#Compute dimensions of compositions by definition
rk = 6 # rk is the rank of the Coxeter group
W = CoxeterGroup(["E",rk])
R = [] # R = [ ribbon numbers ]
for s in range(2^rk):
    R.append(0) # initiate each ribbon number to zero
for w in W:
    j = sum(2^(i-1) for i in w.descents()) # index the descent set of w
    R[j] = R[j] + 1 # add one to the corresponding ribbon number
R.sort(); print(R) # list the ribbon numbers increasingly
for p in [2,3,5,7,11,13]:
    c = [] # c is the composition dimension vector
    for i in range(p):
        c.append(0) # initiate each component of c to zero
    for r in R:
        c[r%p] = c[r%p] + 1 # add one to the component of c corresponding to each ribbon number mod p
    print(p, gcd(c).factor(), [i/gcd(c) for i in c]) # display the prime p and the composition dimension vector c with gcd(c) factored out

k = 4 # Example 3.8 (type A_n, where n is a sum of k distinct nonnegative powers of p)
c = [] # c[p] is the composition dimension p-vector divided by 2^(n-2^k+1)
Pr = [2,3,5,7,11,13,17,19,21,23] # Pr is a list of primes
for p in Pr: # initiate c
    l = []
    for i in range(p):
        l.append(0)
    c.append(l) # initiate c[p]
BL = posets.BooleanLattice(k) #BL is the Boolean lattice of rank k
print(BL.list()); BL.plot() # display BL
for T in Set(range(1,2^k-1)).subsets(): # see Cor. 3.5 for the definition of T
    r = 0
    for f in BL.subposet(T).chains():
        r = r + (-1)^(len(f)) # see Cor. 3.5 for the definition of r
    for j in range(len(Pr)):
        p = Pr[j]; i = r%p 
        if i == 0:
            c[j][i] = c[j][i] + 1  # add one to the component of c[j] corresponding to i
        else:
            c[j][i] = c[j][i] + 1/2 # add half to the component of c[j] corresponding to i
            c[j][p-i] = c[j][p-i] + 1/2  # add half to the component of c[j] corresponding to -i
for i in range(len(Pr)):
    print(Pr[i], c[i])