def test_zzx_gcd():
assert zzx_heu_gcd([], []) == ([], [], [])
assert zzx_mod_gcd([], []) == ([], [], [])
assert zzx_heu_gcd([2], []) == ([2], [1], [])
assert zzx_mod_gcd([2], []) == ([2], [1], [])
assert zzx_heu_gcd([], [2,4]) == ([2,4], [], [1])
assert zzx_mod_gcd([], [2,4]) == ([2,4], [], [1])
assert zzx_heu_gcd([2,4], []) == ([2,4], [1], [])
assert zzx_mod_gcd([2,4], []) == ([2,4], [1], [])
assert zzx_heu_gcd([2], [2]) == ([2], [1], [1])
assert zzx_mod_gcd([2], [2]) == ([2], [1], [1])
assert zzx_heu_gcd([1,2,1], [1]) == ([1], [1, 2, 1], [1])
assert zzx_mod_gcd([1,2,1], [1]) == ([1], [1, 2, 1], [1])
assert zzx_heu_gcd([1,2,1], [2]) == ([1], [1, 2, 1], [2])
assert zzx_mod_gcd([1,2,1], [2]) == ([1], [1, 2, 1], [2])
assert zzx_heu_gcd([2,4,2], [2]) == ([2], [1, 2, 1], [1])
assert zzx_mod_gcd([2,4,2], [2]) == ([2], [1, 2, 1], [1])
assert zzx_heu_gcd([2], [2,4,2]) == ([2], [1], [1, 2, 1])
assert zzx_mod_gcd([2], [2,4,2]) == ([2], [1], [1, 2, 1])
assert zzx_heu_gcd([2,4,2], [1,1]) == ([1, 1], [2, 2], [1])
assert zzx_mod_gcd([2,4,2], [1,1]) == ([1, 1], [2, 2], [1])
assert zzx_heu_gcd([1,1], [2,4,2]) == ([1, 1], [1], [2, 2])
assert zzx_mod_gcd([1,1], [2,4,2]) == ([1, 1], [1], [2, 2])
f, g = [1, -31], [1, 0]
assert zzx_heu_gcd(f, g) == ([1], f, g)
assert zzx_mod_gcd(f, g) == ([1], f, g)
f = [1,8,21,22,8]
g = [1,6,11,6]
h = [1,3,2]
cff = [1,5,4]
cfg = [1,3]
assert zzx_heu_gcd(f, g) == (h, cff, cfg)
assert zzx_mod_gcd(f, g) == (h, cff, cfg)
f = [1,0,0,0,-4]
g = [1,0,4,0, 4]
h = [1,0,2]
cff = [1,0,-2]
cfg = [1,0, 2]
assert zzx_heu_gcd(f, g) == (h, cff, cfg)
assert zzx_mod_gcd(f, g) == (h, cff, cfg)
assert zzx_gcd(f, g) == h
assert zzx_cofactors(f, g) == (h, cff, cfg)
f,g,h = zzX_fateman_poly_F_3(4)
H, cff, cfg = zzX_cofactors(f, g)
assert H == h and zzX_mul(H, cff) == f \
and zzX_mul(H, cfg) == g
def test_zzx_gcd():
assert zzx_heu_gcd([], []) == ([], [], [])
assert zzx_mod_gcd([], []) == ([], [], [])
assert zzx_heu_gcd([2], []) == ([2], [1], [])
assert zzx_mod_gcd([2], []) == ([2], [1], [])
assert zzx_heu_gcd([], [2, 4]) == ([2, 4], [], [1])
assert zzx_mod_gcd([], [2, 4]) == ([2, 4], [], [1])
assert zzx_heu_gcd([2, 4], []) == ([2, 4], [1], [])
assert zzx_mod_gcd([2, 4], []) == ([2, 4], [1], [])
assert zzx_heu_gcd([2], [2]) == ([2], [1], [1])
assert zzx_mod_gcd([2], [2]) == ([2], [1], [1])
assert zzx_heu_gcd([1, 2, 1], [1]) == ([1], [1, 2, 1], [1])
assert zzx_mod_gcd([1, 2, 1], [1]) == ([1], [1, 2, 1], [1])
assert zzx_heu_gcd([1, 2, 1], [2]) == ([1], [1, 2, 1], [2])
assert zzx_mod_gcd([1, 2, 1], [2]) == ([1], [1, 2, 1], [2])
assert zzx_heu_gcd([2, 4, 2], [2]) == ([2], [1, 2, 1], [1])
assert zzx_mod_gcd([2, 4, 2], [2]) == ([2], [1, 2, 1], [1])
assert zzx_heu_gcd([2], [2, 4, 2]) == ([2], [1], [1, 2, 1])
assert zzx_mod_gcd([2], [2, 4, 2]) == ([2], [1], [1, 2, 1])
assert zzx_heu_gcd([2, 4, 2], [1, 1]) == ([1, 1], [2, 2], [1])
assert zzx_mod_gcd([2, 4, 2], [1, 1]) == ([1, 1], [2, 2], [1])
assert zzx_heu_gcd([1, 1], [2, 4, 2]) == ([1, 1], [1], [2, 2])
assert zzx_mod_gcd([1, 1], [2, 4, 2]) == ([1, 1], [1], [2, 2])
f, g = [1, -31], [1, 0]
assert zzx_heu_gcd(f, g) == ([1], f, g)
assert zzx_mod_gcd(f, g) == ([1], f, g)
f = [1, 8, 21, 22, 8]
g = [1, 6, 11, 6]
h = [1, 3, 2]
cff = [1, 5, 4]
cfg = [1, 3]
assert zzx_heu_gcd(f, g) == (h, cff, cfg)
assert zzx_mod_gcd(f, g) == (h, cff, cfg)
f = [1, 0, 0, 0, -4]
g = [1, 0, 4, 0, 4]
h = [1, 0, 2]
cff = [1, 0, -2]
cfg = [1, 0, 2]
assert zzx_heu_gcd(f, g) == (h, cff, cfg)
assert zzx_mod_gcd(f, g) == (h, cff, cfg)
assert zzx_gcd(f, g) == h
assert zzx_cofactors(f, g) == (h, cff, cfg)
f, g, h = zzX_fateman_poly_F_3(4)
H, cff, cfg = zzX_cofactors(f, g)
assert H == h and zzX_mul(H, cff) == f \
and zzX_mul(H, cfg) == g
def test_zzx_gcd():
assert zzx_heu_gcd([], []) == ([], [], [])
assert zzx_mod_gcd([], []) == ([], [], [])
assert zzx_heu_gcd([2], []) == ([2], [1], [])
assert zzx_mod_gcd([2], []) == ([2], [1], [])
assert zzx_heu_gcd([2], [2]) == ([2], [1], [1])
assert zzx_mod_gcd([2], [2]) == ([2], [1], [1])
assert zzx_heu_gcd([1,2,1], [1]) == ([1], [1, 2, 1], [1])
assert zzx_mod_gcd([1,2,1], [1]) == ([1], [1, 2, 1], [1])
assert zzx_heu_gcd([1,2,1], [2]) == ([1], [1, 2, 1], [2])
assert zzx_mod_gcd([1,2,1], [2]) == ([1], [1, 2, 1], [2])
assert zzx_heu_gcd([2,4,2], [2]) == ([2], [1, 2, 1], [1])
assert zzx_mod_gcd([2,4,2], [2]) == ([2], [1, 2, 1], [1])
assert zzx_heu_gcd([2], [2,4,2]) == ([2], [1], [1, 2, 1])
assert zzx_mod_gcd([2], [2,4,2]) == ([2], [1], [1, 2, 1])
assert zzx_heu_gcd([2,4,2], [1,1]) == ([1, 1], [2, 2], [1])
assert zzx_mod_gcd([2,4,2], [1,1]) == ([1, 1], [2, 2], [1])
assert zzx_heu_gcd([1,1], [2,4,2]) == ([1, 1], [1], [2, 2])
assert zzx_mod_gcd([1,1], [2,4,2]) == ([1, 1], [1], [2, 2])
f = [1,8,21,22,8]
g = [1,6,11,6]
h = [1,3,2]
cff = [1,5,4]
cfg = [1,3]
assert zzx_heu_gcd(f, g) == (h, cff, cfg)
assert zzx_mod_gcd(f, g) == (h, cff, cfg)
f = [1,0,0,0,-4]
g = [1,0,4,0, 4]
h = [1,0,2]
cff = [1,0,-2]
cfg = [1,0, 2]
assert zzx_heu_gcd(f, g) == (h, cff, cfg)
assert zzx_mod_gcd(f, g) == (h, cff, cfg)
def test_zzx_gcd():
assert zzx_heu_gcd([], []) == ([], [], [])
assert zzx_mod_gcd([], []) == ([], [], [])
assert zzx_heu_gcd([2], []) == ([2], [1], [])
assert zzx_mod_gcd([2], []) == ([2], [1], [])
assert zzx_heu_gcd([2], [2]) == ([2], [1], [1])
assert zzx_mod_gcd([2], [2]) == ([2], [1], [1])
assert zzx_heu_gcd([1, 2, 1], [1]) == ([1], [1, 2, 1], [1])
assert zzx_mod_gcd([1, 2, 1], [1]) == ([1], [1, 2, 1], [1])
assert zzx_heu_gcd([1, 2, 1], [2]) == ([1], [1, 2, 1], [2])
assert zzx_mod_gcd([1, 2, 1], [2]) == ([1], [1, 2, 1], [2])
assert zzx_heu_gcd([2, 4, 2], [2]) == ([2], [1, 2, 1], [1])
assert zzx_mod_gcd([2, 4, 2], [2]) == ([2], [1, 2, 1], [1])
assert zzx_heu_gcd([2], [2, 4, 2]) == ([2], [1], [1, 2, 1])
assert zzx_mod_gcd([2], [2, 4, 2]) == ([2], [1], [1, 2, 1])
assert zzx_heu_gcd([2, 4, 2], [1, 1]) == ([1, 1], [2, 2], [1])
assert zzx_mod_gcd([2, 4, 2], [1, 1]) == ([1, 1], [2, 2], [1])
assert zzx_heu_gcd([1, 1], [2, 4, 2]) == ([1, 1], [1], [2, 2])
assert zzx_mod_gcd([1, 1], [2, 4, 2]) == ([1, 1], [1], [2, 2])
f = [1, 8, 21, 22, 8]
g = [1, 6, 11, 6]
h = [1, 3, 2]
cff = [1, 5, 4]
cfg = [1, 3]
assert zzx_heu_gcd(f, g) == (h, cff, cfg)
assert zzx_mod_gcd(f, g) == (h, cff, cfg)
f = [1, 0, 0, 0, -4]
g = [1, 0, 4, 0, 4]
h = [1, 0, 2]
cff = [1, 0, -2]
cfg = [1, 0, 2]
assert zzx_heu_gcd(f, g) == (h, cff, cfg)
assert zzx_mod_gcd(f, g) == (h, cff, cfg)