> sage: K.<a> = CyclotomicField(23) > sage: K.class_number() > > ... > > PariError: not enough precomputed primes, need primelimit ~ (35) >
Hah, that's pretty hilarious. :) Actually, what it's telling you is that it needs primes up to a primelimit, and then it doesn't actually put in the primelimit. (This is a bug in our processing of Pari's error messages.) It's then saying that this is PariError #35. The effect is awesome, though. The real answer to your question, though, is that Pari can't provably certify its result for the class number of K without using more than the default number of primes. Of course, it's more than happy to just run along without certifying the result: sage: K.class_number(proof=False) 3 I just ran a GP session, and set it going with a much larger primelimit; it's still computing. So this brings up at least two interesting questions: 1) If we try to compute something for the user, with proof, and Pari tells us that it couldn't do it using whatever information it has prerendered, how many times should we add to that info and try again? For instance, we happily add memory and try again until we're out of memory; should we do the same thing in this case? Should we let the user know? Should we bail out and give a non-verified answer, along with telling the user that this is what we did? 2) Should we have better documentation for certain functions (such as this one!) saying, "Even in moderately sized cases, certifying this result can be computationally intensive. Consider using proof=False." And maybe one last good question: David, were you surprised that Pari/Sage couldn't tell you this? Would you have preferred a non-verified answer (along with information that it wasn't provably correct, of course), what you got, or something else entirely? -cc --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
