On computing factors of cyclotomic polynomials
Number Theory
2010-05-03 v1 Data Structures and Algorithms
Abstract
For odd square-free n > 1 the n-th cyclotomic polynomial satisfies an identity of Gauss. There are similar identity of Aurifeuille, Le Lasseur and Lucas. These identities all involve certain polynomials with integer coefficients. We show how these coefficients can be computed by simple algorithms which require O(n^2) arithmetic operations and work over the integers. We also give explicit formulae and generating functions for the polynomials, and illustrate the application to integer factorization with some numerical examples.
Cite
@article{arxiv.1004.5466,
title = {On computing factors of cyclotomic polynomials},
author = {Richard P. Brent},
journal= {arXiv preprint arXiv:1004.5466},
year = {2010}
}
Comments
21 pages. An old Technical Report, submitted for archival purposes. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub135.html