Annegret Weng on Wed, 8 Dec 1999 17:00:31 +0100 (MEZ)

 relative number fields

```I have a problem concerning pseudo-bases. I do not understand what the
ideal list means.

For example:
I have the number field K=Q(sqrt(3)) generated under gp
by nf=nfinit(x^2-3,0). Now I define an extension L=K(sqrt(a))
generated by the element sqrt(a) where a=7+2*sqrt(3). Since Q(sqrt(3)) has
class number one there must be a relative integral basis for L over K.
And in fact I get such a basis by using the function rnfbasis.

My questions:
Can I get the relative integral basis only by using the
function rnfinit?

Can I use the information from rnf[7] which is
for this example [[Mod(1, y^2 - 3), Mod(1, y^2 - 3)*x + Mod(1, y^2 - 3)],
[[1, 0; 0, 1], [1, 1/2; 0, 1/2]]] ?
(Note that the elements [Mod(1, y^2 -3), Mod(1, y^2 - 3)*x + Mod(1, y^2 - 3)] over O_K generate an order, but
not the maximal order O_L.)

How do I apply the ideal list to the pseudo-basis? I read the explanation
in the User`s Guide but I still don't know how to do it.

Thank you in advance to everyone who will help me.

Annegret

```