def test_DifferentialOperatorEqPoly():
x = symbols('x', integer=True)
R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx')
do = DifferentialOperator([x**2, R.base.zero, R.base.zero], R)
do2 = DifferentialOperator([x**2, 1, x], R)
assert not do == do2
# polynomial comparison issue, see https://github.com/sympy/sympy/pull/15799
# should work once that is solved
# p = do.listofpoly[0]
# assert do == p
p2 = do2.listofpoly[0]
assert not do2 == p2
def test_DifferentialOperator():
x = symbols('x')
R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx')
assert Dx == R.derivative_operator
assert Dx == DifferentialOperator([R.base.zero, R.base.one], R)
assert x * Dx + x**2 * Dx**2 == DifferentialOperator([0, x, x**2], R)
assert (x**2 + 1) + Dx + x * \
Dx**5 == DifferentialOperator([x**2 + 1, 1, 0, 0, 0, x], R)
assert (x * Dx + x**2 + 1 - Dx * (x**3 + x))**3 == (-48 * x**6) + \
(-57 * x**7) * Dx + (-15 * x**8) * Dx**2 + (-x**9) * Dx**3
p = (x * Dx**2 + (x**2 + 3) * Dx**5) * (Dx + x**2)
q = (2 * x) + (4 * x**2) * Dx + (x**3) * Dx**2 + \
(20 * x**2 + x + 60) * Dx**3 + (10 * x**3 + 30 * x) * Dx**4 + \
(x**4 + 3 * x**2) * Dx**5 + (x**2 + 3) * Dx**6
assert p == q