三类根式不等式的有理化与机器证明  

Rationalization and automated proving for three classes of inequalities involving radicals

作　　者：徐嘉[1] 

机构地区：[1]西南民族大学计算机科学与技术学院,四川成都610041

出　　处：《西南民族大学学报（自然科学版）》2016年第2期200-206,共7页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家民委资助项目(14XNZ023);四川省教育厅创新团队(15TD0050)

摘　　要：研究了三类根式不等式的有理化与机器证明.首先给出了三类根式不等式成立的充分必要条件,即等价的有理不等式组.然后介绍了伴随多项式概念,并建立了一个算法Simplex M.Simplex M能够处理带有连结词∧(and)和∨(or)的多项式不等式组.最后给出了大量的应用实例,证实了这一方法的有效性.This paper studies rationalization and automated proving for three classes of inequalities involving radicals. Firstly,the sufficient and necessary conditions for deciding three types of radical inequalities are obtained. Then the adjoint polynomial on a simplex for a given polynomial is introduced. An algorithm Simplex M which can deal with polynomial inequalities with the conjunction ∧（ and） and ∨（ or） is established. Finally,some application examples confirm the effectiveness of this method.

关 键 词：根式不等式 有理化 单纯剖分方法 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]