# Computing Persistent Homology with Various Coefficient Fields in a Single Pass

arXiv: https://arxiv.org/abs/2001.02960 · HTML: https://mlsanity.com/paper/2001.02960/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jan 2020.

## Built on by (most cited first, 1 of 1)

- [Reparameterization through Coverings and Topological Weight Priors](https://mlsanity.com/paper/2604.23804/) (2026)

## Abstract (arXiv)

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.