CM fonts kerning in math superscripts

Question

Using CM fonts with either a traditional engine or XeTeX, an expression such as $D^rf$ produces too much space between the r and the f in the output. It's easy to fix manually by inserting a \!. Is there a systematic way to do this? (I know the issue is the rectangularity of the bounding boxes used for kerning, and perhaps an automatic extra scriptstyle space specified after every superscript.) Other similar expressions with the same problem are $T^kM$, $J^{\ell}g$, etc. I find the kerning of the subscripts good enough. In particular $D^r_xf$ looks OK, although the subscript x could nestle better against the D.

Example

\documentclass[11pt]{amsart}
\begin{document}
$D^rf$  has too much space although $D_xf$ and $D^r_xf$ are OK.
\end{document} 

Answer 1

The simple answer, alas, is that there's no ready-made and automatic way to "fix" the spacing issues you've identified. As DEK notes in the TeXbook, there will always be combinations of letters and/or symbols for which TeX's math-mode spacing rules can be improved by some further tweaking.

Your posting identifies a handful of combinations involving terms in the superscript position whose look can be improved with judicious tweaking. \Gamma_n and P_q are examples of expressions with terms in the subscript position that look better if some tweaking is applied, i.e., if they're written as $\Gamma_{\!n}$ and $P_{\!q}$, respectively.

The TeXbook also mentions double integrals as instances where tweaking is advisable:

• The output of $\int\!\!\int$ looks a lot better than that of $\int\int$, and

• the output of $\displaystyle\int\!\!\!\int$ looks much better than that of $\displaystyle\int\int$.

(Aside: the amsmath package offers the macro \iint, to free users from having to remember to insert those repeated negative thinspaces.)