def test_factor_nc():
x, y = symbols('x,y')
k = symbols('k', integer=True)
n, m, o = symbols('n,m,o', commutative=False)
# mul and multinomial expansion is needed
e = x * (1 + y)**2
assert _mexpand(e) == x + x * 2 * y + x * y**2
def factor_nc_test(e):
ex = _mexpand(e)
assert ex.is_Add
f = factor_nc(ex)
assert not f.is_Add and _mexpand(f) == ex
factor_nc_test(x * (1 + y))
factor_nc_test(n * (x + 1))
factor_nc_test(n * (x + m))
factor_nc_test((x + m) * n)
factor_nc_test(n * m * (x * o + n * o * m) * n)
s = Sum(x, (x, 1, 2))
factor_nc_test(x * (1 + s))
factor_nc_test(x * (1 + s) * s)
factor_nc_test(x * (1 + sin(s)))
factor_nc_test((1 + n)**2)
factor_nc_test((x + n) * (x + m) * (x + y))
factor_nc_test(x * (n * m + 1))
factor_nc_test(x * (n * m + x))
factor_nc_test(x * (x * n * m + 1))
factor_nc_test(x * n * (x * m + 1))
factor_nc_test(x * (m * n + x * n * m))
factor_nc_test(n * (1 - m) * n**2)
factor_nc_test((n + m)**2)
factor_nc_test((n - m) * (n + m)**2)
factor_nc_test((n + m)**2 * (n - m))
factor_nc_test((m - n) * (n + m)**2 * (n - m))
assert factor_nc(n * (n + n * m)) == n**2 * (1 + m)
assert factor_nc(m * (m * n + n * m * n**2)) == m * (m + n * m * n) * n
eq = m * sin(n) - sin(n) * m
assert factor_nc(eq) == eq
eq = (sin(n) + x) * (cos(n) + x)
assert factor_nc(eq.expand()) == eq
# issue sympy/sympy#6534
assert (2 * n + 2 * m).factor() == 2 * (n + m)
# issue sympy/sympy#6701
assert factor_nc(n**k + n**(k + 1)) == n**k * (1 + n)
assert factor_nc((m * n)**k + (m * n)**(k + 1)) == (1 + m * n) * (m * n)**k
# issue sympy/sympy#6918
assert factor_nc(-n * (2 * x**2 + 2 * x)) == -2 * n * x * (x + 1)
assert factor_nc(1 + Mul(Expr(), Expr(), evaluate=False)) == 1 + Expr()**2
def test_diff_wrt_value():
assert Expr()._diff_wrt is False
assert x._diff_wrt is True
assert f(x)._diff_wrt is True
assert Derivative(f(x), x)._diff_wrt is True
assert Derivative(x**2, x)._diff_wrt is False