Effective tests for cyclotomic polynomials

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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.

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Bradford, R. J., & Davenport, J. H. (1989). Effective tests for cyclotomic polynomials. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 358 LNCS, pp. 244–251). Springer Verlag. https://doi.org/10.1007/3-540-51084-2_22

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