非线性代数方程组的正解数

The Number of Positive Solutions of a Nonlinear Algebraic Equition System

利用关于一元多项式实根个数的显式判准、多项式的判别式序列、判别矩阵的顺序主子式序列和Sturm序列的变号数,给出了关于二元非线性代数方程组正解数的一个显式判准(假设方程组的解是有限的).

Using the techniques of explicit criterion to determine the number of real roots of an polynomial, the discriminant sequence of polynomial, the principal minor sequence of the discrimination matrix( cf.[1-2]) and the number of sign changes in the sequence of coefficients of sturm sequence, An explicit criterion to determine the number of positive solutions of a nonlinear algebraic equition system whose solution are finite is given.