Why is a second displaymath instance a short line?

Question

I wanted to change \belowdisplayshortskip to move an equation up onto the preceding line, as there is space for it there, I like things compact in my notes.

However, this also moves equations up, namely those with 2, 4 and 5:

So as I understand it, why is it that display-math counts as a short line? how can I achieve the "moving up" without having space underneath? (\belowdisplayshortskip = 1\baselineskip plus 3.5pt minus 3pt would remedy the overlaps, but creates unnecessary and unwanted space underneath 2 and 5)

MWE:

\documentclass[12pt]{article}
\usepackage{lipsum}
\begin{document}
    % \abovedisplayshortskip = 0pt plus 3pt minus 0pt % default
    % \belowdisplayshortskip = 6.5pt plus 3.5pt minus 3pt % default
    \abovedisplayshortskip = -1\baselineskip plus 3pt minus 0pt
    \belowdisplayshortskip = 6.5pt plus 3.5pt minus 3pt
    \lipsum[1]
    A short line,
    \[ \int \mathrm{1 math}\int \]
    \[ \int \mathrm{2 math}\int \]
    \lipsum[1]
    \[ \int \mathrm{3 math}\int \]
    \[ \int \mathrm{4 math}\int \]
    \[ \int \mathrm{5 math}\int \]
   \lipsum[1]
\end{document}

Answer 1

If you need such compact notes, then you must set the glue values above and below display as follows:

\abovedisplayshortskip = -1\baselineskip
\abovedisplayskip=0pt
\belowdisplayshortskip = 0pt
\belowdisplayskip=0pt

Moreover, define the shortcut:

\def\nd{\predisplaysize=\hsize}

Then you can write:

\lipsum[1]

A short line, 
$$ \int \mathrm{1 math}\int $$
$$\nd \int \mathrm{2 math}\int $$
\lipsum[1]
$$ \int \mathrm{3 math}\int $$
$$\nd \int \mathrm{4 math}\int $$
$$\nd \int \mathrm{5 math}\int $$
\lipsum[1]

It means that if a next display math follows a previous immediately, then you must use \nd inside the next display. It re-assigns the internal value of \predisplaysize to the value as if it were the previous paragraph line full.

Of course, you can add some "plus" values to the glues, but "minus" values does not have sense here.

Answer 2

I think you're after the gather environment (or its non-numbered version gather*) from amsmath:

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{nccmath}
\usepackage{etoolbox}
\BeforeBeginEnvironment{gather*}{\useshortskip}

\usepackage{lipsum}

\begin{document}

    \lipsum[47]
    A short line,
\begin{gather*}
  \int \mathrm{1 math}\int \\
     \int \mathrm{2 math}\int
\end{gather*}
    \lipsum[47]
\begin{gather*}
    \int \mathrm{3 math}\int \\
    \int \mathrm{4 math}\int \\
    \int \mathrm{5 math}\int
\end{gather*}
   \lipsum[47]

\end{document} 

Answer 3

If you want compact notes consider using the savetrees package

\usepackage[extreme]{savetrees}

or some other alternatives as outlined here I'm looking for a compact style for the whole document. Also, for better math typesetting, look into aligned and gather from amsmath.

Output

notice the reduction in lines:

Code

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{lipsum}
\usepackage[extreme]{savetrees}

\begin{document}
\lipsum[47]
A short line,
\begin{gather*}
\int \mathrm{1 math}\int \\
\int \mathrm{2 math}\int
\end{gather*}
\lipsum[47]
\begin{gather*}
\int \mathrm{3 math}\int \\
\int \mathrm{4 math}\int \\
\int \mathrm{5 math}\int
\end{gather*}
\lipsum[47]
\end{document}