def test_PolyElement_cofactors():
R, x, y = ring("x,y", ZZ)
f, g = R(0), R(0)
assert f.cofactors(g) == (0, 0, 0)
f, g = R(2), R(0)
assert f.cofactors(g) == (2, 1, 0)
f, g = R(-2), R(0)
assert f.cofactors(g) == (2, -1, 0)
f, g = R(0), R(-2)
assert f.cofactors(g) == (2, 0, -1)
f, g = R(0), 2*x + 4
assert f.cofactors(g) == (2*x + 4, 0, 1)
f, g = 2*x + 4, R(0)
assert f.cofactors(g) == (2*x + 4, 1, 0)
f, g = R(2), R(2)
assert f.cofactors(g) == (2, 1, 1)
f, g = R(-2), R(2)
assert f.cofactors(g) == (2, -1, 1)
f, g = R(2), R(-2)
assert f.cofactors(g) == (2, 1, -1)
f, g = R(-2), R(-2)
assert f.cofactors(g) == (2, -1, -1)
f, g = x**2 + 2*x + 1, R(1)
assert f.cofactors(g) == (1, x**2 + 2*x + 1, 1)
f, g = x**2 + 2*x + 1, R(2)
assert f.cofactors(g) == (1, x**2 + 2*x + 1, 2)
f, g = 2*x**2 + 4*x + 2, R(2)
assert f.cofactors(g) == (2, x**2 + 2*x + 1, 1)
f, g = R(2), 2*x**2 + 4*x + 2
assert f.cofactors(g) == (2, 1, x**2 + 2*x + 1)
f, g = 2*x**2 + 4*x + 2, x + 1
assert f.cofactors(g) == (x + 1, 2*x + 2, 1)
f, g = x + 1, 2*x**2 + 4*x + 2
assert f.cofactors(g) == (x + 1, 1, 2*x + 2)
R, x, y, z, t = ring("x,y,z,t", ZZ)
f, g = t**2 + 2*t + 1, 2*t + 2
assert f.cofactors(g) == (t + 1, t + 1, 2)
f, g = z**2*t**2 + 2*z**2*t + z**2 + z*t + z, t**2 + 2*t + 1
h, cff, cfg = t + 1, z**2*t + z**2 + z, t + 1
assert f.cofactors(g) == (h, cff, cfg)
assert g.cofactors(f) == (h, cfg, cff)
R, x, y = ring("x,y", QQ)
f = QQ(1,2)*x**2 + x + QQ(1,2)
g = QQ(1,2)*x + QQ(1,2)
h = x + 1
assert f.cofactors(g) == (h, g, QQ(1,2))
assert g.cofactors(f) == (h, QQ(1,2), g)
R, x, y = ring("x,y", RR)
f = 2.1*x*y**2 - 2.1*x*y + 2.1*x
g = 2.1*x**3
h = 1.0*x
assert f.cofactors(g) == (h, f/h, g/h)
assert g.cofactors(f) == (h, g/h, f/h)
