华东师范大学学报(自然科学版) ›› 2014, Vol. 2014 ›› Issue (1): 36-46.

• 应用数学与基础数学 • 上一篇    下一篇

确定有限多个曲面实交集的拓扑

高 犇1,  陈玉福2   

  1. 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
  • 收稿日期:2013-01-01 修回日期:2013-04-01 出版日期:2014-01-25 发布日期:2015-09-25

Determining the topology of real intersection of algebraic surfaces

GAO Ben1,  CHEN Yu-fu2   

  1. 1. College of Mathematics, Taiyuan University of Technology,  Taiyuan 030024, China;
    2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2013-01-01 Revised:2013-04-01 Online:2014-01-25 Published:2015-09-25

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.

关键词: 曲面, 一般位置, 拓扑, 子结式序列

Abstract: 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.

Key words: algebraic surface, generic position, topology, subresultants sequence

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