From: Bob Boyer
To: AIList
Re: A Programming Language for Group Theory (Dept. of Math)
[Forwarded from the UTexas-20 bboard by Laws@SRI-AI.]
DEPARTMENT OF MATHEMATICS COLLOQUIUM
A Programming Language for Group Theory
John Cannon
University of Sydney and Rutgers University
Monday, February 27, 4pm
The past 25 years has seen the emergence of a small but vigorous branch of
group theory which is concerned with the discovery and implementation of
algorithms for computing structural information about both finite and infinite
groups. These techniques have now reached the stage where they are finding
increasing use both in group theory research and in its applications. In order
to make these techniques more generally available, I have undertaken the
development of what in effect is an expert system for group theory.
Major components of the system include a high-level user language (having
a Pascal-like syntax) and an extensive library of group theory algorithms. The
system breaks new ground in that it permits efficient computation with a range
of different types of algebraic structures, sets, sequences, and mappings.
Although the system has only recently been released, already it has been
applied to problems in topology, algebraic number theory, geometry, graphs
theory, mathematical crystalography, solid state physics, numerical analysis
and computational complexity as well as to problems in group theory itself.