Dear Forum members,
We are pleased to inform you that the package ITC has been deposited in
ITC is a package for performing interactively coset enumeration (the
Todd - Coxeter method) on the screen. It is built on the graphic
surface XGAP for GAP4 that has already been accepted as a share
package of GAP4.
ITC allows you to display the coset table, subgroup and relation
tables and to make definitions of coset numbers by clicking into
these. It also can display auxiliary tables such as the list of
definitions made, the list of 'gaps of length 1' or the list of
pending coincidences. Some of the main strategies of coset
enumerations such as HLT, Felsch and minimal gap strategies are
available as well and can either be used to try to close the tables or
to make a prescribed number of definitions using these strategies. The
package also contains two operations for a posteriori 'pruning' a
definition sequence if coincidences have occurred. Scrolling of the
tables allows you to deal with tables much bigger than would fit on
For details about the package see the manual that describes the
functionality and also gives examples of the use of it.
ITC is no competition to coset enumeration programs such as ACE by
George Havas and Colin Ramsay which are designed to handle very big
enumerations with (many) millions of coset numbers, its use should be
primarily in teaching and learning several facets of coset
enumeration, but also to develop new ideas by interactive
experimentation. Some of the examples demonstrate that using these
facilities and the 'pruning' methods can even serve to improve some
frequently investigated challenge problems for 'short' enumerations.
ITC will be submitted to be refereed for acceptance as a GAP share
package. The presently deposited version should be considered as a
beta test version. We have plans for some extensions of the package
in the future, but at present we will very much appreciate feedback
from use of the package.
Volkmar Felsch, Ludger Hippe, and Joachim Neubueser.