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.

REFERENCES

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION

Additional Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications
          Subjects: Very high-level languages; Specialized application languages
      D.3.3 Language Constructs and Features
          Subjects: Abstract data types
      D.3.4 Processors
          Subjects: Run-time environments

General Terms:
Algorithms, Design, Theory