Hyperbolic and Weak Euclidean Polynomials from Wronskian and Leibniz Maps

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.