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arXiv · 2403.08751

Cyclotomic Factors and LRS-Degeneracy

John Abbott·Nico Mexis
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Abstract

We present three new, practical algorithms for polynomials in $\mathbb{Z}[x]$: one to test if a polynomial is cyclotomic, one to determine which cyclotomic polynomials are factors, and one to determine whether the given polynomial is LRS-degenerate. A polynomial is "LRS-degenerate" iff it has two distinct roots $\alpha, \beta$ such that $\beta = \zeta \alpha$ for some root of unity $\zeta$. All three algorithms are based on "intelligent brute force". The first two produce the indexes of the cyclotomic polynomials; the third produces a list of degeneracy orders. The algorithms are implemented in CoCoALib.

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John Abbott, Nico Mexis. 2024-03-13. Cyclotomic Factors and LRS-Degeneracy. https://arxiv.org/abs/2403.08751

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