Bill Allombert on Mon, 15 Sep 2003 15:32:50 +0200

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Re: quadray for subgroup of the ray class group

On Sun, Sep 14, 2003 at 01:51:17PM +0200, Karim BELABAS wrote:
> > 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.

Oh I see.

> > 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.
... of same conductor. 

If you are looking atr a degree 6 extension of same conductor it can
happen that the degree 2 subextension is of a lower conductor, so you will
miss it this way. Also doc is not clear whether they all lie within the
congruence subgroup given.

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

You don't need to build compositum. I woul be more than happy with
outputing a set of polynomials whose compositum is the result 
(à la KANT).