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A Probabilistic Zero-Test for Expressions Involving Roots of Rational Numbers

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Algorithms — ESA’ 98 (ESA 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1461))

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Abstract

Given an expression E using +, −, *, /, with operands from Z and from the set of real roots of integers, we describe a probabilistic algorithm that decides whether E = 0. The algorithms has a one-sided error. If E = 0, then the algorithm will give the correct answer. If E ≠ 0, then the error probability can be made arbitrarily small. The algorithm has been implemented and is expected to be practical.

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Author information

Authors and Affiliations

  1. Institut für Theoretische Informatik, ETH Zürich, ETH Zentrum, CH-8092, Zürich, Switzerland

    Johannes Blömer

Authors
  1. Johannes Blömer
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Editor information

Editors and Affiliations

  1. Dipartimento di Elettronica e Informatica, Università di Padova, via Gradenigo 6/A, I-35131, Padova, Italy

    Gianfranco Bilardi  & Geppino Pucci  & 

  2. Department of Electrical Engineering and Computer Science, The University of Illinois at Chicago, 851 South Morgan Street - 1009 SEO, Chicago, IL, 60607-7053, USA

    Gianfranco Bilardi

  3. Dipartimento di Matematica Applicata e Informatica, Università “Cá Foscari” di Venezia, via Torino 155, I-30173, Venezia Mestre, Italy

    Giuseppe F. Italiano

  4. Dipartimento di Matematica Pura e Applicata, Università di Padova, via Belzoni 7, I-35131, Padova, Italy

    Andrea Pietracaprina

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© 1998 Springer-Verlag Berlin Heidelberg

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Blömer, J. (1998). A Probabilistic Zero-Test for Expressions Involving Roots of Rational Numbers. In: Bilardi, G., Italiano, G.F., Pietracaprina, A., Pucci, G. (eds) Algorithms — ESA’ 98. ESA 1998. Lecture Notes in Computer Science, vol 1461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68530-8_13

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  • DOI: https://doi.org/10.1007/3-540-68530-8_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64848-2

  • Online ISBN: 978-3-540-68530-2

  • eBook Packages: Springer Book Archive

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