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/p-part of a class grouphttp://ask.sagemath.org/question/9849/p-part-of-a-class-group/Hi
I am trying to compute the p-part of a class groups of some number fields. I was hoping to just call G.sylow_subgroup(p), but this function is not implemented for Abelian groups. In addition, invariants doesn't seem to work, for example, if G= C6, then G.invariants() returns [6], which doesn't seem correct.
I would appreciate any advice on how to do this. For example, can I coerce an Abelian Group to just be a finite group?
Note: I asked this on IRC without an answer. I hope it is not bad form to ask it here.
Partial Solution: Elementary divisors and some factorization code gives me what I want. However, it would be nice to be able to coerce an abelian group into a group.lalitkumarjMon, 25 Feb 2013 05:09:12 -0600http://ask.sagemath.org/question/9849/