Polynomial factorisation: an exploration of Lenstra's algorithm

  • JA Abbott
  • JH Davenport
Polynomial Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 378)


We describe various design decisions and problems encountered during the implementation of the Lenstra factoriser [Lenstra82] in REDUCE. A practical viewpoint is taken with descriptions of both successful and unsuccessful attempts at tackling some of the problems. Particular areas considered include bounding coefficients of factors, the Cantor-Zassenhaus factoriser [Cantor81], Hensel lifting, basis reduction, and trial division of polynomials. We give an empirical formula which estimates the running time of our basis reduction routine.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • JA Abbott
    • 1
  • JH Davenport
    • 1
  1. 1.School of Mathematical SciencesUniversity of BathBath, AvonEngland

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