Magma is the latest interactive computer system to be released by the Computational Algebra Group of the School of Mathematics and Statistics at the University of Sydney, Australia. The authors describe the system design as of 1996, including its principles, and some of its theoretical background, scope and use. The design criteria and basis for construction of algebraic objects in this system have undergone further refinement over the years, as it evolved from the earlier Cayley system. While the objects under study may be described precisely, and their representation may be efficient, the user language of the  title  is sketched out rather perfunctorily. The paper does not compare Magma to other systems, nor does it evaluate how effectively the Magma design achieves its goals of universality, precision, notational power, and efficiency.

This system has grown to a monumental size and complexity, as evidenced by additional work by Cannon and his co-authors, including a two-volume Introduction to algebraic programming with Magma [1]. Further details and instructions for purchasing Magma may be found at http://www.maths.usyd.edu.au:8000/comp/magma/ Overview.html.