Karim BELABAS on Thu, 3 Jul 2003 20:21:45 +0200 (MEST) |
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Re: isprime(,2) (again, it seems) |
On Thu, 3 Jul 2003, Phil Carmody wrote: > Looking back through the dev archives (to Jan this year, but not further > back, apologies if this has been mentioned before then) It has not. > it appears that the APRCL in 2.2.5 has a few problems when trying to prove > some numbers of the form Phi(a,b). > > In particular there are two different failure modes. > > 1) *** non invertible matrix in gauss, > e.g. gp > isprime(subst(polcyclo(16),x,16),2) > > 2) Digagreement with isprime(,1) [...] > (18:33) gp > isprime(subst(polcyclo(36),x,125),2) > %7 = 0 Both of them were due to an integer overflow. They should be fixed in the CVS version. The APRCL code is currently in a sorry state: I spent a few days about one year ago cleaning up the original (messy) code; then I received from the original author further patches corresponding to mathematical improvements, but which reintroduced many of the things I had painfully removed [ global variables, various inefficiencies handling t_INTMODs and further unreadable / undocumented hacks ]. The code was still preliminary [ did not contain the Bosma-van der Hulst improvements, didn't use at all partial factorizations of p - 1, p + 1, etc., used a very naïve way of tabulating discrete logs so that it is completely unable to handle numbers around 2000 digits because of memory overflow ]. I let it in as is, waiting for further patches. Unfortunately the latter never came and the code is more or less orphaned at this point. Ugrading it to a decent state would probably require at least one week of my time (full time). I don't think I'll be able to muster that much free time in the near future. Anybody interested in cleaning up / improving that code ? Cheers, and thanks for bringing this up, Karim. -- Karim Belabas Tel: (+33) (0)1 69 15 57 48 Dép. de Mathématiques, Bât. 425 Fax: (+33) (0)1 69 15 60 19 Université Paris-Sud http://www.math.u-psud.fr/~belabas/ F-91405 Orsay (France) http://www.parigp-home.de/ [PARI/GP]