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mathtools.dtx
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mathtools.dtx
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% \iffalse meta-comment
%
% Copyright (C) 2004-2011 by Morten Hoegholm
% Copyright (C) 2012-2019 by Lars Madsen
% Copyright (C) 2020 by Lars Madsen, The LaTeX3 team
%
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either
% version 1.3c of this license or (at your option) any later
% version. The latest version of this license is in
% http://www.latex-project.org/lppl.txt
% and version 1.3c or later is part of all distributions of
% LaTeX version 2008/05/05 or later.
%
% This work has the LPPL maintenance status "maintained".
%
% This Current Maintainer of this work is
% Lars Madsen
%
% This work consists of the main source file mathtools.dtx
% and the derived files
% mathtools.sty, mathtools.pdf, mathtools.ins, mathtools.drv.
%
% Distribution:
% CTAN:macros/latex/contrib/mh/mathtools.dtx
% CTAN:macros/latex/contrib/mh/mathtools.pdf
%
% Unpacking:
% (a) If mathtools.ins is present:
% tex mathtools.ins
% (b) Without mathtools.ins:
% tex mathtools.dtx
% (c) If you insist on using LaTeX
% latex \let\install=y\input{mathtools.dtx}
% (quote the arguments according to the demands of your shell)
%
% Documentation:
% (a) If mathtools.drv is present:
% latex mathtools.drv
% (b) Without mathtools.drv:
% latex mathtools.dtx; ...
% The class ltxdoc loads the configuration file ltxdoc.cfg
% if available. Here you can specify further options, e.g.
% use A4 as paper format:
% \PassOptionsToClass{a4paper}{article}
%
% Programm calls to get the documentation (example):
% pdflatex mathtools.dtx
% makeindex -s gind.ist mathtools.idx
% pdflatex mathtools.dtx
% makeindex -s gind.ist mathtools.idx
% pdflatex mathtools.dtx
%
% Installation:
% TDS:tex/latex/mh/mathtools.sty
% TDS:doc/latex/mh/mathtools.pdf
% TDS:source/latex/mh/mathtools.dtx
%
%<*ignore>
\begingroup
\def\x{LaTeX2e}
\expandafter\endgroup
\ifcase 0\ifx\install y1\fi\expandafter
\ifx\csname processbatchFile\endcsname\relax\else1\fi
\ifx\fmtname\x\else 1\fi\relax
\else\csname fi\endcsname
%</ignore>
%<*install>
\input docstrip.tex
\Msg{************************************************************************}
\Msg{* Installation}
\Msg{* Package: mathtools 2021/03/28 v1.26}
\Msg{************************************************************************}
\keepsilent
\askforoverwritefalse
\preamble
This is a generated file.
Copyright (C) 2002-2011 by Morten Hoegholm
Copyright (C) 2012-2019 by Lars Madsen
Copyright (C) 2020- by Lars Madsen, the LaTeX3 project
This work may be distributed and/or modified under the
conditions of the LaTeX Project Public License, either
version 1.3c of this license or (at your option) any later
version. The latest version of this license is in
http://www.latex-project.org/lppl.txt
and version 1.3c or later is part of all distributions of
LaTeX version 2008/05/04 or later.
This work has the LPPL maintenance status "maintained".
This Current Maintainer of this work is
Lars Madsen and the LaTeX3 project
This work consists of the main source file mathtools.dtx
and the derived files
mathtools.sty, mathtools.pdf, mathtools.ins, mathtools.drv.
\endpreamble
\generate{%
\file{mathtools.ins}{\from{mathtools.dtx}{install}}%
\file{mathtools.drv}{\from{mathtools.dtx}{driver}}%
\usedir{tex/latex/mh}%
\file{mathtools.sty}{\from{mathtools.dtx}{package}}%
}
\obeyspaces
\Msg{************************************************************************}
\Msg{*}
\Msg{* To finish the installation you have to move the following}
\Msg{* file into a directory searched by TeX:}
\Msg{*}
\Msg{* mathtools.sty}
\Msg{*}
\Msg{* To produce the documentation run the file `mathtools.drv'}
\Msg{* through LaTeX.}
\Msg{*}
\Msg{* Happy TeXing!}
\Msg{*}
\Msg{************************************************************************}
\endbatchfile
%</install>
%<*ignore>
\fi
%</ignore>
%<*driver>
\NeedsTeXFormat{LaTeX2e}
\ProvidesFile{mathtools.drv}%
[2021/03/28 v1.28 mathematical typesetting tools]
\documentclass{ltxdoc}
\IfFileExists{fourier.sty}{\usepackage{fourier}}{}
\addtolength\marginparwidth{-25pt}
\usepackage{mathtools}
\setcounter{IndexColumns}{2}
\providecommand*\pkg[1]{\textsf{#1}}
\providecommand*\env[1]{\texttt{#1}}
\providecommand*\email[1]{\href{mailto:#1}{\texttt{#1}}}
\providecommand*\mode[1]{\texttt{[#1]}}
\providecommand*\file[1]{\texttt{#1}}
\usepackage{xcolor,varioref,amssymb}
\makeatletter
\newcommand*\thinfbox[2][black]{\fboxsep0pt\textcolor{#1}{\rulebox{{\normalcolor#2}}}}
\newcommand*\thinboxed[2][black]{\thinfbox[#1]{\ensuremath{\displaystyle#2}}}
\newcommand*\rulebox[1]{%
\sbox\z@{\ensuremath{\displaystyle#1}}%
\@tempdima\dp\z@
\hbox{%
\lower\@tempdima\hbox{%
\vbox{\hrule height\fboxrule\box\z@\hrule height\fboxrule}%
}%
}%
}
\newenvironment{codesyntax}
{\par\small\addvspace{4.5ex plus 1ex}%
\vskip -\parskip
\noindent
\begin{tabular}{|l|}\hline\ignorespaces}%
{\\\hline\end{tabular}\nobreak\par\nobreak
\vspace{2.3ex}\vskip -\parskip\noindent\ignorespacesafterend}
\makeatletter
\newcommand*\FeatureRequest[2]{%
\hskip1sp
\marginpar{%
\parbox[b]{\marginparwidth}{\small\sffamily\raggedright
\strut Feature request by\\#1\\#2%
}
}%
}
\newcommand*\ProvidedBy[2]{%
\hskip1sp
\marginpar{%
\parbox[b]{\marginparwidth}{\small\sffamily\raggedright
\strut Feature provided by\\#1\\#2%
}
}%
}
\newcommand*\SuggestedBy[2]{%
\hskip1sp
\marginpar{%
\parbox[b]{\marginparwidth}{\small\sffamily\raggedright
\strut Suggested by\\#1\\#2%
}
}%
}
\newcommand*\cttPosting[2]{%
\hskip1sp
\marginpar{%
\parbox[b]{\marginparwidth}{\small\sffamily\raggedright
\strut Posted on \texttt{comp.text.tex} \\#1\\#2%
}%
}%
}
\newcommand*\tsxPosting[2]{%
\hskip1sp
\marginpar{%
\parbox[b]{\marginparwidth}{\small\sffamily\raggedright
\strut Posted on \texttt{\small tex.stackexchange.com} \\#1\\#2%
}%
}%
}
\newcommand*\tsxchatPosting[3][Requested on]{%
\hskip1sp
\marginpar{%
\parbox[b]{\marginparwidth}{\small\sffamily\raggedright
\strut #1 \texttt{\scriptsize tex.stackexchange.com chat} \\#2\\#3%
}%
}%
}
\newcommand*\CommentAdded[1]{%
\hskip1sp
\marginpar{%
\parbox[b]{\marginparwidth}{\small\sffamily\raggedright
\strut Comment added\\#1%
}%
}%
}
\expandafter\def\expandafter\MakePrivateLetters\expandafter{%
\MakePrivateLetters \catcode`\_=11\relax
}
\providecommand*\SpecialOptIndex[1]{%
\@bsphack
\index{#1\actualchar{\protect\ttfamily #1}
(option)\encapchar usage}%
\index{options:\levelchar#1\actualchar{\protect\ttfamily #1}\encapchar
usage}\@esphack}
\providecommand*\opt[1]{\texttt{#1}}
\providecommand*\SpecialKeyIndex[1]{%
\@bsphack
\index{#1\actualchar{\protect\ttfamily #1}
(key)\encapchar usage}%
\index{keys:\levelchar#1\actualchar{\protect\ttfamily #1}\encapchar
usage}\@esphack}
\providecommand*\key[1]{\textsf{#1}}
\providecommand*\eTeX{$\m@th\varepsilon$-\TeX}
\def\MTmeta#1{%
\ensuremath\langle
\ifmmode \expandafter \nfss@text \fi
{%
\meta@font@select
\edef\meta@hyphen@restore
{\hyphenchar\the\font\the\hyphenchar\font}%
\hyphenchar\font\m@ne
\language\l@nohyphenation
#1\/%
\meta@hyphen@restore
}\ensuremath\rangle
\endgroup
}
\makeatother
\DeclareRobustCommand\meta{\begingroup\MakePrivateLetters\MTmeta}%
\def\MToarg#1{{\ttfamily[}\meta{#1}{\ttfamily]}\endgroup}
\DeclareRobustCommand\oarg{\begingroup\MakePrivateLetters\MToarg}%
\def\MHmarg#1{{\ttfamily\char`\{}\meta{#1}{\ttfamily\char`\}}\endgroup}
\DeclareRobustCommand\marg{\begingroup\MakePrivateLetters\MHmarg}%
\def\MHarg#1{{\ttfamily\char`\{#1\ttfamily\char`\}}\endgroup}
\DeclareRobustCommand\arg{\begingroup\MakePrivateLetters\MHarg}%
\def\MHcs#1{\texttt{\char`\\#1}\endgroup}
\DeclareRobustCommand\cs{\begingroup\MakePrivateLetters\MHcs}
\def\endverbatim{\if@newlist
\leavevmode\fi\endtrivlist\vspace{-\baselineskip}}
\expandafter\let\csname endverbatim*\endcsname =\endverbatim
\let\MTtheindex\theindex
\def\theindex{\MTtheindex\MakePrivateLetters}
%\usepackage[draft]{fixme}
%\fxsetup{
% multiuser,
%layout=marginnote,
%}
%\providecommand\fxnote[2][]{}
\usepackage{xurl}
\usepackage[final,
hyperindex=false,
colorlinks,
]{hyperref}
\renewcommand*\usage[1]{\textit{\hyperpage{#1}}}
\OnlyDescription
\begin{document}
\DocInput{mathtools.dtx}
\end{document}
%</driver>
% \fi
%
% \changes{v1.19}{2017/03/31}{Updated to match some macro renaming in
% \pkg{mhsetup}}
% \changes{v1.0}{2004/07/26}{Initial release}
%
% \GetFileInfo{mathtools.drv}
%
% \CheckSum{3529}
%
% \title{The \pkg{mathtools} package\thanks{This file has version number
% \fileversion, last revised \filedate.}}
%
% \author{Morten Høgholm, Lars Madsen and the \LaTeX3 project}
% \date{\filedate}
%
% \maketitle
%
% \begin{abstract}
% \noindent The \pkg{mathtools} package is an extension package to
% \pkg{amsmath}. There are two things on \pkg{mathtools}' agenda:
% (1)~correct various bugs/defeciencies in \pkg{amsmath} until
% these are fixed by the \AmS{} and (2)~provide useful tools
% for mathematical typesetting, be it a small macro for
% typesetting a prescript or an underbracket, or entirely new
% display math constructs such as a \env{multlined} environment.
% \end{abstract}
%
% \tableofcontents
%
% \section{Introduction}
%
% Although \pkg{amsmath} provides many handy tools for mathematical
% typesetting, it is nonetheless a static package. This is not a bad
% thing, because what it does, it mostly does quite well and having
% a stable math typesetting package is ``a good thing.'' However,
% \pkg{amsmath} does not fulfill all the needs of the mathematical
% part of the \LaTeX{} community, resulting in many authors writing
% small snippets of code for tweaking the mathematical layout. Some
% of these snippets have also been posted to newsgroups and mailing
% lists over the years, although more often than not without being
% released as stand-alone packages.
%
% The \pkg{mathtools} package is exactly what its name implies: tools
% for mathematical typesetting. It is a collection of many of these
% often needed small tweaks---with some big tweaks added as well. It
% can only do so by having harvesting newsgroups for code and/or you
% writing the maintainers with wishes for code to be included, so if
% you have any good macros or just macros that help you when writing
% mathematics, then don't hesitate to report them.
%
% As of 2020, \pkg{mathtools} (and \pkg{empheq}) is now hosted at the
% \LaTeX3 team GitHub at
% \begin{center}
% \url{https://github.com/latex3/mathtools}
% \end{center}
% So if you have any issue, feel free to register an issue there.
%
% \medskip\noindent
% Update 2013: We now make \cs{(}\cs{)} and \cs[\cs]
% robust (can be disabled via \texttt{nonrobust} package option).
%
% \section{Package loading}
%
%
% The \pkg{mathtools} package requires \pkg{amsmath} but is able to
% pass options to it as well. Thus a line like
% \begin{verbatim}
% \usepackage[fleqn,tbtags]{mathtools}
% \end{verbatim}
% is equivalent to
% \begin{verbatim}
% \usepackage[fleqn,tbtags]{amsmath}
% \usepackage{mathtools}
% \end{verbatim}
%
%
% \subsection{Special \pkg{mathtools} options}
%
% \begin{codesyntax}
% \SpecialOptIndex{fixamsmath}\opt{fixamsmath}\texttt{~~~~}
% \SpecialOptIndex{donotfixamsmathbugs}\opt{donotfixamsmathbugs}
% \end{codesyntax}
% The option \opt{fixamsmath} (default) fixes two bugs in
% \pkg{amsmath}.\footnote{See the online \LaTeX{} bugs database
% \url{http://www.latex-project.org/cgi-bin/ltxbugs2html} under
% \AmS\LaTeX{} problem reports 3591 and 3614.} Should you for some
% reason not want to fix these bugs then just add the option
% \opt{donotfixamsmathbugs} (if you can do it without typos). The
% reason for this extremely long name is that I really don't see why
% you wouldn't want these bugs to be fixed, so I've made it slightly
% difficult not to fix them.
%
% \begin{codesyntax}
% \SpecialOptIndex{allowspaces}\opt{allowspaces}\texttt{~~~~}
% \SpecialOptIndex{disallowspaces}\opt{disallowspaces}
% \end{codesyntax}
% Sometimes \pkg{amsmath} gives you nasty surprises, as here where
% things look seemingly innocent:
% \begin{verbatim}
% \[
% \begin{gathered}
% [p] = 100 \\
% [v] = 200
% \end{gathered}
% \]
% \end{verbatim}
% Without \pkg{mathtools} this will result in this output:
% \[
% \begin{gathered}[c]
% = 100 \\
% [v] = 200
% \end{gathered}
% \]
% Yes, the \texttt{[p]} has been gobbled without any warning
% whatsoever.\footnote{\pkg{amsmath} thought the \texttt[p] was an
% optional argument, checked if it was \texttt{t} or \texttt{b} and
% when both tests failed, assumed it was a \texttt{c}.} This is
% hardly what you'd expect as an end user, as the desired output was
% probably something like this instead:
% \[
% \begin{gathered}[c]
% [p] = 100 \\
% [v] = 200
% \end{gathered}
% \]
% With the option \opt{disallowspaces} (default) \pkg{mathtools}
% disallows spaces in front of optional arguments where it could
% possibly cause problems just as \pkg{amsmath} does with |\\|
% inside the display environments. This includes the environments
% \env{gathered} (and also those shown in \S
% \vref{subsec:gathered}), \env{aligned}, \env{multlined}, and the
% extended \env{matrix}-environments (\S \vref{subsubsec:matrices}).
% If you however want to preserve the more dangerous standard
% optional spaces, simply choose the option \opt{allowspaces}.
%
%
% \section{Tools for mathematical typesetting}
%
% \begin{codesyntax}
% \SpecialUsageIndex{\mathtoolsset}\cs{mathtoolsset}\marg{key val list}
% \end{codesyntax}
% Many of the tools shown in this manual can be turned on and off by
% setting a switch to either true or false. In all cases it is done
% with the command \cs{mathtoolsset}. A typical use could be something like
% \begin{verbatim}
% \mathtoolsset{
% showonlyrefs,
% mathic % or mathic = true
% }
% \end{verbatim}
% More information on the keys later on.
%
% \subsection{Fine-tuning mathematical layout}
%
% Sometimes you need to tweak the layout of formulas a little to get
% the best result and this part of the manual describes the various
% macros \pkg{mathtools} provides for this.
%
% \subsubsection{A complement to \texttt{\textbackslash smash},
% \texttt{\textbackslash llap}, and \texttt{\textbackslash rlap}}
%
% \begin{codesyntax}
% \SpecialUsageIndex{\mathllap}
% \cs{mathllap}\oarg{mathstyle}\marg{math}\texttt{~~}
% \SpecialUsageIndex{\mathclap}
% \cs{mathclap}\oarg{mathstyle}\marg{math}\\
% \SpecialUsageIndex{\mathrlap}
% \cs{mathrlap}\oarg{mathstyle}\marg{math}\texttt{~~}
% \SpecialUsageIndex{\clap}
% \cs{clap}\marg{text}\\
% \SpecialUsageIndex{\mathmbox}
% \cs{mathmbox}\marg{math}\phantom{\meta{mathstyle}}\texttt{~~~~}
% \SpecialUsageIndex{\mathmakebox}
% \cs{mathmakebox}\oarg{width}\oarg{pos}\marg{math}
% \end{codesyntax}
% In \cite{Perlis01}, Alexander R.~Perlis describes some simple yet
% useful macros for use in math displays. For example the display
% \begin{verbatim}
% \[
% X = \sum_{1\le i\le j\le n} X_{ij}
% \]
% \end{verbatim}
% \[
% X = \sum_{1\le i\le j\le n} X_{ij}
% \]
% contains a lot of excessive white space. The idea that comes to
% mind is to fake the width of the subscript. The command
% \cs{mathclap} puts its argument in a zero width box and centers
% it, so it could possibly be of use here.
% \begin{verbatim}
% \[
% X = \sum_{\mathclap{1\le i\le j\le n}} X_{ij}
% \]
% \end{verbatim}
% \[
% X = \sum_{\mathclap{1\le i\le j\le n}} X_{ij}
% \]
% For an in-depth discussion of
% these macros I find it better to read the article; an online
% version can be found at
% \begin{quote}
% \url{http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf}
% \end{quote}
% Note that the definitions shown in the article do not exactly
% match the definitions in \pkg{mathtools}. Besides providing an
% optional argument for specifying the desired math style, these
% versions also work around a most unfortunate \TeX{}
% ``feature.''\footnote{The faulty reboxing procedure.} The
% \cs{smash} macro is fixed too.
%
%
% \subsubsection{Forcing a cramped style}
%
% \begin{codesyntax}
% \SpecialUsageIndex{\cramped}
% \cs{cramped}\oarg{mathstyle}\marg{math}
% \end{codesyntax}
% \cttPosting{Michael Herschorn}{1992/07/21}
% Let's look at another example where we have used \cs{mathclap}:
% \begin{verbatim}
% \begin{equation}\label{eq:mathclap}
% \sum_{\mathclap{a^2<b^2<c}}\qquad
% \sum_{a^2<b^2<c}
% \end{equation}
% \end{verbatim}
% \begin{equation}\label{eq:mathclap}
% \sum_{\mathclap{a^2<b^2<c}}\qquad
% \sum_{a^2<b^2<c}
% \end{equation}
% Do you see the difference? Maybe if I zoomed in a bit:
% \begingroup \fontsize{24}{\baselineskip}\selectfont
% \[
% \sum_{\mathclap{a^2<b^2<c}}\qquad
% \sum_{a^2<b^2<c}
% \]
% \endgroup
% Notice how the limit of the right summation sign is typeset in a
% more compact style than the left. It is because \TeX{} sets the
% limits of operators in a \emph{cramped} style. For each of \TeX'
% four math styles (\cs{displaystyle}, \cs{textstyle},
% \cs{scriptstyle}, and \cs{scriptscriptstyle}), there also exists a
% cramped style that doesn't raise exponents as much. Besides in the
% limits of operators, \TeX{} also automatically uses these cramped
% styles in radicals such as \cs{sqrt} and in the denominators of
% fractions, but unfortunately there are no primitive commands that
% allows you to detect crampedness or switch to it.
%
% \pkg{mathtools} offers the command \cs{cramped} which forces a
% cramped style in normal un-cramped math. Additionally you can
% choose which of the four styles you want it in as well by
% specifying it as the optional argument:
% \begin{verbatim}
% \[
% \cramped{x^2} \leftrightarrow x^2 \quad
% \cramped[\scriptstyle]{x^2} \leftrightarrow {\scriptstyle x^2}
% \]
% \end{verbatim}
% \[
% \cramped{x^2} \leftrightarrow x^2 \quad
% \cramped[\scriptstyle]{x^2} \leftrightarrow {\scriptstyle x^2}
% \]
% You may be surprised how often the cramped style can be
% beneficial to your output. Take a look at this example:
% \begin{verbatim}
% \begin{quote}
% The 2005 Euro\TeX{} conference is held in Abbaye des
% Pr\'emontr\'es, France, marking the 16th ($2^{2^2}$) anniversary
% of both Dante and GUTenberg (the German and French \TeX{} users
% group resp.).
% \end{quote}
% \end{verbatim}
% \begin{quote}
% The 2005 Euro\TeX{} conference is held in Abbaye des
% Pr\'emontr\'es, France, marking the 16th ($2^{2^2}$) anniversary
% of both Dante and GUTenberg (the German and French \TeX{} users
% group resp.).
% \end{quote}
% Typesetting on a grid is generally considered quite desirable, but
% as the second line of the example shows, the exponents of $2$
% causes the line to be too tall for the normal value of
% \cs{baselineskip}, so \TeX{} inserts a \cs{lineskip} (normal value
% is \the\lineskip). In order to circumvent the problem, we can
% force a cramped style so that the exponents aren't raised as much:
% \begin{verbatim}
% \begin{quote}
% The 2005 Euro\TeX{} ... 16th ($\cramped{2^{2^2}}$) ...
% \end{quote}
% \end{verbatim}
% \begin{quote}
% The 2005 Euro\TeX{} conference is held in Abbaye des
% Pr\'emontr\'es, France, marking the 16th ($\cramped{2^{2^2}}$)
% anniversary of both Dante and GUTenberg (the German and French
% \TeX{} users group resp.).
% \end{quote}
%
% \begin{codesyntax}
% \SpecialUsageIndex{\crampedllap}
% \cs{crampedllap}\oarg{mathstyle}\marg{math}\texttt{~~}
% \SpecialUsageIndex{\crampedclap}
% \cs{crampedclap}\oarg{mathstyle}\marg{math}\\
% \SpecialUsageIndex{\crampedrlap}
% \cs{crampedrlap}\oarg{mathstyle}\marg{math}
% \end{codesyntax}
% The commands \cs{crampedllap}, \cs{crampedclap}, and
% \cs{crampedrlap} are identical to the three \cs{mathXlap} commands
% described earlier except the argument is typeset in cramped style.
% You need this in order to typeset \eqref{eq:mathclap} correctly
% while still faking the width of the limit.
% \begin{verbatim}
% \begin{equation*}\label{eq:mathclap-b}
% \sum_{\crampedclap{a^2<b^2<c}}
% \tag{\ref{eq:mathclap}*}
% \end{equation*}
% \end{verbatim}
% \begin{equation*}\label{eq:mathclap-b}
% \sum_{\crampedclap{a^2<b^2<c}}
% \tag{\ref{eq:mathclap}*}
% \end{equation*}
% Of course you could just type
% \begin{verbatim}
% \sum_{\mathclap{\cramped{a^2<b^2<c}}}
% \end{verbatim}
% but it has one major disadvantage: In order for \cs{mathXlap} and
% \cs{cramped} to get the right size, \TeX{} has to process them
% four times, meaning that nesting them as shown above will cause
% \TeX{} to typeset $4^2$ instances before choosing the right one.
% In this situation however, we will of course need the same style
% for both commands so it makes sense to combine the commands in
% one, thus letting \TeX{} make the choice only once rather than
% twice.
%
% \begin{codesyntax}
% \SpecialEnvIndex{crampedsubarray}\cs{begin}\arg{crampedsubarray}\marg{col}
% \meta{contents} \cs{end}\arg{crampedsubarray}\\
% \SpecialUsageIndex{\crampedsubstack}
% \cs{crampedsubstack}\marg{lines separated by \cs{}\cs{}}
% \end{codesyntax}
% \SuggestedBy{Henri Menke}{2019/07/08} If we go back to
% \eqref{eq:mathclap} and apply \cs{substack}, you'll notice that the
% cramped style, the sum would normally apply, is now gone:
% \begin{verbatim}
% \[
% \sum_{\substack{a^2<b^2<c}}\qquad
% \sum_{a^2<b^2<c}
% \]
% \end{verbatim}
% \begingroup \fontsize{24}{\baselineskip}\selectfont
% \[
% \sum_{\substack{a^2<b^2<c}}\qquad
% \sum_{a^2<b^2<c}
% \]
% \endgroup
% We therefore provide a cramped version of
% \cs{substack}.\footnote{\cs{substack} is internally implemented via
% the \env{subarray}-env, so our cramped version of \cs{substack} is implemented via a
% cramped version of this env.}
% \begin{verbatim}
% \[
% \sum_{\crampedsubstack{a^2<b^2<c}}\qquad
% \sum_{a^2<b^2<c}
% \]
% \end{verbatim}
% \begingroup \fontsize{24}{\baselineskip}\selectfont
% \[
% \sum_{\crampedsubstack{a^2<b^2<c}}\qquad
% \sum_{a^2<b^2<c}
% \]
% \endgroup
% Note: We may need to add a similar hook into multlined.
%
%
%
%
%
% \subsubsection{Smashing an operator}
%
%
%
% \begin{codesyntax}
% \SpecialUsageIndex{\smashoperator}
% \cs{smashoperator}\oarg{pos}\marg{operator with limits}
% \end{codesyntax}
% \FeatureRequest{Lars Madsen}{2004/05/04} Above we showed how to get
% \LaTeX{} to ignore the width of the subscript of an
% operator. However this approach takes a lot of extra typing,
% especially if you have a wide superscript, meaning you have to put
% in \cs{crampedclap} in both sub- and superscript. To make things
% easier, \pkg{mathtools} provides a \cs{smashoperator} command,
% which simply ignores the width of the sub- and superscript. It also
% takes an optional argument, \texttt{l}, \texttt{r}, or \texttt{lr}
% (default, \texttt{rl} is an alias for \texttt{lr}), denoting which
% side of the operator should be ignored (smashed).
% \begin{verbatim}
% \[
% V = \sum_{1\le i\le j\le n}^{\infty} V_{ij} \quad
% X = \smashoperator{\sum_{1\le i\le j\le n}^{3456}} X_{ij} \quad
% Y = \smashoperator[r]{\sum\limits_{1\le i\le j\le n}} Y_{ij} \quad
% Z = \smashoperator[l]{\mathop{T}_{1\le i\le j\le n}} Z_{ij}
% \]
% \end{verbatim}
% \[
% V = \sum_{1\le i\le j\le n}^{\infty} V_{ij} \quad
% X = \smashoperator{\sum_{1\le i\le j\le n}^{3456}} X_{ij} \quad
% Y = \smashoperator[r]{\sum\limits_{1\le i\le j\le n}} Y_{ij} \quad
% Z = \smashoperator[l]{\mathop{T}_{1\le i\le j\le n}} Z_{ij}
% \]
% Note that \cs{smashoperator} always sets its argument in display
% style and with limits even if you have used the \opt{nosumlimits}
% option of \pkg{amsmath}. If you wish, you can use shorthands for
% \texttt{\_} and \texttt{\textasciicircum} such as \cs{sb} and
% \cs{sp}.
%
%
% \subsubsection{Adjusting limits of operators}
%
% \begin{codesyntax}
% \SpecialUsageIndex{\adjustlimits}
% \cs{adjustlimits}\marg{operator$\sb1$}\texttt{\_}\marg{limit$\sb1$}
% \marg{operator$\sb2$}\texttt{\_}\marg{limit$\sb2$}
% \end{codesyntax}
% \FeatureRequest{Lars Madsen}{2004/07/09}
% When typesetting two consecutive operators with limits one often
% wishes the limits of the operators were better aligned. Look
% closely at these examples:
% \begin{verbatim}
% \[
% \text{a)} \lim_{n\to\infty} \max_{p\ge n} \quad
% \text{b)} \lim_{n\to\infty} \max_{p^2\ge n} \quad
% \text{c)} \lim_{n\to\infty} \sup_{p^2\ge nK} \quad
% \text{d)} \limsup_{n\to\infty} \max_{p\ge n}
% \]
% \end{verbatim}
% \[
% \text{a)} \lim_{n\to\infty} \max_{p\ge n} \quad
% \text{b)} \lim_{n\to\infty} \max_{p^2\ge n} \quad
% \text{c)} \lim_{n\to\infty} \sup_{p^2\ge nK} \quad
% \text{d)} \limsup_{n\to\infty} \max_{p\ge n}
% \]
% a) looks okay, but b) is not quite as good because the second
% limit ($\cramped{p^2\ge n}$) is significantly taller than the
% first ($n\to\infty$). With c)~things begin to look really bad,
% because the second operator has a descender while the first
% doesn't, and finally we have d)~which looks just as bad as~c). The
% command \cs{adjustlimits} is useful in these cases, as you can
% just put it in front of these consecutive operators and it'll make
% the limits line up.
% \medskip\par\noindent
% \begin{minipage}{\textwidth}
% \begin{verbatim}
% \[
% \text{a)} \adjustlimits\lim_{n\to\infty} \max_{p\ge n} \quad
% \text{b)} \adjustlimits\lim_{n\to\infty} \max_{p^2\ge n} \quad
% \text{c)} \adjustlimits\lim_{n\to\infty} \sup_{p^2\ge nK} \quad
% \text{d)} \adjustlimits\limsup_{n\to\infty} \max_{p\ge n}
% \]
% \end{verbatim}
% \end{minipage}
% \[
% \text{a)} \adjustlimits\lim_{n\to\infty} \max_{p\ge n} \quad
% \text{b)} \adjustlimits\lim_{n\to\infty} \max_{p^2\ge n} \quad
% \text{c)} \adjustlimits\lim_{n\to\infty} \sup_{p^2\ge nK} \quad
% \text{d)} \adjustlimits\limsup_{n\to\infty} \max_{p\ge n}
% \]
% The use of \cs{sb} instead of \texttt{\_} is allowed.
%
%
% \subsubsection{Swapping space above \texorpdfstring{\AmS}{AMS} display math environments }
% \label{sec:swapping}
%
% One feature that the plain old \env{equation} environment has that
% the \AmS\ environments does not (because of technical reasons), is
% the feature of using less space above the equation if the situation
% presents itself. The \AmS\ environments cannot do this, but one can
% manually, using
% \begin{codesyntax}
% \SpecialUsageIndex{\SwapAboveDisplaySkip}
% \cs{SwapAboveDisplaySkip}
% \end{codesyntax}
% as the very first content within an \AmS\ display math
% environment. It will then issue an \cs{abovedisplayshortskip}
% instead of the normal \cs{abovedisplayskip}.
%
% Note it will not work with the \env{equation} or \env{multline} environments.
%
% Here is an example of the effect
% \begin{verbatim}
% \noindent\rule\textwidth{1pt}
% \begin{align*} A &= B \end{align*}
% \noindent\rule\textwidth{1pt}
% \begin{align*}
% \SwapAboveDisplaySkip
% A &= B
% \end{align*}
% \end{verbatim}
% \noindent\rule\textwidth{1pt}
% \begin{align*} A &= B \end{align*}
% \noindent\rule\textwidth{1pt}
% \begin{align*}
% \SwapAboveDisplaySkip
% A &= B
% \end{align*}
%
%
% \subsection{Controlling tags}
%
% In this section various tools for altering the appearance of tags
% are shown. All of the tools here can be used at any point in the
% document but they should probably be affect the whole document, so
% the preamble is the best place to issue them.
%
% \subsubsection{The appearance of tags}
% \begin{codesyntax}
% \SpecialUsageIndex{\newtagform}
% \cs{newtagform}\marg{name}\oarg{inner_format}\marg{left}\marg{right}\\
% \SpecialUsageIndex{\renewtagform}
% \cs{renewtagform}\marg{name}\oarg{inner_format}\marg{left}\marg{right}\\
% \SpecialUsageIndex{\usetagform}
% \cs{usetagform}\marg{name}
% \end{codesyntax}
% Altering the layout of equation numbers in \pkg{amsmath} is not
% very user friendly (it involves a macro with three \texttt{@}'s in
% its name), so \pkg{mathtools} provides an interface somewhat
% reminiscent of the page style concept. This way you can define
% several different tag forms and then choose the one you prefer.
%
% As an example let's try to define a tag form which puts the
% equation number in square brackets. First we define a brand new tag
% form:
% \begin{verbatim}
% \newtagform{brackets}{[}{]}
% \end{verbatim}
% Then we activate it:
% \begin{verbatim}
% \usetagform{brackets}
% \end{verbatim}
% The result is then
% \newtagform{brackets}{[}{]}
% \usetagform{brackets}
% \begin{equation}
% E \neq m c^3
% \end{equation}
%
% Similarly you could define a second version of the brackets that
% prints the equation number in bold face instead
% \begin{verbatim}
% \newtagform{brackets2}[\textbf]{[}{]}
% \usetagform{brackets2}
% \begin{equation}
% E \neq m c^3
% \end{equation}
% \end{verbatim}
% \newtagform{brackets2}[\textbf]{[}{]}
% \usetagform{brackets2}
% \begin{equation}
% E \neq m c^3
% \end{equation}
% When you reference an equation with \cs{eqref}, the tag form in
% effect at the time of referencing controls the formatting, so be
% careful if you use different tag forms throughout your document.
%
% If you want to renew a tag form, then use the command
% \cs{renewtagform}. Should you want to
% return to the standard setting then choose\usetagform{default}
% \begin{verbatim}
% \usetagform{default}
% \end{verbatim}
%
% \changes{v1.12}{2012/05/09}{Added caveat}
% \noindent\textbf{Caveat regarding \pkg{ntheorem}}: If you like to
% change the appearence of the tags \emph{and} you are also using the
% \pkg{ntheorem} package, then please postpone the change of
% appearance until \emph{after} loading \pkg{ntheorem}. (In order to
% do its thing, \pkg{ntheorem} has to mess with the tags\dots)
%
% \subsubsection{Showing only referenced tags}
%
% \begin{codesyntax}
% \SpecialKeyIndex{showonlyrefs}$\key{showonlyrefs}=\texttt{true}\vert\texttt{false}$\\
% \SpecialKeyIndex{showmanualtags}$\key{showmanualtags}=\texttt{true}\vert\texttt{false}$\\
% \SpecialUsageIndex{\refeq}\cs{refeq}\marg{label}
% \end{codesyntax}
% An equation where the tag is produced with a manual \cs{tag*}
% shouldn't be referenced with the normal \cs{eqref} because that
% would format it according to the current tag format. Using just
% \cs{ref} on the other hand may not be a good solution either as
% the argument of \cs{tag*} is always set in upright shape in the
% equation and you may be referencing it in italic text. In the
% example below, the command \cs{refeq} is used to avoid what could
% possibly lead to confusion in cases where the tag font has very
% different form in upright and italic shape (here we switch to
% Palatino in the example):
% \begin{verbatim}
% \begin{quote}\renewcommand*\rmdefault{ppl}\normalfont\itshape
% \begin{equation*}
% a=b \label{eq:example}\tag*{Q\&A}
% \end{equation*}
% See \ref{eq:example} or is it better with \refeq{eq:example}?
% \end{quote}
% \end{verbatim}
% \begin{quote}\renewcommand*\rmdefault{ppl}\normalfont\itshape
% \begin{equation*}
% a=b \label{eq:example}\tag*{Q\&A}
% \end{equation*}
% See \ref{eq:example} or is it better with \refeq{eq:example}?
% \end{quote}
%
%
% Another problem sometimes faced is the need for showing the
% equation numbers for only those equations actually referenced. In
% \pkg{mathtools} this can be done by setting the key
% \key{showonlyrefs} to either true or false by using
% \cs{mathtoolsset}. You can also choose whether or not to show the
% manual tags specified with \cs{tag} or \cs{tag*} by setting the
% option \key{showmanualtags} to true or false.\footnote{I recommend
% setting \key{showmanualtags} to true, else the whole idea of using
% \cs{tag} doesn't really make sense, does it?} For both keys just
% typing the name of it chooses true as shown in the following
% example.
%
% \begin{verbatim}
% \mathtoolsset{showonlyrefs,showmanualtags}
% \usetagform{brackets}
% \begin{gather}
% a=a \label{eq:a} \\
% b=b \label{eq:b} \tag{**}
% \end{gather}
% This should refer to the equation containing $a=a$: \eqref{eq:a}.
% Then a switch of tag forms.
% \usetagform{default}
% \begin{align}
% c&=c \label{eq:c} \\
% d&=d \label{eq:d}
% \end{align}
% This should refer to the equation containing $d=d$: \eqref{eq:d}.
% \begin{equation}
% e=e
% \end{equation}
% Back to normal.\mathtoolsset{showonlyrefs=false}
% \begin{equation}
% f=f
% \end{equation}
% \end{verbatim}
% \mathtoolsset{showonlyrefs,showmanualtags}
% \usetagform{brackets}
% \begin{gather}
% a=a \label{eq:a} \\
% b=b \label{eq:b} \tag{**}
% \end{gather}
% This should refer to the equation containing $a=a$: \eqref{eq:a}.
% Then a switch of tag forms.
% \usetagform{default}
% \begin{align}
% c&=c \label{eq:c} \\
% d&=d \label{eq:d}
% \end{align}
% This should refer to the equation containing $d=d$: \eqref{eq:d}.
% \begin{equation}
% e=e
% \end{equation}
% Back to normal.\mathtoolsset{showonlyrefs=false}
% \begin{equation}
% f=f
% \end{equation}
%
% Note that this feature only works if you use \cs{eqref} or
% \cs{refeq} to reference your equations.
%
% When using \key{showonlyrefs} it might be useful to be able to
% actually add a few equation numbers without directly referring to
% them.
% \begin{codesyntax}
% \SpecialUsageIndex{\noeqref}\cs{noeqref}\marg{label,label,\dots}
% \end{codesyntax}
% \FeatureRequest{Rasmus Villemoes}{2008/03/26}
% The syntax is somewhat similar to \cs{nocite}. If a label in the
% list is undefined we will throw a warning in the same manner as
% \cs{ref}.
%
% \medskip\noindent\textbf{BUG 1:} Unfortunately the use of the
% \key{showonlyref} introduce a bug within amsmath's typesetting
% of formula versus equation number. This bug manifest itself by
% allowing formulas to be typeset close to or over the equation
% number. Currently no general fix is known, other than making sure
% that one's formulas are not long enough to touch the equation