from random import randint
from tqdm import tqdm

F = GF(3301, names=("z", ))

f_a = list(F)

# m = 32
# n = 80

# m = 44
# n = 112

# m = 72
# n = 184

m = 8
n = 20

# m = 2
# n = 5

O = random_matrix(F, (n - m), m)

output = ""
poly_m = []

z = zero_matrix(F, m, (n - m))

for i in range(m):

    P1 = random_matrix(F, (n - m), (n - m))

    for j in range(0, len(P1.rows())):
        for k in range(0, j):
            P1[j, k] = 0

    P2 = random_matrix(F, (n - m), m)
    P3 = -O.T * P1 * O - O.T * P2

    for j in range(0, len(P3.rows())):
        for k in range(j+1, len(P3.rows())):
            P3[j, k] += P3[k, j]
            P3[k, j] = 0

    for i in P1:
        for j in i:
            output += hex(f_a.index(j))[2:]

    for i in P2:
        for j in i:
            output += hex(f_a.index(j))[2:]

    for i in P3:
        for j in i:
            output += hex(f_a.index(j))[2:]

    P = block_matrix([ [P1, P2], [z, P3]])
    poly_m.append(P)

v = matrix(F, n, 1, [randint(0, 1) for i in range(n)])

oil_basis = block_matrix(F, 2, 1, [O, identity_matrix(F, m)])

hint = [zero_matrix(F, n, 1) for i in range(1)]

value = zero_matrix(F, n, 1)

for i in oil_basis.columns():
  for j in range(len(hint)):
    hint[j] += F.random_element() * matrix(F, n, 1, list(i))
  value += F.random_element() * matrix(F, n, 1, list(i))