|
|
from sympy.polys.rings import ring |
|
|
from sympy.polys.domains import ZZ |
|
|
from sympy.polys.heuristicgcd import heugcd |
|
|
|
|
|
|
|
|
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 |
|
|
|
|
|
|
|
|
|
|
|
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 |
|
|
|
|
|
|
|
|
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 test_issue_25793(): |
|
|
R, x = ring("x", ZZ) |
|
|
f = x - 4851 |
|
|
g = f*(2*x + 1) |
|
|
H, cff, cfg = R.dup_zz_heu_gcd(f, g) |
|
|
assert H == f |
|
|
|
|
|
|
