# 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}
}```
• Published 1 December 1982
• Mathematics
• 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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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.
Notation Prologue Chapter I. Lattices 1. Introduction 2. Bases and sublattices 3. Lattices under linear transformation 4. Forms and lattices 5. The polar lattice Chapter II. Reduction 1. Introduction