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On the Computational Hardness of Testing Square-Freeness of Sparse Polynomials

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1719))

Abstract

We show that deciding square-freeness of a sparse univariate polynomial over ZZ and over the algebraic closure of a finite field F p of p elements is NP-hard. We also discuss some related open problems about sparse polynomials.

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, University of Bonn, Römerstrasse 164, 53117, Bonn, Germany

    Marek Karpinski

  2. Dept. of Computing, Macquarie University, Sydney, NSW, 2109, Australia

    Igor Shparlinski

Authors
  1. Marek Karpinski
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  2. Igor Shparlinski
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, University of Hawaii, 2540 Dole St., # 483, Honolulu, HI, 96822, USA

    Marc Fossorier  & Shu Lin  & 

  2. Institute of Industrial Science, University of Tokyo, 7-22-1, Roppongi, Minato-ku, Tokyo, 106, Japan

    Hideki Imai

  3. AAECC/IRIT, Université Paul Sabatier, 118, Route de Narbonne, F31067, Toulouse, Cedex, France

    Alain Poli

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© 1999 Springer-Verlag Berlin Heidelberg

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Karpinski, M., Shparlinski, I. (1999). On the Computational Hardness of Testing Square-Freeness of Sparse Polynomials. In: Fossorier, M., Imai, H., Lin, S., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1999. Lecture Notes in Computer Science, vol 1719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46796-3_47

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  • DOI: https://doi.org/10.1007/3-540-46796-3_47

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66723-0

  • Online ISBN: 978-3-540-46796-0

  • eBook Packages: Springer Book Archive

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