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