Essays in Algebraic Simplification

Abstract

The thesis consists of essays on several aspects of the problem of albegraic simplification by computer. The author first discusses a pattern matching matching system intended to recognize non-obvious occurrences of patterns within algebraic expression. A user of such a system can teach the computer new simplification rules. Then the author reports on new applications of canonical simplification of rational functions. These applications include techniques for picking out coefficients, and for substituting for sums, products, quotients, etc. The final essay is on a new, practical, canonical simplification algorithm for radical expressions (i.e. algebraic expressions including roots of polynomials). The effectiveness of the procedure is assured through proofs of appropriate properties of the simplified forms. Two appendices describe MACSYMA, a computer system for algebraic manipulations, which served as the basis for this work.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1972
Accession Number
AD0740132

Entities

People

  • Richard J. Fateman

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Artificial Intelligence
  • Computations
  • Computer Programming
  • Computer Science
  • Computers
  • Differential Equations
  • Linear Differential Equations
  • Machine Languages
  • Mathematical Analysis
  • Numbers
  • Numerical Analysis
  • Pattern Recognition
  • Programming Languages
  • Rational Numbers
  • Real Numbers
  • Real Variables
  • Theorems

Readers

  • Calculus or Mathematical Analysis
  • Instructional Design and Training Evaluation.
  • Strategic Security Studies