\index in \newcommand breaks MakeIndex

Question

When I use \index, everything is ok, but when I use \newcommand instead, some large symbols can not show:

\documentclass[a4paper,openany,12pt]{amsbook}
\usepackage{imakeidx}
\makeindex[name = index, title = Special Index, columns = 3]
%--------------------------------------------------------
\newcommand{\khm}[1]{#1\index[index]{{#1}}}
%--------------------------------------------------------
\begin{document}
\khm{$\bigcup$} \khm{$<$}
\printindex[index]
\end{document}

The above just show $<$ not $\bigcup$. Could you please help?

Answer 1

If you look in index.idx, which is what LaTeX writes out for later being processed by MakeIndex, you find

\indexentry{{$\DOTSB \bigcup@ \slimits@ $}}{1}
\indexentry{{$<$}}{1}

What happens? When \index is found at the outer level, it enters a “semiverbatim” mode, so \index{$\bigcup$} would write

\indexentry{$\bigcup$}{1}

In particular, what's passed to the eventual \write operation is the string of characters \bigcup, not a command.

In your case, instead, the tokens $\bigcup$ have already been formed and the “semiverbatim” mode can do nothing. And TeX will perform macro expansion during \write.

Solution:

\documentclass[a4paper,openany,12pt]{amsbook}
\usepackage{imakeidx}

\makeindex[name = index, title = Special Index, columns = 3]

\newcommand{\khm}[1]{#1\index[index]{\unexpanded{\unexpanded{#1}}}}

\begin{document}

\khm{$\bigcup$} \khm{$<$}

\printindex[index]

\end{document}

You need two \unexpanded, because TeX would try expansion twice.

The contents of the .idx file is now

\indexentry{$\bigcup $}{1}
\indexentry{$<$}{1}

and the .ind file will be

\begin{theindex}

  \item $<$, 1
  \item $\bigcup $, 1

\end{theindex}

---

Regarding \exists!, you have to take into account that ! is a special character for MakeIndex and has to be quoted. You might go with

\newcommand{\khm}[1]{%
  \begingroup\mathcode`"="8000\relax
  \begingroup\lccode`~=`"\lowercase{\endgroup\let~}\relax
  #1\endgroup\index[index]{\unexpanded{\unexpanded{#1}}}}

so that

\khm{$\exists"!$}

would work as expected. But for this unique case it's much easier and robust to do

$\exists!$\index[index]{$\exists"!$}