Watson Ladd on Mon, 03 Apr 2017 14:13:40 +0200

 Re: Reuse of data in rnfkummer/computing order of galois elements without it

• To: pari-users@pari.math.u-bordeaux.fr
• Subject: Re: Reuse of data in rnfkummer/computing order of galois elements without it
• Date: Mon, 3 Apr 2017 05:13:31 -0700
• Delivery-date: Mon, 03 Apr 2017 14:13:40 +0200
• References: <CACsn0ckn9X0cVMFtirKjgcPrs5qewZTY5AsjFSBHgnM_GyAytA@mail.gmail.com> <20170403102348.GA2683@yellowpig>

On Apr 3, 2017 3:24 AM, "Bill Allombert" <Bill.Allombert@math.u-bordeaux.fr> wrote:
On Sun, Apr 02, 2017 at 09:53:20PM -0700, Watson Ladd wrote:
> 2: Is there a way to determine the maximal order of an element of the
> Galois group of the resulting field without computing the field via
> rnfkummer? I know about bnrgaloismat, but it doesn't seem as though
> the resulting representation of the galois group can be used to find
> the order of elements easily.

Please give an example. Do you mean 'order' as in group theory or
'order' as in 'integral closure' ?

Order as in group theory.

Let K/Q a galois extension, and f a conductor of K that is invariant
by Gal(K/Q).
bnrgaloismatrix gives the action of Gal(K/Q) on Cl_f(K).

bnrisgalois() allows to find the subgroups of Cl_f(K) that gives rise to
Galois extension of Q.

Well, I've already got them: I'm taking a compositum of quadratic extensions L of a field K which will be Galois. I want to throw out L where Gal(L/Q) has an element that is too large.

Cheers,
Bill.