Groups of Lie Type in C++

Abstract

We are looking at groups of Lie type from the point of view of efficient algorithms and efficient data structures. We compute the automorphism group of a Lie group and convert the representation of elements from matrices to words in the generators and back. Our work is based on our own computer algebra system Orbiter, which is a C++ class library with a small front end. The language C++ encourages abstraction and object oriented programming, which are well-suited for mathematical data types. We illustrate this by showing how orbit algorithms for very different groups can be run through the same software interface.