Cyclic polynomials and the multiplication matrices of their roots
Let \(D\) be an integrally closed, characteristic zero domain, \(K\) its field of fractions, and let \(P(x)=\sum_{k=0}^m c_kx^k= \prod_{i=0}^{m-1}(x-\theta_i)\in D[x]\) be a cyclic polynomial. Let \(\tau\) be a generator of \(\text{Gal}(K(\theta_0)/K)\), suppose that \(\tau(\theta_i)=\theta_{i+1}\) (indices mod \(m\)), and \(\text{discr}(\theta_0,\dots,
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