Polynomial recurrences and cyclic resultants
نویسندگان
چکیده
منابع مشابه
Polynomial Recurrences and Cyclic Resultants
Let K be an algebraically closed field of characteristic zero and let f ∈ K[x]. The m-th cyclic resultant of f is rm = Res(f, x m − 1). A generic monic polynomial is determined by its full sequence of cyclic resultants; however, the known techniques proving this result give no effective computational bounds. We prove that a generic monic polynomial of degree d is determined by its first 2d+1 cy...
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Let k be a field of characteristic zero and let f ∈ k[x]. The m-th cyclic resultant of f is rm = Res(f, x − 1). We characterize polynomials having the same set of nonzero cyclic resultants. Generically, for a polynomial f of degree d, there are exactly 2 distinct degree d polynomials with the same set of cyclic resultants as f . However, in the generic monic case, degree d polynomials are uniqu...
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The theory of constant polynomial combinants has been well developed [2] and it is linked to the linear part of the constant Determinantal Assignment problem [1] that provides the unifying description of the pole and zero assignment problems in Linear Systems. Considering the case of dynamic pole, zero assignment problems leads to the emergence of dynamic polynomial combinants. This paper aims ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2006
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-06-08672-2