INTEGER MULTIPLIERS OF REAL POLYNOMIALS WITHOUT NONNEGATIVE ROOTS

Abstract

For a given real polynomial $f$ without nonnegative roots we study monic integer polynomials $g$ such that the product $g f$ has positive (nonnegative, respectively) coefficients. We show that monic integer polynomials~$g$ with these properties can effectively be computed, and we give lower and upper bounds for their degrees. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$