|Bill Allombert on Sat, 20 Oct 2012 22:07:48 +0200|
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|Re: New ellinit interface|
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.