We characterize polynomials having the same set of nonzero cyclic resultants.
Generically, for a polynomial f of degree d, there are exactly 2d−1
distinct degree d polynomials with the same set of cyclic resultants as f.
However, in the generic monic case, degree d polynomials are uniquely
determined by their cyclic resultants. Moreover, two reciprocal
(``palindromic'') polynomials giving rise to the same set of nonzero cyclic
resultants are equal. In the process, we also prove a unique factorization
result in semigroup algebras involving products of binomials. Finally, we
discuss how our results yield algorithms for explicit reconstruction of
polynomials from their cyclic resultants.Comment: 16 pages, Journal of Symbolic Computation, print version with errata
incorporate