Algorithms for localizing roots of a polynomial and the Pisot Vijayaraghavan numbers
R. J. Duffin · Pacific Journal of Mathematics · 1978
Pisot and Vijayaraghavan studied numbers whose mth power is nearly an integer in the sense that the discrepancy vanishes as m becomes infinite.One plus square root two is an example.Algebraic numbers of this type are characterized as algebraic integers whose conjugate roots each have absolute value less than one.This note develops a test for this property.An algorithm is given which determines whether or not one root of a polynomial has absolute value greater than one and all the other roots have absolute value less than one.If n is the degree of the polynomial, this algorithm involves only n rational steps.