Advances and trends in the design and construction of algebraic manipulation systems

ABSTRACT

We compare and contrast several techniques for the implementation of components of an algebraic manipulation system. On one hand is the mathematical-algebraic approach which characterizes (for example) IBM's Scratchpad II. On the other hand is the more ad hoc approach which characterizes many other popular systems (for example, Macsyma, Reduce, Maple, and Mathematica). While the algebraic approach has generally positive results, careful examination suggests that there are significant remaining problems, especially in the representation and manipulation of analytical, as opposed to algebraic mathematics. We describe some of these problems, and some general approaches for solutions.

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INDEX TERMS

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

Additional Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.3 Languages and Systems

          Nouns: MACSYMA

General Terms:
Design, Languages