def test_factorial():
n = Symbol('n', integer=True)
assert str(factorial(-2)) == "zoo"
assert str(factorial(0)) == "1"
assert str(factorial(7)) == "5040"
assert str(factorial(n)) == "factorial(n)"
assert str(factorial(2 * n)) == "factorial(2*n)"
assert str(factorial(factorial(n))) == 'factorial(factorial(n))'
assert str(factorial(factorial2(n))) == 'factorial(factorial2(n))'
assert str(factorial2(factorial(n))) == 'factorial2(factorial(n))'
assert str(factorial2(factorial2(n))) == 'factorial2(factorial2(n))'
assert str(subfactorial(3)) == "2"
assert str(subfactorial(n)) == "subfactorial(n)"
assert str(subfactorial(2 * n)) == "subfactorial(2*n)"
def test_factorial():
n = Symbol('n', integer=True)
assert str(factorial(-2)) == 'zoo'
assert str(factorial(0)) == '1'
assert str(factorial(7)) == '5040'
assert str(factorial(n)) == 'factorial(n)'
assert str(factorial(2 * n)) == 'factorial(2*n)'
assert str(factorial(factorial(n))) == 'factorial(factorial(n))'
assert str(factorial(factorial2(n))) == 'factorial(factorial2(n))'
assert str(factorial2(factorial(n))) == 'factorial2(factorial(n))'
assert str(factorial2(factorial2(n))) == 'factorial2(factorial2(n))'
assert str(subfactorial(3)) == '2'
assert str(subfactorial(n)) == 'subfactorial(n)'
assert str(subfactorial(2 * n)) == 'subfactorial(2*n)'
def test_factorial():
n = Symbol('n', integer=True)
assert str(factorial(-2)) == "zoo"
assert str(factorial(0)) == "1"
assert str(factorial(7)) == "5040"
assert str(factorial(n)) == "factorial(n)"
assert str(factorial(2*n)) == "factorial(2*n)"
assert str(factorial(factorial(n))) == 'factorial(factorial(n))'
assert str(factorial(factorial2(n))) == 'factorial(factorial2(n))'
assert str(factorial2(factorial(n))) == 'factorial2(factorial(n))'
assert str(factorial2(factorial2(n))) == 'factorial2(factorial2(n))'
assert str(subfactorial(3)) == "2"
assert str(subfactorial(n)) == "subfactorial(n)"
assert str(subfactorial(2*n)) == "subfactorial(2*n)"
def test_sympyissue_8730():
assert limit(subfactorial(x), x, oo) == oo
def test_sympyissue_8730():
assert limit(subfactorial(x), x, oo) == oo
def test_subfactorial():
assert all(
subfactorial(i) == ans
for i, ans in enumerate([1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496]))
assert subfactorial(oo) == oo
assert isinstance(subfactorial(Rational(1, 2)), subfactorial)
assert subfactorial(nan) == nan
x = Symbol('x')
assert subfactorial(x).rewrite(uppergamma) == uppergamma(x + 1, -1) / E
tt = Symbol('tt', integer=True, nonnegative=True)
tf = Symbol('tf', integer=True, nonnegative=False)
tn = Symbol('tf', integer=True)
ft = Symbol('ft', integer=False, nonnegative=True)
ff = Symbol('ff', integer=False, nonnegative=False)
fn = Symbol('ff', integer=False)
nt = Symbol('nt', nonnegative=True)
nf = Symbol('nf', nonnegative=False)
nn = Symbol('nf')
te = Symbol('te', even=True, nonnegative=True)
to = Symbol('to', odd=True, nonnegative=True)
assert subfactorial(tt).is_integer
assert subfactorial(tf).is_integer is None
assert subfactorial(tn).is_integer is None
assert subfactorial(ft).is_integer is None
assert subfactorial(ff).is_integer is None
assert subfactorial(fn).is_integer is None
assert subfactorial(nt).is_integer is None
assert subfactorial(nf).is_integer is None
assert subfactorial(nn).is_integer is None
assert subfactorial(tt).is_nonnegative
assert subfactorial(tf).is_nonnegative is None
assert subfactorial(tn).is_nonnegative is None
assert subfactorial(ft).is_nonnegative is None
assert subfactorial(ff).is_nonnegative is None
assert subfactorial(fn).is_nonnegative is None
assert subfactorial(nt).is_nonnegative is None
assert subfactorial(nf).is_nonnegative is None
assert subfactorial(nn).is_nonnegative is None
assert subfactorial(tt).is_even is None
assert subfactorial(tt).is_odd is None
assert subfactorial(te).is_odd is True
assert subfactorial(to).is_even is True