Erratum to “Cyclic resultants” [J. Symbolic Comput. 39 (6) (2005) 653–669]
نویسندگان
چکیده
منابع مشابه
Erratum to "A new algorithm for discussing Gröbner bases with parameters" [J. Symbolic Comput. 33(1-2) (2002) 183-208]
In 2002, the third author has presented the algorithmDisPGB to compute a comprehensiveGröbner system for a parametric ideal in Montes (2002), and has implemented it in Maple. The first release (1.4 of 2002) contains some errors that were fixed in the second release (2.4 of 2004). The two first authors have also implemented this algorithm in Maple, and after testing on several examples, they hav...
متن کاملCyclic resultants
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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We erroneously claim that Lemma 5.1 applies to both non-deterministic and deterministic Benenson automata, while it applies only to deterministic ones. The following corrected lemma holds for both deterministic and non-deterministic Benenson automata. It also exponentially improves on the dependence on D for both for circuit depth and size compared to the paper version. Note that compared with ...
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We consider the family of relative Thue equations x − (t− 1)xy − (t+ 2)xy − y = μ, where the parameter t, the root of unity μ and the solutions x and y are integers in the same imaginary quadratic number field. We prove that there are only trivial solutions (with |x|, |y| ≤ 1), if |t| is large enough or if the discriminant of the quadratic number field is large enough or if Re t = −1/2 (there a...
متن کاملPolynomial 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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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2005
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2005.05.001