def test_subresultants_amv():
x = var('x')
p = x**8 + x**6 - 3*x**4 - 3*x**3 + 8*x**2 + 2*x - 5
q = 3*x**6 + 5*x**4 - 4*x**2 - 9*x + 21
assert subresultants_amv(p, q, x) == subresultants(p, q, x)
assert subresultants_amv(p, q, x)[-1] == sylvester(p, q, x).det()
assert subresultants_amv(p, q, x) != euclid_amv(p, q, x)
amv_factors = [1, 1, -1, 1, -1, 1]
assert subresultants_amv(p, q, x) == [i*j for i, j in zip(amv_factors, modified_subresultants_amv(p, q, x))]
p = x**3 - 7*x + 7
q = 3*x**2 - 7
assert subresultants_amv(p, q, x) == euclid_amv(p, q, x)
def test_subresultants_amv():
x = var('x')
p = x**8 + x**6 - 3*x**4 - 3*x**3 + 8*x**2 + 2*x - 5
q = 3*x**6 + 5*x**4 - 4*x**2 - 9*x + 21
assert subresultants_amv(p, q, x) == subresultants(p, q, x)
assert subresultants_amv(p, q, x)[-1] == sylvester(p, q, x).det()
assert subresultants_amv(p, q, x) != euclid_amv(p, q, x)
amv_factors = [1, 1, -1, 1, -1, 1]
assert subresultants_amv(p, q, x) == [i*j for i, j in zip(amv_factors, modified_subresultants_amv(p, q, x))]
p = x**3 - 7*x + 7
q = 3*x**2 - 7
assert subresultants_amv(p, q, x) == euclid_amv(p, q, x)
def test_euclid_amv():
x = var('x')
p = x**3 - 7*x + 7
q = 3*x**2 - 7
assert euclid_amv(p, q, x)[-1] == sylvester(p, q, x).det()
assert euclid_amv(p, q, x) == subresultants_amv(p, q, x)
p = x**8 + x**6 - 3*x**4 - 3*x**3 + 8*x**2 + 2*x - 5
q = 3*x**6 + 5*x**4 - 4*x**2 - 9*x + 21
assert euclid_amv(p, q, x)[-1] != sylvester(p, q, x, 2).det()
sam_factors = [1, 1, -1, -1, 1, 1]
assert euclid_amv(p, q, x) == [i*j for i,j in zip(sam_factors, sturm_amv(p, q, x))]
def test_euclid_amv():
x = var('x')
p = x**3 - 7*x + 7
q = 3*x**2 - 7
assert euclid_amv(p, q, x)[-1] == sylvester(p, q, x).det()
assert euclid_amv(p, q, x) == subresultants_amv(p, q, x)
p = x**8 + x**6 - 3*x**4 - 3*x**3 + 8*x**2 + 2*x - 5
q = 3*x**6 + 5*x**4 - 4*x**2 - 9*x + 21
assert euclid_amv(p, q, x)[-1] != sylvester(p, q, x, 2).det()
sam_factors = [1, 1, -1, -1, 1, 1]
assert euclid_amv(p, q, x) == [i*j for i,j in zip(sam_factors, sturm_amv(p, q, x))]
def test_modified_subresultants_amv():
x = var('x')
p = x**8 + x**6 - 3*x**4 - 3*x**3 + 8*x**2 + 2*x - 5
q = 3*x**6 + 5*x**4 - 4*x**2 - 9*x + 21
amv_factors = [1, 1, -1, 1, -1, 1]
assert modified_subresultants_amv(p, q, x) == [i*j for i, j in zip(amv_factors, subresultants_amv(p, q, x))]
assert modified_subresultants_amv(p, q, x)[-1] != sylvester(p + x**8, q, x).det()
assert modified_subresultants_amv(p, q, x) != sturm_amv(p, q, x)
p = x**3 - 7*x + 7
q = 3*x**2 - 7
assert modified_subresultants_amv(p, q, x) == sturm_amv(p, q, x)
assert modified_subresultants_amv(-p, q, x) != sturm_amv(-p, q, x)
def test_modified_subresultants_sylv():
x = var('x')
p = x**8 + x**6 - 3*x**4 - 3*x**3 + 8*x**2 + 2*x - 5
q = 3*x**6 + 5*x**4 - 4*x**2 - 9*x + 21
amv_factors = [1, 1, -1, 1, -1, 1]
assert modified_subresultants_sylv(p, q, x) == [i*j for i, j in zip(amv_factors, subresultants_amv(p, q, x))]
assert modified_subresultants_sylv(p, q, x)[-1] != res_q(p + x**8, q, x)
assert modified_subresultants_sylv(p, q, x) != sturm_amv(p, q, x)
p = x**3 - 7*x + 7
q = 3*x**2 - 7
assert modified_subresultants_sylv(p, q, x) == sturm_amv(p, q, x)
assert modified_subresultants_sylv(-p, q, x) != sturm_amv(-p, q, x)
def test_modified_subresultants_bezout():
x = var("x")
p = x**8 + x**6 - 3 * x**4 - 3 * x**3 + 8 * x**2 + 2 * x - 5
q = 3 * x**6 + 5 * x**4 - 4 * x**2 - 9 * x + 21
amv_factors = [1, 1, -1, 1, -1, 1]
assert modified_subresultants_bezout(p, q, x) == [
i * j for i, j in zip(amv_factors, subresultants_amv(p, q, x))
]
assert (modified_subresultants_bezout(p, q, x)[-1] != sylvester(
p + x**8, q, x).det())
assert modified_subresultants_bezout(p, q, x) != sturm_amv(p, q, x)
p = x**3 - 7 * x + 7
q = 3 * x**2 - 7
assert modified_subresultants_bezout(p, q, x) == sturm_amv(p, q, x)
assert modified_subresultants_bezout(-p, q, x) != sturm_amv(-p, q, x)