How to surround multiple-element arguments with parantheses?

Question

A command without brackets specifying the argument takes just the first element after it as an argument, so that a^bc will only have the superscripted b. I would like to exploit this with typeset functions in LaTex like \ln,\sin, and so on. In the case of just one argument, like \ln{a}bc or \ln abc, the function would not be typeset with parentheses. In the case of multiple elements in an argument, like \ln{abc}, there would be parentheses typeset around the argument, the triple product shown.

The motivation for this is the variable need for parentheses in logarithms and readibility of code. For example, I could write \ln{a + b} to unambigiously refer to the logarithm of a sum, and \ln ab to unambigiously refer to the logarithm of a product (by most conventions). Since the logarithm or other mathematical operator is only a standalone typeset, the spurious argument in the absence of bracketing (\ln ab would be equivalent to \ln{a}b) doesn't have an effect on the typesetting. This has an advantage in readibility, for example, contrast \ln\left(a + \frac bc\right) and \ln{a + \frac bc}.

How do I define a command which recognizes how many elements are in the argument and would add parentheses if there are more than one?

Answer 1

My solution uses \@gobble with a simple if-statement to test if a macro argument contains more than one character. There might be better ways to do this. Once you have a macro that adds parentheses on certain conditions, you can add it to any function with \g@addto@macro.

Here is a MWE with examples you mentioned:

\documentclass{article}

\makeatletter
\newcommand{\addparentheses}[1]{%
    \if\@gobble#1\relax\relax#1\else\left(#1\right)\fi
}
\g@addto@macro{\ln}{\addparentheses}
\makeatother

\begin{document}
Tests:

$\ln ab$

$\ln{a}b$

$\ln{a + b}$

$\ln{a + \frac bc}$
\end{document}

Output: