def test_subresultants_rem():
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_rem(p, q, x) == subresultants(p, q, x)
assert subresultants_rem(p, q, x)[-1] == sylvester(p, q, x).det()
assert subresultants_rem(p, q, x) != euclid_amv(p, q, x)
amv_factors = [1, 1, -1, 1, -1, 1]
assert subresultants_rem(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_rem(p, q, x) == euclid_amv(p, q, x)
def test_subresultants_rem():
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_rem(p, q, x) == subresultants(p, q, x)
assert subresultants_rem(p, q, x)[-1] == sylvester(p, q, x).det()
assert subresultants_rem(p, q, x) != euclid_amv(p, q, x)
amv_factors = [1, 1, -1, 1, -1, 1]
assert subresultants_rem(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_rem(p, q, x) == euclid_amv(p, q, x)