#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 |
----------------------------+-----------------------------------------------
Changes (by was):
* summary: [with new patch, needs review] LLL-reduction of elliptic
curve bases (with resulting speed enhancement
to integral_points()) => [with patch, positive
review] LLL-reduction of elliptic curve bases
(with resulting speed enhancement to
integral_points())
Comment:
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).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4525#comment:15>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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