Zero counting for a class of univariate Pfaffian functions

Abstract

We present a new procedure to count the number of real zeros of a class of univariate Pfaffian functions of order 1. The procedure is based on the construction of Sturm sequences for these functions and relies on an oracle for sign determination. In the particular case of E-polynomials, we design an oracle-free effective algorithm solving this task within exponential complexity. In addition, we give an explicit upper bound for the absolute value of the real zeros of an E-polynomial.