Re: Tower field extensions in libPARI

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

On Thu, Mar 19, 2020 at 03:30:52PM +0200, Aleksandr Lenin wrote:
> Bill,
> 
> On 3/19/20 2:33 PM, Bill Allombert wrote:
> > 
> >  a=ffgen((x^2+1)*Mod(1,11),'a);
> >  Ea=ellinit([0,1],a);
> >  [r,m]=ffextend(a,x^6 + (a + 3),'b);
> >  Eb=ellinit(ffmap(m,Ea[1..5]),r);
> >  ellcard(Eb)
> > %12 = 3138424833600
> >  mi=ffinvmap(m);
> >  minpoly(ffmaprel(mi,r))
> > %14 = x^6+(a+3)
> 
> am I getting it right that the proper way to build such an elliptic
> curve is to use T_FFELT elements instead of FpX/FpXQ-s, and my approach
> towards it was incorrect?

Your approach is not incorrect.
The t_FFELT interface is just a wrapper around the FpXQ/Flxq/F2xq
interface.  Whether it is useful to you depend on what you want to do.
(t_FFELT are always absolute).

ffextend return an absolute model for F_11^12, which you could also
obtain using FpX_FpXY_resultant() as I wrote earlier.
Then the curve is defined over this absolute model.

Cheers,
Bill