def test_zzX_wang():
f = zzX_from_poly(W_1)
p = nextprime(zzX_mignotte_bound(f))
assert p == 6291469
V_1, k_1, E_1 = [[1],[]], 1, -14
V_2, k_2, E_2 = [[1, 0]], 2, 3
V_3, k_3, E_3 = [[1],[ 1, 0]], 2, -11
V_4, k_4, E_4 = [[1],[-1, 0]], 1, -17
V = [V_1, V_2, V_3, V_4]
K = [k_1, k_2, k_3, k_4]
E = [E_1, E_2, E_3, E_4]
V = zip(V, K)
A = [-14, 3]
U = zzX_eval_list(f, A)
cu, u = zzx_primitive(U)
assert cu == 1 and u == U == \
[1036728, 915552, 55748, 105621, -17304, -26841, -644]
assert zzX_wang_non_divisors(E, cu, 4) == [7, 3, 11, 17]
assert zzx_sqf_p(u) and zzx_degree(u) == zzX_degree(f)
_, H = zzx_factor_sqf(u)
h_1 = [44, 42, 1]
h_2 = [126, -9, 28]
h_3 = [187, 0, -23]
assert H == [h_1, h_2, h_3]
LC_1 = [[-4], [-4,0]]
LC_2 = [[-1,0,0], []]
LC_3 = [[1], [], [-1,0,0]]
LC = [LC_1, LC_2, LC_3]
assert zzX_wang_lead_coeffs(f, V, cu, E, H, A) == (f, H, LC)
H_1 = [[44L, 42L, 1L], [126L, -9L, 28L], [187L, 0L, -23L]]
C_1 = [-70686, -5863, -17826, 2009, 5031, 74]
H_2 = [[[-4, -12], [-3, 0], [1]], [[-9, 0], [-9], [-2, 0]], [[1, 0, -9], [], [1, -9]]]
C_2 = [[9, 12, -45, -108, -324], [18, -216, -810, 0], [2, 9, -252, -288, -945], [-30, -414, 0], [2, -54, -3, 81], [12, 0]]
H_3 = [[[-4, -12], [-3, 0], [1]], [[-9, 0], [-9], [-2, 0]], [[1, 0, -9], [], [1, -9]]]
C_3 = [[-36, -108, 0], [-27, -36, -108], [-8, -42, 0], [-6, 0, 9], [2, 0]]
T_1 = [[-3, 0], [-2], [1]]
T_2 = [[[-1, 0], []], [[-3], []], [[-6]]]
T_3 = [[[]], [[]], [[-1]]]
assert zzX_diophantine(H_1, C_1, [], 5, p) == T_1
assert zzX_diophantine(H_2, C_2, [-14], 5, p) == T_2
assert zzX_diophantine(H_3, C_3, [-14], 5, p) == T_3
factors = zzX_wang_hensel_lifting(f, H, LC, A, p)
f_1 = zzX_to_poly(factors[0], x, y, z)
f_2 = zzX_to_poly(factors[1], x, y, z)
f_3 = zzX_to_poly(factors[2], x, y, z)
assert f_1 == -(4*(y + z)*x**2 + x*y*z - 1).as_poly(x, y, z)
assert f_2 == -(y*z**2*x**2 + 3*x*z + 2*y).as_poly(x, y, z)
assert f_3 == ((y**2 - z**2)*x**2 + y - z**2).as_poly(x, y, z)
assert f_1*f_2*f_3 == W_1
def test_zzX_wang():
f = zzX_from_poly(W_1)
p = nextprime(zzX_mignotte_bound(f))
assert p == 6291469
V_1, k_1, E_1 = [[1], []], 1, -14
V_2, k_2, E_2 = [[1, 0]], 2, 3
V_3, k_3, E_3 = [[1], [1, 0]], 2, -11
V_4, k_4, E_4 = [[1], [-1, 0]], 1, -17
V = [V_1, V_2, V_3, V_4]
K = [k_1, k_2, k_3, k_4]
E = [E_1, E_2, E_3, E_4]
V = zip(V, K)
A = [-14, 3]
U = zzX_eval_list(f, A)
cu, u = zzx_primitive(U)
assert cu == 1 and u == U == \
[1036728, 915552, 55748, 105621, -17304, -26841, -644]
assert zzX_wang_non_divisors(E, cu, 4) == [7, 3, 11, 17]
assert zzx_sqf_p(u) and zzx_degree(u) == zzX_degree(f)
_, H = zzx_factor_sqf(u)
h_1 = [44, 42, 1]
h_2 = [126, -9, 28]
h_3 = [187, 0, -23]
assert H == [h_1, h_2, h_3]
LC_1 = [[-4], [-4, 0]]
LC_2 = [[-1, 0, 0], []]
LC_3 = [[1], [], [-1, 0, 0]]
LC = [LC_1, LC_2, LC_3]
assert zzX_wang_lead_coeffs(f, V, cu, E, H, A) == (f, H, LC)
H_1 = [[44L, 42L, 1L], [126L, -9L, 28L], [187L, 0L, -23L]]
C_1 = [-70686, -5863, -17826, 2009, 5031, 74]
H_2 = [[[-4, -12], [-3, 0], [1]], [[-9, 0], [-9], [-2, 0]],
[[1, 0, -9], [], [1, -9]]]
C_2 = [[9, 12, -45, -108, -324], [18, -216, -810, 0],
[2, 9, -252, -288, -945], [-30, -414, 0], [2, -54, -3, 81], [12, 0]]
H_3 = [[[-4, -12], [-3, 0], [1]], [[-9, 0], [-9], [-2, 0]],
[[1, 0, -9], [], [1, -9]]]
C_3 = [[-36, -108, 0], [-27, -36, -108], [-8, -42, 0], [-6, 0, 9], [2, 0]]
T_1 = [[-3, 0], [-2], [1]]
T_2 = [[[-1, 0], []], [[-3], []], [[-6]]]
T_3 = [[[]], [[]], [[-1]]]
assert zzX_diophantine(H_1, C_1, [], 5, p) == T_1
assert zzX_diophantine(H_2, C_2, [-14], 5, p) == T_2
assert zzX_diophantine(H_3, C_3, [-14], 5, p) == T_3
factors = zzX_wang_hensel_lifting(f, H, LC, A, p)
f_1 = zzX_to_poly(factors[0], x, y, z)
f_2 = zzX_to_poly(factors[1], x, y, z)
f_3 = zzX_to_poly(factors[2], x, y, z)
assert f_1 == -(4 * (y + z) * x**2 + x * y * z - 1).as_poly(x, y, z)
assert f_2 == -(y * z**2 * x**2 + 3 * x * z + 2 * y).as_poly(x, y, z)
assert f_3 == ((y**2 - z**2) * x**2 + y - z**2).as_poly(x, y, z)
assert f_1 * f_2 * f_3 == W_1
def test_zzx_factor():
assert zzx_factor([ ]) == (0, [])
assert zzx_factor([7]) == (7, [])
f = [1,0,0,1,1]
for i in xrange(0, 20):
assert zzx_factor(f) == (1, [(f, 1)])
assert zzx_factor([2,4]) == \
(2, [([1, 2], 1)])
assert zzx_factor([1,2,2]) == \
(1, [([1,2,2], 1)])
assert zzx_factor([18,12,2]) == \
(2, [([3, 1], 2)])
assert zzx_factor([-9,0,1]) == \
(-1, [([3,-1], 1),
([3, 1], 1)])
assert zzx_factor_sqf([-9,0,1]) == \
(-1, [[3,-1],
[3, 1]])
assert zzx_factor([1,-6,11,-6]) == \
(1, [([1,-3], 1),
([1,-2], 1),
([1,-1], 1)])
assert zzx_factor_sqf([1,-6,11,-6]) == \
(1, [[1,-3],
[1,-2],
[1,-1]])
assert zzx_factor([-1,0,0,0,1,0,0]) == \
(-1, [([1,-1], 1),
([1, 1], 1),
([1, 0], 2),
([1, 0, 1], 1)])
f = [1080, 5184, 2099, 744, 2736, -648, 129, 0, -324]
assert zzx_factor(f) == \
(1, [([5, 24, 9, 0, 12], 1),
([216, 0, 31, 0, -27], 1)])
f = [-29802322387695312500000000000000000000,
0, 0, 0, 0,
2980232238769531250000000000000000,
0, 0, 0, 0,
1743435859680175781250000000000,
0, 0, 0, 0,
114142894744873046875000000,
0, 0, 0, 0,
-210106372833251953125,
0, 0, 0, 0,
95367431640625]
assert zzx_factor(f) == \
(-95367431640625, [([5, -1], 1),
([100, 10, -1], 2),
([625, 125, 25, 5, 1], 1),
([10000, -3000, 400, -20, 1], 2),
([10000, 2000, 400, 30, 1], 2)])
f = zzx_from_dict({10:1, 0:-1})
F_0 = zzx_factor(f, cyclotomic=True)
F_1 = zzx_factor(f, cyclotomic=False)
assert F_0 == F_1 == \
(1, [([1,-1], 1),
([1, 1], 1),
([1,-1, 1,-1, 1], 1),
([1, 1, 1, 1, 1], 1)])
f = zzx_from_dict({10:1, 0:1})
F_0 = zzx_factor(f, cyclotomic=True)
F_1 = zzx_factor(f, cyclotomic=False)
assert F_0 == F_1 == \
(1, [([1, 0, 1], 1),
([1, 0, -1, 0, 1, 0, -1, 0, 1], 1)])
def test_zzx_factor():
assert zzx_factor([]) == (0, [])
assert zzx_factor([7]) == (7, [])
f = [1, 0, 0, 1, 1]
for i in xrange(0, 20):
assert zzx_factor(f) == (1, [(f, 1)])
assert zzx_factor([2,4]) == \
(2, [([1, 2], 1)])
assert zzx_factor([1,2,2]) == \
(1, [([1,2,2], 1)])
assert zzx_factor([18,12,2]) == \
(2, [([3, 1], 2)])
assert zzx_factor([-9,0,1]) == \
(-1, [([3,-1], 1),
([3, 1], 1)])
assert zzx_factor_sqf([-9,0,1]) == \
(-1, [[3,-1],
[3, 1]])
assert zzx_factor([1,-6,11,-6]) == \
(1, [([1,-3], 1),
([1,-2], 1),
([1,-1], 1)])
assert zzx_factor_sqf([1,-6,11,-6]) == \
(1, [[1,-3],
[1,-2],
[1,-1]])
assert zzx_factor([-1,0,0,0,1,0,0]) == \
(-1, [([1,-1], 1),
([1, 1], 1),
([1, 0], 2),
([1, 0, 1], 1)])
f = [1080, 5184, 2099, 744, 2736, -648, 129, 0, -324]
assert zzx_factor(f) == \
(1, [([5, 24, 9, 0, 12], 1),
([216, 0, 31, 0, -27], 1)])
f = [
-29802322387695312500000000000000000000, 0, 0, 0, 0,
2980232238769531250000000000000000, 0, 0, 0, 0,
1743435859680175781250000000000, 0, 0, 0, 0,
114142894744873046875000000, 0, 0, 0, 0, -210106372833251953125, 0, 0,
0, 0, 95367431640625
]
assert zzx_factor(f) == \
(-95367431640625, [([5, -1], 1),
([100, 10, -1], 2),
([625, 125, 25, 5, 1], 1),
([10000, -3000, 400, -20, 1], 2),
([10000, 2000, 400, 30, 1], 2)])
f = zzx_from_dict({10: 1, 0: -1})
F_0 = zzx_factor(f, cyclotomic=True)
F_1 = zzx_factor(f, cyclotomic=False)
assert F_0 == F_1 == \
(1, [([1,-1], 1),
([1, 1], 1),
([1,-1, 1,-1, 1], 1),
([1, 1, 1, 1, 1], 1)])
f = zzx_from_dict({10: 1, 0: 1})
F_0 = zzx_factor(f, cyclotomic=True)
F_1 = zzx_factor(f, cyclotomic=False)
assert F_0 == F_1 == \
(1, [([1, 0, 1], 1),
([1, 0, -1, 0, 1, 0, -1, 0, 1], 1)])
