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.