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中国科学院大学学报 ›› 2010, Vol. 27 ›› Issue (6): 838-846.DOI: 10.7523/j.issn.2095-6134.2010.6.016

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计算紧半代数集的同调方法

高犇, 陈玉福, 张智勇   

  1. 中国科学院研究生院数学科学学院,北京 100049
  • 收稿日期:2009-09-18 发布日期:2010-11-15

A co-homology method for computing compact semi-algebraic sets

GAO Ben, CHEN Yu-Fu, ZHANG Zhi-Yong   

  1. School of Mathematical Sciences,Graduate University,Chinese Academy of Sciences,Beijing 100049,China
  • Received:2009-09-18 Published:2010-11-15

摘要:

提出一个关于计算紧半代数集构成排列的0维Betti-数和1维Betti-数的算法.这个算法的复杂度为单指数复杂度.

关键词: 单纯上同调群, 紧半代数集, 排列, 柱代数分解, 胞腔相邻

Abstract:

We describe an algorithm for computing the zero-th and first Betti numbers of the union of compact semi-algebraic sets.The complexity of the algorithm is single exponential.

Key words: co-homology group, compact semi-algebraic set, arrangement, cylindrical algebraic decomposition, cell adjacency

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