Affiliation:
1. Faculty of Mathematics, University “Al. I. Cuza”, 700506 Iasi, Romania
Abstract
A real univariate polynomial is called hyperbolic or stable if all its roots are real. We search for hyperbolic polynomials of two and three degrees by using the Wronskian map W and a dual map to W called Leibniz, since it involves the classical Leibniz rule for the derivative of a product of functions. In addition to hyperbolicity, we use these two methods to search for a class of polynomials introduced by the first author and now called weak Euclidean.
Reference11 articles.
1. The diagonalization map as submersion, the cubic equation as immersion and Euclidean polynomials;Crasmareanu;Mediterr. J. Math.,2022
2. Kostov, V.P. (2011). Topics on Hyperbolic Polynomials in One Variable, Panoramas et Synthèses.
3. Roots of Garding hyperbolic polynomials;Rainer;Proc. Am. Math. Soc.,2022
4. Nuij type pencils of hyperbolic polynomials;Kurdyka;Can. Math. Bull.,2017
5. Sottile, F. (2011). Real Solutions to Equations from Geometry, American Mathematical Society.