  The persistent homology with coefficients in a field F coincides with the
same for cohomology because of duality. We propose an implementation of a
recently introduced algorithm for persistent cohomology that attaches
annotation vectors with the simplices. We separate the representation of the
simplicial complex from the representation of the cohomology groups, and
introduce a new data structure for maintaining the annotation matrix, which is
more compact and reduces substancially the amount of matrix operations. In
addition, we propose heuristics to simplify further the representation of the
cohomology groups and improve both time and space complexities. The paper
provides a theoretical analysis, as well as a detailed experimental study of
our implementation and comparison with state-of-the-art software for persistent
homology and cohomology.
