Computing Simplicial Homology Based on Efficient Smith Normal Form Algorithms
Computing Simplicial Homology Based on Efficient Smith Normal Form Algorithms
复制标题
基于高效史密斯范式算法的简单同调计算
DOI：
10.1007/978-3-662-05148-1_10
复制
发表时间：
2003
期刊：
影响因子：
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通讯作者：
V. Welker
中科院分区：
文献类型：
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作者：
J. Dumas;F. Heckenbach;D. Saunders;V. Welker
We recall that the calculation of homology with integer coefficients of a simplicial complex reduces to the calculation of the Smith Normal Form of the boundary matrices which in general are sparse. We provide a review of several algorithms for the calculation of Smith Normal Form of sparse matrices and compare their running times for actual boundary matrices. Then we describe alternative approaches to the calculation of simplicial homology. The last section then describes motivating examples and actual experiments with the GAP package that was implemented by the authors. These examples also include as an example of other homology theories some calculations of Lie algebra homology.
DOI：
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发表时间：
2006
期刊：
Integrable systems, geometry, and topology, AMS/IP Studies of Advanced Mathematics, American Mathematical Society 36
影响因子：
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作者：
FURUYA;Jun;Martin Guest
通讯作者：
Martin Guest