Bill Allombert on Wed, 22 Jun 2005 14:01:14 +0200

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Re: Galois test

On Fri, Jun 17, 2005 at 03:38:56PM +0200, Karim Belabas wrote:
> * Ariel Pacetti [2005-06-17 13:56]:
> > Is there a routine for checking wether a number field extension is Galois? 
> > I couldn´t find one, but probably there is some "naive" way to do that 
> > like:
> > 
> > nffactor(nfinit(P),P)
> > 
> > and check wether all the factors have degree one or not. Is there a better 
> > (or faster) way? (like no using nfinit which takes too long if the 
> > polynomial is big enough).
> There's no built-in routine.  You may

You forgot nfgaloisconj. The fact that it does not work well with
polynomial notwithstanding.

We should probably fix it to use factornf on polynomials, and maybe
get rid of the LLL-based variants.