Pisot numbers in the neighborhood of a limit point. II

Let S denote the set of real algebraic integers greater than one, all of whose other conjugates lie within the unit circle. In an earlier paper, we introduced the notion of "width" of a limit point a of S and showed that, if the width of a is smaller than 1.28... then there is an algorithm for determining all members of S in a neighborhood of a. Recently, we introduced the "derived tree" in order to deal with limit points of greater width. Here, we apply these ideas to the study of the limit point a3, the zero of z4 2z3 + ; 1 outside the unit circle. We determine the smallest neighborhood 9X < a3 < 92 of a3 in which all elements of S other than a3 satisfy one of the equations z"(z4 2z3 + z — 1) ± A(z) = 0, where A(z) is one of z} z2 + 1, z3 z + 1 or z4 z3 + z 1. The endpoints 0, and 62 are elements of S of degrees 23 and 42, respectively.