This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-sensitive in the total number of distinct persistent homological features in the diagrams for the different coefficient fields. This computation allows us to infer the prime divisors of the torsion coefficients of the integral homology groups of the topological space at any scale, hence furnishing a more informative description of topology than persistence in a single coefficient field. We provide theoretical complexity analysis as well as detailed experimental results. The code is part of the Gudhi software library.

中文翻译：

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在单程中计算具有各种系数场的持久同源性

本文介绍了一种算法，用于在单个矩阵约简中计算具有各种系数字段的过滤复数的持久同源性。该算法在不同系数字段的图中不同持久同源特征的总数中是输出敏感的。这种计算使我们能够在任何尺度上推断拓扑空间的积分同调群的扭转系数的质因数，因此提供比单一系数场中的持久性更丰富的拓扑描述。我们提供理论复杂性分析以及详细的实验结果。该代码是 Gudhi 软件库的一部分。