Factoring polynomials with rational coefficients

@article{Lenstra1982FactoringPW,
  title={Factoring polynomials with rational coefficients},
  author={A. K. Lenstra and H. Lenstra and L. 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… Expand
3,759 Citations

Figures from this paper

Polynomial-Time Reductions from Multivariate to Bi- and Univariate Integral Polynomial Factorization
  • E. Kaltofen
  • Mathematics, Computer Science
  • SIAM J. Comput.
  • 1985
  • 93
  • PDF
FACTORING MULTIVARIATE POLYNOMIALS OVER LARGE FINITE FIELDS
  • PDF
Factoring bivariate sparse (lacunary) polynomials
  • 27
  • PDF
Factoring Polynomials via Relation-Finding
  • V. Miller
  • Mathematics, Computer Science
  • ISTCS
  • 1992
  • 10
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 35 REFERENCES
Lattices and factorization of polynomials
  • 15
  • PDF
The Hensel Lemma in Algebraic Manipulation
  • D. Yun
  • Mathematics, Computer Science
  • Outstanding Dissertations in the Computer Sciences
  • 1973
  • 53
Generalization of the Euclidean algorithm for real numbers to all dimensions higher than two
  • 90
  • PDF
A remark on the Hensel factorization method
  • 24
  • PDF
A sublinear additive sieve for finding prime number
  • 55
Irreducibility testing and factorization of polynomials
  • L. Adleman, A. Odlyzko
  • Mathematics, Computer Science
  • 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)
  • 1981
  • 3
  • PDF
Irreducibility testing and factorization of polynomials
  • 32
  • PDF
An inequality about factors of polynomials
  • 160
  • PDF
An Introduction to the Theory of Numbers
  • 2,462
...
1
2
3
4
...