Difference substitution and automated inequality proving
Yang Lu · Journal of Guangzhou University · 2006
A program named SDS is designed for polynomial inequality proving,in other words,for decision of nonnegativity of polynomials.The basic idea is: split the variables into smaller nonnegative quantities,then,collect the terms and see whether the coefficients all are nonnegative.The method has been used to prove symmetric polynomial inequalities for so many years that the origin is unavailable.This is a heuristic,not a complete algorithm.However,it was demonstrated to be very efficient in practice.Quite a number of polynomial inequalities was not proven until program SDS is employed.