Re: nfgaloisconj

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

On Tue, Jul 30, 2019 at 11:08:44AM +0200, Bill Allombert wrote:
> It will be difficult to improve nfisincl and nfsplitting. 
> This is a much harder problem than galoisinit.

Thinking about it, there are some possible improvements:

1) if the Galois group is known, then nfsplitting can just write down
the result without any factorization.

2) if the order of the Galois group is not given and the group is not
the symmetric group, then nfsplitting already computes a large part of
nfisincl to check that the tower stops, so we could arrange for
nfsplitting to return also the embeddings.

in fact using G12p, we could return a structure similar to galoisinit,
however we would be missing .gen and .orders, so we would not be able
to compute subgroups with PARI.

Cheers,
Bill