An object-oriented approach to algebra system design

Abstract

This paper describes a new computer algebra system design based on the object-oriented style of programming and an implementation of this design, called Views, written in Smalltalk-80. The design is similar in goals to other 'new' generation computer algebra systems, by allowing the runtime creation of computational domains and providing a way to view these domains as members of categories such as 'group', 'ring' or 'field'. However, Views introduces several unique features. The most notable is the strong distinction made between a domain and its view as a member of a particular category. This distinction between the implementation of a domain and its adherence to a set of algebraic laws allows a great degree of flexibility when choosing the algebraic structures that are to be active during a computation. It also allows for a richer variety of interrelationships among categories than exhibited in other systems.