Trac #34622: partial cleanup in partition.py

some pep8, some code details, one shorter doctest, standard errors, etc

also using formatted strings a little bit

and modern syntax for super()

URL: https://trac.sagemath.org/34622
Reported by: chapoton
Ticket author(s): Frédéric Chapoton
Reviewer(s): Matthias Koeppe

Author: Release Manager