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TitleCyclic resultants
Author(s) Christopher Hillar
TypeArticle in Journal
AbstractWe 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.
KeywordsCyclic resultant, Binomial factorization, Group rings, Toral endomorphisms
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717105000374
LanguageEnglish
JournalJournal of Symbolic Computation
Volume39
Number6
Pages653 - 669
Year2005
Edition0
Translation No
Refereed No
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