def test_genocchi():
genocchis = [1, -1, 0, 1, 0, -3, 0, 17]
for n, g in enumerate(genocchis):
assert genocchi(n + 1) == g
assert genocchi(Symbol('z', zero=True) + 1) == 1
pytest.raises(ValueError, lambda: genocchi(Rational(1, 2)))
m = Symbol('m', integer=True)
n = Symbol('n', integer=True, positive=True)
assert genocchi(2 * n + 1) == 0
assert genocchi(m) == genocchi(m)
assert genocchi(n).rewrite(bernoulli) == 2 * (1 - 2**n) * bernoulli(n)
assert genocchi(x).rewrite(bernoulli) == genocchi(x)
assert genocchi(2 * n).is_odd
assert genocchi(2 * n + 1, evaluate=False).is_odd is None
assert genocchi(4 * n).is_positive
# This should work for 4 * n - 2, but fails due to some variation of issue
# 8632 ((4*n-2).is_positive returns None)
assert genocchi(4 * n + 2).is_negative
assert genocchi(2 * n + 1, evaluate=False).is_negative is None
assert genocchi(m).is_odd is None
assert genocchi(m).is_negative is None
def test_evalf_bernoulli():
pytest.raises(ValueError, lambda: bernoulli(0.5, evaluate=False).evalf())
assert bernoulli(3, evaluate=False).evalf() == 0
def test_bernoulli():
assert bernoulli(0) == 1
assert bernoulli(1) == Rational(-1, 2)
assert bernoulli(2) == Rational(1, 6)
assert bernoulli(3) == 0
assert bernoulli(4) == Rational(-1, 30)
assert bernoulli(5) == 0
assert bernoulli(6) == Rational(1, 42)
assert bernoulli(7) == 0
assert bernoulli(8) == Rational(-1, 30)
assert bernoulli(10) == Rational(5, 66)
assert bernoulli(1000001) == 0
assert bernoulli(0, x) == 1
assert bernoulli(1, x) == x - Rational(1, 2)
assert bernoulli(2, x) == x**2 - x + Rational(1, 6)
assert bernoulli(3, x) == x**3 - (3 * x**2) / 2 + x / 2
# Should be fast; computed with mpmath
b = bernoulli(1000)
assert b.numerator % 10**10 == 7950421099
assert b.denominator == 342999030
b = bernoulli(10**6, evaluate=False).evalf()
assert str(b) == '-2.23799235765713e+4767529'
# Issue sympy/sympy#8527
l = Symbol('l', integer=True)
m = Symbol('m', integer=True, nonnegative=True)
n = Symbol('n', integer=True, positive=True)
assert isinstance(bernoulli(2 * l + 1), bernoulli)
assert isinstance(bernoulli(2 * m + 1), bernoulli)
assert bernoulli(2 * n + 1) == 0
pytest.raises(ValueError, lambda: bernoulli(-20))
assert isinstance(bernoulli(l, x), bernoulli)
def test_evalf_bernoulli():
pytest.raises(ValueError, lambda: bernoulli(0.5, evaluate=False).evalf())
assert bernoulli(3, evaluate=False).evalf() == 0