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Fast Rewriting of Symmetric Polynomials

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Rewriting Techniques and Applications (RTA 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1631))

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Abstract

This note presents a fast version of the classical algorithm to represent any symmetric function in a unique way as a polynomial in the elementary symmetric polynomials by using power sums of variables. We analyze the worst case complexity for both algorithms, the original and the fast version, and confirm our results by empirical run-time experiments. Our main result is a fast algorithm with a polynomial worst case complexity w.r.t. the total degree of the input polynomial compared to the classical algorithm with its exponential worst case complexity. Keywords. Symmetric polynomials, dynamic power sum representation, fast rewriting techniques

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Author information

Authors and Affiliations

  1. Deutsches Fernerkundungsdatenzentrum Algorithmen und Prozessoren, Deutsches Forschungszentrum für Luft- und Raumfahrt e.V. DLR Oberpfaffenhofen, 82234, Weßling, Germany

    Manfred G#x00F6;bel

Authors
  1. Manfred G#x00F6;bel
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University at Albany — SUNY, Albany, NY, 12222, USA

    Paliath Narendran

  2. LORIA — INRIA Lorraine 615, rue du Jardin Botanique, F-54602, Villers les Nancy, Cedex, France

    Michael Rusinowitch

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© 1999 Springer-Verlag Berlin Heidelberg

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G#x00F6;bel, M. (1999). Fast Rewriting of Symmetric Polynomials. In: Narendran, P., Rusinowitch, M. (eds) Rewriting Techniques and Applications. RTA 1999. Lecture Notes in Computer Science, vol 1631. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48685-2_29

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  • DOI: https://doi.org/10.1007/3-540-48685-2_29

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66201-3

  • Online ISBN: 978-3-540-48685-5

  • eBook Packages: Springer Book Archive

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