On 7 Sep, 01:45, "William Stein" <[EMAIL PROTECTED]> wrote:
> On 9/6/07, Bill Hart <[EMAIL PROTECTED]> wrote:
>
> > The question is, which algorithm does SAGE currently use?
>
> For class groups?
Yes.
> If so, it uses pari, then calls the
> bnfcertify command after doing the computation.
OK.
>
> > Does it
> > really provide a proven result?
>
> Assuming pari works correctly.
>
> > Is it proven to terminate?
>
> I don't know.
In Pari I very much doubt it.
>
> > Can it
> > provide a certificate that I can check in less time than doing the
> > computation again?
I don't believe you can. bnfcertify is probably the best you can do.
>
> I don't know.
>
> > How can I be sure the result is valid?
>
> You can't really.
It relies on primes being prime. So I claim it actually doesn't remove
the GRH. I'm happy to be proved wrong.
I agree in principal that algorithms should not rely on conjectures,
especially ones that not everyone believes. But I have some
reservations about this in practice. Anyone trusting a CAS to produce
correct proven results has obviously not been told recently that the
third prime is 6.
Bill.
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