Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10325743 | Journal of Symbolic Computation | 2005 | 17 Pages |
Abstract
We characterize polynomials having the same set of nonzero cyclic resultants. Generically, for a polynomial f of degree d, there are exactly 2dâ1 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.
Related Topics
Physical Sciences and Engineering
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Authors
Christopher J. Hillar,