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中文摘要：
近年来由杨路等提出了一种利用逐次差分代换以证明多项式非负性的方法,并在MAPLE平台编写了相应程序。但是,对于某些多项式的非负性却无法在一定时间内给出有效证明。文章改进了逐次差分代换的判定方法,可以较好的解决这一类问题。
英文摘要：
Recently a method based on successive difference substitution has been developed by Yang to prove positive semi-definition of polynomials, and its corresponding program tsds has been realized in MAPLE. However some polynomials cannot be definitely judged by it. In this paper, the method is improved so as to verify these polynomials automatically.
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