def test_gf_berlekamp():
f = gf_from_int_poly([1, -3, 1, -3, -1, -3, 1], 11)
Q = [[1, 0, 0, 0, 0, 0], [3, 5, 8, 8, 6, 5], [3, 6, 6, 1, 10, 0],
[9, 4, 10, 3, 7, 9], [7, 8, 10, 0, 0, 8], [8, 10, 7, 8, 10, 8]]
V = [[1, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0], [0, 0, 7, 9, 0, 1]]
assert gf_Qmatrix(f, 11, ZZ) == Q
assert gf_Qbasis(Q, 11, ZZ) == V
assert gf_berlekamp(f, 11, ZZ) == \
[[1, 1], [1, 5, 3], [1, 2, 3, 4]]
f = [1, 0, 1, 0, 10, 10, 8, 2, 8]
Q = [[1, 0, 0, 0, 0, 0, 0, 0], [2, 1, 7, 11, 10, 12, 5, 11],
[3, 6, 4, 3, 0, 4, 7, 2], [4, 3, 6, 5, 1, 6, 2, 3],
[2, 11, 8, 8, 3, 1, 3, 11], [6, 11, 8, 6, 2, 7, 10, 9],
[5, 11, 7, 10, 0, 11, 7, 12], [3, 3, 12, 5, 0, 11, 9, 12]]
V = [[1, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 0, 9, 5, 1, 0],
[0, 9, 11, 9, 10, 12, 0, 1]]
assert gf_Qmatrix(f, 13, ZZ) == Q
assert gf_Qbasis(Q, 13, ZZ) == V
assert gf_berlekamp(f, 13, ZZ) == \
[[1, 3], [1, 8, 4, 12], [1, 2, 3, 4, 6]]
def test_gf_berlekamp():
f = gf_from_int_poly([1,-3,1,-3,-1,-3,1], 11)
Q = [[1, 0, 0, 0, 0, 0],
[3, 5, 8, 8, 6, 5],
[3, 6, 6, 1,10, 0],
[9, 4,10, 3, 7, 9],
[7, 8,10, 0, 0, 8],
[8,10, 7, 8,10, 8]]
V = [[1, 0, 0, 0, 0, 0],
[0, 1, 1, 1, 1, 0],
[0, 0, 7, 9, 0, 1]]
assert gf_Qmatrix(f, 11, ZZ) == Q
assert gf_Qbasis(Q, 11, ZZ) == V
assert gf_berlekamp(f, 11, ZZ) == \
[[1, 1], [1, 5, 3], [1, 2, 3, 4]]
f = [1,0,1,0,10,10,8,2,8]
Q = [[1, 0, 0, 0, 0, 0, 0, 0],
[2, 1, 7,11,10,12, 5,11],
[3, 6, 4, 3, 0, 4, 7, 2],
[4, 3, 6, 5, 1, 6, 2, 3],
[2,11, 8, 8, 3, 1, 3,11],
[6,11, 8, 6, 2, 7,10, 9],
[5,11, 7,10, 0,11, 7,12],
[3, 3,12, 5, 0,11, 9,12]]
V = [[1, 0, 0, 0, 0, 0, 0, 0],
[0, 5, 5, 0, 9, 5, 1, 0],
[0, 9,11, 9,10,12, 0, 1]]
assert gf_Qmatrix(f, 13, ZZ) == Q
assert gf_Qbasis(Q, 13, ZZ) == V
assert gf_berlekamp(f, 13, ZZ) == \
[[1, 3], [1, 8, 4, 12], [1, 2, 3, 4, 6]]