An effective decision method for semidefinite polynomials

摘要

The purpose of this paper is to present an effective method of deciding the semidefiniteness of multivariate polynomials with coefficients in a computable ordered field, which admits an effective method of finding an isolating set for every non-zero univariate polynomial. Based on this method, the decision of the semidefiniteness of a multivariate polynomial may be reduced to testing some resulted polynomials in fewer variables, of which the total degrees and the term numbers do not exceed those of the given polynomial. With the aid of the computer algebra system Maple, our method is used to solve several examples.