Operate on all strings in any math environment

Question

I want to create an environment that will search through all of the math in it, to make some changes. So, I want something like a way to apply \regex_extract_all to search through everything which is in math mode in my environment.

I'm leaning towards using latex3, however I'm also considering luatex if that would be considerably easier. In that case, something like Automatically colourize all occurrences of certain strings (different colouring for different sets of words) is similar to what I want, however I want to apply it only within math mode, rather than to the whole document.

I've looked into applying commands to math mode, and it's been looking like I could perhaps use a combination of \regex_extract_all and \everymath however I'm worried about how it would work with other math environments like align equation or even just display mode. These questions:

\everymath, AMS equations, beamer, and tikz not working together

How to color certain commands/environments?

seem to indicate that it's non-trivial to operate on all math-mode text, and they both seem to use workarounds that might not work universally? I'm not sure. Would using \everymath, \everydisplay work for this case?

As a minimal example, if I were trying to make every occurrence of i as a variable red I'd want this code

\DeclarePairedDelimiter\norm{\lVert}{\rVert}
\begin{document}

$i+2=3$

\begin{myEnv}
  This is a test about i

  $\sin(\theta)+\sum_{i=0}^\infty ix^i$
  \begin{equation*}
     \norm{i} = \begin{cases}
      i & \text{if } i \geq 0 \\
      -i & \text{if } i < 0 
    \end{cases}
  \end{equation*}

  $$(x_i) = 1/i$$
\end{myEnv}
\end{document}

to generate a document where the "i"s in "i+2=3" on top and in "This is a test about i" are untouched, the "i"s in the words "if" are untouched, and the commands \sin and \infty still work, but the other "i"s used as a variable are made red.

Answer 1

Solving the problem in full generality is something I wouldn't try.

Here's the solution for making i variables red.

\documentclass{article}
\usepackage{amsmath,mathtools,xcolor}

\DeclarePairedDelimiter\norm{\lVert}{\rVert}

\newenvironment{myEnv}
 {\edef\redi{{\noexpand\textcolor{red}{\mathchar\the\mathcode`i}}}%
  \begingroup\lccode`~=`i \lowercase{\endgroup\let~}\redi
  \renewcommand{\sin}{\mathop{\textnormal{\textup{sin}}}}%
  \mathcode`i="8000 }
 {}

\begin{document}

$i+2=3$

\begin{myEnv}
This is a test about $i$

$\sin(\theta)+\sum_{i=0}^\infty ix^i$
\begin{equation*}
\norm{i} = 
  \begin{cases}
  i & \text{if } i \geq 0 \\
  -i & \text{if } i < 0 
  \end{cases}
\end{equation*}
Some text containing some letters,
\[
(x_{i}) = 1/i
\]
\end{myEnv}

$i+2=3$

\end{document}