def test_modified_subresultants_pg():
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_pg(p, q, x) == [i*j for i, j in zip(amv_factors, subresultants_pg(p, q, x))]
assert modified_subresultants_pg(p, q, x)[-1] != sylvester(p + x**8, q, x).det()
assert modified_subresultants_pg(p, q, x) != sturm_pg(p, q, x)
p = x**3 - 7*x + 7
q = 3*x**2 - 7
assert modified_subresultants_pg(p, q, x) == sturm_pg(p, q, x)
assert modified_subresultants_pg(-p, q, x) != sturm_pg(-p, q, x)
def test_modified_subresultants_pg():
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_pg(p, q, x) == [i*j for i, j in zip(amv_factors, subresultants_pg(p, q, x))]
assert modified_subresultants_pg(p, q, x)[-1] != sylvester(p + x**8, q, x).det()
assert modified_subresultants_pg(p, q, x) != sturm_pg(p, q, x)
p = x**3 - 7*x + 7
q = 3*x**2 - 7
assert modified_subresultants_pg(p, q, x) == sturm_pg(p, q, x)
assert modified_subresultants_pg(-p, q, x) != sturm_pg(-p, q, x)
def test_sturm_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 sturm_amv(p, q, x)[-1] != sylvester(p, q, x, 2).det()
sam_factors = [1, 1, -1, -1, 1, 1]
assert sturm_amv(p, q, x) == [i*j for i,j in zip(sam_factors, euclid_amv(p, q, x))]
p = -9*x**5 - 5*x**3 - 9
q = -45*x**4 - 15*x**2
assert sturm_amv(p, q, x, 1)[-1] == sylvester(p, q, x, 1).det()
assert sturm_amv(p, q, x)[-1] != sylvester(p, q, x, 2).det()
assert sturm_amv(-p, q, x)[-1] == sylvester(-p, q, x, 2).det()
assert sturm_pg(-p, q, x) == modified_subresultants_pg(-p, q, x)
def test_sturm_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 sturm_amv(p, q, x)[-1] != sylvester(p, q, x, 2).det()
sam_factors = [1, 1, -1, -1, 1, 1]
assert sturm_amv(p, q, x) == [i*j for i,j in zip(sam_factors, euclid_amv(p, q, x))]
p = -9*x**5 - 5*x**3 - 9
q = -45*x**4 - 15*x**2
assert sturm_amv(p, q, x, 1)[-1] == sylvester(p, q, x, 1).det()
assert sturm_amv(p, q, x)[-1] != sylvester(p, q, x, 2).det()
assert sturm_amv(-p, q, x)[-1] == sylvester(-p, q, x, 2).det()
assert sturm_pg(-p, q, x) == modified_subresultants_pg(-p, q, x)