Fix powsimp issues #9183, #10095, and KeyError

[ylemkimon]

• Fixed powsimp raising ValueError when base is float and Pow is argument of Mul. Since multiplicity expects integer or rational but powsimp doesn't checks it, it raises ValueError: fixes simplify throws unexpected ValueError #9183
• Fixed Pow.as_numer_denom() returning nan when either numerator or denominator of base is 1 and exp is infinite. Since 1**oo is NaN, numerator or denominator becomes NaN: fixes simplify((1/(2*E))**oo) returns nan #10095
• Fixed powsimp raising KeyError in common_b[b] = common_b[b] + e, when one base is Float and another is equal Rational(Integer). This seems to be caused by a == b doesn't imply hash(a) == hash(b) for floats #11707.

Thing(s) to consider: Should we automatically evaluate k**oo to zero where k is in (-1, 1), i.e., (1/(2*E))**oo?

[asmeurer]

Should we automatically evaluate k**oo to zero where k is in (-1, 1),

I don't think automatic evaluation should use evalf at all. That can be slow in general and automatic stuff should be fast (see also https://github.com/sympy/sympy/wiki/Automatic-Simplification). Those examples you gave all work because the power can be implemented directly on the Number object itself without any actual numeric evaluation (for instance, E (actually exp) knows that the power of -oo is 0.

Inside a simplification function like powsimp however it makes sense.

[ylemkimon]

@asmeurer I've been mistaken assumptions like .is_positive do not use evalf.

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Added another commit.

[asmeurer]

If you need an actual rational number you should use is_Rational or isinstance(b, Rational). is_rational will also be True for things like Symbol('x', rational=True).

[asmeurer]

I have just the one comment. +1 to merge once it is fixed.

[ylemkimon]

@asmeurer Fixed 😄