Cyclotomic Factors and LRS-Degeneracy
arxiv(2024)
摘要
We present three new, practical algorithms for polynomials in
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 α, β such that β = ζα for
some root of unity ζ. 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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