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;
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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.
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页码：395 / 401
页数：6
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