def test_dmp_zz_wang():
p = ZZ(nextprime(dmp_zz_mignotte_bound(w_1, 2, ZZ)))
assert p == ZZ(6291469)
t_1, k_1, e_1 = dmp_normal([[1], []], 1, ZZ), 1, ZZ(-14)
t_2, k_2, e_2 = dmp_normal([[1, 0]], 1, ZZ), 2, ZZ(3)
t_3, k_3, e_3 = dmp_normal([[1], [1, 0]], 1, ZZ), 2, ZZ(-11)
t_4, k_4, e_4 = dmp_normal([[1], [-1, 0]], 1, ZZ), 1, ZZ(-17)
T = [t_1, t_2, t_3, t_4]
K = [k_1, k_2, k_3, k_4]
E = [e_1, e_2, e_3, e_4]
T = zip(T, K)
A = [ZZ(-14), ZZ(3)]
S = dmp_eval_tail(w_1, A, 2, ZZ)
cs, s = dup_primitive(S, ZZ)
assert cs == 1 and s == S == \
dup_normal([1036728, 915552, 55748, 105621, -17304, -26841, -644], ZZ)
assert dmp_zz_wang_non_divisors(E, cs, 4, ZZ) == [7, 3, 11, 17]
assert dup_sqf_p(s, ZZ) and dup_degree(s) == dmp_degree(w_1, 2)
_, H = dup_zz_factor_sqf(s, ZZ)
h_1 = dup_normal([44, 42, 1], ZZ)
h_2 = dup_normal([126, -9, 28], ZZ)
h_3 = dup_normal([187, 0, -23], ZZ)
assert H == [h_1, h_2, h_3]
lc_1 = dmp_normal([[-4], [-4, 0]], 1, ZZ)
lc_2 = dmp_normal([[-1, 0, 0], []], 1, ZZ)
lc_3 = dmp_normal([[1], [], [-1, 0, 0]], 1, ZZ)
LC = [lc_1, lc_2, lc_3]
assert dmp_zz_wang_lead_coeffs(w_1, T, cs, E, H, A, 2, ZZ) == (w_1, H, LC)
H_1 = [
dmp_normal(t, 0, ZZ)
for t in [[44L, 42L, 1L], [126L, -9L, 28L], [187L, 0L, -23L]]
]
H_2 = [
dmp_normal(t, 1, ZZ)
for t in [[[-4, -12], [-3, 0], [1]], [[-9, 0], [-9], [-2, 0]],
[[1, 0, -9], [], [1, -9]]]
]
H_3 = [
dmp_normal(t, 1, ZZ)
for t in [[[-4, -12], [-3, 0], [1]], [[-9, 0], [-9], [-2, 0]],
[[1, 0, -9], [], [1, -9]]]
]
c_1 = dmp_normal([-70686, -5863, -17826, 2009, 5031, 74], 0, ZZ)
c_2 = dmp_normal(
[[9, 12, -45, -108, -324], [18, -216, -810, 0],
[2, 9, -252, -288, -945], [-30, -414, 0], [2, -54, -3, 81], [12, 0]],
1, ZZ)
c_3 = dmp_normal(
[[-36, -108, 0], [-27, -36, -108], [-8, -42, 0], [-6, 0, 9], [2, 0]],
1, ZZ)
T_1 = [dmp_normal(t, 0, ZZ) for t in [[-3, 0], [-2], [1]]]
T_2 = [dmp_normal(t, 1, ZZ) for t in [[[-1, 0], []], [[-3], []], [[-6]]]]
T_3 = [dmp_normal(t, 1, ZZ) for t in [[[]], [[]], [[-1]]]]
assert dmp_zz_diophantine(H_1, c_1, [], 5, p, 0, ZZ) == T_1
assert dmp_zz_diophantine(H_2, c_2, [ZZ(-14)], 5, p, 1, ZZ) == T_2
assert dmp_zz_diophantine(H_3, c_3, [ZZ(-14)], 5, p, 1, ZZ) == T_3
factors = dmp_zz_wang_hensel_lifting(w_1, H, LC, A, p, 2, ZZ)
assert dmp_expand(factors, 2, ZZ) == w_1
def test_dmp_zz_wang():
p = ZZ(nextprime(dmp_zz_mignotte_bound(w_1, 2, ZZ)))
assert p == ZZ(6291469)
t_1, k_1, e_1 = dmp_normal([[1],[]], 1, ZZ), 1, ZZ(-14)
t_2, k_2, e_2 = dmp_normal([[1, 0]], 1, ZZ), 2, ZZ(3)
t_3, k_3, e_3 = dmp_normal([[1],[ 1, 0]], 1, ZZ), 2, ZZ(-11)
t_4, k_4, e_4 = dmp_normal([[1],[-1, 0]], 1, ZZ), 1, ZZ(-17)
T = [t_1, t_2, t_3, t_4]
K = [k_1, k_2, k_3, k_4]
E = [e_1, e_2, e_3, e_4]
T = zip(T, K)
A = [ZZ(-14), ZZ(3)]
S = dmp_eval_tail(w_1, A, 2, ZZ)
cs, s = dup_primitive(S, ZZ)
assert cs == 1 and s == S == \
dup_normal([1036728, 915552, 55748, 105621, -17304, -26841, -644], ZZ)
assert dmp_zz_wang_non_divisors(E, cs, 4, ZZ) == [7, 3, 11, 17]
assert dup_sqf_p(s, ZZ) and dup_degree(s) == dmp_degree(w_1, 2)
_, H = dup_zz_factor_sqf(s, ZZ)
h_1 = dup_normal([44, 42, 1], ZZ)
h_2 = dup_normal([126, -9, 28], ZZ)
h_3 = dup_normal([187, 0, -23], ZZ)
assert H == [h_1, h_2, h_3]
lc_1 = dmp_normal([[-4], [-4,0]], 1, ZZ)
lc_2 = dmp_normal([[-1,0,0], []], 1, ZZ)
lc_3 = dmp_normal([[1], [], [-1,0,0]], 1, ZZ)
LC = [lc_1, lc_2, lc_3]
assert dmp_zz_wang_lead_coeffs(w_1, T, cs, E, H, A, 2, ZZ) == (w_1, H, LC)
H_1 = [ dmp_normal(t, 0, ZZ) for t in [[44L,42L,1L],[126L,-9L,28L],[187L,0L,-23L]] ]
H_2 = [ dmp_normal(t, 1, ZZ) for t in [[[-4,-12],[-3,0],[1]],[[-9,0],[-9],[-2,0]],[[1,0,-9],[],[1,-9]]] ]
H_3 = [ dmp_normal(t, 1, ZZ) for t in [[[-4,-12],[-3,0],[1]],[[-9,0],[-9],[-2,0]],[[1,0,-9],[],[1,-9]]] ]
c_1 = dmp_normal([-70686,-5863,-17826,2009,5031,74], 0, ZZ)
c_2 = dmp_normal([[9,12,-45,-108,-324],[18,-216,-810,0],[2,9,-252,-288,-945],[-30,-414,0],[2,-54,-3,81],[12,0]], 1, ZZ)
c_3 = dmp_normal([[-36,-108,0],[-27,-36,-108],[-8,-42,0],[-6,0,9],[2,0]], 1, ZZ)
T_1 = [ dmp_normal(t, 0, ZZ) for t in [[-3,0],[-2],[1]] ]
T_2 = [ dmp_normal(t, 1, ZZ) for t in [[[-1,0],[]],[[-3],[]],[[-6]]] ]
T_3 = [ dmp_normal(t, 1, ZZ) for t in [[[]],[[]],[[-1]]] ]
assert dmp_zz_diophantine(H_1, c_1, [], 5, p, 0, ZZ) == T_1
assert dmp_zz_diophantine(H_2, c_2, [ZZ(-14)], 5, p, 1, ZZ) == T_2
assert dmp_zz_diophantine(H_3, c_3, [ZZ(-14)], 5, p, 1, ZZ) == T_3
factors = dmp_zz_wang_hensel_lifting(w_1, H, LC, A, p, 2, ZZ)
assert dmp_expand(factors, 2, ZZ) == w_1
def test_dup_zz_factor():
assert dup_zz_factor([], ZZ) == (0, [])
assert dup_zz_factor([7], ZZ) == (7, [])
assert dup_zz_factor([-7], ZZ) == (-7, [])
assert dup_zz_factor_sqf([], ZZ) == (0, [])
assert dup_zz_factor_sqf([7], ZZ) == (7, [])
assert dup_zz_factor_sqf([-7], ZZ) == (-7, [])
assert dup_zz_factor([2,4], ZZ) == \
(2, [([1, 2], 1)])
assert dup_zz_factor_sqf([2,4], ZZ) == \
(2, [([1, 2], 1)])
f = [1, 0, 0, 1, 1]
for i in xrange(0, 20):
assert dup_zz_factor(f, ZZ) == (1, [(f, 1)])
assert dup_zz_factor([1,2,2], ZZ) == \
(1, [([1,2,2], 1)])
assert dup_zz_factor([18,12,2], ZZ) == \
(2, [([3, 1], 2)])
assert dup_zz_factor([-9,0,1], ZZ) == \
(-1, [([3,-1], 1),
([3, 1], 1)])
assert dup_zz_factor_sqf([-9,0,1], ZZ) == \
(-1, [[3,-1],
[3, 1]])
assert dup_zz_factor([1,-6,11,-6], ZZ) == \
(1, [([1,-3], 1),
([1,-2], 1),
([1,-1], 1)])
assert dup_zz_factor_sqf([1,-6,11,-6], ZZ) == \
(1, [[1,-3],
[1,-2],
[1,-1]])
assert dup_zz_factor([3,10,13,10], ZZ) == \
(1, [([1,2], 1),
([3,4,5], 1)])
assert dup_zz_factor_sqf([3,10,13,10], ZZ) == \
(1, [[1,2],
[3,4,5]])
assert dup_zz_factor([-1,0,0,0,1,0,0], ZZ) == \
(-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 dup_zz_factor(f, ZZ) == \
(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 dup_zz_factor(f, ZZ) == \
(-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 = dup_from_raw_dict({10: 1, 0: -1}, ZZ)
F_0 = dup_zz_factor(f, ZZ, cyclotomic=True)
F_1 = dup_zz_factor(f, ZZ, 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 = dup_from_raw_dict({10: 1, 0: 1}, ZZ)
F_0 = dup_zz_factor(f, ZZ, cyclotomic=True)
F_1 = dup_zz_factor(f, ZZ, cyclotomic=False)
assert F_0 == F_1 == \
(1, [([1, 0, 1], 1),
([1, 0, -1, 0, 1, 0, -1, 0, 1], 1)])
def test_dup_zz_factor():
assert dup_zz_factor([], ZZ) == (0, [])
assert dup_zz_factor([7], ZZ) == (7, [])
assert dup_zz_factor([-7], ZZ) == (-7, [])
assert dup_zz_factor_sqf([], ZZ) == (0, [])
assert dup_zz_factor_sqf([7], ZZ) == (7, [])
assert dup_zz_factor_sqf([-7], ZZ) == (-7, [])
assert dup_zz_factor([2,4], ZZ) == \
(2, [([1, 2], 1)])
assert dup_zz_factor_sqf([2,4], ZZ) == \
(2, [([1, 2], 1)])
f = [1,0,0,1,1]
for i in xrange(0, 20):
assert dup_zz_factor(f, ZZ) == (1, [(f, 1)])
assert dup_zz_factor([1,2,2], ZZ) == \
(1, [([1,2,2], 1)])
assert dup_zz_factor([18,12,2], ZZ) == \
(2, [([3, 1], 2)])
assert dup_zz_factor([-9,0,1], ZZ) == \
(-1, [([3,-1], 1),
([3, 1], 1)])
assert dup_zz_factor_sqf([-9,0,1], ZZ) == \
(-1, [[3,-1],
[3, 1]])
assert dup_zz_factor([1,-6,11,-6], ZZ) == \
(1, [([1,-3], 1),
([1,-2], 1),
([1,-1], 1)])
assert dup_zz_factor_sqf([1,-6,11,-6], ZZ) == \
(1, [[1,-3],
[1,-2],
[1,-1]])
assert dup_zz_factor([3,10,13,10], ZZ) == \
(1, [([1,2], 1),
([3,4,5], 1)])
assert dup_zz_factor_sqf([3,10,13,10], ZZ) == \
(1, [[1,2],
[3,4,5]])
assert dup_zz_factor([-1,0,0,0,1,0,0], ZZ) == \
(-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 dup_zz_factor(f, ZZ) == \
(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 dup_zz_factor(f, ZZ) == \
(-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 = dup_from_raw_dict({10:1, 0:-1}, ZZ)
config.setup('USE_CYCLOTOMIC_FACTOR', True)
F_0 = dup_zz_factor(f, ZZ)
config.setup('USE_CYCLOTOMIC_FACTOR', False)
F_1 = dup_zz_factor(f, ZZ)
assert F_0 == F_1 == \
(1, [([1,-1], 1),
([1, 1], 1),
([1,-1, 1,-1, 1], 1),
([1, 1, 1, 1, 1], 1)])
config.setup('USE_CYCLOTOMIC_FACTOR')
f = dup_from_raw_dict({10:1, 0:1}, ZZ)
config.setup('USE_CYCLOTOMIC_FACTOR', True)
F_0 = dup_zz_factor(f, ZZ)
config.setup('USE_CYCLOTOMIC_FACTOR', False)
F_1 = dup_zz_factor(f, ZZ)
assert F_0 == F_1 == \
(1, [([1, 0, 1], 1),
([1, 0, -1, 0, 1, 0, -1, 0, 1], 1)])
config.setup('USE_CYCLOTOMIC_FACTOR')
