[GAP Forum] Request for advice

[Nilo de Roock]

Hi GAP forum members,

I appreciate any advice, hints, ideas concerning the following...

A bit of background: I consider myself an abstract algebra self-student,
that is: i have learned everything I know through self-study. That would not
have been possible without Mathematica, and more recently GAP. My career,
work, is in IT consultancy. Mathematics however, is in my
heart, I am sure you'll understand.

Although there is already an Abstract Algebra package for Mathematica
available, it is limited and no longer maintained. (
http://www.central.edu/eaam/index.asp ) It is my goal to develop a Group
Theory package for Mathematica. I'll make it a project of 1, maybe 2 years.
This project is ( nothing more than ) an instrument to bring my
understanding of Group theory to a deeper level. Sofare about my plans.

My ambitions are the following. ( Initially ) I do not want to invent
algorithms, I want to study them and implement them in the Mathematica
programming language. Since GAP is ( or very close to ) the centre of the
state-of-the-art of Computational Group Theory / Algebra, I intend to use
the GAP algorithms, if at all possible. If I understand it correct the
knowledge in GAP is free to use as long as it is referenced. As far as
functionality is concerned I aim for what is available in the nice Open
Source program Group Explorer 2.0 ( http://groupexplorer.sourceforge.net/ )
plus Character Tables, Table of Marks and the Cycle Graph of a group. More
than enough to do, I might say. Group Explorer is rather limited in the
groups it can handle: all groups of order =< 20, three of order 24 and A5. I
intend to be able to handle much more groups than that. The key to solving
that issue is imo using better, faster algorithms. Hence, GAP.

To the point. I am looking for ( the papers which contain ) the algorithms
on which GAP has been built, restricted to Group Theory, Representation
Theory, Vector Spaces and Matrices. What is really an issue in my situation
though, is that, since I don't work at a university, I do not have access to
the paid journals.

Before you may decide this message is outside the context of the GAP forum I
would like to add that it is my ultimate goal to add code to GAP itself and
publish about that, and the sooner the better. In order to achieve that I
must practice first.

Thanks for reading.

Kind regards,
nilo de roock