Computing the Betti Numbers of Arrangements in Practice

机译：在实践中计算安排的贝蒂数

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We describe an algorithm for computing the zero-th and the first Betti numbers of the union of n simply connected compact semi-algebraic sets in R~k, where each such set is defined by a constant number of polynomials of constant degrees. The complexity of the algorithm is O(n~3). We also describe an implementation of this algorithm in the particular case of arrangements of ellipsoids in R~3 and describe some of our results.

机译：我们描述了一种算法，用于计算R〜k中n个简单连接的紧半代数集的并集的第零个和第一个Betti数，其中每个这样的集合由恒定次数的恒定次数的多项式定义。该算法的复杂度为O（n〜3）。我们还描述了在R〜3中椭球排列的特定情况下该算法的实现，并描述了一些结果。

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来源
《International Workshop on Computer Algebra in Scientific Computing(CASC 2005); 20050912-16; Kalamata(GR)》|2005年|P.13-31|共19页
会议地点 Kalamata(GR)
作者
Saugata Basu; Michael Kettner;
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作者单位

School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA;

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原文格式 PDF
正文语种 eng
中图分类计算技术、计算机技术;代数、数论、组合理论;
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Computing the Betti Numbers of Arrangements in Practice

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