Factoring polynomials with rational coefficients

@article{Lenstra1982FactoringPW,
  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},
  year={1982},
  volume={261},
  pages={515-534}
}
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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