def test_branch_bug():
# TODO combsimp cannot prove that the factor is unity
assert powdenest(integrate(erf(x**3), x, meijerg=True).diff(x),
polar=True) == 2*erf(x**3)*gamma(Rational(2, 3))/3/gamma(Rational(5, 3))
assert integrate(erf(x**3), x, meijerg=True) == \
2*x*erf(x**3)*gamma(Rational(2, 3))/(3*gamma(Rational(5, 3))) \
- 2*gamma(Rational(2, 3))*lowergamma(Rational(2, 3), x**6)/(3*sqrt(pi)*gamma(Rational(5, 3)))
def test_branch_bug():
# TODO combsimp cannot prove that the factor is unity
assert powdenest(integrate(erf(x**3), x, meijerg=True).diff(x),
polar=True) == 2*erf(x**3)*gamma(Rational(2, 3))/3/gamma(Rational(5, 3))
assert integrate(erf(x**3), x, meijerg=True) == \
2*x*erf(x**3)*gamma(Rational(2, 3))/(3*gamma(Rational(5, 3))) \
- 2*gamma(Rational(2, 3))*lowergamma(Rational(2, 3), x**6)/(3*sqrt(pi)*gamma(Rational(5, 3)))
def test_issue_5805():
arg = ((gamma(x) * hyper((), (), x)) * pi)**2
assert powdenest(arg) == (pi * gamma(x) * hyper((), (), x))**2
assert arg.is_positive is None
def test_powdenest_polar():
x, y, z = symbols('x y z', polar=True)
assert powdenest((x * y * z)**a) == x**a * y**a * z**a
assert powdenest((x**a * y**b)**c) == x**(a * c) * y**(b * c)
assert powdenest(((x**a)**b * y**c)**c) == x**(a * b * c) * y**(c**2)
def test_powdenest():
from diofant import powdenest
from diofant.abc import x, y, z, a, b
p, q = symbols('p q', positive=True)
i, j = symbols('i,j', integer=True)
assert powdenest(x) == x
assert powdenest(x + 2 *
(x**(2 * a / 3))**(3 * x)) == (x + 2 *
(x**(2 * a / 3))**(3 * x))
assert powdenest((exp(2 * a / 3))**(3 * x)) # -X-> (exp(a/3))**(6*x)
assert powdenest((x**(2 * a / 3))**(3 * x)) == ((x**(2 * a / 3))**(3 * x))
assert powdenest(exp(3 * x * log(2))) == 2**(3 * x)
assert powdenest(sqrt(p**2)) == p
i, j = symbols('i,j', integer=True)
eq = p**(2 * i) * q**(4 * i)
assert powdenest(eq) == (p * q**2)**(2 * i)
# -X-> (x**x)**i*(x**x)**j == x**(x*(i + j))
assert powdenest((x**x)**(i + j))
assert powdenest(exp(3 * y * log(x))) == x**(3 * y)
assert powdenest(exp(y * (log(a) + log(b)))) == (a * b)**y
assert powdenest(exp(3 * (log(a) + log(b)))) == a**3 * b**3
assert powdenest(((x**(2 * i))**(3 * y))**x) == ((x**(2 * i))**(3 * y))**x
assert powdenest(((x**(2 * i))**(3 * y))**x,
force=True) == x**(6 * i * x * y)
assert powdenest(((x**(2*a/3))**(3*y/i))**x) == \
(((x**(2*a/3))**(3*y/i))**x)
assert powdenest((x**(2 * i) * y**(4 * i))**z,
force=True) == (x * y**2)**(2 * i * z)
assert powdenest((p**(2 * i) * q**(4 * i))**j) == (p * q**2)**(2 * i * j)
e = ((p**(2 * a))**(3 * y))**x
assert powdenest(e) == e
e = ((x**2 * y**4)**a)**(x * y)
assert powdenest(e) == e
e = (((x**2 * y**4)**a)**(x * y))**3
assert powdenest(e) == ((x**2 * y**4)**a)**(3 * x * y)
assert powdenest((((x**2*y**4)**a)**(x*y)), force=True) == \
(x*y**2)**(2*a*x*y)
assert powdenest((((x**2*y**4)**a)**(x*y))**3, force=True) == \
(x*y**2)**(6*a*x*y)
assert powdenest((x**2 * y**6)**i) != (x * y**3)**(2 * i)
x, y = symbols('x,y', positive=True)
assert powdenest((x**2 * y**6)**i) == (x * y**3)**(2 * i)
assert powdenest((x**(2 * i / 3) *
y**(i / 2))**(2 * i)) == (x**Rational(4, 3) * y)**(i**2)
assert powdenest(sqrt(x**(2 * i) * y**(6 * i))) == (x * y**3)**i
assert powdenest(4**x) == 2**(2 * x)
assert powdenest((4**x)**y) == 2**(2 * x * y)
assert powdenest(4**x * y) == 2**(2 * x) * y
def test_sympyissue_5805():
arg = ((gamma(x)*hyper((), (), x))*pi)**2
assert powdenest(arg) == (pi*gamma(x)*hyper((), (), x))**2
assert arg.is_positive is None
def test_powdenest_polar():
x, y, z = symbols('x y z', polar=True)
assert powdenest((x*y*z)**a) == x**a*y**a*z**a
assert powdenest((x**a*y**b)**c) == x**(a*c)*y**(b*c)
assert powdenest(((x**a)**b*y**c)**c) == x**(a*b*c)*y**(c**2)
def test_powdenest():
x, y = symbols('x,y')
p, q = symbols('p q', positive=True)
i, j = symbols('i,j', integer=True)
assert powdenest(x) == x
assert powdenest(x + 2*(x**(2*a/3))**(3*x)) == (x + 2*(x**(2*a/3))**(3*x))
assert powdenest((exp(2*a/3))**(3*x)) # -X-> (exp(a/3))**(6*x)
assert powdenest((x**(2*a/3))**(3*x)) == ((x**(2*a/3))**(3*x))
assert powdenest(exp(3*x*log(2))) == 2**(3*x)
assert powdenest(sqrt(p**2)) == p
i, j = symbols('i,j', integer=True)
eq = p**(2*i)*q**(4*i)
assert powdenest(eq) == (p*q**2)**(2*i)
# -X-> (x**x)**i*(x**x)**j == x**(x*(i + j))
assert powdenest((x**x)**(i + j))
assert powdenest(exp(3*y*log(x))) == x**(3*y)
assert powdenest(exp(y*(log(a) + log(b)))) == (a*b)**y
assert powdenest(exp(3*(log(a) + log(b)))) == a**3*b**3
assert powdenest(((x**(2*i))**(3*y))**x) == ((x**(2*i))**(3*y))**x
assert powdenest(((x**(2*i))**(3*y))**x, force=True) == x**(6*i*x*y)
assert powdenest(((x**(2*a/3))**(3*y/i))**x) == \
(((x**(2*a/3))**(3*y/i))**x)
assert powdenest((x**(2*i)*y**(4*i))**z, force=True) == (x*y**2)**(2*i*z)
assert powdenest((p**(2*i)*q**(4*i))**j) == (p*q**2)**(2*i*j)
e = ((p**(2*a))**(3*y))**x
assert powdenest(e) == e
e = ((x**2*y**4)**a)**(x*y)
assert powdenest(e) == e
e = (((x**2*y**4)**a)**(x*y))**3
assert powdenest(e) == ((x**2*y**4)**a)**(3*x*y)
assert powdenest((((x**2*y**4)**a)**(x*y)), force=True) == \
(x*y**2)**(2*a*x*y)
assert powdenest((((x**2*y**4)**a)**(x*y))**3, force=True) == \
(x*y**2)**(6*a*x*y)
assert powdenest((x**2*y**6)**i) != (x*y**3)**(2*i)
x, y = symbols('x,y', positive=True)
assert powdenest((x**2*y**6)**i) == (x*y**3)**(2*i)
assert powdenest((x**(2*i/3)*y**(i/2))**(2*i)) == (x**Rational(4, 3)*y)**(i**2)
assert powdenest(sqrt(x**(2*i)*y**(6*i))) == (x*y**3)**i
assert powdenest(4**x) == 2**(2*x)
assert powdenest((4**x)**y) == 2**(2*x*y)
assert powdenest(4**x*y) == 2**(2*x)*y
