Cyclic Resultants

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dc.creatorHillar, Christopher J.
dc.date2004-01-18
dc.date2005-04-28
dc.date.accessioned2026-07-07T05:04:38Z
dc.date.available2026-07-07T05:04:38Z
dc.descriptionWe characterize polynomials having the same set of nonzero cyclic resultants. Generically, for a polynomial $f$ of degree $d$, there are exactly $2^{d-1}$ 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.
dc.description16 pages, Journal of Symbolic Computation, print version with errata incorporated
dc.identifierhttps://arxiv.org/abs/math/0401220
dc.identifierhttp://arxiv.org/abs/math/0401220
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69883
dc.subjectCommutative Algebra
dc.subjectRings and Algebras
dc.titleCyclic Resultants
dc.typetext

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