  A polynomial is expansive if all of its roots lie outside the unit circle. We
define some special determinants involving the coefficients of a real
polynomial and formulate necessary and sufficient conditions for expansivity
using these determinants. We show how these conditions can be turned into an
algorithm, which, for integer polynomials, avoids exponential coefficient
growth. We also examine the question how close the roots of an expansive
polynomial can be to the unit circle if the coefficients are integers. We give
several lower bounds on this distance in terms of different measures of the
polynomial (e.g. its height). The simplest one is derived by Liouville's
inequality, but then we improve this result and give different bounds using our
special determinants.
