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Factoring Polynomials and 0—1 Vectors

  • Mark van Hoeij
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2146)

Abstract

A summary is given of an algorithm, published in [4], that uses lattice reduction to handle the combinatorial problem in the factoring algorithm of Zassenhaus. Contrary to Lenstra, Lenstra and Lovász, the lattice reduction is not used to calculate coefficients of a factor but is only used to solve the combinatorial problem, which is a problem with much smaller coefficients and dimension. The factors are then constructed efficiently in the same way as in Zassenhaus’ algorithm.

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References

  1. 1.
    H. Zassenhaus, On Hensel Factorization, I., Journal of Number Theory 1, 291–311 (1969).zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    A.K. Lenstra, H.W. Lenstra and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann. 261, 515–534 (1982).zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    V. Miller, Factoring polynomials via Relation-Finding. ISTCS’92, Springer Lecture Notes in Computer Science 601, 115–121 (1992).Google Scholar
  4. 4.
    M. van Hoeij, Factoring polynomials and the knapsack problem, preprint available from http://www.math.fsu.edu/~hoeij/ accepted for Journal of Number Theory (2000).

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Mark van Hoeij
    • 1
  1. 1.Department of MathematicsFlorida State UniversityTallahassee

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