def test_separatevars_advanced_factor():
    x,y,z = symbols('x,y,z')
    assert separatevars(1 + log(x)*log(y) + log(x) + log(y)) == (log(x) + 1)*(log(y) + 1)
    assert separatevars(1 + x - log(z) - x*log(z) - exp(y)*log(z) - x*exp(y)*log(z) + x*exp(y) + exp(y)) == \
        -((x + 1)*(log(z) - 1)*(exp(y) + 1))
    x, y = symbols('x,y', positive=True)
    assert separatevars(1 + log(x**log(y)) + log(x*y)) == (log(x) + 1)*(log(y) + 1)

def test_separatevars_advanced_factor():
    # If factor() is ever improved to factor non-symbolic expressions, this
    # should XPASS
    assert separatevars(1 + log(x)*log(y) + log(x) + log(y)) == (log(x) + 1)*(log(y) + 1)
    assert separatevars(1 + x - log(z) - x*log(z) - exp(y)*log(z) - \
        x*exp(y)*log(z) + x*exp(y) + exp(y)) == \
        (1 + x)*(1 - log(z))*(1 + exp(y))
    x, y = symbols('xy', positive=True)
    assert separatevars(1 + log(x**log(y)) + log(x*y)) == (log(x) + 1)*(log(y) + 1)

def test_separatevars():
    x,y,z,n = symbols('xyzn')
    assert separatevars(2*n*x*z+2*x*y*z) == 2*x*z*(n+y)
    assert separatevars(x*z+x*y*z) == x*z*(1+y)
    assert separatevars(pi*x*z+pi*x*y*z) == pi*x*z*(1+y)
    assert separatevars(x*y**2*sin(x) + x*sin(x)*sin(y)) == x*(sin(y) + y**2)*sin(x)
    assert separatevars(x*exp(x+y)+x*exp(x)) == x*(1 + exp(y))*exp(x)
    assert separatevars((x*(y+1))**z) == x**z*(1 + y)**z
    assert separatevars(1+x+y+x*y) == (x+1)*(y+1)
    assert separatevars(y / pi * exp(-(z - x) / cos(n))) == y * exp((x - z) / cos(n)) / pi
    # 1759
    p=Symbol('p',positive=True)
    assert separatevars(sqrt(p**2 + x*p**2)) == p*sqrt(1 + x)
    assert separatevars(sqrt(y*(p**2 + x*p**2))) == p*sqrt(y)*sqrt(1 + x)

def test_separatevars():
    x,y,z,n = symbols('xyzn')
    assert separatevars(2*n*x*z+2*x*y*z) == 2*x*z*(n+y)
    assert separatevars(x*z+x*y*z) == x*z*(1+y)
    assert separatevars(pi*x*z+pi*x*y*z) == pi*x*z*(1+y)
    assert separatevars(x*y**2*sin(x) + x*sin(x)*sin(y)) == x*(sin(y) + y**2)*sin(x)
    assert separatevars(x*exp(x+y)+x*exp(x)) == x*(1 + exp(y))*exp(x)
    assert separatevars((x*(y+1))**z) == x**z*(1 + y)**z
    assert separatevars(1+x+y+x*y) == (x+1)*(y+1)

def test_separatevars():
    x,y,z,n = symbols('x,y,z,n')
    assert separatevars(2*n*x*z+2*x*y*z) == 2*x*z*(n+y)
    assert separatevars(x*z+x*y*z) == x*z*(1+y)
    assert separatevars(pi*x*z+pi*x*y*z) == pi*x*z*(1+y)
    assert separatevars(x*y**2*sin(x) + x*sin(x)*sin(y)) == x*(sin(y) + y**2)*sin(x)
    assert separatevars(x*exp(x+y)+x*exp(x)) == x*(1 + exp(y))*exp(x)
    assert separatevars((x*(y+1))**z).is_Pow # != x**z*(1 + y)**z
    assert separatevars(1+x+y+x*y) == (x+1)*(y+1)
    assert separatevars(y / pi * exp(-(z - x) / cos(n))) == y * exp((x - z) / cos(n)) / pi
    # 1759
    p=Symbol('p',positive=True)
    assert separatevars(sqrt(p**2 + x*p**2)) == p*sqrt(1 + x)
    assert separatevars(sqrt(y*(p**2 + x*p**2))) == p*sqrt(y*(1 + x))
    assert separatevars(sqrt(y*(p**2 + x*p**2)), force=True) == p*sqrt(y)*sqrt(1 + x)
    # 1766
    assert separatevars(sqrt(x*y)).is_Pow
    assert separatevars(sqrt(x*y), force=True) == sqrt(x)*sqrt(y)
    # 1858
    # any type sequence for symbols is fine
    assert separatevars(((2*x+2)*y), dict=True, symbols=()) == {'coeff': 2, x: x + 1, y: y}
    # separable
    assert separatevars(((2*x+2)*y), dict=True, symbols=[]) == {'coeff': 2, x: x + 1, y: y}
    assert separatevars(((2*x+2)*y), dict=True) == {'coeff': 2, x: x + 1, y: y}
    assert separatevars(((2*x+2)*y), dict=True, symbols=None) == {'coeff': 2*y*(x + 1)}
    # not separable
    assert separatevars(2*x+y, dict=True, symbols=()) is None
    assert separatevars(2*x+y, dict=True) is None
    assert separatevars(2*x+y, dict=True, symbols=None) == {'coeff': 2*x + y}