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Computer Algebra pp 11–43Cite as

Algebraic Simplification

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Part of the book series: Computing Supplementa ((COMPUTING,volume 4))

Abstract

Some basic techniques for the simplification of terms are surveyed. In two introductory sections the problem of canonical algebraic simplification is formally stated and some elementary facts are derived that explain the fundamental role of simplification in Computer algebra. In the subsequent sections two major groups of simplification techniques are presented: special techniques for simplifying terms over numerical domains and completion algorithms for simplification with respect to sets of equations. Within the first group canonical simplification algorithms for polynomials, rational expressions, radical expressions and transcendental expressions are treated (Sections 3–7). As examples for completion algorithms the Knuth-Bendix algorithm for rewrite rules and an algorithm for completing bases of polynomial ideals are described (Sections 8–11).

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Authors and Affiliations

  1. Institut für Mathematik, Johannes-Kepler-Universität Linz, Altenbergerstrasse 69, A-4040, Linz, Austria

    Prof. Dr. B. Buchberger

  2. Institut für Informatik I, Universität Karlsruhe Zirkel 2, D-7500, Karlsruhe, Federal Republic of Germany

    Prof. Dr. R. Loos

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  2. Prof. Dr. R. Loos
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Editors and Affiliations

  1. Institut für Mathematik, Johannes Kepler Universität, Linz, Austria

    Bruno Buchberger

  2. Computer Science Department, University of Wisconsin-Madison, Madison, Wis., USA

    George Edwin Collins

  3. Institut für Informatik I, Universität Karlsruhe, Federal Republic of Germany

    Rüdiger Loos

  4. Institut für Informatik und Numerische Mathematik, Universität Innsbruck, Austria

    Rudolf Albrecht

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© 1983 Springer-Verlag/Wien

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Buchberger, B., Loos, R. (1983). Algebraic Simplification. In: Buchberger, B., Collins, G.E., Loos, R., Albrecht, R. (eds) Computer Algebra. Computing Supplementa, vol 4. Springer, Vienna. https://doi.org/10.1007/978-3-7091-7551-4_2

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  • DOI: https://doi.org/10.1007/978-3-7091-7551-4_2

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-81776-6

  • Online ISBN: 978-3-7091-7551-4

  • eBook Packages: Springer Book Archive

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