How to avoid using curly braces when placing a \DeclareMathOperator command in subscript or superscript, while preserving spacing?

Question

Let's say in my preamble I define \DeclareMathOperator\rad{rad} and have the text

Let $f$ be a smooth function and $f^{\rad}$ its radial symmetrization.

It is inconvenient to have to enclose the \rad in curly braces. I could work around it by defining it as \newcommand\rad{{\operatorname{rad}}} instead. But at another place in my document I write

Let $n$ be a positive integer and $2 \rad(n)$ be twice its radical.

If I use \newcommand\rad{{\operatorname{rad}}}, there is no space between 2 and rad. (See newcommand vs. DeclareMathOperator)

So my question is: How can I allow a command to be used directly in superscript or subscript, while preserving the correct spacing when it is appears in the middle of a formula?

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Related: Double subscript error with \newcommand?

Answer 1

If you just use \rad in exponents and not really as an operator, then defining

\newcommand{\rad}{{\mathrm{rad}}}

will let you type

f^\rad

Note that \DeclareMathOperator is not a shorthand for getting \mathrm.

If you need \rad as an operator in other contexts, then no, you can't, for the same reason that ^\notin will produce an error.

On the other hand, is there a real reason for sparing a couple of braces? Any good TeX editor will supply the braces as soon as you enter ^. Adding them always will save you from head scratching when something goes wrong.