Re: New elldata package minor update (updated generators)

[John Cremona <john.cremona@gmail.com>]

On Wed, 3 Mar 2021 at 14:30, Bill Allombert
<Bill.Allombert@math.u-bordeaux.fr> wrote:
>
> On Wed, Mar 03, 2021 at 10:11:56AM +0000, John Cremona wrote:
> > ? E = ellinit([0, 0, 1, -79, 342])
> > %1 = [0, 0, 1, -79, 342, 0, -158, 1369, -6241, 3792, -295704,
> > -19047851, -54526169088/19047851, Vecsmall([1]), [Vecsmall([128,
> > -1])], [0, 0, 0, 0, 0,
> > 0, 0, 0]]
> > ? ellglobalred(E)
> > %2 = [19047851, [1, 0, 0, 0], 1, Mat([19047851, 1]), [[1, 5, 0, 1]]]
> > ? ellrank(E)
> > %3 = [5, 5, [[5, 8], [0, 18], [10, 23], [12, 33], [4, 9]]]
> > ? ##
> >   ***   last result computed in 32 ms.
> >
> > This compares rather well with mwrank (3.5s, but only 396ms without
> > saturation, which is a fairer comparison, though Bill has a good
> > saturation implementation on the way).
>
> Indeed, I recently added a function ellsaturation that you can use if
> you know the bound. If I read correctly, mwrank uses bound 1000 in
> this example so:
>
> ? ellsaturation(E,%[3],1000)
>   *** ellsaturation: Warning: increasing stack size to 16000000.
> %3 = [[5,8],[0,18],[10,23],[12,33],[4,9]]
> ? ##
>   ***   last result computed in 334 ms.
>
> Obviously the next step would be for ellsaturation to compute the bound
> itself.

In this case the bound is 265.  If you run mwrank with command line
parameters -S -1 -v 3 you can see this:  "-S" is a saturation bound,
but if you give it -1 it computes the bound itself.  "-v 3" is a
verbosity level; the saturation bound is not displayed with "-v 2",
though perhaps it should be.  ("-v 1" is the default.)  Also (since I
am here), option "-o" outputs the points in PARI/GP format:

$ echo [0,0,1,-79,342] | mwrank -q -S -1 -v 0 -o
[[5],[[-10,11],[-39/4,105/8],[-8,21],[-7,23],[-6,24]]]

I seem to remember that I put that in at Karim's request, since he
once wrote a wrapper for this in GP.  Thanks to Bill that is now
surely redundant!

John
>
> Cheers,
> Bill.
>