How to globally put subscripts in math-mode in upright font using amsmath?

Question

I'm often apply the subscript environment in math-mode to assign e.g. materials to material properties, $\eta_{oil}$, $\lambda_{air}$, etc. Not very mathematical but hey, I'm an engineer ;-)

I'm applying the amsmath package, so this puts the subscript in italics as most other letters. I don't want that. Of course there are numerous ways to change this locally ($\eta_{\mathrm{oil}}$ feels most appropriate), but this is cumbersome.

So is there a nice, slick TeXy way to address this? Possibly applying anything like \DeclareMathSomething{}{}{}{}?

I'd like to do that globally since 99% of my usage of $_{}$ is not related to variables. And in the very few situations the subscript is an variable, I still could use $_{\mathnormal{}}$...

I'm grateful for all suggestions.

Answer 1

I'd use a different character for this. Here I use ! for upright subscripts (and define \exclam if you need ! in math mode as itself.

\documentclass{article}
\usepackage{amsmath}

\begingroup\lccode`~=`!
\lowercase{\endgroup\def~}#1{_{\mathrm{#1}}}
\mathchardef\exclam=\mathcode`!
\AtBeginDocument{\mathcode`!=\string"8000 }

\begin{document}
$a_{x}+b!{eff}=n\exclam$
\end{document}

When a character is given \mathcode 32768 ("8000 is the hexadecimal for it and \string is a precaution against babel doing strange things) it has a peculiar behavior. It performs normally in text mode, but when found in math mode it becomes like a macro, more precisely like an active character.

A definition of ! as active character must be present; the trick

\begingroup\lccode`~=`!
\lowercase{\endgroup\def~}#1{_{\mathrm{#1}}}

is the same as

{\catcode`!=\active \gdef!#1{_{\mathrm{#1}}}

but I prefer avoiding \gdef whenever it's possible. So when TeX finds ! in math mode it looks for an argument and transforms it into _{\mathrm{<argument>}}, which is precisely what you're after.

Finally, \mathchardef\exclam=\mathcode`! defines \exclam to produce the same that would be produced by ! in math mode if we hadn't redefined it.

---

If you don't plan using only ASCII letters in your subscripts, then you should change \mathrm into \textnormal, so also accented letters are allowed (and spaces are respected).

Answer 2

I usually use something like the following:

\newcommand{\mstr}[1]   {\ensuremath{\mathit{#1}}}
\newcommand{\subs}[2]   {#1\mstr{_#2}}

Of course, you could e.g. change \mathit to \mathrm. Then use it like

\subs{x}{y}