A math-font-size-knowledgeable \raisebox

Question

I would like to some symbols lower than others in a math formula, without size change, for example

\def\abcd#1#2{\left[\raisebox{-.4em}{{\ensuremath{#1}}}\kern-.3em\setminus\kern-.2em#2\right]}
$\abcd{X_1}{X_2}$

which gives

But when I use this notation in a subscript position $$\bigoplus_{\abcd{X_1}{X_2}}$$, the left glyph remains at normalsize (because of the \raisebox acting like a \hbox and ignoring the fact that it is located in a subscript):

How can I define a math-font-size-knowledgeable \raisebox command?

Answer 1

You can use \mathpalette plain TeX macro:

\def\abcd#1#2{\left[\mathpalette\abcdA{#1}\mkern-6mu{\setminus}#2\right]}
\def\abcdA#1#2{\lower.4em\hbox{$#1#2$}}

Moreover, the \setminus is re-typed as Ord using {\setminus}, so you needn't compensate the space after it by negative kern. And the first negative kern is expressed in mu units in order to work in script sizes too.

Answer 2

You don't have to guess the amount of lowering. It's necessary to use \mathpalette in order to use the right font size. See The mysteries of \mathpalette

\documentclass{article}
\usepackage{amsmath}

\makeatletter

\newcommand{\abcd}[2]{\left[\mathpalette\abcd@{#1}\backslash#2\right]}
\newcommand{\abcd@}[2]{%
  % #1 = math style
  % #2 = text to be lowered
  \raisebox{%
    % we make it so that the top of the
    % lowered part is at the formula axis
    \dimexpr-\height+\abcd@fontdimen{#1}%
  }{%
    % we don't want that \scriptspace kicks in
    \scriptspace=\z@
    % the part to be lowered
    $\m@th#1#2$%
  }%
}
\newcommand{\abcd@fontdimen}[1]{%
  % the height of the formula axis is \fontdimen22 <math font of family 2>
  \fontdimen22
  \ifx#1\displaystyle\textfont\else
  \ifx#1\textstyle\textfont\else
  \ifx#1\scriptstyle\scriptfont\else
  \scriptscriptfont\fi\fi\fi 2
}
\makeatother

\begin{document}

\[
\abcd{X_1}{X_2}\qquad\bigoplus_{\abcd{X_1}{X_2}}
\]
\[
\abcd{X}{Y}\qquad\bigoplus_{\abcd{X}{Y}}
\]

\end{document}