ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sat, 08 Jul 2017 12:52:42 -0500How to compute a cyclic subgroup of a class group?http://ask.sagemath.org/question/38198/how-to-compute-a-cyclic-subgroup-of-a-class-group/ Hello, I am quite new to computing in Sage and I am stuck at this point. Please help me out. I am going to use algebraic number theory notation without explaining them in detail. All computations are in quadratic fields.
What I have :
- $\Delta_p=p^2\Delta_K$ where $p$ is a prime, $\Delta_K=-pq$ and $\Delta_K\equiv 1$ mod $4$
- I computed the class group, $C(\Delta_p)$ in Sage
What I want :
- Set $f=[(p^2,p)]$ in $C(\Delta_p)$ where $(p^2,p)$ is the standard representation of an ideal of norm $p^2$
- Set $F=\langle f \rangle$
My question is :
- How to get that cyclic subgroup $F$?
I have been looking at AbelianGroup and ClassGroup in Sage but I am not quite understanding how to use these to actually get what I want.
Any help in this matter would be greatly appreciated.jakkeonSat, 08 Jul 2017 12:52:42 -0500http://ask.sagemath.org/question/38198/