Re: New GP function ellrank (2-descent)

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Fri, Feb 05, 2021 at 04:53:27PM +0100, Bill Allombert wrote:
> Dear PARI developers,
> 
> I have added a new GP function 'ellrank' to the master branch.
> This is a port of Denis Simon GP script ellQ.gp.
> However the interface is different, it returns [r,R,V] where r is a
> lower bound for the rank, R is an upper bound and V is a list of point.
> 
> It should compare favorably to John Cremona mwrank (which use a
> different algorithm), except it does not do saturation yet, but this
> will be added soon.

I have added a GP function ellsaturation that can be used to saturate
the points.

{ E=ellinit([0,1,0,-19357973048906456166239827272707359553313344,
    21187731957757821187375878909257489490487412099497964528006317056]);
}
R = ellrank(E,100);
R1=matdet(ellheightmatrix(E,R[3]))
\\%3 = 29871087490016654.513984426820550500851
S = ellsaturation(E, R[3],200);
R2=matdet(ellheightmatrix(E,S))
\\%5 = 312848498549.62405624139280925577340965
R1/R2
\\%6 = 95480.999999999999999999999999999999760

Cheers,
Bill