Dear Forum members,
I have the pleasure to announce the release of the new GAP 4 share package ACE.
ACE stands for 'Advanced Coset Enumerator' and several of you will
know or have heard of the standalone program of the same name by
George Havas and Colin Ramsay.
In fact the new share package builds on this C program. The extensive
GAP interface has been written by
Greg Gamble and Alexander Hulpke.
The method of coset enumeration, also known as the Todd - Coxeter
method, is one of the main work horses for the computational
investigation of finitely presented groups. Given a finite
presentation for a group G and generators for a subgroup H of G as
words in the generators of G, the method tries to find a (transitive)
permutation representation of G on the (right) cosets of H (in the
form of a 'coset table' of H in G) and thus also the index of H in G.
The method that was first described by Todd and Coxeter in 1936 allows
many variations, often referred to as 'strategies'. It has been
implemented several times; its implementation in ACE not only provides
the possibility to choose from very many strategies but is tuned for
extreme speed and for doing enumerations when the index of H in G may
reach well into several millions. Moreover ACE provides functionality
to further investigate G using the coset table or parts thereof.
The GAP interface allows one to use ACE in three different ways:
- ACE can replace the built-in GAP Todd-Coxeter method,
- ACE can be called non-interactively, i.e. a particular enumeration
task can be sent to ACE with fixed parameters for the specification of
the strategy to be used,
- ACE can be used interactively from GAP thus availing the full
flexibilty of the standalone ACE to the GAP user.
The interactive link of GAP and ACE, written by Greg Gamble, makes use
of the i/o streams that Steve Linton has implemented in GAP. It may be
hoped that this link can also serve as a model for linking other
standalones with strong interactive features to GAP.
The program comes with an extensive manual explaining terminology and
functionality of ACE and its GAP interface and providing many examples
of use. The manual and the web page for ACE provide pointers to the
literature on coset enumeration. A README is also provided.
I am sure that GAP users will welcome that this powerful program is
now available to them comfortably from GAP in such a way that its
results can directly be further processed in GAP.
PS: Since the ANU website is currently not up-to-date, if you want to
access an Australian site to obtain the ACE share package, for the
time being please visit the following URL: