William, the trac ticket should read > 10^15, not < 10^15. Bill.
On 7 Sep, 18:23, "William Stein" <[EMAIL PROTECTED]> wrote: > On 9/7/07, John Cremona <[EMAIL PROTECTED]> wrote: > > > On 9/7/07, Bill Hart <[EMAIL PROTECTED]> wrote: > > > Are there other algorithms available in SAGE from Pari that rely on > > > conjectures? This would include the stuff for totally real fields that > > > relies on the Stark conjectures. > > > mwrank uses the pari library for factorization of integers, so the > > correctness of mwrank funtions (and in particular, elliptic curve > > ranks) relies on pari giving actual prime numbers when asked to > > factor. > > Wow, that's not good. Thanks for pointing this out! > I've made this trac #622, in case anybody wants to > fix it in SAGE very soon: > > http://trac.sagemath.org/sage_trac/ticket/622 > > > > > The pari manual says (about factor(x)): > > > If $x$ is of type integer or rational, the factors are \var{pseudoprimes} > > (see \kbd{ispseudoprime}), and in general not rigorously proven primes. In > > fact, any factor which is $\leq 10^{15}$ is a genuine prime number. Use > > \kbd{isprime} to prove primality of other factors, > > > I would need to change the mwrank code to test "primes" > 10^15 for > > primality as recommended. A better solution would be to ask the pari > > developers to add an optional "proof=true" flag to factor() which does > > the isprime() calls automatically. I will do that. > > > John > > -- > > John Cremona > > -- > William Stein > Associate Professor of Mathematics > University of Washingtonhttp://www.williamstein.org --~--~---------~--~----~------------~-------~--~----~ 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://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
