Forcing \savebox to use correct mode

Question

I found myself wanting to use a construct of the following type:

\newsavebox{\mybox}
\newcommand{\mycommand}[1]{\savebox{\mybox}{#1}\reflectbox{\usebox{\mybox}}}

The problem is that I want the content of the box to be typeset in the "correct" mode. In other words, if \mycommand is used in math mode, #1 should automatically be typeset in math mode. Furthermore, if \mycommand is used inside a subscript in math mode, then #1 should be typeset as a subscript, etc. Essentially, if it weren't for the presence of \reflectbox, \mycommand should be completely "transparent".

Answer 1

The \ThisStyle{...\SavedStyle...} syntax of the scalerel package allows precisely this to be done.

In the MWE I show: text mode (row 1); textstyle and displaystyle math (row 2); scriptstyle and scriptscriptstyle (row 3); combined effect of normal math and subscripted \mycommand (row 4).

\documentclass{amsart}
\usepackage{scalerel}
\newsavebox{\mybox}
\newcommand{\mycommand}[1]{%
  \ThisStyle{\ifmmode%
    \savebox{\mybox}{$\SavedStyle#1$}%
    \reflectbox{\usebox{\mybox}}%
  \else%
    \savebox{\mybox}{#1}%
    \reflectbox{\usebox{\mybox}}%
  \fi%
}}
\begin{document}
\mycommand{abc}

$\mycommand{\sum_{i=1}^N abc}\quad\displaystyle\mycommand{\sum_{i=1}^N abc} $

$\scriptstyle \mycommand{abc}\quad\scriptscriptstyle \mycommand{abc}$

$Z_{\mycommand{Z}}$
\end{document}