RankedMax and Max do not behave identically

Question

I have spent three hours debugging some code and at the end I think I found a bug. Otherwise I cannot explain what I am seeing:

When I want to use RankedMax on nested sublists, Mathematica freaks out, but it works all smooth as I expect when I use Max.

Try:

tab = Table[{i, j, k}, {i, 1, 2}, {j, 1, 3}, {k, 1, 4}] // TableForm
Map[Function[{x}, x/Max[x]], tab] // TableForm
Map[Function[{x}, x/RankedMax[x, 1]], tab] // TableForm

The last line will cause an error, and I do not understand why, because the documentation says:

RankedMax[{Subscript[x, 1],...,Subscript[x, m]},1] is equivalent to Max[{Subscript[x, 1],...,Subscript[x, m]}].

Why is this happening? Do I understand something incorrectly?

Answer 1

I suspect this has to do with the fact that Max has attribute Flat, and RankedMax hasn't. To get the same behaviour, you could do

(tab = Table[{i, j, k}, {i, 1, 2}, {j, 1, 3}, {k, 1, 4}]) // TableForm
Map[Function[{x}, x/Max[x]], tab] // TableForm
Map[Function[{x}, x/RankedMax[Flatten[x], 1]], tab] // TableForm

As an aside, // binds stronger than = which means that is you do something like

a = b // TableForm

this is interpreted as a = TableForm[b] which is probably not what you want if you want to use a for further calculations. To prevent this you can use brackets to group the right terms together, i.e. (a = b) // TableForm.