Algorithmic Number Theory

Symbolic and Algebraic Computation

Volume 358 of the series Lecture Notes in Computer Science pp 244-251

Date:

Effective tests for cyclotomic polynomials

  • R. J. BradfordAffiliated withSchool of Mathematical Sciences, University of Bath
  • , J. H. DavenportAffiliated withSchool of Mathematical Sciences, University of Bath

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Abstract

We present two efficient tests that determine if a given polynomial is cyclotomic, or is a product of cyclotomics. The first method uses the fact that all the roots of a cyclotomic polynomial are roots of unity, and the second the fact that the degree of a cyclotomic polynomial is a value of φ(n), for some n. We can also find the cyclotomic factors of any polynomial.