Re: Artin's method for class field computation

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

On Fri, Apr 30, 2021 at 11:33:44AM +0200, Aurel Page wrote:
> Hi Lucas,
> 
> There would be no problem implementing the method you suggest to deal with
> prime power degree extensions, but we chose to implement bnrclassfield by
> relying on the historical function rnfkummer, and at the moment we don't
> have plans to implement the other method although it could be useful in some
> cases.
> Algorithmically, the best method depends on the ramification of the
> intermediate extensions involved. What is costly in explicit class field
> theory using kummer theory is that to construct a cyclic extension of degree
> n of K, you have to compute the class group and units of K(zeta_n).
> - If you directly do the extension of degree p^m, you have to do this
> computation for K(zeta_p^m).

Note that together with your algorithm for bnfinit of compositum,
this method could be quite useful!

Cheers,
Bill.