Re: the minimal polynomial over the composite field

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

On Wed, Oct 09, 2019 at 12:46:15PM +0900, macsyma wrote:
> Factoring by galoisfixedfield(,,2) is attractive, 
> but it seems time-consuming to put together preparations for that.

This is true. galoissplittinginit is doing much more initialization
that what you need. You need much smaller bound.

> > Also your example x^n-2 are very sparse which make computation
> > faster compared to generic example.
> How about 2*(1+x)^n-x^n (dense and having an isomorphic splitting field) ? 

This is not a good idea: polredbest will reduce it to x^25-2 in 104ms.

I think you should allow for the number field discriminant to get
larger, not the model.

I am concerned that optimizing the program for such easy case will
make it slower when trying large example.

I suggest you try polynomial from Klüners-Malle database:
<http://galoisdb.math.upb.de>
You can search for the property 'is solvable'.

Cheers,
Bill.