Characterization of expansive polynomials by special determinants

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