Fast Modular Algorithms for Squarefree Factorization and Hermite Integration

  • Jürgen Gerhard


We present new modular algorithms for the squarefree factorization of a primitive polynomial in ℤ[x] and for computing the rational part of the integral of a rational function in ℚ(x). We analyze both algorithms with respect to classical and fast arithmetic and argue that the latter variants are – up to logarithmic factors – asymptotically optimal. Even for classical arithmetic, the integration algorithm is faster than previously known methods.

Keywords: Chinese Remainder Algorithm, Computing time analysis, Fast algorithms, Hermite integration, Modular algorithms, Rational reconstruction, Squarefree factorization, Symbolic integration. 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Jürgen Gerhard
    • 1
  1. 1.Universität-GH Paderborn, Fachbereich Mathematik/Informatik, 33095 Paderborn, Germany (e-mail:

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