【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.更多还原

【Abstract】 In this paper,the set of m-th equal partition points of n-simplex is defined by 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.更多还原