Re: the minimal polynomial over the composite field

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

On Thu, Oct 03, 2019 at 11:01:13AM +0200, Bill Allombert wrote:
> This version was lackig one improvement, so I updated again.

I have made a new version again of the branch bill-nfsplitting,
which is faster in hard cases.

Now the time are:

? G=galoissplittinginit(x^17-2);
  ***   last result computed in 4,732 ms.
? P=x^17-2;Q=nfsplitting(P,17*16);nfisincl(P,Q);
  ***   last result computed in 4,325 ms.

Some comments:
galoisinitfromaut is performing initialization to some
p-adic accuracy required for arbitary use of galoisfixedfields later.
Obviously if you know which subgroups you need in advance, you can do
the initialization to the p-adic accuracy you actually need.

Also your example x^n-2 are very sparse which make computation
faster compared to generic example.

Cheers,
Bill