Some simple code for computing the probabilistic zeta function of a poset lattice, as defined in Shala22. There is also a function to look for lattices which are weakly coset-like (WCL) but not strongly coset-like (SCL).
To install, simply copy the file and run load("main.sage") in the same directory.
L = d_partition_lattice(2,3)
prob_zeta_fn(L)
# Returns (30/15^s - 15/5^s + 1, True)
# Find counterexamples for the assertion WCL => SCL:
test_all(10,10)