ENH: Shall we let pd.NA * 0 equals to zero?

[tushushu]

Is your feature request related to a problem?

I found that:

pd.NA ** 0 # The result is 1
pd.NA * 0 # The result is pd.NA

Describe the solution you'd like

Personally, I think the pow and mul method shoulds be consistent. The results should be both NA or both numbers.
Solution 1:

pd.NA ** 0 # The result is pd.NA
pd.NA * 0 # The result is pd.NA

Solution 2:

pd.NA ** 0 # The result is 1
pd.NA * 0 # The result is 0

PS: I assume the pd.NA is not infinite.

[TomAugspurger]

xref #29997.

PS: I assume the pd.NA is not infinite.

I think that's the issue. Similar to how np.inf * 0 isn't defined (returns np.nan) we don't know what the output of pd.NA * 0 should be. That differs from pd.NA ** 0 which is 1 by definition.

[tushushu]

That makes sense. But NA**0 == 1 is also confusing, shouldn't it be 1 or 1.0? How do we know the NA is representing a integer?

[TomAugspurger]

I think that gets into a larger discussion around "typed NA" (or NA[T]). #28095

[tushushu]

Thanks @TomAugspurger for sharing these discussions, it's really insightful.