The Todd–Coxeter procedure

Many computer algebra systems, such as GAP, provide implementations of the Todd–Coxeter coset enumeration procedure. There are also sophisticated standalone implementations, such as ACE (which is also available as a GAP package). In spite of this, I have written yet another implementation, called Toddcox. It is a toy version, intended for pedagogical use.

I plan to use Toddcox in my graduate algebra course. I've also written a brief introduction to the Todd–Coxeter procedure for that course.

My goals in writing Toddcox were the following:

• A student should be able to learn how to use it in a few minutes.
• It should work reasonably quickly on small examples.
• The code should be transparent; anyone who is familiar with the language (C++) should be able to read the code and see how it relates to standard treatments of coset enumeration (such as the one in Handbook of Computational Group Theory by Holt et al).

To obtain Toddcox, visit the download page. More information, including sample runs of the program, can be found on the documentation page.

I do not expect to spend a lot of time developing the program further, since it suffices for my purposes. But I will certainly try to fix any bugs that are reported, and I will try to implement suggestions for improvement if they're not too difficult and they don't detract from the goals stated above. I would appreciate hearing from anyone who uses the program, and I would especially appreciate hearing about any improvements that you make.

Toddcox is free software, licensed under the GNU General Public License GPLv3.

Ken Brown
Department of Mathematics
Cornell University
Ithaca, NY 14853
Email: kbrown@cornell.edu