86 lines
1.9 KiB
Python
86 lines
1.9 KiB
Python
|
|
||
|
|
||
|
# This file was *autogenerated* from the file get_basis.sage
|
||
|
from sage.all_cmdline import * # import sage library
|
||
|
|
||
|
_sage_const_3301 = Integer(3301); _sage_const_8 = Integer(8); _sage_const_20 = Integer(20); _sage_const_0 = Integer(0); _sage_const_1 = Integer(1); _sage_const_2 = Integer(2)
|
||
|
from random import randint
|
||
|
from tqdm import tqdm
|
||
|
|
||
|
F = GF(_sage_const_3301 , names=("z", ))
|
||
|
|
||
|
f_a = list(F)
|
||
|
|
||
|
# m = 32
|
||
|
# n = 80
|
||
|
|
||
|
# m = 44
|
||
|
# n = 112
|
||
|
|
||
|
# m = 72
|
||
|
# n = 184
|
||
|
|
||
|
m = _sage_const_8
|
||
|
n = _sage_const_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(_sage_const_0 , len(P1.rows())):
|
||
|
for k in range(_sage_const_0 , j):
|
||
|
P1[j, k] = _sage_const_0
|
||
|
|
||
|
P2 = random_matrix(F, (n - m), m)
|
||
|
P3 = -O.T * P1 * O - O.T * P2
|
||
|
|
||
|
for j in range(_sage_const_0 , len(P3.rows())):
|
||
|
for k in range(j+_sage_const_1 , len(P3.rows())):
|
||
|
P3[j, k] += P3[k, j]
|
||
|
P3[k, j] = _sage_const_0
|
||
|
|
||
|
for i in P1:
|
||
|
for j in i:
|
||
|
output += hex(f_a.index(j))[_sage_const_2 :]
|
||
|
|
||
|
for i in P2:
|
||
|
for j in i:
|
||
|
output += hex(f_a.index(j))[_sage_const_2 :]
|
||
|
|
||
|
for i in P3:
|
||
|
for j in i:
|
||
|
output += hex(f_a.index(j))[_sage_const_2 :]
|
||
|
|
||
|
P = block_matrix([ [P1, P2], [z, P3]])
|
||
|
poly_m.append(P)
|
||
|
|
||
|
v = matrix(F, n, _sage_const_1 , [randint(_sage_const_0 , _sage_const_1 ) for i in range(n)])
|
||
|
|
||
|
oil_basis = block_matrix(F, _sage_const_2 , _sage_const_1 , [O, identity_matrix(F, m)])
|
||
|
|
||
|
hint = [zero_matrix(F, n, _sage_const_1 ) for i in range(_sage_const_1 )]
|
||
|
|
||
|
value = zero_matrix(F, n, _sage_const_1 )
|
||
|
|
||
|
for i in oil_basis.columns():
|
||
|
for j in range(len(hint)):
|
||
|
hint[j] += F.random_element() * matrix(F, n, _sage_const_1 , list(i))
|
||
|
value += F.random_element() * matrix(F, n, _sage_const_1 , list(i))
|
||
|
|
||
|
|
||
|
|
||
|
for P in poly_m:
|
||
|
print(value.T * (P + P.T) * hint[_sage_const_0 ])
|
||
|
|
||
|
|