def test_multiplicity(): for b in range(2, 20): for i in range(100): assert multiplicity(b, b**i) == i assert multiplicity(b, (b**i) * 23) == i assert multiplicity(b, (b**i) * 1000249) == i # Should be fast assert multiplicity(10, 10**10023) == 10023 # Should exit quickly assert multiplicity(10**10, 10**10) == 1 # Should raise errors for bad input pytest.raises(ValueError, lambda: multiplicity(1, 1)) pytest.raises(ValueError, lambda: multiplicity(1, 2)) pytest.raises(ValueError, lambda: multiplicity(1.3, 2)) pytest.raises(ValueError, lambda: multiplicity(2, 0)) pytest.raises(ValueError, lambda: multiplicity(1.3, 0)) # handles Rationals assert multiplicity(10, Rational(30, 7)) == 0 assert multiplicity(Rational(2, 7), Rational(4, 7)) == 1 assert multiplicity(Rational(1, 7), Rational(3, 49)) == 2 assert multiplicity(Rational(2, 7), Rational(7, 2)) == -1 assert multiplicity(3, Rational(1, 9)) == -2
def eval(cls, arg, base=None): from diofant import unpolarify arg = sympify(arg) if base is not None: base = sympify(base) if base == 1: if arg == 1: return S.NaN else: return S.ComplexInfinity try: # handle extraction of powers of the base now # or else expand_log in Mul would have to handle this n = multiplicity(base, arg) if n: den = base**n if den.is_Integer: return n + log(arg // den) / log(base) else: return n + log(arg / den) / log(base) else: return log(arg)/log(base) except ValueError: pass if base is not S.Exp1: return cls(arg)/cls(base) else: return cls(arg) if arg.is_Number: if arg is S.Zero: return S.ComplexInfinity elif arg is S.One: return S.Zero elif arg is S.Infinity: return S.Infinity elif arg is S.NegativeInfinity: return S.Infinity elif arg.is_Rational: if arg.q != 1: return cls(arg.p) - cls(arg.q) if arg.is_Pow and arg.base is S.Exp1 and arg.exp.is_extended_real: return arg.exp elif arg.func is exp_polar: return unpolarify(arg.exp) if arg.is_number: if arg.is_negative: return S.Pi * S.ImaginaryUnit + cls(-arg) elif arg is S.ComplexInfinity: return S.ComplexInfinity elif arg is S.Exp1: return S.One # don't autoexpand Pow or Mul (see the issue 3351): if not arg.is_Add: coeff = arg.as_coefficient(S.ImaginaryUnit) if coeff is not None: if coeff is S.Infinity: return S.Infinity elif coeff is S.NegativeInfinity: return S.Infinity elif coeff.is_Rational: if coeff.is_nonnegative: return S.Pi * S.ImaginaryUnit * S.Half + cls(coeff) else: return -S.Pi * S.ImaginaryUnit * S.Half + cls(-coeff)