2009/5/21 Robert Miller <rlmills...@gmail.com>:
>
> ratpoints is a program for finding points of bounded height on curves
> of the form
>
> y^2 = a_n x^n + ... + a_1 x + a_0.
>
> A version of ratpoints was the starting point of John Cremona's
> mwrank, but since then there have been substantial improvements. I
> have been working on a Sage-native implementation of 2-descent on
> elliptic curves, using ratpoints, GMP, and FLINT. It is significantly
> faster than Magma, which is significantly faster than mwrank (at least
> on the curves I've been looking at-- I haven't done extensive
> benchmarking yet).
>
> The webpage for the software is here:
>
> http://www.mathe2.uni-bayreuth.de/stoll/programs/index.html
>
> The trac ticket is here:
>
> http://trac.sagemath.org/sage_trac/ticket/5854
>
> There are some memory leaks in ratpoints, but we will work on fixing
> these next week at Dagstuhl.
>
> Statistics:
> spkg size: 255K
> time to build: 5.6 secs
>
> What does everyone think?
I will certainly be checking this out! Two points before I do:
1. For years after Magma re-implemented mwrank (I gave them my code,
no license, but they wrote tehor own impelmentation) John Cannon was
frustrated that it remained slower than mwrank itself. I had not
noticed that that had changed. On the other hand tehre are things in
mwrank (e.g. second descents) which are not -- I think -- in Magma,
and testing curves in the database is a bit too easy.
2. It is not true to say that "A version of ratpoints was the starting
point of ... mwrank", not at all. mwrank does 2-descent, during the
course of which it has to search for points on such curves. For the
first 10 years of mwrank that was done by my own code. Then Stoll's
ratpoints came along which did that part faster (but did no kind of
descent at all, it was just a fast point search); so I adapted it and
put it into mwrank in 1999. My older searching code is still in
there, in fact if you change line 61 of src/qrank/mrank1.cc from this:
#define QSIEVE_OPT 0 // uses Stoll's sieve
so something else it wil still work (or it did last time I tried it,
so not guaranteed).
I'm looking forward to working on this. Note that what Robert has
done goes way way beyond the current title of #5854 ("Include Michael
Stoll's ratpoints in Sage"); it also implements a complete native
Sage version of (a lot of) mwrank, and he has done it remarkably fast.
Well done!
John
> >
>
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