Factoring polynomials with rational coefficients

  title={Factoring polynomials with rational coefficients},
  author={Arjen K. Lenstra and Hendrik W. Lenstra and L{\'a}szl{\'o} Mikl{\'o}s Lov{\'a}sz},
  journal={Mathematische Annalen},
In this paper we present a polynomial-time algorithm to solve the following problem: given a non-zero polynomial fe Q(X) in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q(X). It is well known that this is equivalent to factoring primitive polynomials feZ(X) into irreducible factors in Z(X). Here we call f~ Z(X) primitive if the greatest common divisor of its coefficients (the content of f) is 1. Our algorithm performs well in practice, cf. (8… 

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  • 1990
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  • Computer Science, Mathematics
  • 1992
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  • D. Yun
  • Mathematics
    Outstanding Dissertations in the Computer Sciences
  • 1973
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  • L. AdlemanA. Odlyzko
  • Mathematics
    22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)
  • 1981
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  • E. T.
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  • 1946
THIS book must be welcomed most warmly into X the select class of Oxford books on pure mathematics which have reached a second edition. It obviously appeals to a large class of mathematical readers.

An Introduction to the Geometry of Numbers

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