Re: New ellinit interface

[Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>]

On Sat, Oct 20, 2012 at 09:23:08PM +0200, Karim Belabas wrote:
> * Bill Allombert [2012-10-20 17:03]:
> > t_ELL_Q: curves over Q. (Is it easy to find an integral, (possibly non minimal) model ?)
>
> Yes it is: ellintegralmodel uses only a partial factorization of
> involved denominators.

So eventually we can precompute an ellintegralmodel and add it to the
type specific data.

> > t_ELL_Qp: curves defined over Q, seen over Qp.  (not supported yet)
> > t_ELL_Fp: curves over F_p
> > t_ELL_Fq: curves over F_q
> 
> We're missing
> 
>   t_ELL_K: curves over number fields
>   t_ELL_Kv: curves over local fields (completion of #field K at prime v)
> 
> almost nothing is implemented yet [ we have the ellnflocalred() script,
> Francois Brunault's implementation of Tate reduction algorithm; my new
> elltors() code using division polynomials can also trivially be adapted 
> to handle torsion over number fields ].
> 
> It would be a pity not to include this, given PARI's current strong
> points in algebraic number theory. And we want to include Denis Simon
> script as well :-)

Sure but we can add new type when the implementation follow. In particular
we cannot define the type specific data without an implementation.

Cheers,
Bill.