#4525: [with patch, needs review] LLL-reduction of elliptic curve bases (with
resulting speed enhancement to integral_points())
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Reporter: cremona | Owner: was
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.2.1
Component: number theory | Resolution:
Keywords: elliptic curve |
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Comment (by cremona):
The second patch 10903.patch implements another speedup, in the function
integral_points_with_bounded_mw_coefficients(), which I have moved outside
the integral_points() function (mainly for ease of testing). We still
loop through all relevant linear combinations as real points, but instead
of computing each linear combo from scratch we do so in a more incremental
way, since most of the time we get the next combo by adding a single
point.
Apply after the previous patch. Timings:
rank 3 [0,0,1,-7,6] : old 0.33s, new 0.16s
rank 4 [0,0,1,-7,36]: old 15.4s, new 4.24s
rank 5 [0,0,1,-79,342]: old 273s, new 64s
with presumably even better factors for larger examples. (I still have
not completed a rank 8 example, but one day I will!).
By the way, for that rank 5 example I had to find the gens first with
"proof=False" and then manually use E._set_rank() and E._set_gens(). We
might want to add the proof flag to integral points, just to apply to the
MW basis part of the computation.
PS Since I moved the function it is not so easy to see what has changed,
sorry. Basically the old lines 4228-4242 are replaced by the new lines
4491-4526.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4525#comment:4>
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