确定有限多个曲面实交集的拓扑  

Determining the topology of real intersection of algebraic surfaces

作　　者：高犇[1] 陈玉福[2] 

机构地区：[1]太原理工大学数学学院,太原030024 [2]中国科学院大学数学科学学院,北京100049

出　　处：《华东师范大学学报（自然科学版）》2014年第1期36-46,共11页Journal of East China Normal University(Natural Science)

摘　　要：提出一个关于计算曲面实交集拓扑的有效算法,其中曲面由有限多个实系数三元多项式所定义.这个算法使用了实交集至多两个投影的拓扑信息.在此过程中,必须使得有限多个曲面满足一定的条件,这些条件通过线性坐标变换可以得到,并且应用一些方法来检测这些条件是否满足.This paper gave an algorithm for computing in an efficient way the topology of the real intersection of algebraic surfaces, which are defined by a finite family of trivariate polynomials with coefficients in R. The algorithm is based on the computation of the graphs which are the intersection of at most two projections. For this purpose, some conditions, which be obtained by some linearly change of coordinates were fultiued, and some methods for checking these conditions were presented.

关 键 词：曲面 一般位置 拓扑 子结式序列 

分 类 号：O154[理学—数学]