Karim Belabas on Tue, 13 Dec 2005 19:44:02 +0100 |
[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]
Re: modular exponentiation |
* John Jones [2005-12-13 18:00]: > > (14:15) gp > k = 10000000000; N = 123456; > > (14:15) gp > Mod(10,N)^k > > *** Warning: multiword exponent in Fl_pow. [...] > The way it is, it looks like gp is warning the user that the answer > might be wrong because it cannot handle an exponent so large. I think > that is a really bad message to send to the users. If the warning is > there to say "this computation can probably be done more efficiently by > ...", then that is what it should say. OK, I've changed it to: (19:32) gp > Mod(10,123456)^10000000000 *** Warning: large exponent in Mod(a,N)^n: reduce n mod phi(N). > Personally, I don't think gp should give such warnings at all. In this > case, it is ironic that gp gives a warning since gp could do everything > itself: it could test the size of the modulus and the exponent to decide > if the exponent should be reduced modulo phi(N). But it doesn't do that, > because it would be a waste of time? I'd rather warn the user that he's doing something stupid, than to silently spend twice as much time (or worse!) for these (trivial) computations. Cheers, Karim. -- Karim Belabas Tel: (+33) (0)5 40 00 26 17 Universite Bordeaux 1 Fax: (+33) (0)5 40 00 69 50 351, cours de la Liberation http://www.math.u-bordeaux.fr/~belabas/ F-33405 Talence (France) http://pari.math.u-bordeaux.fr/ [PARI/GP]