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Counting Reducible, Powerful, and Relatively Irreducible Multivariate Polynomials over Finite Fields

(Extended Abstract)
  • Joachim von zur Gathen
  • Alfredo Viola
  • Konstantin Ziegler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6034)

Abstract

We present counting methods for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones (divisible by the sth power of a nonconstant polynomial), and the relatively irreducible ones (irreducible but reducible over an extension field). One approach employs generating functions, another one a combinatorial method. They yield approximations with relative errors that essentially decrease exponentially in the input size.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Joachim von zur Gathen
    • 1
  • Alfredo Viola
    • 2
    • 3
  • Konstantin Ziegler
    • 1
  1. 1.B-ITUniversität BonnBonnGermany
  2. 2.Instituto de ComputaciónUniversidad de la RepúblicaMontevideoUruguay
  3. 3.Associate Member of LIPN - CNRS UMR 7030Université de Paris-NordVilletaneuseFrance

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