from itertools import combinations
from sympy import Matrix, lcm
from fractions import Fraction

f = open('output.txt', 'w')

l1 = Matrix([[1, 0, 0, 0]])
l2 = Matrix([[1, 1, 0, 0]])
l3 = Matrix([[2, 1, 1, 0]])
l4 = Matrix([[Fraction(3, 2), Fraction(1, 2), Fraction(1, 2), Fraction(1, 2)]])

weights = [l1, l2, l3, l4]
weight_Mat = Matrix([l1, l2, l3, l4])

e1 = Matrix([[0, 1, -1, 0]])
e2 = Matrix([[0, 0, 1, -1]])
e3 = Matrix([[0, 0, 0, 1]])
e4 = Matrix([[Fraction(1, 2), Fraction(-1, 2), Fraction(-1, 2), Fraction(-1, 2)]])

basis = [e1, e2, e3, e4]

rank = len(basis)

W = [weight_Mat]

i = 0
while i != len(W):
    weight = W[i]
    for e_i in basis:
        a = weight - ((2 * (weight * e_i.T) / (e_i * e_i.T)) * e_i)
        t = False
        for elem in W:
            if a == elem:
                t = True
                break
        if not t:
            W.append(a)
    i += 1

S = weights

i = 0
while i != len(S):
    weight = S[i]
    for e_i in basis:
        a = weight - ((2 * (weight * e_i.T) / (e_i * e_i.T)) * e_i)
        t = False
        for elem in S:
            if a == elem or a == -elem:
                t = True
                break
        if not t:
            S.append(a)
    i += 1

X_set = set()
for vectors in combinations(S, rank - 1):
    A = Matrix([vectors[0], vectors[1], vectors[2]])
    if A.rank() == rank - 1:
        v = A.nullspace()[0]
        m = lcm([val.q for val in v])
        solve = m * v
        X_set.add(tuple(solve))
        X_set.add(tuple(-solve))

X_list = list()
for vector in X_set:
    X_list.append(Matrix(vector))

sep = 5

mask = [[0] * 37776] * 1152

print(mask)

for i in range(len(W)):
    for j in range(len(X_list)):
        sc_vect = W[i] * X_list[j]
        cnt_plus = 0
        for i in range(rank):
            if sc_vect[i] > 0:
                cnt_plus += 1
        if cnt_plus == rank:
            mask[i][j] = 1

f.write(str(mask))

f.close()