def test_coeff():
assert (x + 1).coeff(x + 1) == 1
assert (3 * x).coeff(0) == 0
assert (z * (1 + x) * x ** 2).coeff(1 + x) == z * x ** 2
assert (1 + 2 * x * x ** (1 + x)).coeff(x * x ** (1 + x)) == 2
assert (1 + 2 * x ** (y + z)).coeff(x ** (y + z)) == 2
assert (3 + 2 * x + 4 * x ** 2).coeff(1) == 0
assert (3 + 2 * x + 4 * x ** 2).coeff(-1) == 0
assert (3 + 2 * x + 4 * x ** 2).coeff(x) == 2
assert (3 + 2 * x + 4 * x ** 2).coeff(x ** 2) == 4
assert (3 + 2 * x + 4 * x ** 2).coeff(x ** 3) == 0
assert (-x / 8 + x * y).coeff(x) == -S(1) / 8 + y
assert (-x / 8 + x * y).coeff(-x) == S(1) / 8
assert (4 * x).coeff(2 * x) == 0
assert (2 * x).coeff(2 * x) == 1
assert (-oo * x).coeff(x * oo) == -1
n1, n2 = symbols("n1 n2", commutative=False)
assert (n1 * n2).coeff(n1) == 1
assert (n1 * n2).coeff(n2) == n1
assert (n1 * n2 + x * n1).coeff(n1) == 1 # 1*n1*(n2+x)
assert (n2 * n1 + x * n1).coeff(n1) == n2 + x
assert (n2 * n1 + x * n1 ** 2).coeff(n1) == n2
assert (n1 ** x).coeff(n1) == 0
assert (n1 * n2 + n2 * n1).coeff(n1) == 0
assert (2 * (n1 + n2) * n2).coeff(n1 + n2, right=1) == n2
assert (2 * (n1 + n2) * n2).coeff(n1 + n2, right=0) == 2
f = Function("f")
assert (2 * f(x) + 3 * f(x).diff(x)).coeff(f(x)) == 2
expr = z * (x + y) ** 2
expr2 = z * (x + y) ** 2 + z * (2 * x + 2 * y) ** 2
assert expr.coeff(z) == (x + y) ** 2
assert expr.coeff(x + y) == 0
assert expr2.coeff(z) == (x + y) ** 2 + (2 * x + 2 * y) ** 2
assert (x + y + 3 * z).coeff(1) == x + y
assert (-x + 2 * y).coeff(-1) == x
assert (x - 2 * y).coeff(-1) == 2 * y
assert (3 + 2 * x + 4 * x ** 2).coeff(1) == 0
assert (-x - 2 * y).coeff(2) == -y
assert (x + sqrt(2) * x).coeff(sqrt(2)) == x
assert (3 + 2 * x + 4 * x ** 2).coeff(x) == 2
assert (3 + 2 * x + 4 * x ** 2).coeff(x ** 2) == 4
assert (3 + 2 * x + 4 * x ** 2).coeff(x ** 3) == 0
assert (z * (x + y) ** 2).coeff((x + y) ** 2) == z
assert (z * (x + y) ** 2).coeff(x + y) == 0
assert (2 + 2 * x + (x + 1) * y).coeff(x + 1) == y
assert (x + 2 * y + 3).coeff(1) == x
assert (x + 2 * y + 3).coeff(x, 0) == 2 * y + 3
assert (x ** 2 + 2 * y + 3 * x).coeff(x ** 2, 0) == 2 * y + 3 * x
assert x.coeff(0, 0) == 0
assert x.coeff(x, 0) == 0
n, m, o, l = symbols("n m o l", commutative=False)
assert n.coeff(n) == 1
assert y.coeff(n) == 0
assert (3 * n).coeff(n) == 3
assert (2 + n).coeff(x * m) == 0
assert (2 * x * n * m).coeff(x) == 2 * n * m
assert (2 + n).coeff(x * m * n + y) == 0
assert (2 * x * n * m).coeff(3 * n) == 0
assert (n * m + m * n * m).coeff(n) == 1 + m
assert (n * m + m * n * m).coeff(n, right=True) == m # = (1 + m)*n*m
assert (n * m + m * n).coeff(n) == 0
assert (n * m + o * m * n).coeff(m * n) == o
assert (n * m + o * m * n).coeff(m * n, right=1) == 1
assert (n * m + n * m * n).coeff(n * m, right=1) == 1 + n # = n*m*(n + 1)
def test_coeff():
assert (x + 1).coeff(x + 1) == 1
assert (3 * x).coeff(0) == None
assert (z * (1 + x) * x**2).coeff(1 + x) == z * x**2
assert (1 + 2 * x * x**(1 + x)).coeff(x * x**(1 + x)) == 2
assert (1 + 2 * x**(y + z)).coeff(x**(y + z)) == 2
assert (3 + 2 * x + 4 * x**2).coeff(1) == None
assert (3 + 2 * x + 4 * x**2).coeff(-1) == None
assert (3 + 2 * x + 4 * x**2).coeff(x) == 2
assert (3 + 2 * x + 4 * x**2).coeff(x**2) == 4
assert (3 + 2 * x + 4 * x**2).coeff(x**3) == None
assert (-x / 8 + x * y).coeff(x) == -S(1) / 8 + y
assert (-x / 8 + x * y).coeff(-x) == S(1) / 8
assert (4 * x).coeff(2 * x) == None
assert (2 * x).coeff(2 * x) == 1
n1, n2 = symbols('n1 n2', commutative=False)
assert (n1 * n2).coeff(n1) == 1
assert (n1 * n2).coeff(n2) == n1
assert (n1 * n2 + x * n1).coeff(n1) == 1 # 1*n1*(n2+x)
assert (n2 * n1 + x * n1).coeff(n1) == n2 + x
assert (n2 * n1 + x * n1**2).coeff(n1) == n2
assert (n1**x).coeff(n1) == None
assert (n1 * n2 + n2 * n1).coeff(n1) == None
assert (2 * (n1 + n2) * n2).coeff(n1 + n2, right=1) == n2
assert (2 * (n1 + n2) * n2).coeff(n1 + n2, right=0) == 2
f = Function('f')
assert (2 * f(x) + 3 * f(x).diff(x)).coeff(f(x)) == 2
expr = z * (x + y)**2
expr2 = z * (x + y)**2 + z * (2 * x + 2 * y)**2
assert expr.coeff(z) == (x + y)**2
assert expr.coeff(x + y) == None
assert expr2.coeff(z) == (x + y)**2 + (2 * x + 2 * y)**2
assert (x + y + 3 * z).coeff(1) == x + y
assert (-x + 2 * y).coeff(-1) == x
assert (x - 2 * y).coeff(-1) == 2 * y
assert (3 + 2 * x + 4 * x**2).coeff(1) == None
assert (-x - 2 * y).coeff(2) == -y
assert (x + sqrt(2) * x).coeff(sqrt(2)) == x
assert (3 + 2 * x + 4 * x**2).coeff(x) == 2
assert (3 + 2 * x + 4 * x**2).coeff(x**2) == 4
assert (3 + 2 * x + 4 * x**2).coeff(x**3) == None
assert (z * (x + y)**2).coeff((x + y)**2) == z
assert (z * (x + y)**2).coeff(x + y) == None
assert (2 + 2 * x + (x + 1) * y).coeff(x + 1) == y
n, m, o, l = symbols('n m o l', commutative=False)
assert n.coeff(n) == 1
assert y.coeff(n) == None
assert (3 * n).coeff(n) == 3
assert (2 + n).coeff(x * m) == None
assert (2 * x * n * m).coeff(x) == 2 * n * m
assert (2 + n).coeff(x * m * n + y) == None
assert (2 * x * n * m).coeff(3 * n) == None
assert (n * m + m * n * m).coeff(n) == 1 + m
assert (n * m + m * n * m).coeff(n, right=True) == m # = (1 + m)*n*m
assert (n * m + m * n).coeff(n) == None
assert (n * m + o * m * n).coeff(m * n) == o
assert (n * m + o * m * n).coeff(m * n, right=1) == 1
assert (n * m + n * m * n).coeff(n * m, right=1) == 1 + n # = n*m*(n + 1)