An improved algorithm for deciding semi-definite polynomials

In this paper, a new algorithm is presented for deciding the semi-definiteness 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. This algorithm is an improvement of the method presented in Ref. [24]. The technique in this paper is to compute triangular decompositions of polynomial systems into regular chains.