LaTeX color setting for math mode

Question

I'm wondering if it's possible to do something like this in LaTeX:

For all numbers (0, 1, ..., 9) in math mode, color it red. For alphabets (a, b, ..., z, A, B, ..., Z) in math mode, color it green. For everything else in math mode, color it blue.

I want to make my document more colorful, but doing manual coloring takes too much time!

Answer 1

With no warranty of any kind!

\documentclass{article}
\usepackage{color}


\makeatletter
\def\colorizemath #1#2{%
    \expandafter\mathchardef\csname orig:math:#1\endcsname\mathcode`#1
    \mathcode`#1="8000
    \toks@\expandafter{\csname orig:math:#1\endcsname}%
    \begingroup
       \lccode`~=`#1
       \lowercase{%
    \endgroup
       \edef~{{\noexpand\color{#2}\the\toks@}}}%
   }
\@for\@tempa:=a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z\do{%
    \expandafter\colorizemath\@tempa{green}}
\@for\@tempa:=A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z\do{%
    \expandafter\colorizemath\@tempa{green}}
\@for\@tempa:=0,1,2,3,4,5,6,7,8,9\do{%
    \expandafter\colorizemath\@tempa{red}}
\makeatother

\everymath{\color{blue}}
\everydisplay{\color{blue}}

\begin{document}\thispagestyle{empty}

Hello $world$. Do you know that $E=mc^2$? 

\[ \widehat f(\omega) = \int_{-\infty}^\infty f(x) e^{-2\pi i \omega x}\,dx\]

\[ (I - M)^{-1} = \sum_{k=0}^\infty M^k\]
\end{document}

Let me add, with regards to \everymath and \everydisplay that it would have been better to do:

\everymath\expandafter{\the\everymath \color{blue}}
\everydisplay\expandafter{\the\everydisplay \color{blue}}

This preserves, rather than erases, the previously stored data in these token lists. (I just checked and Lamport's book does not have a single mention of token list, and even the word token is not to be found (it seems) in the entire book...). Admittedly, packages who put things in them should do that At Begin Document so even the brutal way used in my initial code, as long as it is in the preamble, is maybe not that destructive. People interested in token lists can learn about it in, for example, TeX by Topic by Victor Eijkhout (texdoc topic).

Answer 2

With unicode-math you can customize colors quite a lot, by specifying the font for different ranges, where a range can be a font command, e.g. \mathit, \mathbf etc., or a Unicode range. Color settings won't affect fraction lines and the horizontal line in square roots, as explained in color of unicode-math in xetex, but adding \everymath{\color{blue}} \everydisplay{\color{blue}} as in user700902's answer fixes that. No idea why the hat is red.

unicode-math requires that one compiles with xelatex or lualatex.

\documentclass{article}
\usepackage{unicode-math,color}
\setmathfont[Color=0000FF]{xits-math.otf}
\setmathfont[range={\mathit,\mathup,\mathbfup},Color=00FF00]{xits-math.otf} % mathup is used for operators I think, \mathbf actually gives \mathbfup it seems 
\setmathfont[range=\mathit/{greek,Greek},Color=0000FF]{xits-math.otf} % sets greek letters to blue
\setmathfont[range="0030-"0039,Color=FF0000]{xits-math.otf} % unicode hex range of 0-9
\everymath{\color{blue}}
\everydisplay{\color{blue}}
\begin{document}
Hello $world$. Do you know that $E=mc^2$? 
\[
\widehat f(\omega) = \int_{-\infty}^\infty f(x) e^{-2\pi i \omega x}\,dx
\]
And \( \tan x = \sin x /\cos x \).
\[ (I - M)^{-1} = \sum_{k=0}^\infty M^k\]

Even fractions and square roots \(\frac{\sqrt{x+1}}{x+1}\)
\[
\frac{\sqrt{x+1}}{x+1}
\]

\end{document}