and none (I think) of #random.
Note that these Heegner examples are often going to be problematical since
in many cases the point computed is approximately (0:1:0), i.e. the z in
CC is approximately a period. In such examples it might be better just to
output E.period_lattice().coordinates(z) rather than
E.elliptic_exponential(z). However, I have adjusted the test for being
integral (i.e. for z to b in the period lattice) in a way that I hope is a
reasonable compromise: namely that the coordinates w.r.t. the lattice
basis should be approximately integral in the sense that their fractional
part is at most {{{2^(0.8*prec)}}}.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8820#comment:28>
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