Abstract data types in computer algebra

Abstract

The theory of abstract data types was developed in the late 1970s and the 1980s by several people, including the “ADJ” group, whose work influenced the design of Axiom. One practical manifestation of this theory was the OBJ-3 system. An area of computing that cries out for this approach is computer algebra, where the objects of discourse are mathematical, generally satisfying various algebraic rules. There have been various theoretical studies of this in the literature: [36,42,45] to name but a few. The aim of this paper is to report on the practical applications of this theory within computer algebra, and also to outline some of the theoretical issues raised by this practical application. We also give a substantial bibliography.