On Symbolic-Numeric Solving of Sine-Polynomial Equations

Abstract

This paper deals with the localization of all the real roots of sine-polynomials. D. Richardson (1991, in “effective Methods in Algebraic Geometry,” pp. 427–440, Birkhäuser, Basel) has already studied this type of analytic function. He showed how to find the number of real roots in a bounded interval. Here we propose an algorithm which determines whether a sine-polynomial has a finite number of real roots or not. Moreover in the finite case we construct an explicit interval containing all of them. We also construct a generalized exclusion method to find all the real roots in a bounded interval and we adapt it to the infinite case.