Bill Allombert on Tue, 4 Mar 2003 14:08:09 +0100

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Re: relative basis for Z_L over Z_K

On Mon, Mar 03, 2003 at 05:55:21PM +0100, Markus Endres wrote:
> hi
> I guess it's not very difficult but I don't know how to do that.
> let L|K|Q a tower of fields given by nfinit() or bnfinit(). now, one can
> compute an integral basis for Z_L and Z_K with L.zk resp. K.zk. 
> but both are expressed on the powers of alpha resp. theta, when
> K=Q(theta), L=K(alpha). that means, that the basis is given over Q, the
> rationals. 
> what I need ist the basis of Z_L expressed over Z_K.

You should try rnfpseudobasis. Note that if Z_K is not principal,
there is no true basis for Z_L as a Z_K modules, hence the pseudo.

More generally look at the rnf* class fucntions.