Re: thue() wants more than 4GB stack

[Max Alekseyev <maxale@gmail.com>]

On Mon, Feb 8, 2010 at 7:36 AM, Karim Belabas
<Karim.Belabas@math.u-bordeaux1.fr> wrote:
> * Max Alekseyev [2010-02-05 19:27]:
>> I wonder whether this behavior is intended?
>>
>> ? thue(thueinit(-3711916*x^4 - 161330*x^3 + 178491*x^2 - 365*x - 19),344622096)
>> Â *** thue: Warning: Non trivial conditional class group.
>> Â *** The result returned by 'thue' is conditional on the GRH.
>> Â *** Â at top-level: thue(thueinit(-37119
>> Â *** Â Â Â Â Â Â Â Â ^--------------------
>> Â *** thue: the PARI stack overflows !
>> Â current stack size: 4294967296 (4096.000 Mbytes)
>> Â [hint] you can increase GP stack with allocatemem()
>
> Intended, no. Expected, yes :-)
>
>> This is rather unusual example since many other thue() computations I
>> performed were not so eager for memory.
>
> After a simple change of variable, the algorithm needs to solve
>
> ÂK = bnfinit(x^4+365*x^3-3391329*x^2+58240130*x+25460031844);
> Âa = -461794186226632896;
> Âbnfisintnorm(K, a)
>
> Unfortunately, 'a' has many prime divisors (with moderately large
> valuations), in fact 18 prime ideal divisors, producing a huge number of
> potential solutions, about half of which should yield actual solutions
> since the class number of K is 2.
>
> It is not clean whether these solutions can actually fit in physical
> memory (I'll double check this, maybe there is some simple obstruction
> and no solution after all...).

Kurt Foster informed me that the equation I was trying to solve does
not have solutions neither modulo 7^3, nor modulo 3^3, which can be
easily verified by brute-force.
It would be helpful if PARI/GP performed some similar checks (maybe,
optionally by user's request) before going into heavy number-theoretic
machinery.

Regards,
Max