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 Washington
http://www.williamstein.org
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