Re: ellap hangs on a large-ish prime

[Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>]

On Tue, Feb 02, 2010 at 10:06:36AM -0400, Jeremy Porter wrote:
> Thanks to all for the very speedy responses!
> 
> In any case, the problem seems to be solved in the current svn.
> > The original poster's gp script
> >
> > E = ellinit([0,0,1,-1,0]);
> > P = 2486152157;
> > ellap(E, P)
> >
> > returns -13740 in no time.
> >
> 
> I also get this answer in no time if I compile the older 2.3.4 (stable)
> version of GP myself on any of the systems I have at my disposal; however
> using the version of GP installed through the Ubuntu repositories will have
> ellap() hang, on various architectures. Is it possible (out of the purview
> of this list, I recognize) that some compilation option for the Ubuntu
> package is to blame?

This is because you did not pass the flag --with-gmp to Configure, so you
do not use the GMP kernel.

The bug is caused by an incorrect use of modBIL(y) where y is 0. When using
the GMP kernel this return a random value, so the match fails. With the
pari kernel this always returns 2 so the match succeed.

Now y=0 can only happen for 2-torsion points, but the code in the developement
version handle 2-torsion points separately, so it is not affected.

Cheers,
Bill