Latex Equations: Colour all instances of symbol

Question

I (and most humans) find equations a lot easier to read when certain variables are highlighted. For example:

$$
0 = \frac{\partial}{\partial\color{blue}{z_l}}\big(\|h(z_{l-1})\cdot w_l-\color{blue}{z_l}\| + \lambda \| h(\color{blue}{z_l})\cdot w_{l+1} - z_{l+1}\| \big) 
$$

Gives a visually appealing:

My question: Is there some way to do this without explicitly filling the equation with these \color commands? Ideally, I would not have to change the equations at all, and could just define a block around the equation that takes care of the colouring. I'm looking for something like defining a block of code where you automatically replace all instances of z_l with \color{blue}{z_l}.

To be clear, I am aware of the "Find -> Replace" function of most editors, but this isn't what I'm looking for - I want to be decorate my equations without messing up the equation code itself.

Answer 1

(edited/simplified the code after OP clarified that only z_l instances need to be colored for now)

You could achieve your objective by using LuaLaTeX and taking a preprocessor-based approach, as is done in the following example.

% !TeX program = lualatex
\documentclass[letterpaper]{article}
\usepackage{xcolor,mathtools}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}

\usepackage{luacode}
% The lua function 'color_zl' does the actual work
\begin{luacode}
function color_zl ( s ) 
  s = string.gsub ( s , "z_l" , "\\textcolor{blue}{%0}" )
  return s
end
\end{luacode}

% The lua function is assigned to 'process_input_buffer' callback:
\newcommand{\ZColorOn}{\directlua{luatexbase.add_to_callback(
  "process_input_buffer", color_zl , "color_zl" )}}
\newcommand{\ZColorOff}{\directlua{luatexbase.remove_from_callback(
  "process_input_buffer", "color_zl" )}}

\begin{document}
\ZColorOn % turn on automatic coloring of "z_l" terms
\[
0 = \frac{\partial}{\partial z_l}\bigl(
          \norm[\big]{h(z_{l-1})\cdot w_l-z_l} 
+ \lambda \norm[\big]{h(z_l)\cdot w_{l+1} - z_{l+1}} \bigr) 
\]

\ZColorOff % turn off automatic coloring of "z_l" terms
\[
0 = \frac{\partial}{\partial z_l}\bigl(
          \norm[\big]{h(z_{l-1})\cdot w_l-z_l} 
+ \lambda \norm[\big]{h(z_l)\cdot w_{l+1} - z_{l+1}} \bigr) 
\]
\end{document}

---

Addendum If you wanted to typeset in blue all instances of z with any subscript, not just z_l, you should modify the Lua function by enabling a couple of pattern-matching operations:

function color_zl ( s ) 
  s = string.gsub ( s , "z_%b{}" , "\\textcolor{blue}{%0}" )
  s = string.gsub ( s , "z_(%w)" , "\\textcolor{blue}{%0}" )
  return s
end

The first pattern, %b{}, matches a matching pair of curly braces with any content. The second pattern, %w, matches a single alphanumeric character, e.g., l, 1, etc.

Answer 2

Just try to make your own definition for that. As a starting point a example for your case:

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

\def\zl{{\ensuremath{\color{blue} z_l}}}

\begin{document}
\[0 = \frac{\partial}{\partial\zl}\big(\|h(z_{l-1})\cdot w_l-\zl\| + \lambda \| h(\zl)\cdot w_{l+1} - z_{l+1}\| \big) \]
\end{document}

Answer 3

You do not have to have markup (or Lua) to colour math tokens for example

\documentclass{article}
\usepackage{color}

\mathchardef\zmath\mathcode`z
\mathcode`z="8000

{\makeatletter
\def~{\@ifnextchar_{\zzm}{\zmath}}
\catcode`z\active
\global\let z~
}

\def\zzl{l}
\def\zzm_#1{%
 \def\tmp{#1}%
  \ifx\tmp\zzl
  \textcolor{blue}{\zmath_{l}}%
  \else
    \zmath_{#1}%
  \fi}

\begin{document}
\[
0 = \frac{\partial}{\partial z_l}\bigl(\|h(z_{l-1})\cdot w_l-z_l\| + 
\lambda \| z_l)\cdot w_{l+1} - z_{l+1}\| \big) 
\]
\end{document}

Answer 4

I was quite fed up with writing X_{\mathit{y}} to get proper index y following the variable X. You seem to have simillar problem. My solution, adapted to your case, was:

\newcommand[2][blue]{\foo}{{\ensuremath{\color{#1}#2}}}

And usage is simple:

Variable \foo{b} is emphasized blue and variable \foo[red]{r} is emphasized red.