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