Avoid brackets with a command having an optional argument as subscript

Question

I have the following code:

\documentclass{article}
\newcommand{\quot}[3][c]{\frac{#2}{#3#1}}
\begin{document}
\LARGE
$A_\frac{a}{bc}$
$A_{\quot{a}{b}}$
$A_{\quot[d]{a}{b}}$
\end{document}

If I write $A_\quot{a}{b}$ instead of $A_{\quot{a}{b}}$

or $A_\quot[d]{a}{b}$ instead of $A_{\quot[d]{a}{b}}$ I get an error.

! Missing { inserted.

Is it possible to modify my \quot command in order to suppress the extra brackets?

Answer 1

$A_\frac{a}{bc}$ works because _ does expansion in order to find a left brace, which may also be implicit. Thus the expansion of \frac is pursued all the way, since the usual definition is

% latex.ltx, line 4260:
\def\frac#1#2{{\begingroup#1\endgroup\over#2}}

and so the { before \begingroup is scanned when the arguments have already been absorbed.

This doesn't happen with \quot, because it has an optional argument, so the expansion ends at \kernel@ifnextchar because this macro begins with \let.

Adding a pair of braces to the definition, like in

\newcommand{\quot}[3][c]{{\frac{#2}{#3#1}}}

will not solve the issue. You could do it in an indirect way:

\newcommand{\quot}{\bgroup\innerquot}
\newcommand{\innerquot}[3][c]{\frac{#2}{#3#1}\egroup}

but I recommend getting the habit of using braces around subscripts. If you try

$A_\notin$

you'll probably understand why. And no, there's no way to make \notin work in subscript without braces, that is, one needs to type $A_{\notin}$. The trick above works because \quot will make an ordinary symbol and the braces do no harm when used in text style.