n-单形的m阶等分点集与零多项式的判定  

The Set of m-th Equal Partition Points of n-Simplex and Decision of the Zero Polynomial

作　　者：徐嘉[1] 姚勇[2] 张景中[2] 

机构地区：[1]西南民族大学计算机科学与技术学院,成都610041 [2]中国科学院成都计算机应用研究所,成都610041

出　　处：《数学学报（中文版）》2014年第2期311-320,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家重点基础研究发展计划(2011CB302412);国家自然科学基金资助项目(11001228);西南民族大学中央高校基本科研业务费专项资金(12NZYTH04)

摘　　要：通过递归方法定义了N-单形的m阶等分点集.证明了n元m次多项式f为零多项式的充要条件是:f在任意n-单形的m阶等分点处的取值为0.然后将这一结果应用到插值方法的适定点问题和几何定理机器证明的数值并行法.In this paper, the set of m-th equal partition points of n-simplex is definedby recursion. A necessary and sufficient condition for deciding the zero polynomial is presented, i.e., for a polynomial f of m degree in n variables, it is the zero polynomial iff it vanishes at m-th equal partition points of an arbitrary n-simplex. As applications,this result is presented on the properly posed set of nodes for interpolation and the parallel numerical method of mechanical theorem proving.

关 键 词：n-单形 等分点集 零多项式 

分 类 号：O187.2[理学—数学]