This is an excellent idea. Obviously, for every package Sage
includes, as much of its functionality as possible should be made
available ! But this does take time and effort.
I am CC-ing this to sage-nt since if we are going to discuss how to do
this in detail that might be the best forum.
John
2008/10/28 Pablo De Napoli <[EMAIL PROTECTED]>:
>
> Hi,
>
> I'm reading the notes of William's talk "Three Lectures about Explicit
> Methods in Number Theory Using Sage", that are indeed very interesting.
>
> It comments that Sage includes functionallity to compute the zeros of L-series
> of elliptic curves, by doing
>
> sage: E = EllipticCurve('389a1')
> sage: L = E.lseries()
>
> sage: L.zeros(10)
> [0.000000000, 0.000000000, 2.87609907, 4.41689608, 5.79340263,
> 6.98596665, 7.47490750, 8.63320525, 9.63307880, 10.3514333]
>
> It comments that
> " Rubinstein's program can also do similar computations for a wide class
> of L-functions, though not all of this functionality is as easy to use from
> Sage as for elliptic curves."
>
> It would be nice to functionallity for computing other L-functions that
> appears in number theory. The most basic one would: compute the L-series
> associated with a Dirichlet character, and been able to do some simmilar
> computation like
>
> sage: G=DirichletGroup(10)
> sage: c=G[1]
> sage: L=c.lseries()
> sage: L.zeros(10)
>
> Also one could like to do similar computations for instance with Dedekind zeta
> function of a number fileld, something like...
>
> sage: K.<sqrt2> = QuadraticField(2)
> sage: Z.DedekindZeta()
> sage: Z.zeros(10)
>
> Would it be possible to implement such a functionallity in Sage?
> Perhaps we would need a more more flexible class for representing L-series.
>
> best regards
> Pablo
>
>
> >
>
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