Beyond Descartes’ rule of signs

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Constructive Mathematical Analysis
Volume:6 Issue:2
Beyond Descartes’ rule of signs

Beyond Descartes’ rule of signs

Pages : 128-141

View : 40 | Download : 33

Publication Date : 2023-06-15

Article Type : Research Paper

Abstract :We consider real univariate polynomials with all roots real. Such a polynomial with c sign changes and p sign preservations in the sequence of its coefficients has c positive and p negative roots counted with multiplicity. Suppose that all moduli of roots are distinct; we consider them as ordered on the positive half-axis. We ask the question: If the positions of the sign changes are known, what can the positions of the moduli of negative roots be? We prove several new results which show how far from trivial the answer to this question is.
Keywords : real polynomial in one variable, hyperbolic polynomial, sign pattern, Descartes rule of signs

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