def test_coeff():
from sympy.abc import x, y, z
from sympy import sqrt
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)
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():
from sympy.abc import x, y, z
from sympy import sqrt
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)