Is it possible to create a macro that changes when $\mathrm$ is applied to it?

Question

I would like to define a macro

\newcommand{\III}{I\hspace{-0.2em}I\hspace{-0.2em}I}

in such a way that when I type

$ \mathrm{\III} $

in math-mode, the compiler will compile

$ \mathrm{I\hspace{-0.05em}I\hspace{-0.05em}I} $

instead. Is there any way to do this?

Answer 1

You can set a spacing for the case when \mathnormal is in force and less space for other math groups.

\documentclass{article}

\usepackage{amsmath}

\newcommand{\III}{{I\IIIspace I\IIIspace I}}
\newcommand{\IIIspace}{%
  \mspace{%
    \ifnum\mathgroup=-1
      -5mu
    \else
      -2mu
    \fi
  }%
}

\begin{document}

$\III\ne\mathrm{\III}\ne\mathbf{\III}$

\end{document}

A different implementation, where in case of \mathnormal we use \mathit (and suppress the italic correction by inserting a suitable subscript that nullifies \scriptspace.

\documentclass{article}

\usepackage{amsmath}

\newcommand{\III}{%
  \ifnum\mathgroup=-1
    \expandafter\mathit
  \fi
  {I_{\kern-\scriptspace}\mspace{-2mu}I_{\kern-\scriptspace}\mspace{-2mu}I}%
}

\begin{document}

$\III\ne\mathrm{\III}\ne\mathbf{\III}$

$\scriptstyle\III\mathrm{\III}\mathbf{\III}$

$\scriptscriptstyle\III\mathrm{\III}\mathbf{\III}$

\end{document}

Answer 2

You can test the current value of \fam register:

\def\III{I\ikern I\ikern I}
\def\ikern{\mkern-\ifnum\fam<0 4.5mu\else 1.5mu \fi}

$\III \quad \rm \III$

\bye

Answer 3

To answer what your title ask:

I do not dare to recommend this since \mathrm doesn't take any arguments, I suspect something bad happens.

Both examples below prints hello world

\documentclass{article}
\begin{document}
  \newif\ifMathrm
  \newcommand\mathrmNew[1]{\Mathrmtrue\mathrm{#1}\Mathrmfalse}
  \newcommand\hello{\ifMathrm world\else hello\fi}
  \[ \hello~\mathrm{\hello} \]
\end{document}

It would be a little bit better to make \mathrmNew that toggles a flag. This is better because it doesn't execute the if-statements everytime \mathrm is called. Like this:

\documentclass{article}
\begin{document}
  \newif\ifMathrm
  \newcommand{\mathrmNew}[1]{\Mathrmtrue\mathrm{#1}\Mathrmfalse}
  \newcommand{\hello}{\ifMathrm world\else hello\fi}
  \[ \hello~\mathrmNew{\hello} \]
\end{document}