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Generalized Polynomial Remainder Sequences

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Book cover Computer Algebra

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

Abstract

Given two polynomials over an integral domain, the problem is to compute their polynomial remainder sequence (p.r.s.) over the same domain. Following Habicht, we show how certain powers of leading coefficients enter systematically all following remainders. The key tool is the subresultant chain of two polynomials. We study the primitive, the reduced and the improved subresultant p.r.s. algorithm of Brown and Collins as basis for Computing polynomial greatest common divisors, resultants or Sturm sequences. Habicht’s subresultant theorem allows new and simple proofs of many results and algorithms found in different ways in Computer algebra.

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Author information

Authors and Affiliations

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

    Prof. Dr. R. Loos

Authors
  1. Prof. Dr. R. Loos
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Editor information

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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Loos, R. (1983). Generalized Polynomial Remainder Sequences. 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_9

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  • DOI: https://doi.org/10.1007/978-3-7091-7551-4_9

  • 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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