Bill Allombert on Fri, 05 Feb 2021 16:53:29 +0100


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New GP function ellrank (2-descent)


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.
If the full gorup is determined, r==R==#V.

? E = ellinit([-157^2,0]);
? ellrank(E)
%2 = [1,1,[]]
The rank is 1 but no points was found.
It is possible to ask ellrank to try harder
? ellrank(E,10)
%5 =
[1,1,[[-43565582610691407250551997/609760250665615167250729,562653616877773225244609387368307126580/476144382506163554005382044222449067]]]

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.

Finally, I like to thanks Denis Simon for improving ellQ.gp over all
this years.

Cheers,
Bill