How to make multiple variables take the same width in math mode?

Question

I would like to use characters as variable names and adjust their width to all be the maximum width of a character. This way, brackets around them would align nicely as shown in the example below. Instead of stretching the characters, I would like them to match width by adding whitespace to the left and right of the character. I'm aware of \hphantom{} but what I need here is to "fill up" the width of one character to that of another.

Example:

\begin{aligned}
&\operatorname{I}[a; c] \\
&\operatorname{I}[w; a] \\
&\operatorname{I}[c; w]
\end{aligned}

Output:

Answer 1

You could use eqparbox. In the first example, the objects are centered in the allotted space, in the second one the alignment is right and left.

The tags are arbitrary, you need to use different ones for each application.

\documentclass{article}
\usepackage{amsmath}
\usepackage{eqparbox}

\newcommand{\q}[3][c]{%
  % #1 (optional) = alignment, default c
  % #2 = tag
  % #3 = object
  \eqmakebox[#2][#1]{$#3$}%
}

\begin{document}

\[
\begin{aligned}
&\operatorname{I}[\q{1}{a}; \q{2}{c}] \\
&\operatorname{I}[\q{1}{w}; \q{2}{a}] \\
&\operatorname{I}[\q{1}{c}; \q{2}{w}]
\end{aligned}
\]

\[
\begin{aligned}
&\operatorname{I}[\q[r]{1}{a}; \q[l]{2}{c}] \\
&\operatorname{I}[\q[r]{1}{w}; \q[l]{2}{a}] \\
&\operatorname{I}[\q[r]{1}{c}; \q[l]{2}{w}]
\end{aligned}
\]

\end{document}

Answer 2

As long as you don't need separate equation numbers on various lines, you could use TABstack alignment

\documentclass{article}
\usepackage{amsmath,tabstackengine}
\TABstackMath
\setstacktabulargap{0pt}
\setstackgap{L}{1.2\baselineskip}
\begin{document}
\[
\tabularCenterstack{rcccl}{
\operatorname{I}[&a&;& c&] \\
\operatorname{I}[&w&;& a&] \\
\operatorname{I}[&c&;& w&]
}
\]
\end{document}

Answer 3

This soulution is based on \hbox to and on the guess of "a good constant" for this application of type "Op[a;b]"

\def\operatorname#1[#2;#3]{#1\hbox to2.5em{$[\hss#2;\hss#3\hss]$}}

Test: $\operatorname{I}[a; c]$\par
Test: $\operatorname{I}[w; a]$\par
Test: $\operatorname{I}[i; j]$\par
Test: $\operatorname{I}[m; w]$\par

\bye