Is it possible to have a "real" \belowdisplayshortskip?

Question

I think this is a tough one. Have you ever wondered why TeX sometimes produces vertical spacing around equations that is far from satisfactory? An example:

\documentclass{article}
\setlength{\textheight}{2.93cm}
\begin{document}
A short line,
\[ a = b_{11}^2 b_{12}^2 b_{13}^2 b_{14}^2, \]
a long line containing superscripts $\delta^{22}\beta^{22}$,
almost touching the above formula,
\[ c = d, \]
and another short line,
\[ e = f. \]
\end{document}

produces

In my opinion, the vertical space after the first display is much too small, whereas after the second one it's too large.

Before I ask the question, I'd like to explain this behaviour: The first text line is short and doesn't overlap the diplay that follows, so TeX put only little vertical space in between, namely \abovedisplayshortskip. This is good. Now there is also \belowdisplayshortskip, but this doesn't behave as you might expect: It does control the vertical space after the display, but the space becomes small if the line above the display is short (which I find weird). This also explains why the space after the second display is large.

Now my question: Is there any way to obtain a \belowdisplayshortskip that becomes short if there is no overlap after the display? My fear is that in TeX/LaTeX the answer is no, but maybe with XeTeX or LuaTeX one can do something?

(I do have a fix for the problem, but this fix is also far from satisfactory. I set \belowdisplayshortskip=9pt plus 3pt minus 5pt, and then after each display where there is no overlap with the next line, I put a macro that makes the vertical space shorter. This is a real nuisance if one makes changes in the text.)

Answer 1

Finding better ways to handle displayed math including (sub)formulanumbers is on the todo list for luatex, but in the current situation even in luatex doing this is far from trivial.

The issue is that the engine puts the display on the page as a full-width line, and it takes considerable effort to extract the actual width(s) from that, even with luatex node processing.

Answer 2

An edit pushed up this question to the front page, so here's my take:

\documentclass{article}
\begin{document}
A short line,
\[ a = b_{11}^2 b_{12}^2 b_{13}^2 b_{14}^2, \]
a long line containing superscripts $\delta^{22}\beta^{22}$,
almost touching the above formula,
\[ c = d, \]
and another short line,
\[ e = f \]
followed by a longer line that we want to go beyond the limit so it wraps.

\bigskip\hrule\bigskip

\belowdisplayshortskip=\belowdisplayskip

A short line,
\[ a = b_{11}^2 b_{12}^2 b_{13}^2 b_{14}^2, \]
a long line containing superscripts $\delta^{22}\beta^{22}$,
almost touching the above formula,
\[ c = d, \]
and another short line,
\[ e = f \]
followed by a longer line that we want to go beyond the limit so it wraps.
\end{document}

TeX uses \belowdisplayshortskip if it used \abovedisplayshortskip before the display, but the parameters are independent: there's no law that imposes

\belowdisplayshortskip=\abovedisplayshortskip

and the parameter can be set to whatsoever value one wants. Setting it equal to \belowdisplayskip seems quite drastic, though.

Doing automatic adjustments might be really difficult; one can think of changing the parameter locally.

\documentclass{article}
\begin{document}
A short line,
\begingroup\belowdisplayshortskip=\belowdisplayskip
\[
  a = b_{11}^2 b_{12}^2 b_{13}^2 b_{14}^2,
\]\endgroup
a long line containing superscripts $\delta^{22}\beta^{22}$,
almost touching the above formula,
\[ c = d, \]
and another short line,
\[ e = f \]
followed by a longer line that we want to go beyond the limit so it wraps.
\end{document}