Parenthesise math expression if it contains operator

Question

Imagine I have written several fractions of the form $\frac{V+W}{U}$ and decide later that I want them to be displayed as a slashed fraction instead. In the group where I want this to happen, I can always do \renewcommand\frac[2]{#1/#2}. However, I would like to add parenthesis to the numerator (or the denominator) only if it contains a mathop. At least, this seems to me a suitable first heuristic for deciding whether the numerator (denominator) is to be parenthesised or not.

Does anyone know how to achieve this?

Answer 1

Here, I search for +, -, \bullet, and \cdot, but you can add more operators to the \setsepchar list.

Also, if the operator is leading, such as -3, I do not add parens. You could change that by commenting the line \ignoreemptyitems.

EDITED to workaround a strange error when \sim appears by itself as an argument to \inlinefrac.

\documentclass{article}
\usepackage{listofitems}
\newcommand\inlinefrac[2]{
  \setsepchar{+||-||\bullet||\cdot||\oplus}
  \ignoreemptyitems
  \readlist*\xator{ #1}
  \ifnum\listlen\xator[]>1\relax(#1)\else{#1}\fi
  /
  \readlist*\xator{ #2}
  \ifnum\listlen\xator[]>1\relax(#2)\else{#2}\fi
}
\begin{document}
\[
  \frac{2}{3}\quad\let\frac\inlinefrac\frac{2}{3}
\]
\[
  \frac{2}{-3}\quad\let\frac\inlinefrac\frac{2}{-3}
\]
\[
  \frac{2+x}{3}\quad\let\frac\inlinefrac\frac{2+x}{3}
\]
\[
  \frac{2\bullet x}{3\cdot y}\quad\inlinefrac{2\bullet x}{3\cdot y}
\]
\centering$\inlinefrac{M\oplus N}{\sim}$
\end{document}

Answer 2

I propose an \ifrac command. If given with * it will call \inlinefrac, but it will also obey the setting done by \fractionsinline (local setting).

This way it's easy to switch from one form to the other, by adding or removing *. You can also use \inlinefrac directly.

Symbols that trigger the parentheses need not be the same in the numerator and the denominator: multiplication symbols should trigger parentheses in the denominator only.

\documentclass{article}
\usepackage{amsmath}
\usepackage{xparse}

\ExplSyntaxOn

\NewDocumentCommand{\ifrac}{smm}
 {
  \IfBooleanTF { #1 }
   { \inlinefrac { #2 } { #3 } }
   {
    \bool_if:NTF \l_bubaya_frac_inline_bool
     {
      \inlinefrac { #2 } { #3 }
     }
     {
      \frac { #2 } { #3 }
     }
   }
 }

\bool_new:N \l_bubaya_frac_inline_bool

% extend the regex at will; \+ and \- stand for + and -,
% \c{command name} for a control sequence
\regex_const:Nn \c_bubaya_frac_num_regex { \+ | \- | \c{sin} | \c{cos} }
\regex_const:Nn \c_bubaya_frac_den_regex { \c{cdot} | \c{times} | \c{bullet} }

\NewDocumentCommand{\fractionsinline}{}
 {
  \bool_set_true:N \l_bubaya_frac_inline_bool
 }

\NewDocumentCommand{\inlinefrac}{mm}
 {
  \regex_match:NnTF \c_bubaya_frac_num_regex { #1 } { (#1) } { #1 }
  /
  \regex_match:NnTF \c_bubaya_frac_num_regex { #2 }
   {
    (#2)
   }
   {
    \regex_match:NnTF \c_bubaya_frac_den_regex { #2 } { (#2) } { #2 }
   }
 }

\ExplSyntaxOff

\begin{document}
\begin{gather*}
  \ifrac{2}{3}\qquad\ifrac*{2}{3}
\\
  \ifrac{2}{-3}\qquad\ifrac*{2}{-3}
\\
  \fractionsinline
  \ifrac{2}{-3}\qquad\ifrac{2}{-3}
\\
  \inlinefrac{2+x}{3}
\\
  \ifrac{\sin x}{x}\qquad\ifrac*{\sin x}{x}
\\
\end{gather*}

\fractionsinline
\begin{gather*}
  \ifrac{2+x}{3}
\\
  \ifrac{2\bullet x}{3\cdot y}
\\
  \ifrac{\sin x}{x}
\end{gather*}

\end{document}

Answer 3

An alternative with the same idea as @Steven's solution but by using xstring package.

\documentclass{article}
\usepackage{xstring}
\renewcommand\frac[2]{\IfSubStr{#1}{+}{(#1)}{\IfSubStr{#1}{-}{(#1)}{#1}}/\IfSubStr{#2}{+}{(#2)}{\IfSubStr{#2}{-}{(#2)}{#2}}}
\begin{document}
\(\frac{5}{10}=0.5\) but \(\frac{5+1}{10}=0.6\) and \(\frac{7}{10+4}=0.5\) but \(\frac{14+1}{6+1.5}=2\)
\end{document}

PS: I suggest Steven's solution as easier to expanded for more cases, but had already created this code before see his answer and thus, posted.