Is it possible to define a command taking an optional star and working in a subscript?

Question

Note: this is more or less a cross-post from my blog. I hope this is acceptable, especially that this is a genuine question!

I’m currently writing a (longish) document on mathematics. Among other things, I write about the Hausdorff metric, which I denote by $d_H$. Since this notation appears quite often, I decided to write a command for it:

\newcommand{\dH}{{d_H}}

The additional braces are there, because sometimes I want to talk about a ball with respect to the Hausdorff metric, denoted by $B_{d_H}$ – for that, I wanted to write B_\dH. Without the extra braces this won’t work (for obvious reasons).

So far, so good. But there’s another catch: I want a similar notion to the Hausdorff metric (call it a Haudorff quasimetric), which I denote by $d_H^*$. With my definition, \dH^* won’t work (I want the star to be above the subscript). So I wanted to be clever, and use an optional star; this way, I could write \dH or \dH*. I did this:

\newcommand{\dH}{\@ifstar{d_H^*}{d_H}}

But my ability to write B_\dH is lost now! And of course, adding braces around \@ifstar won’t help: it will then never “see” the star. (Note: I know that xparse makes defining commands with optional stars easier, but I expect it won't help with my problem.)

Personally, I can see no way out of this dilemma. It’s not a big deal, I can write B_{\dH} (which is cleaner LaTeX syntax anyway), but I’m curious whether there’s any way to eat this cake and have it, too.

Answer 1

Delay the closing of the group: after _, one can use \bgroup.

\documentclass{article}
\makeatletter
\newcommand\dH{\bgroup d_H\@ifstar{^*\egroup}{\egroup}}
\makeatother

\begin{document}
$B_\dH$ and $B_\dH*$
\end{document}

But avoid it.