On 10/29/07, John Cremona <[EMAIL PROTECTED]> wrote:
> On 29/10/2007, Martin Albrecht <[EMAIL PROTECTED]> wrote:
> > On Monday 29 October 2007, John Cremona wrote:
> > > Since you have a lot more things to add to your list, you should
> > > delete the p-adic arithmetic item, since that already exists in pari.
> > > (I am not saying taht the capabilities are the same, but I have been
> > > using pari/gp for p-adic arithmetic for years).
> >
> > as far as I know is the p-adics project in Sage way more ambitious than what
> > is implemented in Pari and thus I think it is okay to list it. I might be
> > wrong, though, as I never work with it.
>
> I'm sure your right about the ambitiousness! But it's not true to say
> that "arithmetic with $p$-adic numbers" was "not implemented before in
> the
> open-source world", that's all. Even if you added "advanced" before
> "arithmetic", some pari people might object since pari does have (for
> example) quite a lot of p-adic analytic functions, polynomial
> factorization and root-finding, ...
There are numerous models and variants of p-adic arithmetic that
David Roe has spent months and months implementing for Sage which are not
available at all in any other open source package. At least one
of them ("lazy p-adics") is also not available in any other package.
So in fact it is true to say that "certain models of arithmetic with
$p$-adic numbers" was "not implemented before in the open source
world". There are also new algorithms for arithmetic in polynomial
rings over the p-adics (and with matrices?) that are only in Sage.
-- William
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