[Tex/LaTex] Auto-pagebreak in align environment: Is it possible

alignamsmathpage-breakingwarnings

I have a one-line statement of a theorem and a page-long proof of it. I have kept the proof inside

\begin{align*}
...
\end{align*}

Since there is no break TeXMaker keeps the whole proof in a single page. As a result, the previous page looks like: Theorem 2.2 in the first line, and the statement in the last line. The middle of the page shows a great white eternal void and the output shows the warning message:

"Underfull \vbox has occured while \output is active []"

How do I get rid of this? Is there anyway for the align environment to understand the turn of a page and generate auto-pagebreak? Is there any alternative to align which does not have this difficulty?

Best Answer

See the section “Vertical spacing and page breaks in multiline displays” in the amsmath documentation (texdoc amsmath or texdoc amsldoc). It says:

When the amsmath package is in use page breaks between equation lines are normally disallowed; the philosophy is that page breaks in such material should receive individual attention from the author. […]

If you prefer a strategy of letting page breaks fall where they may, even in the middle of a multi-line equation, then you might put \allowdisplaybreaks[1] in the preamble of your document. An optional argument 1–4 can be used for finer control: [1] means allow page breaks, but avoid them as much as possible; values of 2,3,4 mean increasing permissiveness.

You can read the documentation for more options.

Related Solutions

[Tex/LaTex] thmtools: How to prevent pagebreak between theorem and proof

Given that the theorem and proof environments are quite separate, it's indeed a bit tricky to forbid categorically all pagebreaks between them. All I can suggest is that you load the package needspace and insert the command

\Needspace{3\baselineskip}

close to the end of the statement of the theorem/corollary/whatever; note the uppercase N at the start of the macro. According to the manual of the needspace package, the command "\Needspace{} is less efficient [than \needspace{}] but reserves the requested space exactly. It should only be used between paragraphs." Given that you're basically facing this situation, you may want to give it a try.

You'll probably have to practice a bit to determine the best placement of this command and the number of baseline skips you require in order to always get at least two lines of the proof statement to show up on the same page as the associated theorem.

[Tex/LaTex] How to add partial horizontal lines in horizontally aligned math environments

The answer of egreg has the tiny drawback, that the values for \tleq has to be found manually. This answer fills the gap.

Package amsmath processes its equations twice. In the first run, the widths are measured. The switch \ifmeasure@ is true during this measuring phase. In the second run the equations are actually typeset. Depending on the measured widths of the first run amsmath is now able to move the equation number if necessary, for example.

Also environment alignat* stores the widths of the cells and calculates the maximal widths of the columns.

After the measuring phase the widths of the columns are available in macro \maxcolumn@width. The values are prefixed with \or for easy use with \ifcase, e.g.:

\or 23.1945pt \or 25.221pt \or 10.00002pt \or 12.77773pt \or 54.77959pt \or 62.81717pt \or 74.90263pt \or 0.0pt \or 0.0pt

Count register \column@ holds the current column number.

The following example defines the macro \tline that uses these data to draw a line with the width of the current column. In right aligned columns it is placed after the cell contents, in left aligned columns \tline should start the cell.

\documentclass{article}
\usepackage{amsmath}

\makeatletter
\newcommand*{\tline}{%
  \ifmeasuring@
    % first measuring run
  \else
    % second run
    % \typeout{\meaning\maxcolumn@widths}% debug info
    \ifodd\column@
      \expandafter\rlap
    \else
      \expandafter\llap
    \fi
    {% 
      \vrule height-1ex depth \dimexpr1ex+.4pt\relax width
      \ifcase\numexpr\column@+1\expandafter\relax
      \maxcolumn@widths
      \fi
    }%
  \fi
}
\makeatother

\begin{document}

\begin{alignat*}{4}
a^1 x^\star &\leq b_1 &\quad& \Rightarrow & \delta_1 a^1 x^\star &\leq
\delta_1 b_1 \\
a^2 x^\star &\leq b_2 &&      \Rightarrow & \delta_2 a^2 x^\star &\leq
\delta_2 b_2 \\[-4.5pt]
        &\;\;\vdots   &&  \;\;\vdots      &                  &\;\;\vdots \\
a^m x^\star &\leq b_m &&      \Rightarrow & \delta_m a^m x^\star
\tline&\tline \leq\delta_m b_m \quad (+) \\
&&&& \sum_{1 \leq i \leq m} \delta_i a^i x^\star &\leq \delta_i b_i &
\quad\Rightarrow \delta^t A x^\star \leq \delta^t b
\end{alignat*}

\end{document}

Remark:

The space above \vdots is a little large for my taste, macro \vdots already adds 6pt at the top of the dots. Therefore I have reduced it a bit.

`\cline` in `alignat*` and better vertical centered dots

An easier solution is \cline, it also works in environment alignat*, only the space before needs some adjusting.
\rvdots of egreg's answer (see Qrrbrbirlbel's comment) cheats a little, it reduces the height by 1pt. The example below defines \mvdots that uses \vcenter instead of \vbox that reduces the asymmetry by participating the descender.

Example file:

\documentclass{article}
\usepackage{amsmath}

\makeatletter
\DeclareRobustCommand{\mvdots}{%
  \vcenter{%
    \baselineskip4\p@\lineskiplimit\z@
    \hbox{.}\hbox{.}\hbox{.}%
  }%
}
\makeatother

\begin{document}

\begin{alignat*}{4}
a^1 x^\star &\leq b_1 &\quad& \Rightarrow & \delta_1 a^1 x^\star &\leq
\delta_1 b_1 \\
a^2 x^\star &\leq b_2 &&      \Rightarrow & \delta_2 a^2 x^\star &\leq
\delta_2 b_2 \\
        &\;\;\mvdots   &&  \;\;\mvdots      &                  &\;\;\mvdots \\
a^m x^\star &\leq b_m &&      \Rightarrow & \delta_m a^m x^\star
& \leq\delta_m b_m \quad (+) \\[-2ex]
\cline{5-6}
&&&&\sum_{1 \leq i \leq m} \delta_i a^i x^\star &\leq \delta_i b_i &
\quad\Rightarrow \delta^t A x^\star \leq \delta^t b
\end{alignat*}

\end{document}

Best Answer

Related Solutions

[Tex/LaTex] thmtools: How to prevent pagebreak between theorem and proof

[Tex/LaTex] How to add partial horizontal lines in horizontally aligned math environments

\cline in alignat* and better vertical centered dots

Related Question

`\cline` in `alignat*` and better vertical centered dots