Re: FFELT: how to recover the field?

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

On Sun, Dec 09, 2007 at 07:46:30PM +0100, Jeroen Demeyer wrote:
> Bill Allombert wrote:
> >Why are sqrtn(x,p) and x^(1/p) less obvious ?
> 
> Karim Belabas wrote:
> >What's wrong with sqrtn(x,p) ?
> 
> Okay, true.  I guess I was thinking too much as a programmer instead of
> a mathematician.  By the way, these functions don't work for finite
> field POLMODs, so it's not *that* obvious :-)

Fixing this limitation was one of the motivation of adding FFELT.

> Karim Belabas wrote:
> >It doesn't seem to be possible currently (only x.p and x.pol work).
> >I'll add x.mod to the allowed member functions
> 
> Maybe you could also add lift(x) to make things more analogous to POLMODs.

What should lift return ? a POLMOD by analogy to INTMOD ? 

FFELTs are not supposed to be analogous to POLMODs, but rather to 
INTMODs. Also there is a technical limitation: FFELTs do not respect
variables priorities (which make them much less troublesome to use than
POLMODs) so if you allow to lift the FFELT coefficients of a polynomial,
you might end up with a invalid polynomial.

Cheers,
Bill.