def test_dmp_subresultants():
R, x, y = ring("x,y", ZZ)
assert R.dmp_resultant(0, 0) == 0
assert R.dmp_prs_resultant(0, 0)[0] == 0
assert R.dmp_zz_collins_resultant(0, 0) == 0
assert R.dmp_qq_collins_resultant(0, 0) == 0
assert R.dmp_resultant(1, 0) == 0
assert R.dmp_resultant(1, 0) == 0
assert R.dmp_resultant(1, 0) == 0
assert R.dmp_resultant(0, 1) == 0
assert R.dmp_prs_resultant(0, 1)[0] == 0
assert R.dmp_zz_collins_resultant(0, 1) == 0
assert R.dmp_qq_collins_resultant(0, 1) == 0
f = 3 * x**2 * y - y**3 - 4
g = x**2 + x * y**3 - 9
a = 3 * x * y**4 + y**3 - 27 * y + 4
b = -3 * y**10 - 12 * y**7 + y**6 - 54 * y**4 + 8 * y**3 + 729 * y**2 - 216 * y + 16
r = R.dmp_LC(b)
assert R.dmp_subresultants(f, g) == [f, g, a, b]
assert R.dmp_resultant(f, g) == r
assert R.dmp_prs_resultant(f, g)[0] == r
assert R.dmp_zz_collins_resultant(f, g) == r
assert R.dmp_qq_collins_resultant(f, g) == r
f = -x**3 + 5
g = 3 * x**2 * y + x**2
a = 45 * y**2 + 30 * y + 5
b = 675 * y**3 + 675 * y**2 + 225 * y + 25
r = R.dmp_LC(b)
assert R.dmp_subresultants(f, g) == [f, g, a]
assert R.dmp_resultant(f, g) == r
assert R.dmp_prs_resultant(f, g)[0] == r
assert R.dmp_zz_collins_resultant(f, g) == r
assert R.dmp_qq_collins_resultant(f, g) == r
R, x, y, z, u, v = ring("x,y,z,u,v", ZZ)
f = 6 * x**2 - 3 * x * y - 2 * x * z + y * z
g = x**2 - x * u - x * v + u * v
r = y**2*z**2 - 3*y**2*z*u - 3*y**2*z*v + 9*y**2*u*v - 2*y*z**2*u \
- 2*y*z**2*v + 6*y*z*u**2 + 12*y*z*u*v + 6*y*z*v**2 - 18*y*u**2*v \
- 18*y*u*v**2 + 4*z**2*u*v - 12*z*u**2*v - 12*z*u*v**2 + 36*u**2*v**2
assert R.dmp_zz_collins_resultant(f, g) == r.drop(x)
R, x, y, z, u, v = ring("x,y,z,u,v", QQ)
f = x**2 - QQ(1, 2) * x * y - QQ(1, 3) * x * z + QQ(1, 6) * y * z
g = x**2 - x * u - x * v + u * v
r = QQ(1,36)*y**2*z**2 - QQ(1,12)*y**2*z*u - QQ(1,12)*y**2*z*v + QQ(1,4)*y**2*u*v \
- QQ(1,18)*y*z**2*u - QQ(1,18)*y*z**2*v + QQ(1,6)*y*z*u**2 + QQ(1,3)*y*z*u*v \
+ QQ(1,6)*y*z*v**2 - QQ(1,2)*y*u**2*v - QQ(1,2)*y*u*v**2 + QQ(1,9)*z**2*u*v \
- QQ(1,3)*z*u**2*v - QQ(1,3)*z*u*v**2 + u**2*v**2
assert R.dmp_qq_collins_resultant(f, g) == r.drop(x)
Rt, t = ring("t", ZZ)
Rx, x = ring("x", Rt)
f = x**6 - 5 * x**4 + 5 * x**2 + 4
g = -6 * t * x**5 + x**4 + 20 * t * x**3 - 3 * x**2 - 10 * t * x + 6
assert Rx.dup_resultant(
f, g) == 2930944 * t**6 + 2198208 * t**4 + 549552 * t**2 + 45796
def test_dmp_subresultants():
R, x, y = ring("x,y", ZZ)
assert R.dmp_resultant(0, 0) == 0
assert R.dmp_prs_resultant(0, 0)[0] == 0
assert R.dmp_zz_collins_resultant(0, 0) == 0
assert R.dmp_qq_collins_resultant(0, 0) == 0
assert R.dmp_resultant(1, 0) == 0
assert R.dmp_resultant(1, 0) == 0
assert R.dmp_resultant(1, 0) == 0
assert R.dmp_resultant(0, 1) == 0
assert R.dmp_prs_resultant(0, 1)[0] == 0
assert R.dmp_zz_collins_resultant(0, 1) == 0
assert R.dmp_qq_collins_resultant(0, 1) == 0
f = 3*x**2*y - y**3 - 4
g = x**2 + x*y**3 - 9
a = 3*x*y**4 + y**3 - 27*y + 4
b = -3*y**10 - 12*y**7 + y**6 - 54*y**4 + 8*y**3 + 729*y**2 - 216*y + 16
r = R.dmp_LC(b)
assert R.dmp_subresultants(f, g) == [f, g, a, b]
assert R.dmp_resultant(f, g) == r
assert R.dmp_prs_resultant(f, g)[0] == r
assert R.dmp_zz_collins_resultant(f, g) == r
assert R.dmp_qq_collins_resultant(f, g) == r
f = -x**3 + 5
g = 3*x**2*y + x**2
a = 45*y**2 + 30*y + 5
b = 675*y**3 + 675*y**2 + 225*y + 25
r = R.dmp_LC(b)
assert R.dmp_subresultants(f, g) == [f, g, a]
assert R.dmp_resultant(f, g) == r
assert R.dmp_prs_resultant(f, g)[0] == r
assert R.dmp_zz_collins_resultant(f, g) == r
assert R.dmp_qq_collins_resultant(f, g) == r
R, x, y, z, u, v = ring("x,y,z,u,v", ZZ)
f = 6*x**2 - 3*x*y - 2*x*z + y*z
g = x**2 - x*u - x*v + u*v
r = y**2*z**2 - 3*y**2*z*u - 3*y**2*z*v + 9*y**2*u*v - 2*y*z**2*u \
- 2*y*z**2*v + 6*y*z*u**2 + 12*y*z*u*v + 6*y*z*v**2 - 18*y*u**2*v \
- 18*y*u*v**2 + 4*z**2*u*v - 12*z*u**2*v - 12*z*u*v**2 + 36*u**2*v**2
assert R.dmp_zz_collins_resultant(f, g) == r.drop(x)
R, x, y, z, u, v = ring("x,y,z,u,v", QQ)
f = x**2 - QQ(1,2)*x*y - QQ(1,3)*x*z + QQ(1,6)*y*z
g = x**2 - x*u - x*v + u*v
r = QQ(1,36)*y**2*z**2 - QQ(1,12)*y**2*z*u - QQ(1,12)*y**2*z*v + QQ(1,4)*y**2*u*v \
- QQ(1,18)*y*z**2*u - QQ(1,18)*y*z**2*v + QQ(1,6)*y*z*u**2 + QQ(1,3)*y*z*u*v \
+ QQ(1,6)*y*z*v**2 - QQ(1,2)*y*u**2*v - QQ(1,2)*y*u*v**2 + QQ(1,9)*z**2*u*v \
- QQ(1,3)*z*u**2*v - QQ(1,3)*z*u*v**2 + u**2*v**2
assert R.dmp_qq_collins_resultant(f, g) == r.drop(x)
Rt, t = ring("t", ZZ)
Rx, x = ring("x", Rt)
f = x**6 - 5*x**4 + 5*x**2 + 4
g = -6*t*x**5 + x**4 + 20*t*x**3 - 3*x**2 - 10*t*x + 6
assert Rx.dup_resultant(f, g) == 2930944*t**6 + 2198208*t**4 + 549552*t**2 + 45796
