Karim BELABAS on Sun, 14 Sep 2003 13:51:17 +0200 (MEST)

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Re: quadray for subgroup of the ray class group

On Sun, 14 Sep 2003, Bill Allombert wrote:
> I would like to compute Hilbert class field of non-maximal order.
> This corresponds to a subgroup of the ray class group of the maximal
> order. Is there any possibility to use quadray to compute defining
> polynomials for subgroups of the ray class group?

for real fields, use bnrstark. For imaginary ones, you'll have to
implement it.

> By the way, I think the documentation of quadclassunit should
> enphasize it can handles non fundamental discriminants.

It can't. It very often does, which is very different...

So it should in fact emphasize the opposite.

> We should probably change rnfkummer to handle squarefree order.

Possibly. But the simplest [ and fastest ] way to use rnfkummer is simply
rnfkummer(, p) to output all extensions of (prime) degree p in a single call.

Building compositums and identifying the right extensions is essentially
straightforward, but a user interface would be rather awkward.

Karim Belabas                     Tel: (+33) (0)1 69 15 57 48
Dép. de Mathématiques, Bât. 425   Fax: (+33) (0)1 69 15 60 19
Université Paris-Sud              http://www.math.u-psud.fr/~belabas/
F-91405 Orsay (France)            http://www.parigp-home.de/  [PARI/GP]