  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.
