The paper describes design ideas and implementation techniques for a computer algebra system written in the object-oriented language Smalltalk-80. The design goals are similar to other new generation computer algebra systems, the best-known of these being new SCRATCHPAD [1].

One feature of new algebra systems is that they enable the programmer to specify algorithms in their most general algebraic setting. For specific computational domains algorithms can be automatically derived from the general specification. The major contribution of the paper is that greater flexibility than in other new generation systems is given in the choice of an algebraic setting for a particular computational domain. The authors also show that the dynamic type concept built into the underlying Smalltalk language simplifies the design of the system. In the section on implementation techniques, they discuss different ways of improving the creation speed of the dynamic objects that are used to represent algebraic settings and computational domains. However, they do not try to convince their readers that their system is (or could be made) as fast as other algebra systems.

The paper is required reading for people working with the design and development of computer algebra systems. It also has tutorial value--it describes the common design goals of the new generation computer algebra systems. It is easy to understand even for those not involved in the design and development of computer algebra systems. The length of the paper is suitable for its purpose. It gives references to recent similar work, including Jenks’s paper [1].