def test_gf_from_dict():
f = {11: 12, 6: 2, 0: 25}
g = [1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3]
assert gf_from_dict(f, 11, ZZ) == g
f = {11: -5, 4: 0, 3: 1, 0: 12}
g = [6, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]
assert gf_from_dict(f, 11, ZZ) == g
def test_gf_from_dict():
f = {11: 12, 6: 2, 0: 25}
g = [1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3]
assert gf_from_dict(f, 11, ZZ) == g
f = {11: -5, 4: 0, 3: 1, 0: 12}
g = [6, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]
assert gf_from_dict(f, 11, ZZ) == g
def test_gf_squarefree():
assert gf_sqf_list([], 11, ZZ) == (0, [])
assert gf_sqf_list([1], 11, ZZ) == (1, [])
assert gf_sqf_list([1, 1], 11, ZZ) == (1, [([1, 1], 1)])
assert gf_sqf_p([], 11, ZZ) is True
assert gf_sqf_p([1], 11, ZZ) is True
assert gf_sqf_p([1, 1], 11, ZZ) is True
f = gf_from_dict({11: 1, 0: 1}, 11, ZZ)
assert gf_sqf_p(f, 11, ZZ) is False
assert gf_sqf_list(f, 11, ZZ) == \
(1, [([1, 1], 11)])
f = [1, 5, 8, 4]
assert gf_sqf_p(f, 11, ZZ) is False
assert gf_sqf_list(f, 11, ZZ) == \
(1, [([1, 1], 1),
([1, 2], 2)])
assert gf_sqf_part(f, 11, ZZ) == [1, 3, 2]
f = [1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0]
assert gf_sqf_list(f, 3, ZZ) == \
(1, [([1, 0], 1),
([1, 1], 3),
([1, 2], 6)])
def test_gf_from_to_dict():
f = {11: 12, 6: 2, 0: 25}
F = {11: 1, 6: 2, 0: 3}
g = [1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3]
assert gf_from_dict(f, 11, ZZ) == g
assert gf_to_dict(g, 11) == F
f = {11: -5, 4: 0, 3: 1, 0: 12}
F = {11: -5, 3: 1, 0: 1}
g = [6, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]
assert gf_from_dict(f, 11, ZZ) == g
assert gf_to_dict(g, 11) == F
assert gf_to_dict([10], 11, symmetric=True) == {0: -1}
assert gf_to_dict([10], 11, symmetric=False) == {0: 10}
def test_gf_ddf():
f = gf_from_dict({15: ZZ(1), 0: ZZ(-1)}, 11, ZZ)
g = [([1, 0, 0, 0, 0, 10], 1), ([1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], 2)]
assert gf_ddf_zassenhaus(f, 11, ZZ) == g
assert gf_ddf_shoup(f, 11, ZZ) == g
f = gf_from_dict({63: ZZ(1), 0: ZZ(1)}, 2, ZZ)
g = [([1, 1], 1), ([1, 1, 1], 2), ([1, 1, 1, 1, 1, 1, 1], 3),
([
1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1,
1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1,
0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1
], 6)]
assert gf_ddf_zassenhaus(f, 2, ZZ) == g
assert gf_ddf_shoup(f, 2, ZZ) == g
f = gf_from_dict({
6: ZZ(1),
5: ZZ(-1),
4: ZZ(1),
3: ZZ(1),
1: ZZ(-1)
}, 3, ZZ)
g = [([1, 1, 0], 1), ([1, 1, 0, 1, 2], 2)]
assert gf_ddf_zassenhaus(f, 3, ZZ) == g
assert gf_ddf_shoup(f, 3, ZZ) == g
f = ZZ.map([1, 2, 5, 26, 677, 436, 791, 325, 456, 24, 577])
g = [([1, 701], 1), ([1, 110, 559, 532, 694, 151, 110, 70, 735, 122], 9)]
assert gf_ddf_zassenhaus(f, 809, ZZ) == g
assert gf_ddf_shoup(f, 809, ZZ) == g
p = ZZ(nextprime(int((2**15 * pi).evalf())))
f = gf_from_dict({15: 1, 1: 1, 0: 1}, p, ZZ)
g = [([1, 22730, 68144], 2),
([1, 64876, 83977, 10787, 12561, 68608, 52650, 88001, 84356], 4),
([1, 15347, 95022, 84569, 94508, 92335], 5)]
assert gf_ddf_zassenhaus(f, p, ZZ) == g
assert gf_ddf_shoup(f, p, ZZ) == g
def test_gf_ddf():
f = gf_from_dict({15: ZZ(1), 0: ZZ(-1)}, 11, ZZ)
g = [([1, 0, 0, 0, 0, 10], 1),
([1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], 2)]
assert gf_ddf_zassenhaus(f, 11, ZZ) == g
assert gf_ddf_shoup(f, 11, ZZ) == g
f = gf_from_dict({63: ZZ(1), 0: ZZ(1)}, 2, ZZ)
g = [([1, 1], 1),
([1, 1, 1], 2),
([1, 1, 1, 1, 1, 1, 1], 3),
([1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0,
0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0,
0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1], 6)]
assert gf_ddf_zassenhaus(f, 2, ZZ) == g
assert gf_ddf_shoup(f, 2, ZZ) == g
f = gf_from_dict({6: ZZ(1), 5: ZZ(-1), 4: ZZ(1), 3: ZZ(1), 1: ZZ(-1)}, 3, ZZ)
g = [([1, 1, 0], 1),
([1, 1, 0, 1, 2], 2)]
assert gf_ddf_zassenhaus(f, 3, ZZ) == g
assert gf_ddf_shoup(f, 3, ZZ) == g
f = [1, 2, 5, 26, 677, 436, 791, 325, 456, 24, 577]
g = [([1, 701], 1),
([1, 110, 559, 532, 694, 151, 110, 70, 735, 122], 9)]
assert gf_ddf_zassenhaus(f, 809, ZZ) == g
assert gf_ddf_shoup(f, 809, ZZ) == g
p = ZZ(nextprime(int((2**15 * pi).evalf())))
f = gf_from_dict({15: 1, 1: 1, 0: 1}, p, ZZ)
g = [([1, 22730, 68144], 2),
([1, 64876, 83977, 10787, 12561, 68608, 52650, 88001, 84356], 4),
([1, 15347, 95022, 84569, 94508, 92335], 5)]
assert gf_ddf_zassenhaus(f, p, ZZ) == g
assert gf_ddf_shoup(f, p, ZZ) == g
def test_gf_factor():
assert gf_factor([], 11, ZZ) == (0, [])
assert gf_factor([1], 11, ZZ) == (1, [])
assert gf_factor([1, 1], 11, ZZ) == (1, [([1, 1], 1)])
assert gf_factor_sqf([], 11, ZZ) == (0, [])
assert gf_factor_sqf([1], 11, ZZ) == (1, [])
assert gf_factor_sqf([1, 1], 11, ZZ) == (1, [[1, 1]])
config.setup('GF_FACTOR_METHOD', 'berlekamp')
assert gf_factor_sqf([], 11, ZZ) == (0, [])
assert gf_factor_sqf([1], 11, ZZ) == (1, [])
assert gf_factor_sqf([1, 1], 11, ZZ) == (1, [[1, 1]])
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor_sqf([], 11, ZZ) == (0, [])
assert gf_factor_sqf([1], 11, ZZ) == (1, [])
assert gf_factor_sqf([1, 1], 11, ZZ) == (1, [[1, 1]])
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor_sqf(ZZ.map([]), 11, ZZ) == (0, [])
assert gf_factor_sqf(ZZ.map([1]), 11, ZZ) == (1, [])
assert gf_factor_sqf(ZZ.map([1, 1]), 11, ZZ) == (1, [[1, 1]])
f, p = ZZ.map([1, 0, 0, 1, 0]), 2
g = (1, [([1, 0], 1), ([1, 1], 1), ([1, 1, 1], 1)])
config.setup('GF_FACTOR_METHOD', 'berlekamp')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor(f, p, ZZ) == g
g = (1, [[1, 0], [1, 1], [1, 1, 1]])
config.setup('GF_FACTOR_METHOD', 'berlekamp')
assert gf_factor_sqf(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor_sqf(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor_sqf(f, p, ZZ) == g
f, p = gf_from_int_poly([1, -3, 1, -3, -1, -3, 1], 11), 11
g = (1, [([1, 1], 1), ([1, 5, 3], 1), ([1, 2, 3, 4], 1)])
config.setup('GF_FACTOR_METHOD', 'berlekamp')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor(f, p, ZZ) == g
f, p = [1, 5, 8, 4], 11
g = (1, [([1, 1], 1), ([1, 2], 2)])
config.setup('GF_FACTOR_METHOD', 'berlekamp')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor(f, p, ZZ) == g
f, p = [1, 1, 10, 1, 0, 10, 10, 10, 0, 0], 11
g = (1, [([1, 0], 2), ([1, 9, 5], 1), ([1, 3, 0, 8, 5, 2], 1)])
config.setup('GF_FACTOR_METHOD', 'berlekamp')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor(f, p, ZZ) == g
f, p = gf_from_dict({32: 1, 0: 1}, 11, ZZ), 11
g = (1, [([1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 10], 1),
([1, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 10], 1)])
config.setup('GF_FACTOR_METHOD', 'berlekamp')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor(f, p, ZZ) == g
f, p = gf_from_dict({32: ZZ(8), 0: ZZ(5)}, 11, ZZ), 11
g = (8, [([1, 3], 1), ([1, 8], 1), ([1, 0, 9], 1), ([1, 2, 2], 1),
([1, 9, 2], 1), ([1, 0, 5, 0, 7], 1), ([1, 0, 6, 0, 7], 1),
([1, 0, 0, 0, 1, 0, 0, 0, 6], 1), ([1, 0, 0, 0, 10, 0, 0, 0,
6], 1)])
config.setup('GF_FACTOR_METHOD', 'berlekamp')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor(f, p, ZZ) == g
f, p = gf_from_dict({63: ZZ(8), 0: ZZ(5)}, 11, ZZ), 11
g = (8, [([1, 7], 1), ([1, 4, 5], 1), ([1, 6, 8, 2], 1), ([1, 9, 9, 2], 1),
([1, 0, 0, 9, 0, 0, 4], 1), ([1, 2, 0, 8, 4, 6, 4], 1),
([1, 2, 3, 8, 0, 6, 4], 1), ([1, 2, 6, 0, 8, 4, 4], 1),
([1, 3, 3, 1, 6, 8, 4], 1), ([1, 5, 6, 0, 8, 6, 4], 1),
([1, 6, 2, 7, 9, 8, 4], 1), ([1, 10, 4, 7, 10, 7, 4], 1),
([1, 10, 10, 1, 4, 9, 4], 1)])
config.setup('GF_FACTOR_METHOD', 'berlekamp')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor(f, p, ZZ) == g
# Gathen polynomials: x**n + x + 1 (mod p > 2**n * pi)
p = ZZ(nextprime(int((2**15 * pi).evalf())))
f = gf_from_dict({15: 1, 1: 1, 0: 1}, p, ZZ)
assert gf_sqf_p(f, p, ZZ) is True
g = (1, [([1, 22730, 68144], 1), ([1, 81553, 77449, 86810, 4724], 1),
([1, 86276, 56779, 14859, 31575], 1),
([1, 15347, 95022, 84569, 94508, 92335], 1)])
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor(f, p, ZZ) == g
g = (1, [[1, 22730, 68144], [1, 81553, 77449, 86810, 4724],
[1, 86276, 56779, 14859, 31575],
[1, 15347, 95022, 84569, 94508, 92335]])
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor_sqf(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor_sqf(f, p, ZZ) == g
# Shoup polynomials: f = a_0 x**n + a_1 x**(n-1) + ... + a_n
# (mod p > 2**(n-2) * pi), where a_n = a_{n-1}**2 + 1, a_0 = 1
p = ZZ(nextprime(int((2**4 * pi).evalf())))
f = ZZ.map([1, 2, 5, 26, 41, 39, 38])
assert gf_sqf_p(f, p, ZZ) is True
g = (1, [([1, 44, 26], 1), ([1, 11, 25, 18, 30], 1)])
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor(f, p, ZZ) == g
g = (1, [[1, 44, 26], [1, 11, 25, 18, 30]])
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor_sqf(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor_sqf(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'other')
pytest.raises(KeyError, lambda: gf_factor([1, 1], 11, ZZ))
config.setup('GF_FACTOR_METHOD')
def test_gf_factor_sqf():
assert gf_factor_sqf([], 11, ZZ) == (0, [])
assert gf_factor_sqf([1], 11, ZZ) == (1, [])
assert gf_factor_sqf([1, 1], 11, ZZ) == (1, [[1, 1]])
assert gf_factor_sqf([2, 3], 11, ZZ) == (2, [[1, 7]])
with config.using(gf_factor_method='berlekamp'):
assert gf_factor_sqf([], 11, ZZ) == (0, [])
assert gf_factor_sqf([1], 11, ZZ) == (1, [])
assert gf_factor_sqf([1, 1], 11, ZZ) == (1, [[1, 1]])
assert gf_factor_sqf([1, 0], 11, ZZ) == (1, [[1, 0]])
with config.using(gf_factor_method='zassenhaus'):
assert gf_factor_sqf([], 11, ZZ) == (0, [])
assert gf_factor_sqf([1], 11, ZZ) == (1, [])
assert gf_factor_sqf([1, 1], 11, ZZ) == (1, [[1, 1]])
assert gf_factor_sqf([1, 0], 11, ZZ) == (1, [[1, 0]])
with config.using(gf_factor_method='shoup'):
assert gf_factor_sqf([], 11, ZZ) == (0, [])
assert gf_factor_sqf([1], 11, ZZ) == (1, [])
assert gf_factor_sqf([1, 1], 11, ZZ) == (1, [[1, 1]])
assert gf_factor_sqf([1, 0], 11, ZZ) == (1, [[1, 0]])
f, p = [1, 0, 0, 1, 0], 2
g = (1, [[1, 0],
[1, 1],
[1, 1, 1]])
with config.using(gf_factor_method='berlekamp'):
assert gf_factor_sqf(f, p, ZZ) == g
with config.using(gf_factor_method='zassenhaus'):
assert gf_factor_sqf(f, p, ZZ) == g
with config.using(gf_factor_method='shoup'):
assert gf_factor_sqf(f, p, ZZ) == g
# Gathen polynomials: x**n + x + 1 (mod p > 2**n * pi)
p = ZZ(nextprime(int((2**15*pi))))
f = gf_from_dict({15: 1, 1: 1, 0: 1}, p, ZZ)
g = (1, [[1, 22730, 68144],
[1, 81553, 77449, 86810, 4724],
[1, 86276, 56779, 14859, 31575],
[1, 15347, 95022, 84569, 94508, 92335]])
with config.using(gf_factor_method='zassenhaus'):
assert gf_factor_sqf(f, p, ZZ) == g
with config.using(gf_factor_method='shoup'):
assert gf_factor_sqf(f, p, ZZ) == g
# Shoup polynomials: f = a_0 x**n + a_1 x**(n-1) + ... + a_n
# (mod p > 2**(n-2) * pi), where a_n = a_{n-1}**2 + 1, a_0 = 1
p = ZZ(nextprime(int((2**4*pi))))
f = [1, 2, 5, 26, 41, 39, 38]
g = (1, [[1, 44, 26],
[1, 11, 25, 18, 30]])
with config.using(gf_factor_method='zassenhaus'):
assert gf_factor_sqf(f, p, ZZ) == g
with config.using(gf_factor_method='shoup'):
assert gf_factor_sqf(f, p, ZZ) == g
def test_gf_factor():
assert gf_factor([], 11, ZZ) == (0, [])
assert gf_factor([1], 11, ZZ) == (1, [])
assert gf_factor([1, 1], 11, ZZ) == (1, [([1, 1], 1)])
assert gf_factor_sqf([], 11, ZZ) == (0, [])
assert gf_factor_sqf([1], 11, ZZ) == (1, [])
assert gf_factor_sqf([1, 1], 11, ZZ) == (1, [[1, 1]])
config.setup('GF_FACTOR_METHOD', 'berlekamp')
assert gf_factor_sqf([], 11, ZZ) == (0, [])
assert gf_factor_sqf([1], 11, ZZ) == (1, [])
assert gf_factor_sqf([1, 1], 11, ZZ) == (1, [[1, 1]])
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor_sqf([], 11, ZZ) == (0, [])
assert gf_factor_sqf([1], 11, ZZ) == (1, [])
assert gf_factor_sqf([1, 1], 11, ZZ) == (1, [[1, 1]])
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor_sqf([], 11, ZZ) == (0, [])
assert gf_factor_sqf([1], 11, ZZ) == (1, [])
assert gf_factor_sqf([1, 1], 11, ZZ) == (1, [[1, 1]])
f, p = [1, 0, 0, 1, 0], 2
g = (1, [([1, 0], 1),
([1, 1], 1),
([1, 1, 1], 1)])
config.setup('GF_FACTOR_METHOD', 'berlekamp')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor(f, p, ZZ) == g
g = (1, [[1, 0],
[1, 1],
[1, 1, 1]])
config.setup('GF_FACTOR_METHOD', 'berlekamp')
assert gf_factor_sqf(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor_sqf(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor_sqf(f, p, ZZ) == g
f, p = gf_from_int_poly([1, -3, 1, -3, -1, -3, 1], 11), 11
g = (1, [([1, 1], 1),
([1, 5, 3], 1),
([1, 2, 3, 4], 1)])
config.setup('GF_FACTOR_METHOD', 'berlekamp')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor(f, p, ZZ) == g
f, p = [1, 5, 8, 4], 11
g = (1, [([1, 1], 1), ([1, 2], 2)])
config.setup('GF_FACTOR_METHOD', 'berlekamp')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor(f, p, ZZ) == g
f, p = [1, 1, 10, 1, 0, 10, 10, 10, 0, 0], 11
g = (1, [([1, 0], 2), ([1, 9, 5], 1), ([1, 3, 0, 8, 5, 2], 1)])
config.setup('GF_FACTOR_METHOD', 'berlekamp')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor(f, p, ZZ) == g
f, p = gf_from_dict({32: 1, 0: 1}, 11, ZZ), 11
g = (1, [([1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 10], 1),
([1, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 10], 1)])
config.setup('GF_FACTOR_METHOD', 'berlekamp')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor(f, p, ZZ) == g
f, p = gf_from_dict({32: ZZ(8), 0: ZZ(5)}, 11, ZZ), 11
g = (8, [([1, 3], 1),
([1, 8], 1),
([1, 0, 9], 1),
([1, 2, 2], 1),
([1, 9, 2], 1),
([1, 0, 5, 0, 7], 1),
([1, 0, 6, 0, 7], 1),
([1, 0, 0, 0, 1, 0, 0, 0, 6], 1),
([1, 0, 0, 0, 10, 0, 0, 0, 6], 1)])
config.setup('GF_FACTOR_METHOD', 'berlekamp')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor(f, p, ZZ) == g
f, p = gf_from_dict({63: ZZ(8), 0: ZZ(5)}, 11, ZZ), 11
g = (8, [([1, 7], 1),
([1, 4, 5], 1),
([1, 6, 8, 2], 1),
([1, 9, 9, 2], 1),
([1, 0, 0, 9, 0, 0, 4], 1),
([1, 2, 0, 8, 4, 6, 4], 1),
([1, 2, 3, 8, 0, 6, 4], 1),
([1, 2, 6, 0, 8, 4, 4], 1),
([1, 3, 3, 1, 6, 8, 4], 1),
([1, 5, 6, 0, 8, 6, 4], 1),
([1, 6, 2, 7, 9, 8, 4], 1),
([1, 10, 4, 7, 10, 7, 4], 1),
([1, 10, 10, 1, 4, 9, 4], 1)])
config.setup('GF_FACTOR_METHOD', 'berlekamp')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor(f, p, ZZ) == g
# Gathen polynomials: x**n + x + 1 (mod p > 2**n * pi)
p = ZZ(nextprime(int((2**15 * pi).evalf())))
f = gf_from_dict({15: 1, 1: 1, 0: 1}, p, ZZ)
g = (1, [([1, 22730, 68144], 1),
([1, 81553, 77449, 86810, 4724], 1),
([1, 86276, 56779, 14859, 31575], 1),
([1, 15347, 95022, 84569, 94508, 92335], 1)])
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor(f, p, ZZ) == g
g = (1, [[1, 22730, 68144],
[1, 81553, 77449, 86810, 4724],
[1, 86276, 56779, 14859, 31575],
[1, 15347, 95022, 84569, 94508, 92335]])
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor_sqf(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor_sqf(f, p, ZZ) == g
# Shoup polynomials: f = a_0 x**n + a_1 x**(n-1) + ... + a_n
# (mod p > 2**(n-2) * pi), where a_n = a_{n-1}**2 + 1, a_0 = 1
p = ZZ(nextprime(int((2**4 * pi).evalf())))
f = [1, 2, 5, 26, 41, 39, 38]
g = (1, [([1, 44, 26], 1),
([1, 11, 25, 18, 30], 1)])
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor(f, p, ZZ) == g
g = (1, [[1, 44, 26],
[1, 11, 25, 18, 30]])
config.setup('GF_FACTOR_METHOD', 'zassenhaus')
assert gf_factor_sqf(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'shoup')
assert gf_factor_sqf(f, p, ZZ) == g
config.setup('GF_FACTOR_METHOD', 'other')
pytest.raises(KeyError, lambda: gf_factor([1, 1], 11, ZZ))
config.setup('GF_FACTOR_METHOD')
# IPoly interface:
R, t = ring("t", FF(11))
assert R.gf_factor_sqf(2*t + 3) == (2, [t + 7])