Re: ellap hangs on a large-ish prime

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

On Mon, Feb 01, 2010 at 09:50:24PM -0400, Jeremy Porter wrote:
> Greetings,
> 
> In iteratively computing values of ellap(E,P) for the curve E =
> ellinit([0,0,1,-1,0]) for primes P of increasing size, I noticed that when P
> = 2486152157 my iteration would hang. Primes in a similar range (i.e.,
> nextprime(P+1) = 2486152159) are computed in well under a second, however I
> left this value of P to compute overnight without result.
> 
> I initially noticed this when using libpari in a C program, then confirmed
> it with the GP calculator. An example follows:
> 
> E = ellinit([0,0,1,-1,0]);
> P = 2486152157;
> isprime(P)
> ellap(E, nextprime(P+1))
> ellap(E, P)

I can reproduce this bug, I will investigate more.

> On the Intel i5 system, I do not encounter this problem if I download the
> latest source (pari-2.3.4.tar.gz) and simply run ./Configure with 'make
> all'. Doing this, the same ellap(E, P) call as above returns (correctly, I
> believe) -13740.

This is due to the difference of multiprecision kernel: You need
to pass --with-gmp to Configure to use the GMP multiprecision kernel.
Unfortunately, this bug only occurs when using the GMP kernel, so
it occur with the Ubuntu build but not with your manual build.

This bugs "disappeared" in the developpement branch in revision 8814.
I do not know yet why it disappeared, but I will investigate.

Cheers,
Bill.