Awesome Mike - thanks for working on this!

On Mon, Mar 8, 2010 at 6:58 PM, Mike OS <mosul...@math.sdsu.edu> wrote:
>
> I have some funding from my university to develop materials in SAGE
> for use in my classes. The focus of the project is developing
> educational materials but we'd also like to  contribute to SAGE
> development. I posted to sage-edu about educational issues.   This
> post concerns development, specifically groups in SAGE and the
> relationship with GAP. I've hired two students, Rhea Morton and
> Ryan Rosenbaum to work on the project, and we would like some
> guidance on how we can contribute.
>
> Some observations:
>
> A. William started a  libgap, analogous to libsing, but it has lain
> fallow for a while.  As we understand things, there is a somewhat
> different challenge with GAP.    Much of Singular's functionality is
> written in C so that SAGE can access it via Cython,   whereas much of
> GAP is written in GAP's own language, so pexpect is required to access
> it.    How does this affect goals for libgap? Does this mean that
> libgap will be inherently limited in  efficiency or functionality?
>
> B.  The class Group seems to only loosely combine the different
> types of groups: permutation groups, abelian groups and matrix groups.
> For example, subgroup is not implemented for matrix groups.
> Also, the unit group of a ring (like U_n= Z_n*) and finitely
> presented
> groups aren't implemented (that we coud find).
> Should these be implemented in SAGE via GAP or have their own
> existence in SAGE?  What are the goals for improvement of the Group
> functionality?
>
> C.  Rhea is preparing a homomorphism package that exposes GAP's group
> homomorphism functions. In order to work it requires SAGE groups with
> GAP compatible generators. It doesn't work with the Integer ring, for
> example, because the Integer class doesn't extend from sage.groups. In
> addition, it works closely with the FreeGroup class so both would have
> to be submitted for it to be of much utility. Rhea has tested it with
> the FreeGroup class, SAGE DihedralGroup, and SAGE SymmetricGroup.
> The documentation and test cases are still being prepared.
>
> Comments?
>
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