How to define a command that can be used as a superscript without {} and that can have a subscript

Question

I have used \theta hundreds of times in my document. Now I decided that I would like all thetas to be in red color.

So I would like to redefine the command \theta to create a red theta.

MWE:

\documentclass{article}
\usepackage{xcolor}
\let\oldtheta\theta
\renewcommand{\theta}{\mathcolor{red}{\oldtheta}}
\newcommand{\thetaWrongSpacing}{{\mathcolor{red}{\oldtheta}}}
\begin{document}
$M^\theta$ %gives error message
$\theta_1\oldtheta_1$ %works perfectly
$M^\thetaWrongSpacing$ %works perfectly
$\thetaWrongSpacing_1$ %wrong spacing
$M^\alpha$ % seems to work perfectly, but David Carlisle says this should not be used according to the LaTeX manual
\end{document}

but then $M^\theta$ results in an error. I can fix this by enclosing the definition of the command with {}, but then the spacing is not correct.

How can I redefine \theta in the preamble without making any change within the document?

PS: \renewcommand{\theta}{\begingroup\mathcolor{red}{\oldtheta}\endgroup} does also produce an error for $M^\theta$ and flaws the spacing of \theta_1.

Answer 1

The reason of bad spacing with colorized theta in you example is due to old concept of colors implementation. The colors in pdftex or XeTeX is based on inserted \pdcolorstacks (roughly speaking). They must be inserted when a color change starts and when the color is returned back, then it is inserted too. Roughly speaking:

{color-change text}_subscript

expands to

{pdfcolorstack text}pdfcolorstack_subscript

and the secnod pdfcolorstack is the reason of the problem.

On the other hand, if we are using a modern concept of colors (using attributes, provided by LuaTeX), then there isn't problem with spacing. For example, in OpTeX:

\let\oritheta=\theta
\def\theta{{\Red\oritheta}}
Test $a^\theta$ and $\theta_1$.
\bye

Spacing is correct. Or you can use LuaLaTeX with appropriate coloring package based on color attributes.

Note1: your macro with \begingroup...\endgroup doesn't solve the spacing problem for subscripts. The \pdfcolorstack is here too and the unwanted kern 0.2779pt (from italic correction of theta) is here too. Your comment "works perfectly" in your source file isn't true.

Note2 (due to the discussion here): TeX was designed for humans, they create and read the source files of TeX. It is much more comfortable to write $M^\theta$ than $M^{\theta}$. So, we cannot prohibit the first syntax which is more suitable for humans.

Answer 2

As wipet mentioned, you can use Lua attributes to color the glyphs without changing the spacing. In LaTeX you can do that using the package luacolor.

Result with xcolor

\documentclass{article}
\usepackage{xcolor}
\let\oldtheta\theta
\renewcommand*{\theta}{{\mathcolor{red}\oldtheta}}
\begin{document}

    $M^\theta M^\oldtheta$
$\theta_1 \oldtheta_1$

% check that the spacing is the same 
$M^\theta$\llap{$M^\oldtheta$}

$\theta_1$\llap{$\oldtheta_1$}

\end{document}

Result with luacolor

\documentclass{article}
\usepackage{luacolor}
\let\oldtheta\theta
\renewcommand*{\theta}{{\color{red}\oldtheta}}
\begin{document}

    $M^\theta M^\oldtheta$
$\theta_1 \oldtheta_1$

% check that the spacing is the same 
$M^\theta$\llap{$M^\oldtheta$}

$\theta_1$\llap{$\oldtheta_1$}

\end{document}