  In a recent work, the authors established a refinement of the well-known 1958
result of Vietoris on nonnegative cosine polynomials.
  In four places of the proof, use was made of the classical Sturm Theorem on
determining the number of real roots of an algebraic polynomials in a given
interval. Although absolutely rigorous, the Sturm procedure involves lengthy
technical computations carried out with the help of the software MAPLE 13. This
article provides such details which were omitted in the article presenting the
recent work.
