#4525: [with new patch, needs 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 cremona):
* summary: [with patch, needs work] LLL-reduction of elliptic curve
bases (with resulting speed enhancement to
integral_points()) => [with new patch, needs
review] LLL-reduction of elliptic curve bases
(with resulting speed enhancement to
integral_points())
Comment:
The new patch trac-4525-combined.patch replaces all earlier ones by
combining them, and also fixes the bug William found (fix due to Tobias)
with an associated doctest. I checked all was well for curves in the
database up to conductor about 170.
The patch is based on 3.2 (since I have not yet built any 3.2.1s). Tested
on 32- and 64-bit linux.
Remarks on testing (especially against Magma): (1) unless you have a very
recent version of Magma the Magma output may sometimes be wrong (from
x-coordinates repeated to crashes). (2) For small examples like this most
of the time is spent finding the MW basis. For better time comparisons
you should (a) use the optional database, which includes generators, in
Sage and (b) precompute the generators in Magma medfore asking for the
integral points. I did this before the initial release of the code, and
one day I'll do it again.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4525#comment:13>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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