Is it likely that in the future, there will be interest in computing persistent homology over the integers (or other PIDs)?

Currently, persistent homology is usually done over a field (like $\mathbb{Z}/2$), as the algorithms for producing the barcode only work for a field.

However, working over a field loses a lot of information. Also, there are algorithms that can compute the persistent groups over a PID (http://geometry.stanford.edu/papers/zc-cph-05/zc-cph-05.pdf Section 5).

Thanks for any help. References will be very welcome.