Computer algebra

  • Authors:
  • Franz Winkler;Gaston H. Gonnet;Dominik W. Gruntz;Laurent Bernardin

  • Affiliations:
  • -;-;-;-

  • Venue:
  • Encyclopedia of Computer Science
  • Year:
  • 2003

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Abstract

Computer algebra is a branch of scientific computation. There are several characteristic features that distinguish computer algebra from numerical analysis, the other principal branch of scientific computation. (1) Computer algebra involves computation in algebraic structures, such as finitely presented groups, polynomial rings, rational function fields, algebraic and transcendental extensions of the rational numbers, or differential and difference fields. (2) Computer algebra manipulates formulas. Whereas in numerical computation the input and output of algorithms are basically (integer or floating point) numbers, the input and output of computer algebra algorithms are generally formulas. So, typically, instead of computing