代数曲面对应多项式的质公因子存在性研究  

Research on Existence of Common Prime Factors of Polynomial Corresponding to Algebraic Surface

作　　者：张敬 宋文建 崔利宏 

机构地区：[1]辽宁师范大学,辽宁 大连

出　　处：《应用数学进展》2021年第11期3668-3672,共5页Advances in Applied Mathematics

摘　　要：Bezout定理在证明二元插值适定结点组构造方法时起到了重要的作用,但不能直接简单推广至三维空间,该文针对这个问题以平面中的相关理论为参照,以代数曲面与多项式相关理论为基础,对何时代数曲面对应多项式有质公因子进行了研究,给出了判断空间代数曲面对应多项式是否有质公因子的一种方法。Bezout’s theorem plays an important role in proving the constructive methods of properly posed set of nodes for binary interpolation, but it cannot be directly extended to three-dimensional space. In order to address this problem, this paper investigated relevant theories on the plane, explored relevant theories of algebraic surfaces and polynomials to explain the instances during which polynomial corresponding to algebraic surface can have common prime factors, and proposed a method to judge whether the polynomial corresponding to algebraic surface has common prime factors.

关 键 词：代数曲面 多项式 不可约公因子 结式 

分 类 号：O15[理学—数学]