On May 2, 2008, at 3:45 PM, William Stein wrote:
> The complexity mostly depends on the precision one uses in > computing a certain Euler product approximation to zeta > and also the number of factors in the product. If you look > at the PARI source code the comments do *not* inspire confidence in > its correctness. I had a student give a provable bound on precision > and number of factors needed and wasn't able to get anything > as good as what PARI uses. > > Here's the funny part of the PARI code (in trans3.c): > > /* 1.712086 = ??? */ > t = log( gtodouble(d) ) + (n + 0.5) * log(n) - n*(1+log2PI) + > 1.712086; One way to check it is to use the bernoulli_mod_p_single() function, which computes B_k mod p for a single p and k, and uses a completely independent algorithm. sage: x = bernoulli(240000) sage: p = next_prime(500000) sage: bernoulli_mod_p_single(p, 240000) 498812 sage: x % p 498812 sage: p = next_prime(10^6) sage: bernoulli_mod_p_single(p, 240000) 841174 sage: x % p 841174 So I would say the answer is correct. david --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
