  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.
