Max Alekseyev on Mon, 08 Feb 2010 20:23:50 +0100 |
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Re: thue() wants more than 4GB stack |
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