Is there a package to differently color nested expressions in the output?

Question

Say I have an expressions like $(\sin(x-3(z^{(x-2)^2}))+1)^2$ with many nested expressions. To better visualize this in the output (and to help finding missing delimiters when proof-reading) I'd like to have nested expressions and their delimiter show up in a different color than its surrounding. Is there a package for that purpose?

Answer 1

I am not aware of any packages that do this. A relatively easy way is to redefine ( and ) as command sequences that keep count of the level and change the colour accordingly. That would look like this:

\documentclass{article}

\usepackage{xcolor}

\makeatletter
\let\dotlessi\i
\catcode`(=\active
\catcode`)=\active
\newcounter{nestlvl}
\setcounter{nestlvl}{1}
\newcounter{temp}
\newcommand{\colorlst}{black,blue,red,green,yellow,brown}
\def({%
  \setcounter{temp}{0}%
  \addtocounter{nestlvl}{1}%
  \@for\i:=\colorlst\do{%
    \stepcounter{temp}%
    \ifnum\arabic{temp}<\arabic{nestlvl}%
      \color{\i}%
    \fi%
  }%
  \char`(%
}
\def){%
  \setcounter{temp}{0}%
  \addtocounter{nestlvl}{-1}%
  \ifnum\arabic{nestlvl}<0%
    \message{nesting error}%
  \fi%
  \char`)%
  \@for\i:=\colorlst\do{%
    \stepcounter{temp}%
    \ifnum\arabic{temp}<\arabic{nestlvl}%
      \color{\i}%
    \fi%
  }%
}
\let\i\dotlessi
\makeatother
\begin{document}
  (test(multi(levels)colors)like this)
\end{document}

The amount of colors specified this way is limited, I couldn't think of something more elegant right now. Perhaps somebody has a suggestion how colors can be picked in a better way.

The result:

And your example:

Note the exponents have the colour of the parentheses group they are in, this might not be what you actually want. It would require a bit of additional code to fix this. I think it looks horrible, but that is mainly due to the poor choice of colours on my end.