A high-performance algorithm for calculating cyclotomic polynomials

The nth cyclotomic polynomial, n(z), is the monic polynomial whose (n) distinct roots are the nth primitive roots of unity. n(z) can be computed efficiently as a quotient of terms of the form (1 - zd ) by way of a method the authors call the Sparse Power Series algorithm. We improve on this algorithm in three steps, ultimately deriving a fast, recursive algorithm to calculate n(z). The new algorithm, which we have implemented in C, allows us to compute n(z) for n > 109 in less than one minute.

• Type: Journal
• Year: 2010
• Where: CAP
• Authors: Andrew Arnold, Michael B. Monagan
• Keywords: Algorithm, CAP 2010, Distributed And Parallel Computing, Nth Cyclotomic Polynomial, Nth Primitive Roots