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Bill Allombert on Thu, 07 Mar 2024 19:15:52 +0100
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Re: question on inconsistent results for a curve and ellrank() command
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- To: pari-users@pari.math.u-bordeaux.fr
- Subject: Re: question on inconsistent results for a curve and ellrank() command
- From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>
- Date: Thu, 7 Mar 2024 19:15:44 +0100
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On Thu, Mar 07, 2024 at 08:34:20AM +0100, Aurel Page wrote:
> Dear Randall,
>
> Bill will confirm, but I think ellrank uses a random search, so the points
> found may not be the same on several runs. I don't think this has anything
> to do with the precision.
Precisely, if you do not use effort, the algorithm is mostly deterministic.
Otherwise the algorithm pick random Selmer class representative to build
quartics to find points on them, so you might not always find the same
number of points.
Now the effort parameter increases both the number of quartics to check, and the
height bound for the search on each of them.
However, the choice of growth of parameters is probably not optimal, but it is
difficult to compare the effect of any choices.
One can do:
? E=ellinit([0,12304376939822994932659524,0,-3648259547053109398533591982691229700073064038400,0]);
? F=ellrankinit(E);
? R=ellrank(F)
%3 = [0,6,0,[]]
? R=ellrank(E,1,R[4])
%4 = [0,6,0,[]]
? R=ellrank(E,2,R[4])
%5 = [2,6,0,[[-1406975789099557808651520,5167717070222070579741742214157519360]]]
? R=ellrank(E,3,R[4])
%6 = [2,6,0,[[-1406975789099557808651520,5167717070222070579741742214157519360],[-999779060917633308399360,3866142351194747967608412122674782720]]]
? R=ellrank(E,4,R[4])
%7 = [4,6,0,[[-6105797019069920466053760,15917389406358134595823780451205131520],[-1406975789099557808651520,5167717070222070579741742214157519360],[-999779060917633308399360,3866142351194747967608412122674782720]]]
Cheers,
Bill.