#4525: [with patch, positive review] LLL-reduction of elliptic curve bases (with
resulting speed enhancement to integral_points())
----------------------------+-----------------------------------------------
Reporter: cremona | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-3.2.1
Component: number theory | Resolution:
Keywords: elliptic curve |
----------------------------+-----------------------------------------------
Comment (by cremona):
Replying to [comment:15 was]:
> I strongly recommend adding this as a doctest. It takes 11 seconds
without database_cremona, and about 2.5 seconds with, so should be marked
#long, probably:
>
> sage: [len(e.integral_points(both_signs=False)) for e in
cremona_curves([1..100])] # long
> [2, 0, 2, 3, 2, 1, 3, 0, 2, 4, 2, 4, 3, 0, 0, 1, 2, 1, 2, 0, 2, 1, 0, 1,
3, 3, 1, 1, 4, 2, 3, 2, 0, 0, 5, 3, 2, 2, 1, 1, 1, 0, 1, 3, 0, 1, 0, 1, 1,
3, 6, 1, 2, 2, 2, 0, 0, 2, 3, 1, 2, 2, 1, 1, 0, 3, 2, 1, 0, 1, 0, 1, 3, 3,
1, 1, 5, 1, 0, 1, 1, 0, 1, 2, 0, 2, 0, 1, 1, 3, 1, 2, 2, 4, 4, 2, 1, 0, 0,
5, 1, 0, 1, 2, 0, 2, 2, 0, 0, 0, 1, 0, 3, 1, 5, 1, 2, 4, 1, 0, 1, 0, 1, 0,
1, 0, 2, 2, 0, 0, 1, 0, 1, 1, 4, 1, 0, 1, 1, 0, 4, 2, 0, 1, 1, 2, 3, 1, 1,
1, 1, 6, 2, 1, 1, 0, 2, 0, 6, 2, 0, 4, 2, 2, 0, 0, 1, 2, 0, 2, 1, 0, 3, 1,
2, 1, 4, 6, 3, 2, 1, 0, 2, 2, 0, 0, 5, 4, 1, 0, 0, 1, 0, 2, 2, 0, 0, 2, 3,
1, 3, 1, 1, 0, 1, 0, 0, 1, 2, 2, 0, 2, 0, 0, 1, 2, 0, 0, 4, 1, 0, 1, 1, 0,
1, 2, 0, 1, 4, 3, 1, 2, 2, 1, 1, 1, 1, 6, 3, 3, 3, 3, 1, 1, 1, 1, 1, 0, 7,
3, 0, 1, 3, 2, 1, 0, 3, 2, 1, 0, 2, 2, 6, 0, 0, 6, 2, 2, 3, 4, 6, 5, 1, 0,
6, 1, 0, 3, 1, 1, 2, 3, 1, 2, 1, 1, 0, 1, 0, 1, 0, 5, 5, 2, 2, 0, 0, 1, 0,
0, 0, 0, 1, 1, 1, 1]
>
> I believe the output numbers are right. Two of them disagree with magma
(that 92 example), but in those two cases magma is wrong, as you mention
above.
>
> Positive review (but please add the above doctest).
Done in trac-4525-combined-2.patch which *replaces*
trac-4525-combined.patch .
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4525#comment:16>
Sage <http://sagemath.org/>
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