Betti Numbers of Semialgebraic Sets Defined by Quantifier-Free Formulae

被引：0

作者：

Andrei Gabrielov

Nicolai Vorobjov

机构：

[1] Department of Mathematics,

[2] Purdue University,undefined

[3] West Lafayette,undefined

[4] IN 47907,undefined

[5] Department of Computer Science,undefined

[6] University of Bath,undefined

[7] Bath BA2 7AY,undefined

来源：

Discrete & Computational Geometry | 2005年 / 33卷

关键词：

Computational Mathematic; Betti Number; Atomic Formula; Boolean Combination; Distinct Polynomial;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Let X be a semialgebraic set in Rn defined by a Boolean combination of atomic formulae of the kind h * 0 where * \in { >, \ge, = }, deg(h) < d, and the number of distinct polynomials h is k. We prove that the sum of Betti numbers of X is less than O(k2d)n.

引用

页码：395 / 401

页数：6

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