Since I have started to package this myself I should explain what it does. The HAP package can compute Homolgy and persistent Homology. See https://www.gap-system.org/Manuals/pkg/hap-1.25/www/SideLinks/About/twoTutorials.html
Another tool that might be able to do that is singular. I do however find HAP easier to use. Sincerely, Joachim -- Papier ist gebundenes CO2. Bitte drucken Sie diese EMail aus und archivieren Sie sie.