\abovedisplayskip and related commands

\abovedisplayskip is one of 4 commands to control the amount of glue (flexible space) that TEX engines add before, and after, a displayed equation:

• \abovedisplayskip[=] glue
• \belowdisplayskip[=] glue
• \abovedisplayshortskip[=] glue
• \belowdisplayshortskip[=] glue

where glue is some “flexible space” and the “[=]” indicates that an optional “=” can follow after the command.

usage example \abovedisplayskip=12pt plus 3pt minus 9pt ( the “=” sign) is optional).

Each of the 4 commands above can be used to set (store) your preferred glue value that TEX can use when typesetting display mathematics.

Choosing which glues to use

As with most TEX algorithms, a full description needs to address many fine details but, to a first approximation, TEX checks whether the last line in the paragraph and the equation “overlap”: the outcome of that comparison determines which glue to place above and below the equation. In practice, TEX also tests for the presence of an equation number.

If the equation is preceded by a “sufficiently short” line the glue stored in \abovedisplayshortskip will be inserted above the equation and the glue value stored in \belowdisplayshortskip will be inserted after it. For longer lines (or longer equations), TEX will instead insert the glue \abovedisplayskip above the equation and \belowdisplayskip below it.

A detailed explanation of exactly how TEX chooses which glue to place above a display equation (\abovedisplayskip or \abovedisplayshortskip) or below it (\belowdisplayskip or \belowdisplayshortskip) can be found on pages 188–9 of The TEXbook.

Examples

For demonstration purposes, we’ll use some “extreme” values for the various glues so that their effect is clearly visible. We’ll choose \abovedisplayshortskip=-20pt which will moves a display equation upwards by 20pt if that equation is preceded by a sufficiently short line. We’ll also use \belowdisplayshortskip=100pt to set the glue (100 pt) inserted below the displayed equation. Here, we’ll use the Schrödinger equation as the basis for illustrating the effect of these commands:

\[ \frac{\hbar^2}{2m}\nabla^2\Psi + V(\mathbf{r})\Psi
= -i\hbar \frac{\partial\Psi}{\partial t} \]

which produces the following mathematics:

\[ \frac{\hbar ^2}{2m}\nabla ^2\Psi + V(\mathbf{r})\Psi = -i\hbar \frac{\partial \Psi }{\partial t} \] The following example uses the “extreme” glue values mentioned above:

\abovedisplayshortskip=-20pt
\belowdisplayshortskip=100pt
\noindent A short last line...
\[ \frac{\hbar^2}{2m}\nabla^2\Psi + V(\mathbf{r})\Psi
= -i\hbar \frac{\partial\Psi}{\partial t} \]
... a short concluding line.

The following graphic shows the results:

As you can see, the Schrödinger equation has been shifted upwards by 20pt with 100pt of space added below it.

However, if we now use a much wider equation with \abovedisplayshortskip=-20pt and \belowdisplayshortskip=100pt or increase the length of the last line in our paragraph those two glue settings are ignored because the displayed equation “overlaps” the last line. Here, TEX now uses the glues \abovedisplayskip above the equation and \belowdisplayskip below it. Here, we have not set values for \abovedisplayskip or \belowdisplayskip but simply use their default values:

\abovedisplayshortskip=-20pt
\belowdisplayshortskip=100pt
\noindent A short last line...
\[\int_{x^2 + y^2 \leq R^2} f(x,y)\,dx\,dy
= \int_{\theta=0}^{2\pi} \int_{r=0}^R
f(r\cos\theta,r\sin\theta) r\,dr\,d\theta.\]
... a short concluding line.

The following graphic shows the results:

Now we’ll typeset the the Schrödinger equation but make sure the last line is longer:

\abovedisplayshortskip=-20pt
\belowdisplayshortskip=100pt
\noindent A longer last line now precedes our Schr\"{o}dinger equation. As a result,
\TeX{} will use the glues \verb|\abovedisplayskip| above the equation and
\verb|\belowdisplayskip| below it, ignoring the ‘‘extreme’’ values we supplied:
\verb|\abovedisplayshortskip=-20pt| and \verb|\belowdisplayshortskip=100pt|.
\[ \frac{\hbar^2}{2m}\nabla^2\Psi + V(\mathbf{r})\Psi
= -i\hbar \frac{\partial\Psi}{\partial t} \]
... a short concluding line.

The following graphic shows the results:

Related commands

• \displaywidth[=] dimension
• \displayindent[=] dimension
• \predisplaysize[=] dimension

where dimension is a lenth in units understood by TEX. The “[=]” indicates that an optional equals follows after the command.