Polynomial factorization by root approximation

  • Arjen K. Lenstra
Pactorization And GCD Computations
Part of the Lecture Notes in Computer Science book series (LNCS, volume 174)


We show that a constructive version of the fundamental theorem of algebra [3], combined with the basis reduction algorithm from [1], yields a polynomial-time algorithm for factoring polynomials in one variable with rational coefficients.


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  1. 1.
    A.K. Lenstra, H.W. Lenstra, Jr., L. Lovász, Factoring polynomials with rational coefficients, Math. Ann. 261 (1972), 515–534.Google Scholar
  2. 2.
    M. Mignotte, An inequality about factors of polynomials, Math. Comp. 28 (1974), 1153–1157.Google Scholar
  3. 3.
    A. Schönhage, The fundamental theorem of algebra in terms of computational complexity, manuscript, 1982.Google Scholar
  4. 4.
    A. Schönhage, Factorization of univariate integer polynomials by diophantine approximation and by an improved basis reduction algorithm, manuscript, 1983.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Arjen K. Lenstra
    • 1
  1. 1.Centrum voor wiskunde en informaticaAmsterdamThe Netherlands

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