def test_heugcd_univariate_integers():
R, x = ring("x", ZZ)
f = x**4 + 8 * x**3 + 21 * x**2 + 22 * x + 8
g = x**3 + 6 * x**2 + 11 * x + 6
h = x**2 + 3 * x + 2
cff = x**2 + 5 * x + 4
cfg = x + 3
assert heugcd(f, g) == (h, cff, cfg)
f = x**4 - 4
g = x**4 + 4 * x**2 + 4
h = x**2 + 2
cff = x**2 - 2
cfg = x**2 + 2
assert heugcd(f, g) == (h, cff, cfg)
f = x**8 + x**6 - 3 * x**4 - 3 * x**3 + 8 * x**2 + 2 * x - 5
g = 3 * x**6 + 5 * x**4 - 4 * x**2 - 9 * x + 21
h = 1
cff = f
cfg = g
assert heugcd(f, g) == (h, cff, cfg)
f = - 352518131239247345597970242177235495263669787845475025293906825864749649589178600387510272*x**49 \
+ 46818041807522713962450042363465092040687472354933295397472942006618953623327997952*x**42 \
+ 378182690892293941192071663536490788434899030680411695933646320291525827756032*x**35 \
+ 112806468807371824947796775491032386836656074179286744191026149539708928*x**28 \
- 12278371209708240950316872681744825481125965781519138077173235712*x**21 \
+ 289127344604779611146960547954288113529690984687482920704*x**14 \
+ 19007977035740498977629742919480623972236450681*x**7 \
+ 311973482284542371301330321821976049
g = 365431878023781158602430064717380211405897160759702125019136*x**21 \
+ 197599133478719444145775798221171663643171734081650688*x**14 \
- 9504116979659010018253915765478924103928886144*x**7 \
- 311973482284542371301330321821976049
# TODO: assert heugcd(f, f.diff(x))[0] == g
f = 1317378933230047068160 * x + 2945748836994210856960
g = 120352542776360960 * x + 269116466014453760
h = 120352542776360960 * x + 269116466014453760
cff = 10946
cfg = 1
assert heugcd(f, g) == (h, cff, cfg)
def test_issue_10996():
R, x, y, z = ring("x,y,z", ZZ)
f = (
12 * x ** 6 * y ** 7 * z ** 3
- 3 * x ** 4 * y ** 9 * z ** 3
+ 12 * x ** 3 * y ** 5 * z ** 4
)
g = (
-48 * x ** 7 * y ** 8 * z ** 3
+ 12 * x ** 5 * y ** 10 * z ** 3
- 48 * x ** 5 * y ** 7 * z ** 2
+ 36 * x ** 4 * y ** 7 * z
- 48 * x ** 4 * y ** 6 * z ** 4
+ 12 * x ** 3 * y ** 9 * z ** 2
- 48 * x ** 3 * y ** 4
- 9 * x ** 2 * y ** 9 * z
- 48 * x ** 2 * y ** 5 * z ** 3
+ 12 * x * y ** 6
+ 36 * x * y ** 5 * z ** 2
- 48 * y ** 2 * z
)
H, cff, cfg = heugcd(f, g)
assert H == 12 * x ** 3 * y ** 4 - 3 * x * y ** 6 + 12 * y ** 2 * z
assert H * cff == f and H * cfg == g
def _gcd_ZZ(f, g):
return heugcd(f, g)
def test_heugcd_multivariate_integers():
R, x, y = ring("x,y", ZZ)
f, g = 2 * x ** 2 + 4 * x + 2, x + 1
assert heugcd(f, g) == (x + 1, 2 * x + 2, 1)
f, g = x + 1, 2 * x ** 2 + 4 * x + 2
assert heugcd(f, g) == (x + 1, 1, 2 * x + 2)
R, x, y, z, u = ring("x,y,z,u", ZZ)
f, g = u ** 2 + 2 * u + 1, 2 * u + 2
assert heugcd(f, g) == (u + 1, u + 1, 2)
f, g = z ** 2 * u ** 2 + 2 * z ** 2 * u + z ** 2 + z * u + z, u ** 2 + 2 * u + 1
h, cff, cfg = u + 1, z ** 2 * u + z ** 2 + z, u + 1
assert heugcd(f, g) == (h, cff, cfg)
assert heugcd(g, f) == (h, cfg, cff)
R, x, y, z = ring("x,y,z", ZZ)
f, g, h = R.fateman_poly_F_1()
H, cff, cfg = heugcd(f, g)
assert H == h and H * cff == f and H * cfg == g
R, x, y, z, u, v = ring("x,y,z,u,v", ZZ)
f, g, h = R.fateman_poly_F_1()
H, cff, cfg = heugcd(f, g)
assert H == h and H * cff == f and H * cfg == g
R, x, y, z, u, v, a, b = ring("x,y,z,u,v,a,b", ZZ)
f, g, h = R.fateman_poly_F_1()
H, cff, cfg = heugcd(f, g)
assert H == h and H * cff == f and H * cfg == g
R, x, y, z, u, v, a, b, c, d = ring("x,y,z,u,v,a,b,c,d", ZZ)
f, g, h = R.fateman_poly_F_1()
H, cff, cfg = heugcd(f, g)
assert H == h and H * cff == f and H * cfg == g
R, x, y, z = ring("x,y,z", ZZ)
f, g, h = R.fateman_poly_F_2()
H, cff, cfg = heugcd(f, g)
assert H == h and H * cff == f and H * cfg == g
f, g, h = R.fateman_poly_F_3()
H, cff, cfg = heugcd(f, g)
assert H == h and H * cff == f and H * cfg == g
R, x, y, z, t = ring("x,y,z,t", ZZ)
f, g, h = R.fateman_poly_F_3()
H, cff, cfg = heugcd(f, g)
assert H == h and H * cff == f and H * cfg == g
def test_heugcd_univariate_integers():
R, x = ring("x", ZZ)
f = x ** 4 + 8 * x ** 3 + 21 * x ** 2 + 22 * x + 8
g = x ** 3 + 6 * x ** 2 + 11 * x + 6
h = x ** 2 + 3 * x + 2
cff = x ** 2 + 5 * x + 4
cfg = x + 3
assert heugcd(f, g) == (h, cff, cfg)
f = x ** 4 - 4
g = x ** 4 + 4 * x ** 2 + 4
h = x ** 2 + 2
cff = x ** 2 - 2
cfg = x ** 2 + 2
assert heugcd(f, g) == (h, cff, cfg)
f = x ** 8 + x ** 6 - 3 * x ** 4 - 3 * x ** 3 + 8 * x ** 2 + 2 * x - 5
g = 3 * x ** 6 + 5 * x ** 4 - 4 * x ** 2 - 9 * x + 21
h = 1
cff = f
cfg = g
assert heugcd(f, g) == (h, cff, cfg)
f = (
-352518131239247345597970242177235495263669787845475025293906825864749649589178600387510272 * x ** 49
+ 46818041807522713962450042363465092040687472354933295397472942006618953623327997952 * x ** 42
+ 378182690892293941192071663536490788434899030680411695933646320291525827756032 * x ** 35
+ 112806468807371824947796775491032386836656074179286744191026149539708928 * x ** 28
- 12278371209708240950316872681744825481125965781519138077173235712 * x ** 21
+ 289127344604779611146960547954288113529690984687482920704 * x ** 14
+ 19007977035740498977629742919480623972236450681 * x ** 7
+ 311973482284542371301330321821976049
)
g = (
365431878023781158602430064717380211405897160759702125019136 * x ** 21
+ 197599133478719444145775798221171663643171734081650688 * x ** 14
- 9504116979659010018253915765478924103928886144 * x ** 7
- 311973482284542371301330321821976049
)
# TODO: assert heugcd(f, f.diff(x))[0] == g
f = 1317378933230047068160 * x + 2945748836994210856960
g = 120352542776360960 * x + 269116466014453760
h = 120352542776360960 * x + 269116466014453760
cff = 10946
cfg = 1
assert heugcd(f, g) == (h, cff, cfg)
def test_heugcd_multivariate_integers():
R, x, y = ring("x,y", ZZ)
f, g = 2 * x**2 + 4 * x + 2, x + 1
assert heugcd(f, g) == (x + 1, 2 * x + 2, 1)
f, g = x + 1, 2 * x**2 + 4 * x + 2
assert heugcd(f, g) == (x + 1, 1, 2 * x + 2)
R, x, y, z, u = ring("x,y,z,u", ZZ)
f, g = u**2 + 2 * u + 1, 2 * u + 2
assert heugcd(f, g) == (u + 1, u + 1, 2)
f, g = z**2 * u**2 + 2 * z**2 * u + z**2 + z * u + z, u**2 + 2 * u + 1
h, cff, cfg = u + 1, z**2 * u + z**2 + z, u + 1
assert heugcd(f, g) == (h, cff, cfg)
assert heugcd(g, f) == (h, cfg, cff)
R, x, y, z = ring("x,y,z", ZZ)
f, g, h = R.fateman_poly_F_1()
H, cff, cfg = heugcd(f, g)
assert H == h and H * cff == f and H * cfg == g
R, x, y, z, u, v = ring("x,y,z,u,v", ZZ)
f, g, h = R.fateman_poly_F_1()
H, cff, cfg = heugcd(f, g)
assert H == h and H * cff == f and H * cfg == g
R, x, y, z, u, v, a, b = ring("x,y,z,u,v,a,b", ZZ)
f, g, h = R.fateman_poly_F_1()
H, cff, cfg = heugcd(f, g)
assert H == h and H * cff == f and H * cfg == g
R, x, y, z, u, v, a, b, c, d = ring("x,y,z,u,v,a,b,c,d", ZZ)
f, g, h = R.fateman_poly_F_1()
H, cff, cfg = heugcd(f, g)
assert H == h and H * cff == f and H * cfg == g
R, x, y, z = ring("x,y,z", ZZ)
f, g, h = R.fateman_poly_F_2()
H, cff, cfg = heugcd(f, g)
assert H == h and H * cff == f and H * cfg == g
f, g, h = R.fateman_poly_F_3()
H, cff, cfg = heugcd(f, g)
assert H == h and H * cff == f and H * cfg == g
R, x, y, z, t = ring("x,y,z,t", ZZ)
f, g, h = R.fateman_poly_F_3()
H, cff, cfg = heugcd(f, g)
assert H == h and H * cff == f and H * cfg == g
