Mak Trifkovic on Tue, 05 Jul 2005 05:19:53 +0200

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Re: Class groups

I have a quadratic extension K/F of arbitrary number fields, F with class number one. I have an order O in K (not necessarily maximal), and I would like to have an explicit set of representatives for Pic(O), e.g. as rank 2 lattices over O_F.

Now I know PARI doesn't come anywhere near to having a command to do this, so I've been trying to use various bnr commands. Some questions:

1) Is there documentation for the precise structure of the output of bnrinit? Does it actually initialize the class field of a given conductor, or at least give me the relative polynomial?

b) Is there any way of finding the polynomial for a subfield of the ray class field given by a congruence subgroup in the case where the base field is not real (so bnrstark doesn't apply)?