from itertools import combinations

def level(M):
    return M.denominator() # not documented enough :(

def create_matrix(CT):
    AS = RootSystem(CT).ambient_space()
    return Matrix([[r.associated_coroot().inner_product(v) for r in AS.positive_roots()] for v in AS.fundamental_weights()])

def calculate_levels(CT):
    M = create_matrix(CT)
    allrows = list(range(M.nrows()))
    res = dict()
    print(binomial(M.ncols(), M.nrows()))
    # for cols in Subsets(range(M.ncols()), M.nrows()): # much slower?
    for cols in combinations(range(M.ncols()), M.nrows()):
        res[cols]=0
        try:
            sM = M[allrows, cols].inverse()
            res[cols] = level(sM)
        except:
            res[cols] = 0
    return res