On Apr 17, 2007, at 3:44 PM, DanK wrote:
> > Hi, > > for low p the computations are no problem and the time shown in the > results seemed to be correct. But by larger p around 100000 it takes > about 5 to 8 hours on the wall clock and the results seem tob be > correct, but the time is negative. Two comments. First, I've studied that paper before (cyclotomic invariants to twelve million, or whatever it is), and there is no way it should be taking you 5 to 8 hours to handle p = 100000. The computation of the bernoulli numbers mod p should easily dominate the computation. The verification of vandiver's conjecture once that information is computed should be extremely fast. I might be getting this wrong --- it's been several years --- but I'm reasonably sure this is correct. So for p = 100000 that part of the computation should be taking a small fraction of a second on any modern hardware. I think probably you are doing the modular arithmetic inefficiently. As I have mentioned before on this list, if you want to compute 2^n mod X, where n is very large, you should *not* do (2^n)%X, because then the machine has to actually compute 2^n *as an integer* and then reduce mod X. You should instead use the SAGE object Integers(X) to construct a ring in which to perform the computation. Secondly, regarding the negative time, I'm starting to suspect a resolution problem with the cputime() function on your platform. Perhaps the clock is wrapping around to zero after a certain amount of time. What kind of machine and operating system are you running on? You could try performing an experiment where you just print out cputime() once a minute for a few hours and see if you get back to zero again. David --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@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-support URLs: http://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
