判别三元多项式的正半定性及软件实现

DETERMINATION POSITIVE SEMI DEFINITE OF POLYNOMIALS WITH THREE INDETERMINATES AND SOFTWARE IMPLEMENTATION

本文应用符号（文字）系数多项式的完全判别系统来研究四元齐次多项式或三元非齐次多项式的正半定性质，我们采用计算机代数软件ＭＡＰＬＥ和图形技术，将整个平面划分成有限个区域，在每个区域里通过代表点确定多项式的正半定性质。本方法直观、可靠、易于理解，并有助于对多项式的进一步研究。

In this paper we developed a decision algorithm for positive/negative semidefinite of homogeneous polynomials with four indeterminates or nonhomogeneous polynomials with three indeterminates,applying the theory of complete determinant system of polynomials with symbolic coefficients established recently in.Using the computer algebra software MAPLE and graphic technique ,we devide the whole plane into a finite number of regions,each of them is repressnted by a point inside it,and the given polynomial is either positive semi definite or negative semi definite.Our method is effcient and intuitive,and is conducive for further study on polynomials.