Generalized Budan–Fourier theorem and virtual roots
نویسندگان
چکیده
منابع مشابه
Generalized Budan-Fourier theorem and virtual roots
The notion of virtual root was introduced in [5] in the case of polynomials. The virtual roots provide d continuous “root fonctions” on the space all real polynomials of a given degree d, with an interlacing property linking virtual roots of P and virtual roots of P ′. From a computational point of view, there is no need to know the coefficients with infinite precision in order to compute the v...
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The Generalized Principal Ideal Theorem is one of the cornerstones of dimension theory for Noetherian rings. For an R-module M, we identify certain submodules of M that play a role analogous to that of prime ideals in the ring R. Using this definition, we extend the Generalized Principal Ideal Theorem to modules.
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Given a degree n univariate polynomial f(x), the Budan-Fourier function Vf (x) counts the sign changes in the sequence of derivatives of f evaluated at x. The values at which this function jumps are called the virtual roots of f , these include the real roots of f and any multiple root of its derivatives. This concept was introduced (by an equivalent property) by Gonzales-Vega, Lombardi, Mahé i...
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ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2005
ISSN: 0885-064X
DOI: 10.1016/j.jco.2004.11.003