[Tex/LaTex] How to use a forward slash to display a fraction

fractionsmacrosmath-mode

Using $\frac{x + 5}{y - 4}$ can make equations very long and difficult to read. I'd prefer to be able to write $(x + 5)/(y - 4)$ and have it interpreted as $\frac{x + 5}{y - 4}$. How could I write a command that does this?

Best Answer

Here's a LuaLaTeX-based solution. It consists of two LaTeX macros, called \InlineToDispOn and \InlineToDispOff, and a Lua function called inline_to_disp. When activated via \InlineToDispOn, the Lua function scans all lines of input and replaces all instances of (...)/(...) with \frac{...}{...}. (The parentheses that encase the numerator and denominator terms are stripped off.)

Some additional comments:

  • Use the macro \InlineToDispOff to deactivate the Lua function. This may be needed if your document has passages which much be reproduced verbatim.

  • Nested matching parentheses in the numerator or denominator are ok, but only the outermost ones are processed. Hence, (2(x+5))/(y-4) will be transformed to \frac{2(x+5)}{y-4}.

  • Whitespace to the left and right of the / division symbol is allowed.

  • Per your write-up, the replacement operation requires both the numerator and denominator to be encased in pairs of matching parentheses.

    • By design, the Lua function inline_to_disp does not operate on expressions such as x/y, (a)/b, or c/(d).

    • If you have an expression of the form (x+5)/(y-4) but do not want it to be changed to \frac{x+5}{y-4}, change it to, say, (x+5){}/(y-4). The empty math group, {}, will assure that the gsub function inside inline_to_disp does not perform a successful match.

  • Any number of instances of (...)/(...) may occur on a given input line. (See below for examples.)

  • No input sanity checking of any kind is performed.

    • If the numerator and denominator terms are not syntactically valid from a LaTeX point of view and/or if the parentheses that encase the numerator and denominator terms are not matched, Latex will generate various mysterious warning and error messages.

    • The Lua function also doesn't check whether (...)/(...) occurs in (display or inline) math mode; if it occurs in text mode, Latex will crash with a comment that, you guessed it, \frac is not allowed to occur in text mode. This is, I trust, not much of a constraint since you're looking, in part, to replace various existing \frac expressions.

In the following screenshot, the upper row is typeset in \textstyle, while the lower one is typeset in \displaystyle:

enter image description here

% !TEX TS-program = lualatex
\documentclass{article}
\usepackage{luacode} % for 'luacode' environment
\begin{luacode}

function inline_to_disp ( s ) 
  s = s:gsub ( "(%b())%s-/%s-(%b())" , function (u,v)
               u = u:sub(2,-2)  -- strip off the parentheses
               v = v:sub(2,-2)
               return "\\frac{"..u.."}{"..v.."}" 
           end )
  return s
end

\end{luacode}

%% LaTeX-side code:
\newcommand\InlineToDispOn{\directlua{%
  luatexbase.add_to_callback("process_input_buffer", 
  inline_to_disp, "InlineToDisp" )}}
\newcommand\InlineToDispOff{\directlua{%
  luatexbase.remove_from_callback("process_input_buffer", 
  "InlineToDisp" )}}
\AtBeginDocument{\InlineToDispOn} %activate by default

\begin{document}
$(x+5)/(y-4) \quad (x) / (y) \quad (2(x+5))/(y-4) \quad 2(x+5)/ (y-4) \quad x/y$

\bigskip
$\displaystyle % same as above, but now with \displaystyle instead of \textstyle
 (x+5)/(y-4) \quad (x) / (y) \quad (2(x+5))/(y-4) \quad 2(x+5)/ (y-4) \quad x/y$
\end{document}
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