def _eval_expand_log(self, deep=True, **hints): from diofant import unpolarify, expand_log from diofant.concrete import Sum, Product force = hints.get('force', False) if (len(self.args) == 2): return expand_log(self.func(*self.args), deep=deep, force=force) arg = self.args[0] if arg.is_Integer: # remove perfect powers p = perfect_power(int(arg)) if p is not False: return p[1]*self.func(p[0]) elif arg.is_Mul: expr = [] nonpos = [] for x in arg.args: if force or x.is_positive or x.is_polar: a = self.func(x) if isinstance(a, log): expr.append(self.func(x)._eval_expand_log(**hints)) else: expr.append(a) elif x.is_negative: a = self.func(-x) expr.append(a) nonpos.append(S.NegativeOne) else: nonpos.append(x) return Add(*expr) + log(Mul(*nonpos)) elif arg.is_Pow: if force or (arg.exp.is_extended_real and arg.base.is_positive) or \ arg.base.is_polar: b = arg.base e = arg.exp a = self.func(b) if isinstance(a, log): return unpolarify(e) * a._eval_expand_log(**hints) else: return unpolarify(e) * a elif isinstance(arg, Product): if arg.function.is_positive: return Sum(log(arg.function), *arg.limits) return self.func(arg)
def test_perfect_power(): assert perfect_power(0) is False assert perfect_power(1) is False assert perfect_power(2) is False assert perfect_power(3) is False assert perfect_power(4) == (2, 2) assert perfect_power(14) is False assert perfect_power(25) == (5, 2) assert perfect_power(22) is False assert perfect_power(22, [2]) is False assert perfect_power(137**(3*5*13)) == (137, 3*5*13) assert perfect_power(137**(3*5*13) + 1) is False assert perfect_power(137**(3*5*13) - 1) is False assert perfect_power(103005006004**7) == (103005006004, 7) assert perfect_power(103005006004**7 + 1) is False assert perfect_power(103005006004**7 - 1) is False assert perfect_power(103005006004**12) == (103005006004, 12) assert perfect_power(103005006004**12 + 1) is False assert perfect_power(103005006004**12 - 1) is False assert perfect_power(2**10007) == (2, 10007) assert perfect_power(2**10007 + 1) is False assert perfect_power(2**10007 - 1) is False assert perfect_power((9**99 + 1)**60) == (9**99 + 1, 60) assert perfect_power((9**99 + 1)**60 + 1) is False assert perfect_power((9**99 + 1)**60 - 1) is False assert perfect_power((10**40000)**2, big=False) == (10**40000, 2) assert perfect_power(10**100000) == (10, 100000) assert perfect_power(10**100001) == (10, 100001) assert perfect_power(13**4, [3, 5]) is False assert perfect_power(3**4, [3, 10], factor=0) is False assert perfect_power(3**3*5**3) == (15, 3) assert perfect_power(2**3*5**5) is False assert perfect_power(2*13**4) is False assert perfect_power(2**5*3**3) is False assert perfect_power(25751251501**3, big=False) == (25751251501, 3) assert perfect_power(2575122501**3, big=False) == (2575122501, 3)