简单剖分上的多元样条理想Grbner基  

The multivariate spline ideal Grbner bases on the simple partition

作　　者：许景飞[1] 

机构地区：[1]赣南师范学院数学与计算机科学学院,江西赣州341000

出　　处：《辽宁师范大学学报（自然科学版）》2008年第3期270-274,共5页Journal of Liaoning Normal University:Natural Science Edition

摘　　要：多项式理想的Grbner基理论及其算法作为计算代数的重要内容,在多项式系统的求解以及极限环构造方面也有着广泛的应用.通过引用多项式理想Grbner基的一些基本理论,给出了只有两个胞腔的多元样条理想的Grbner基及约化Grbner基的定义,并给出构造Grbner基的相应算法,然后用实例说明算法的可行性.最后,对更复杂的多个胞腔的情形进行了初步讨论,提出了需要进一步解决的一些问题.The theory and algorithm of the polynomial ideal Grobner base one important content of calculation algebra, and have been widely applied in the solution of polynomial systems and the construction of limit cycles. In this paper, we firstly gave out the definitions of Grobner base and reduced Grobner base on multivariate spline ideal with only two cells, basing on some fundamental theories of the polynomial ideal Grobner bases. Then, we designed an algorithm for Grobner bases and showed the feasibility of the algorithm with an example. At last, we simply discussed the more complex condition for the cases with many cells and pointed out some problems needed further study.

关 键 词：多元样条 样条理想 GROBNER基 

分 类 号：O241.5[理学—计算数学]