Hi Nils,

There is a working patch for finitely generated abelian groups, which
builds on the ZZ-modules routines and some similar code for finite
groups.

http://trac.sagemath.org/sage_trac/ticket/9773

Patch needs docs, and a couple of fixups, but there are some working
examples (like multiplicative group of units mod n).

I plan to take this up again this summer, but would move it up on my
schedule if there was a co-conspirator interested in improving,
expanding and reviewing.

But maybe you just want modules and not groups.  Volker is right, the
FGP_Module's will do much of what you want.

Rob

On May 4, 3:13 pm, Nils Bruin <[email protected]> wrote:
> Does anybody know the current state-of-the-art in sage to compute with
> finitely generated Z-modules (i.e., finitely generated abelian
> groups)? The operations I would be looking for are
>  - sums, intersections and quotients of/by submodules
>  - homomorphisms between Z-modules
>  - computing kernel and image of a homomorphism as submodules
>  - computing images and pre-images of elements under homomorphisms
> The categories AbelianGroup (which is multiplicative but still
> describes as isomorphic to something that is written additively) and
> AdditiveAbelianGroup do not seem to have homomorphisms implemented for
> them ...

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