中文摘要：

设计了一个试探性的计算机程序SDS，用于证明多项式不等式，或等价地，用于判定多项式的非负性．将各变量按一定方式分割成较小的非负量，将变量替换后的多项式合并同类项，然后看是否所有的系数都是非负的．该方法不是完备的，但实验结果表明该程序对许多情况有效．不少次数较高或变量较多的多项式，除了SDS，还没有任何其他软件能做．

英文摘要：

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.