How to change color of operators (lim, log, etc.)?

Question

How can I change the color of operators like "log", "lim" or the root symbol of \sqrt command?

Answer 1

You could tap into the primitive \mathop:

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

\let\oldmathop\mathop
\def\mathop#1{\oldmathop{\textcolor{red}{#1}}}
\let\oldsurd\surd
\def\surd{\textcolor{red}{\oldsurd}}

\begin{document}
\[
  \abc d \quad
  \sin \theta \quad
  \log_e \quad
  \lim_{x \rightarrow 0} \quad
  \int_a^b \quad
  \sqrt[n]{} \quad
  \surd
\]

\end{document}

The above is not thoroughly tested though...

Answer 2

Here's a possibility; I wouldn't hack into \mathop, which is a primitive also used in several other situations (in \overset, for instance).

\documentclass{article}
\usepackage{xcolor,amsmath,xpatch,letltxmacro}
\DeclareMathOperator{\abc}{abc}

\xpatchcmd{\qopname}{#3}{\textcolor{red}{#3}}{}{}
\LetLtxMacro\latexsqrt\sqrt
\RenewDocumentCommand{\sqrt}{om}{%
  \colorlet{current}{.}
  \IfNoValueTF{#1}
    {\textcolor{red}{\latexsqrt{\textcolor{current}{#2}}}}%
    {\textcolor{red}{\latexsqrt[#1]{\textcolor{current}{#2}}}}%
}


\begin{document}
\[
  \abc d \quad
  \sin \theta \quad
  \log_e \quad
  \lim_{x \rightarrow 0} \quad
  \int_a^b \quad
  \sqrt{2} \quad
  \sqrt[3]{x+1}
\]

\end{document}

The redefined \sqrt command works also with \leftroot and \uproot.

A variant coloring different the various operators and also for defining new ones to have colors. The commands given as first argument to \colorizeoperator should already been defined and be operators of \lim type.

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

\newcommand{\colorizeoperator}[2]{%
  % #1 = operator, #2 = color
  \begingroup\def\qopname##1##2##3{%
    \xdef#1{%
      \noexpand\qopname
      \unexpanded{##1}%
      ##2%
      {\begingroup\noexpand\color{#2}##3\endgroup}%
    }%
  }%
  #1%
  \endgroup
}
\makeatletter
\newcommand{\DeclareColoredMathOperator}{%
  \@ifstar
    {\def\DCMO@@{\DeclareMathOperator*}\DCMO@}
    {\def\@DCMO{\DeclareMathOperator}\DCMO@}%
}
\newcommand\DCMO@[3]{%
  % #1 = operator, #2 = name, #3 = color
  \DCMO@@{#1}{\begingroup\color{#3}#2\endgroup}%
}
\makeatother

\colorizeoperator{\lim}{blue}
\colorizeoperator{\sin}{red!60}
\DeclareColoredMathOperator*{\argmin}{arg\,min}{green}
\DeclareColoredMathOperator{\tors}{tors}{green!20!blue}

\begin{document}
\[
\lim_{x\to0}x=\sin0-\argmin_x 0+\tors
\]
\end{document}

Answer 3

FWIW, in ConTeXt you can change the color of operators using

\setupmathematics[functioncolor=red]

and change the color of \sqrt using

\setupmathradical[color=blue]

Here is a minimal example:

\setupmathematics[functioncolor=red]
\setupmathradical[color=blue]

\starttext
\startformula
\sqrt{\log\left( \frac{ \sin x } { \cos x } \right)}
\stopformula
\stoptext

which gives

This only affects operators, so commands like \stackrel, \underset, etc. that use \mathop in the background continue to work as expected.

Answer 4

Here's a LuaLaTeX-based solution. The solution doesn't modify the definition of \log, \sin, \cos, etc. Instead, it sets up a Lua function (called color_op) that encases these directives in {\color{<color>}...} wrappers, while ensuring that the now colored objects maintain the spacing properties of objects of type mathop. The Lua function, in turn, is assigned to the process_input_buffer callback, which operates at a very early stage of processing -- before TeX itself does most of its processing.

This setup may, at least at first, seem to be more involved than approaches that modify the low-level macros \mathop and \qopname directly. An upside is that it's possible to assign distinct colors to each "math operator". Another upside is that -- as long as one has at least some familiarity with Lua's pattern matching syntax -- it's straightforward to deal with complicated \sqrt cases, such as $\sqrt[\leftroot{-2}\uproot{2}\beta]{k}$. This code snippet is, by the way, not of my own invention! It comes from the user guide of the amsmath package.

% !TEX TS-program = lualatex
\documentclass{article}
\usepackage[dvipsnames,x11names,svgnames]{xcolor} % lots of predefined colors...
\usepackage{amsmath} % for "\leftroot" and "\uproot" macros

\usepackage{luacode}
\begin{luacode}
in_verbatim_env = false
function color_op (line)
  if string.find ( line , "\\begin{[vV]erbatim}" ) then
    in_verbatim_env = true
  elseif string.find ( line , "\\end{[vV]erbatim}" ) then
    in_verbatim_env = false
  else
    if not in_verbatim_env then
      line = string.gsub ( line, "\\log", "\\mathop{\\color{blue}%0}" )
      line = string.gsub ( line, "\\sin", "\\mathop{\\color{magenta}%0}" )
      line = string.gsub ( line, "\\cos", "\\mathop{\\color{SeaGreen}%0}" )
      line = string.gsub ( line, "\\lim", "\\mathop{\\color{cyan}%0}" )

      line = string.gsub ( line, "(\\sqrt)%s-(%b{})", 
                                 "{\\color{brown}%1{\\color{black}%2}}" )
      line = string.gsub ( line, "(\\sqrt%s-%b[])%s-(%b{})", 
                                 "{\\color{red}%1{\\color{black}%2}}" ) 
    end
  end
  return line
end
luatexbase.add_to_callback ( "process_input_buffer", color_op, "color_op" )
\end{luacode}

\begin{document}    
$\log(z)$, 
$\sin\theta$,
$\lim_{x\to\infty} u(x)$

\medskip
$\sqrt{2}$, $\sqrt [\leftroot{-2}\uproot{2}\beta] {k}$, 
$\displaystyle\sqrt[3]{\int_0^1 \frac{\sin x}{\cos x}\,dx}$
\end{document}

Answer 5

The Unicode engines luatex and xetex have the advantage, that colour is taken as a property of the font itself, rather than being added on top of it.

The unicode-math allows to load Unicode math fonts with a certain colour specification. Here we first of all load Latin Modern Math for the entire math mode and proceed to load Latin Modern Math for the glyphs from the \mathop range and \sqrt with the colour specification red. Similar for the operator font.

As you can see in the output, the horizontal bar of the radical is not coloured red. This is due to the fact that the bar is not a math glyph, but a \vrule, which is not a even a glyph.

\documentclass{article}
\usepackage{mathtools,unicode-math,xcolor}

\setmathfont{Latin Modern Math}
\setmathfont{Latin Modern Math}[range={\mathop,\sqrt}, Color=red]
\setmathfontface\mathlm{Latin Modern Math}[Color=red]
\setoperatorfont\mathlm

\DeclareMathOperator{\abc}{abc}
\begin{document}
\[
  \abc d \quad
  \sin \theta \quad
  \log_e \quad
  \lim_{x \rightarrow 0} \quad
  \int_a^b \quad
  \sqrt{2} \quad
  \sqrt[3]{x+1}
\]
\end{document}

Answer 6

As @Christian Hupfer suggested in his comment.

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

\begin{document}

\begin{align*}
\textcolor{black!50!green}{A} &= \color{red}{\sqrt{   \color{blue}{aaa}} }                    \\
\textcolor{black!50!blue}{B} &= \color{black!70}{\lim_{ \color{cyan}{t \rightarrow \infty}} }  \\
\textcolor{green}{C} &= \color{black!10!yellow}{\log_{2}}   \color{blue}{x}
\end{align*}

\end{document}