path: root/macros/latex/contrib/delimset/delimset.dtx

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% delimset.dtx Copyright (C) 2016-2018 Niklas Beisert
%
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either version 1.3
% 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
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% The Current Maintainer of this work is Niklas Beisert.
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% and the derived files delimset.sty and dlmssamp.tex
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%<package|sample>\NeedsTeXFormat{LaTeX2e}[1996/12/01]
%<package>\ProvidesPackage{delimset}[2018/12/30 v1.1 convenient size control for delimiter sets]
%<sample>\ProvidesFile{dlmssamp.tex}[2018/12/30 v1.1 sample for delimset]
%<*driver>
%\ProvidesFile{delimset.drv}[2018/12/30 v1.1 delimset Reference Manual file]
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\documentclass{ltxdoc}

\usepackage[margin=35mm]{geometry}
\usepackage{hyperref}
\usepackage{hyperxmp}
\usepackage[usenames]{color}
\usepackage{amsmath,amsfonts}

\hypersetup{colorlinks=true}
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\hypersetup{pdfsource={}}
\hypersetup{pdflang={en-UK}}
\hypersetup{pdfcopyright={Copyright 2016-2018 Niklas Beisert.
  This work may be distributed and/or modified under the
  conditions of the LaTeX Project Public License, either version 1.3
  of this license or (at your option) any later version.}}
\hypersetup{pdflicenseurl={http://www.latex-project.org/lppl.txt}}
\hypersetup{pdfcontactaddress={ETH Zurich, ITP, HIT K, Wolfgang-Pauli-Strasse 27}}
\hypersetup{pdfcontactpostcode={8093}}
\hypersetup{pdfcontactcity={Zurich}}
\hypersetup{pdfcontactcountry={Switzerland}}
\hypersetup{pdfcontactemail={nbeisert@itp.phys.ethz.ch}}
\hypersetup{pdfcontacturl={http://people.phys.ethz.ch/\xmptilde nbeisert/}}

\newcommand{\secref}[1]{\hyperref[#1]{section \ref*{#1}}}

\parskip1ex
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\begin{document}

\title{The \textsf{delimset} Package}
\hypersetup{pdftitle={The delimset Package}}
\author{Niklas Beisert\\[2ex]
  Institut f\"ur Theoretische Physik\\
  Eidgen\"ossische Technische Hochschule Z\"urich\\
  Wolfgang-Pauli-Strasse 27, 8093 Z\"urich, Switzerland\\[1ex]
  \href{mailto:nbeisert@itp.phys.ethz.ch}
  {\texttt{nbeisert@itp.phys.ethz.ch}}}
\hypersetup{pdfauthor={Niklas Beisert}}
\hypersetup{pdfsubject={Manual for the LaTeX2e Package delimset}}
\date{30 December 2018, \textsf{v1.1}}
\maketitle

\begin{abstract}\noindent
\textsf{delimset} is a \LaTeXe{} package to typeset and declare
sets of delimiters in math mode whose size can be adjusted conveniently.
\end{abstract}

\begingroup
\parskip0ex
\tableofcontents
\endgroup

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}

In ordinary \TeX{} and \LaTeX{}, delimiters in math and physics expressions
(brackets such as parentheses, braces, but also
absolute values, sets, pairings, bra-kets and quantum expectation values,
commutators, \ldots)
are typically coded by their respective symbols.
For example:
%
\[
\begin{aligned}
|[(ax+b)x+c]| &\to [(ax+b)x+c]
\\
|\{1,2,3,\ldots\}| &\to \{1,2,3,\ldots\}
\\
|(v,w)| &\to (v,w)
\\
|\langle\psi\vert M\vert\psi\rangle| &\to \langle\psi\vert M\vert\psi\rangle
\\
|(x^2+px+q)\vert_{-p/2}| &\to (x^2+px+q)\vert_{-p/2}
\\&\ldots
\end{aligned}
\]
%
In order to adjust the size of delimiters, the modifiers
|\big|, |\Big|, |\bigg|, |\Bigg| are used.
More importantly the construct
{|\left*| \ldots [|\middle*|] \ldots  |\right*|}
adjusts the size of delimiters to the contents:
\[
\Bigg[\bigg[\Big[\big[[*]\big]\Big]\bigg]\Bigg],
\qquad
\left\{\frac{p}{q} \middle\vert p,q\in\mathbb{Z}, q\neq 0 \right\}
\]
%
These modifiers allow to construct expressions involving delimiters
conveniently and with a large amount of flexibility.

However, once an expression has been typeset in this way,
it takes some efforts to modify, if needed.
At least, one has to take care of both delimiters at the same time
and change their size or type accordingly.
For example, $\hat X$ in the expression |(A\hat{X}+B)|
has an extended height that calls for bigger delimiters.
Ideally, one would use |\left(...\right)|
to find the correct size.
Unfortunately, in this case, the smallest size of delimiters
that covers the height of $\hat X$ is equivalent to |\Big|,
which feels somewhat too big. For aesthetic reasons one might thus prefer
the size |\big(...\big)|:
%
\[
\begin{aligned}
|(A\hat{X}+B)|
&\to(A\hat{X}+B)
\\
|\left(A\hat{X}+B\right)|
&\to\left(A\hat{X}+B\right)
\\
|\Big(A\hat{X}+B\Big)|
&\to\Big(A\hat{X}+B\Big)
\\
|\big(A\hat{X}+B\big)|
&\to\big(A\hat{X}+B\big)
\end{aligned}
\]

The package \textsf{delimset} provides mechanisms to declare sets of delimiters
whose size can be adjusted conveniently by simple optional parameters.
For example, it provides a general purpose bracket |\brk|
which can be used as follows:
\[
\begin{aligned}
|\brk{A\hat{X}+B}|&\to(A\hat{X}+B)
\\
|\brk*{A\hat{X}+B}|&\to\mathopen{}\mathclose{\left(A\hat{X}+B\right)}
\\
|\brk2{A\hat{X}+B}|&\to\Bigl(A\hat{X}+B\Bigr)
\\
|\brk!{A\hat{X}+B}|&\to\bigl(A\hat{X}+B\bigr)
\end{aligned}
\]
%
It also allows to change the type of bracket conveniently:
%
\[
\begin{aligned}
|\brk{ax+b}|
&\to(ax+b)
\\
|\brk[s]{ax+b}|
&\to[ax+b]
\\
|\brk[c]{ax+b}|
&\to\{ax+b\}
\\
|\brk[a]{ax+b}|
&\to\langle ax+b\rangle
\end{aligned}
\]
%
These features can be combined and used, e.g., in nested brackets
in order to distinguish the levels by shape and size:
%
\[
|\brk[s]!{\brk{ax+b}x+c}|
\to\bigl[(ax+b)x+c\bigr]
\]
%
All of this can of course be achieved with the conventional
tools of \TeX{} with comparable effort,
but the more complicated and nested the expressions get,
the more difficult it will be to adjust them
to obtain a visually acceptable result.

The main functionality of the package is based on a
versatile mechanism to specify sets of delimiters, e.g.:
\[
\begin{aligned}
|\delim<>{ax+b}|
&\to\langle ax+b\rangle
\\
|\delimpair{[}{[.],}{[}!{a}{b}|
&\to \bigl[a, b\bigr[
\\
|\delimtriple<\vert\vert>*{\psi}{A^\dagger}{\psi}|
&\to\left\langle\psi\middle\vert A^\dagger\middle\vert \psi\right\rangle
\end{aligned}
\]
%
The command |\delim| can be used on the fly, but also
in definitions of custom delimiter sets such as:
%
\[
|\newcommand{\comm}{\delimpair{[}{[.],}{]}}|
\]
%
Note that the definition of |\comm| does not specify any arguments.
They are nevertheless read by the incomplete definition of |\delimpair|
from the what follows |\comm|.
In particular, this incomplete definition
enables the correct parsing of the optional size specifier,
e.g.:
%
\[
|\comm!{P}{\psi(x)}| \to \bigl[P,\psi(x)\bigr]
\]
%
The package also provides a mechanism to declare
delimited sets more flexibly.
The above definition could be written as follows:
%
\[
\begin{aligned}
&|\DeclareMathDelimiterSet{\comm}[2]|
\\
&\qquad |{\selectdelim[l]{[}{#1},{#2}\selectdelim[r]{]}}|
\end{aligned}
\]

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Delimiter Sizes for Math Styles}

In plain \LaTeXe{}
the size modifiers |\big|, |\Big|, |\bigg|, |\Bigg| have the shortcoming
that they are based on a fixed font size of 10pt.
More precisely, they use a vertical phantom of
height 8.5pt, 11.5pt, 14.5pt or 17.5pt, respectively
to set the height of the delimiter.
The package \textsf{amsmath} corrects for font size
by instead placing a (centred) vertical phantom of
height 1.2, 1.8, 2.4 or 3 times the size
of the currently selected math font
(height plus depth of |\Mathstrutbox@|).

Unfortunately, it does not account for
the currently selected math style.
Therefore, the size of delimiters in sub/superscripts
cannot be adjusted appropriately,
\unskip\footnote{Arguably, it is bad typesetting practice
to have too complicated expressions in sub/superscripts.}
they come out way too big:
%
\[
|e^{\big(ax+b\big)}| \to e^{\big(ax+b\big)}
\]
%
This package modifies the definitions of
the size modifiers (of \textsf{amsmath})
to automatically adjust to sub/superscripts
(subject to availability):
%
\[
\makeatletter
|e^{\big(ax+b\big)}| \to e^{\left(\vcenter to 0.7\big@size{}ax+b\right)}
\makeatother
\]

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Spacing and Math Classes}

Another shortcoming of the variable-size delimiters is that
the spacing is noticeably different from their fixed-size counterparts:
%
\[
\begin{aligned}
|\square(ax+b)\square|
&\to \square(ax+b)\square
\\
|\square\left(ax+b\right)\square|
&\to \square\left(ax+b\right)\square
\\
|\square\bigl(ax+b\bigr)\square|
&\to \square\bigl(ax+b\bigr)\square
\\
|\square\left(ax+\big.b\right)\square|
&\to \square\left(ax+\big.b\right)\square
\end{aligned}
\]
%
Often the construct |\left*| \ldots|\right*|
leaves a large amount of space around it.
A suitable way to fix this problem
is to adjust the math class as follows:
%
\[
\begin{aligned}
|\square(ax+b)\square|
&\to \square(ax+b)\square
\\
|\square\mathopen{}\mathclose{\left(ax+b\right)}\square|
&\to \square\mathopen{}\mathclose{\left(ax+b\right)}\square
\end{aligned}
\]
%
This makes the expression look like |\mathopen| from the left
and like |\mathclose| from the right. Importantly,
the delimited expression should be contained in
the |\mathclose| block so as to place any following
sub/superscripts at the appropriate height.
Unfortunately, the fix is too elaborate
in comparison to the benefits of appropriate spacing.
For practical purposes, consistent spacing can only be achieved
by a more convenient mechanism.

On a related note, it is important to correctly specify
the math class (|\mathopen|\hspace{0pt}/\hspace{0pt}|\mathclose|)
for the delimiters, for example:
\[
\begin{aligned}
|\big(-1\big)| &\to \big(-1\big)
\\
|\bigl(-1\bigr)| &\to \bigl(-1\bigr)
\end{aligned}
\]
%
The math class can also make a major difference for intermediate delimiters,
e.g.:
\[
\begin{aligned}
|\bigl\langle\psi\big\vert\psi\bigr\rangle|
&\to \bigl\langle\psi\big\vert\psi\bigr\rangle
\\
|\bigl\langle\psi\bigm\vert\psi\bigr\rangle|
&\to \bigl\langle\psi\bigm\vert\psi\bigr\rangle
\\
|\bigl\langle\psi\mathbin\big\vert\psi\bigr\rangle|
&\to \bigl\langle\psi\mathbin\big\vert\psi\bigr\rangle
\\
|\bigl\langle\psi\mathpunct\big\vert\psi\bigr\rangle|
&\to \bigl\langle\psi\mathpunct\big\vert\psi\bigr\rangle
\end{aligned}
\]
%
Depending on the particular situation,
any of these expressions may be the most appropriate representation.

The package \textsf{delimset} automatically takes care of the math classes
of the left and right delimiters. It also offers several choices for
intermediate delimiters to take the context into account.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Philosophy}

Semantic typesetting is one of the philosophies behind \LaTeX{}:
The author should focus on the content
while the layout is taken care of by the engine.
The (body of a) source file largely codes the contents of the document,
while the layout is largely specified
by the kernel, classes, styles and macro definitions
(in the preamble).
In order for the separation of content and layout to work well,
the meaning of the content must be accurately specified by the source file
so that the appropriate layout can be applied to it.
For example, a left bracket `|(|' can have many meanings,
which the engine could not possibly guess.
Even a simple compound expression such as |[A,B]| could
have different meanings depending on context
such as a compact interval or a commutator.
A semantic coding of the latter two concepts
such as |\intv{A}{B}| vs.\ |\comm{A}{B}|
clearly distinguishes between them.
This allows the typesetting engine to represent them appropriately
in every situation.
It also allows to consistently define or adjust
the typeset representation globally
according to one's taste, such as $[A,B]$ vs.\ $[A;B]$.
The price to pay is a larger number of abstract commands
(which possibly evaluate to the same expression)
and using them to specify the semantics throughout the source file
(or at least where practical and useful).
Conversely, the price to pay for an immediate typesetting scheme is that
all notations need to be fixed at the start, and later adjustments require
an elaborate search and replacement
of (somewhat ambiguous) patterns like |[|$x$|,|$y$|]|.

Another distinction between \TeX{} and \LaTeX{} is that the former
frequently uses free-format expressions such as $|{x\over y}|$
whereas the latter normally uses structured commands with arguments
such as $|\frac{x}{y}|$.
In that sense, the construct {|\left(ax+b\right)|}
belongs to the world of \TeX{}, whereas an expression like
{|\delim()*{ax+b}|} fits the \LaTeX{} framework better.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Related CTAN Packages}

There are at least three other packages which offer a similar functionality:
%
\begin{itemize}
\item
The package \href{http://ctan.org/pkg/delim}{\textsf{delim}} supplies a command
|\delimdef| to declare a set of delimiters
which is similar to the present |\DeclareMathDelimiterSet|.
The size of delimiters to be used in each case
is then specified by a prefix command such as |\mbig| or |\mauto|.
\item
The package \href{http://ctan.org/pkg/mathtools}{\textsf{mathtools}}
supplies commands |\DeclarePairedDelimiter...| (among many other things)
which are similar to the present |\DeclareMathDelimiterSet|.
The size of delimiters to be used in each case
is then specified by an optional argument
such as `|*|' or |[\big]|.
\item
The package \href{http://ctan.org/pkg/delimseasy}{\textsf{delimseasy}}
defines a collection of useful delimiters such as |\prn| for
round parentheses or |\sqpr| square parentheses.
Modifier letters can be prepended and appended to adjust their size.
\end{itemize}
%
A functionality of the present package
not offered by any of the above packages is
to typeset delimiters on the fly, e.g.:
%
\[
|\delim<\vert>!{\psi}{\psi}|
\to\bigl\langle\psi\big\vert\psi\bigr\rangle
\]
%
The mechanism to specify the size is leaner in the sense that it uses
only a single character and a single command.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Usage}

To use the package \textsf{delimset} add the command
\begin{center}|\usepackage{delimset}|\end{center}
to the preamble of your \LaTeX{} document.
If not yet present,
the package \textsf{amsmath} will be loaded automatically.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Inline Usage}
\label{sec:delimcommands}

The package provides three general purpose commands
to compose delimiter sets with one, two or three encapsulated expressions:
%
\[
\begin{aligned}
&|\delim{|\emph{l}|}{|\emph{r}|}|\emph{size}|{|\emph{expr}|}|
\\
&|\delimpair{|\emph{l}|}{|\emph{m}|}{|\emph{r}|}|
\emph{size}|{|\emph{expr1}|}{|\emph{expr2}|}|
\\
&|\delimtriple{|\emph{l}|}{|\emph{m1}|}{|\emph{m2}|}{|\emph{r}|}|
\emph{size}|{|\emph{expr1}|}{|\emph{expr2}|}{|\emph{expr3}|}|
\end{aligned}
\]
%
The expression(s) \emph{expr(n)} will be surrounded by the
delimiters \emph{l} and \emph{r}
and, in the case of more than one expression,
they will be separated by the delimiters \emph{m(n)}:
\[
\emph{l}\ \emph{expr}\ \emph{r},
\qquad
\emph{l}\ \emph{expr1}\ \emph{m}\ \emph{expr2}\ \emph{r},
\qquad
\emph{l}\ \emph{expr1}\ \emph{m1}\ \emph{expr2}\
\emph{m2}\ \emph{expr3}\ \emph{r}
\]

Here, \emph{l} and \emph{r} have to be
math delimiters (symbols which can be used for |\left| and |\right|) or
the dot `.' for the null delimiter.
The separators \emph{m(n)} can be plain math delimiters as well, but they can
also be compound expression of the form |[|\emph{class}|]|\emph{delim}
where \emph{class} specifies
the intended math class of the delimiter \emph{delim}:
%
\[
\begin{aligned}{}
\left.\begin{array}{r}
\emph{delim}\\|{|\emph{delim}|}|\\|{[]|\emph{delim}|}|
\end{array}\right\}
&\qquad\text{class }|\mathord|\text{ (similar to }|\big|)
\\
|{[l]|\emph{delim}|}|&\qquad
\text{class }|\mathopen|\text{ (similar to }|\bigl|
\text{, not for use in }|\delim...|)
\\
|{[r]|\emph{delim}|}|&\qquad
\text{class }|\mathclose|\text{ (similar to }|\bigr|
\text{, not for use in }|\delim...|)
\\
|{[o]|\emph{delim}|}|&\qquad
\text{class }|\mathopen|\text{ (similar to }|\bigl|)
\\
|{[c]|\emph{delim}|}|&\qquad
\text{class }|\mathclose|\text{ (similar to }|\bigr|)
\\
|{[m]|\emph{delim}|}|&\qquad
\text{class }|\mathrel|\text{ (similar to }|\bigm|)
\\
|{[p]|\emph{delim}|}|&\qquad
\text{class }|\mathpunct|\text{ (similar to }|\bigp|)
\\
|{[b]|\emph{delim}|}|&\qquad
\text{class }|\mathbin|\text{ (similar to }|\bigb|)
\\
|{[.]|\emph{expr}|}|&\qquad
\text{no size adjustment, \emph{expr} can be any expression}
\end{aligned}
\]
%
Note that the left and right delimiters \emph{l} and \emph{r} effectively
have |[l]| and |[r]| prepended, respectively,
and therefore they must be a plain math delimiter.
Conversely, the immediate delimiters \emph{m(n)} must not
have the |[l]| and |[r]| classes
because the latter must appear precisely once
and they are already taken by \emph{l} and \emph{r};
use classes |[o]| and |[c]| instead.

The optional size modifier \emph{size} should take one of the following values:
\[
\begin{aligned}{}
\emph{empty}, \emph{anything else}, |0|&\qquad \text{default size}
\\
|!|, |+|, |1|&\qquad \text{size }|\big|\text{ (|!| is preferred)}
\\
|2|&\qquad \text{size }|\Big|
\\
|3|&\qquad \text{size }|\bigg|
\\
|4|&\qquad \text{size }|\Bigg|
\\
|*|&\qquad \text{variable size }|\left...\right|
\end{aligned}
\]

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Declarations}

The above constructs can be used to define new delimiter commands via:
%
\[
|\newcommand{\|\emph{name}|}{\delim...{|\emph{l}|}...{|\emph{r}|}}|
\]
%
Here it makes sense to drop all arguments starting
with the size modifier \emph{size} from the definition.
The \TeX{} parsing mechanism will then automatically
use the tokens following |\|\emph{name} including the optional size modifier.
If the encapsulated expression(s) are to be passed as explicit arguments
to |\|\emph{name}, one will have to find an alternative way to pass the
optional size argument.

The above declarations via |\delim...|
should be sufficient for almost all situations.
However, there is an even more flexible way to declare delimiter sets:
\[
|\DeclareMathDelimiterSet{\|\emph{name}|}[|\emph{narg}|]{|\emph{expr}|}|
\]
%
The syntax of this command is equivalent to the one of |\newcommand|.
The difference is that the command |\|\emph{name} first looks
for the optional size modifier \emph{size} as
described above in \secref{sec:delimcommands}.
It remembers the desired size for evaluating the macro \emph{expr}.
Then it parses the arguments as if the command
was declared by |\newcommand|.

As usual, the macro \emph{expr} contains the command arguments
specified by |#1|, |#2|, \ldots. Note that these should
be encapsulated in groups |{#1}|, |{#2}|, \ldots,
in order to prevent them from overwriting definitions
at the level of the current group.
It should also contain the desired math delimiters
specified by:
%
\[
|\selectdelim[|\emph{class}|]{|\emph{delim}|}|
\]
%
Here, the sizes are adjusted automatically
according to the previously specified modifier \emph{size}.
The math classes must be in proper sequence,
i.e.\ the first and last ones must be |l| and |r|, respectively,
while the intermediate ones can be anything by |l| and |r|,
see \secref{sec:delimcommands}.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Default Declarations}
\label{sec:defaultcommands}

The package predefines four commonly used sets of delimiters:
%
\begin{itemize}
\item
|\brk[|\emph{type}|]|\emph{size}|{|\emph{expr}|}| represents
a standard bracket around a single expression \emph{expr}.
The type of bracket can be specified by the optional
argument \emph{type}:
\[
\text{\emph{empty} or |[r]|: round }(x),\quad
\text{|[s]|: square }[x],\quad
\text{|[c]|: curly }\{x\},\quad
\text{|[a]|: angle }\langle x\rangle
\]
\item
|\eval[|\emph{type}|]|\emph{size}|{|\emph{expr}|}| represents
evaluation of a functional expression \emph{expr}.
The type of bracket can be specified by the optional
argument \emph{type}:
\[
\text{\emph{empty} or |[v]|: }f(x)\vert_{a},\qquad
\text{|[s]|: }[f(x)]_{a}^{b}
\]
\item
|\abs|\emph{size}|{|\emph{expr}|}| represents
the absolute value $\lvert\emph{expr}\rvert$.
\item
|\norm|\emph{size}|{|\emph{expr}|}| represents
the norm $\lVert\emph{expr}\rVert$.
\end{itemize}
%
The above definitions can be suppressed by
setting the package option |stddef| to |false|,
see \secref{sec:packageoptions}.
The package also defines some extended sets of delimiters as follows:
%
\begin{itemize}
\item
|\pair|\emph{size}|{|\emph{expr1}|}{|\emph{expr2}|}| represents
a pair(ing) $(\emph{expr1},\emph{expr2})$.
\item
|\set|\emph{size}|{|\emph{expr}|}| represents
the set $\{\emph{expr}\}$.
\item
|\setcond|\emph{size}|{|\emph{expr}|}{|\emph{cond}|}| represents
a set with condition $\{\emph{expr}\vert\emph{cond}\}$.
\item
|\intv[|\emph{type}|]|\emph{size}|{|\emph{expr1}|}{|\emph{expr2}|}| represents
an interval from \emph{expr1} to \emph{expr2}.
The in/\hspace{0pt}exclusion of the bounds can be specified by the optional
argument \emph{type}:
\[
\text{\emph{empty} or |[c]|: closed }[a,b],\qquad
\text{|[o]|: open }]a,b[,\qquad
\begin{array}{l}
\text{|[l]|: left-open }]a,b]
\\
\text{|[r]|: right-open }[a,b[
\end{array}
\]
\item
|\avg|\emph{size}|{|\emph{expr}|}| represents
some average $\langle\emph{expr}\rangle$.
\item
|\corr|\emph{size}|{|\emph{expr}|}| represents
some correlator $\langle\emph{expr}\rangle$.
\item
|\comm|\emph{size}|{|\emph{expr1}|}{|\emph{expr2}|}| represents
the commutator $[\emph{expr1},\emph{expr2}]$.
\item
|\acomm|\emph{size}|{|\emph{expr1}|}{|\emph{expr2}|}| represents
the anti-commutator $\{\emph{expr1},\emph{expr2}\}$.
\item
|\bra|\emph{size}|{|\emph{expr}|}| represents
a bra-vector $\langle\emph{expr}\rvert$ in quantum mechanics.
\item
|\ket|\emph{size}|{|\emph{expr}|}| represents
a ket-vector $\lvert\emph{expr}\rangle$ in quantum mechanics.
\item
|\setcond|\emph{size}|{|\emph{expr1}|}{|\emph{expr2}|}| represents
a bra-ket contraction $\langle\emph{expr1}\vert\emph{expr2}\rangle$.
\end{itemize}
The extended definitions need to be activated by
the package option |extdef|, see \secref{sec:packageoptions}.

If the representations of the above delimiters do not suit the purpose
or taste of the user, they can be redefined with |\renewcommand|.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Auxiliary Commands}
\label{sec:auxcommands}

In addition to the |\bigl|, |\bigr| and |\bigm| commands
(as well as their |\Big.|, |\bigg.| and |\Bigg.| counterparts),
the package defines two additional sets |\bigp| and |\bigb|
(and counterparts).
Here |\bigp| implies the math class |\mathpunct|
and |\bigb| the class |\mathbin|.

Furthermore, the package overloads the size calculation in the |\big...|
commands to properly account for the math styles in sub/superscripts
(|\scriptstyle|) and nested sub/\hspace{0pt}superscripts (|\scriptscriptstyle|).
The latter behaviour can be controlled by
the package option |scriptstyle|, see \secref{sec:packageoptions}.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Package Options}
\label{sec:packageoptions}

Options can be passed to the package by
\[
|\usepackage[|\emph{opts}|]{delimset}|
\qquad
\text{or}
\qquad
|\PassOptionsToPackage{|\emph{opts}|}{delimset}|
\]
%
Here \emph{opts} is a comma-separated list of the available options:
%
\begin{itemize}
\item
|stddef|[|=true|$\vert$|false|]
controls the activation of standard delimiter definitions specified in
\secref{sec:defaultcommands}.
If no value is given |true| is assumed; initially set to |true|.
\item
|extdef|[|=true|$\vert$|false|]
controls the activation of extended delimiter definitions specified in
\secref{sec:defaultcommands}.
If no value is given |true| is assumed; initially set to |false|.
\item
|scriptstyle|[|=true|$\vert$|false|]
controls the overwriting of size modifiers explained
in \secref{sec:auxcommands}.
If no value is given |true| is assumed; initially set to |true|.
\end{itemize}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Information}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Copyright}

Copyright \copyright{} 2016--2018 Niklas Beisert

This work may be distributed and/or modified under the
conditions of the \LaTeX{} Project Public License, either version 1.3
of this license or (at your option) any later version.
The latest version of this license is in
  \url{http://www.latex-project.org/lppl.txt}
and version 1.3 or later is part of all distributions of \LaTeX{}
version 2005/12/01 or later.

This work has the LPPL maintenance status `maintained'.

The Current Maintainer of this work is Niklas Beisert.

This work consists of the files |README.txt|, |delimset.ins| and |delimset.dtx|
as well as the derived files |delimset.sty|, |dlmssamp.tex| and |delimset.pdf|.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Files and Installation}

The package consists of the files
%
\begin{center}
\begin{tabular}{ll}
    |README.txt|   & readme file \\
    |delimset.ins| & installation file \\
    |delimset.dtx| & source file \\
    |delimset.sty| & package file \\
    |dlmssamp.tex| & sample file \\
    |delimset.pdf| & manual
\end{tabular}
\end{center}
%
The distribution consists of the files
|README.txt|, |delimset.ins| and |delimset.dtx|.
%
\begin{itemize}
\item
Run (pdf)\LaTeX{} on |delimset.dtx|
to compile the manual |delimset.pdf| (this file).
\item
Run \LaTeX{} on |delimset.ins| to create the package |delimset.sty|
and the sample |dlmssamp.tex|.
Copy the file |delimset.sty| to an appropriate directory of your \LaTeX{}
distribution, e.g.\ \textit{texmf-root}|/tex/latex/delimset|.
\end{itemize}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Interaction with CTAN Packages}

The package relies on other packages:
\begin{itemize}
\item
This package relies on some functionality of the package \textsf{amsmath}
by using and overwriting some native code.
Compatibility with the \textsf{amsmath} package
has been tested with v2.15d (2016/06/28).
\item
This package uses the package \textsf{keyval} from the \textsf{graphics} bundle
to process optional arguments to the package options.
Compatibility with the \textsf{keyval} package
has been tested with v1.15 (2014/10/28).
\end{itemize}
%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Feature Suggestions}

% specify width of null delimiter?
% automatic nesting of bracket types?
% make optional arguments work for DeclareMathDelimiterSet?
% add pfrac for fraction a/b in text mode
% handle cramped style properly (perhaps impossible)
% outer decorations for delimiters e.g. _y<a,b>_x
% freestyle delimiter with size adjustment replacement \size{\rangle}_x

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Revision History}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\paragraph{v1.1:} 2018/12/30

\begin{itemize}
\item
classes added, class and size selection mechanism simplified
\end{itemize}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\paragraph{v1.01:} 2018/01/17

\begin{itemize}
\item
manual rearranged
\end{itemize}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\paragraph{v1.0:} 2016/11/01

\begin{itemize}
\item
extended standard definitions
\item
manual and installation package added
\item
first version published on CTAN
\end{itemize}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\paragraph{v0.5--0.7:} 2016/05/08 -- 2016/09/04

\begin{itemize}
\item
basic functionality
\item
standard definitions
\end{itemize}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\appendix

\settowidth\MacroIndent{\rmfamily\scriptsize 000\ }

 \DocInput{delimset.dtx}

\end{document}
%</driver>
% \fi
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{Sample File}
%\iffalse
%<*sample>
%\fi
%
% In this section we provide a \LaTeX{} example how to use
% some of the \textsf{delimset} features.
%
% Preamble and beginning of document body:
%
%    \begin{macrocode}
\documentclass[12pt]{article}

\usepackage[margin=2cm]{geometry}
\usepackage{amsmath,amsfonts}
\usepackage{delimset}

\begin{document}
%    \end{macrocode}

sizes for default brackets:
%    \begin{macrocode}
\[
\brk0{x},\quad
\brk1{x},\quad
\brk2{x},\quad
\brk3{x},\quad
\brk4{x}
\]
%    \end{macrocode}

styles for default brackets:
%    \begin{macrocode}
\[
\brk[r]{x},\quad
\brk[s]{x},\quad
\brk[c]{x},\quad
\brk[a]{x}
\]
%    \end{macrocode}

nested brackets:
%    \begin{macrocode}
\[
\brk[c]2{\brk[s]!{\brk{ax+b}x+c}x+d}
\]
%    \end{macrocode}

default absolute value, norm and default evaluations:
%    \begin{macrocode}
\[
\abs*{\frac{ax+b}{cx+d}},\qquad
\norm*{\frac{ax+b}{cx+d}},\qquad
\eval*{\frac{ax+b}{cx+d}}_{x=0},\qquad
\eval[s]*{\frac{ax+b}{cx+d}}_{x=0}^{x=\infty}
\]
%    \end{macrocode}

outer delimiter spacing:
%    \begin{macrocode}
\begin{align*}
&\square\brk0{x}\square,&&\square\brk1{A^k}\square,
\\
&\square\brk*{x}\square,&&\square\brk*{A^k}\square
\end{align*}
%    \end{macrocode}

delimiter sizes in exponents:
%    \begin{macrocode}
\[
e^{\brk{ax+b}},\qquad
e^{\brk!{ax+b}}
\]
%    \end{macrocode}

delimiter declaration:
%    \begin{macrocode}
\DeclareMathDelimiterSet{\braket}[2]
  {\selectdelim[l]<#1\selectdelim|#2\selectdelim[r]>}
\[
\braket!{\psi}{\psi},
\quad
\braket*{\psi}{\psi\big.}
\]
%    \end{macrocode}

delimiter usage:
%    \begin{macrocode}
\[
\delimpair<|>!{\psi}{\psi}
\]
%    \end{macrocode}

conditional set, alternative layouts:
%    \begin{macrocode}
\[
\delimpair\{{[m]|}\}!{2n}{n\in\mathbb{Z}},
\qquad
\delimpair\{{[b]|}\}!{2n}{n\in\mathbb{Z}},
\qquad
\delimpair\{{[p]|}\}!{2n}{n\in\mathbb{Z}},
\qquad
\delimpair\{|\}!{2n}{n\in\mathbb{Z}},
\qquad
\delimpair\{{[.];}\}!{2n}{n\in\mathbb{Z}}
\]
conditional set, alternative layouts with variable size:
\[
\delimpair\{{[m]|}\}*{2n}{n\in\mathbb{Z}\big.},
\qquad
\delimpair\{{[b]|}\}*{2n}{n\in\mathbb{Z}\big.},
\qquad
\delimpair\{{[p]|}\}*{2n}{n\in\mathbb{Z}\big.},
\qquad
\delimpair\{|\}*{2n}{n\in\mathbb{Z}\big.},
\qquad
\delimpair\{{[.];}\}*{2n}{n\in\mathbb{Z}\big.}
\]
%    \end{macrocode}

delimiter definition:
%    \begin{macrocode}
\newcommand{\comm}{\delimpair[{[.],}]}
\[
\comm!{\comm{A}{B}}{C}
+\comm!{\comm{B}{C}}{A}
+\comm!{\comm{C}{A}}{B}
=0
\]
%    \end{macrocode}

alternative representation:
%    \begin{macrocode}
\renewcommand{\comm}{\delimpair[{[.];}]}
\[
\comm!{\comm{A}{B}}{C}
+\comm!{\comm{B}{C}}{A}
+\comm!{\comm{C}{A}}{B}
=0
\]
%    \end{macrocode}

% end of document body:
%    \begin{macrocode}
\end{document}
%    \end{macrocode}
%\iffalse
%</sample>
%\fi
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{Implementation}
%\iffalse
%<*package>
%\fi
%
% In this section we describe the package |delimset.sty|.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Required Packages.}
%
% The package loads the packages \textsf{amsmath} and \textsf{keyval}
% if not yet present.
% \textsf{amsmath} is used for basic delimiter size functionality.
% \textsf{keyval} is used for extended options processing.
%    \begin{macrocode}
\RequirePackage{amsmath}
\RequirePackage{keyval}
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Package Options.}
%
% The package has some boolean \textsf{keyval} options
% which can be set to |true| or |false|.
%    \begin{macrocode}
\newif\ifdlm@std\dlm@stdtrue
\newif\ifdlm@ext\dlm@extfalse
\newif\ifdlm@script\dlm@scripttrue

\def\dlm@group{dlm@}
\define@key{\dlm@group}{stddef}[true]{\csname dlm@std#1\endcsname}
\define@key{\dlm@group}{extdef}[true]{\csname dlm@ext#1\endcsname}
\define@key{\dlm@group}{scriptstyle}[true]{\csname dlm@script#1\endcsname}

\DeclareOption*{\expandafter\setkeys\expandafter\dlm@group%
  \expandafter{\CurrentOption}}
\ProcessOptions
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Internal Definitions.}
%
% Overwrite the \textsf{amsmath} command |\bBigg@|
% to select the size according to the present math style
% (uses the \textsf{amsmath} definitions |\@mathmeasure| and |\big@size|).
% This code is activated only if
% the package option |scriptstyle| is set to |true|.
%
%    \begin{macrocode}
\ifdlm@script
\def\bBigg@choice#1#2#3#4{%
  {\@mathmeasure\z@{\nulldelimiterspace\z@}%
     {\big@size#2\big@size#1\left#4\vcenter to#3\big@size{}\right.}%
   \box\z@}}
\def\bBigg@#1#2{{\mathchoice%
  {\bBigg@choice{\displaystyle}{1}{#1}{#2}}%
  {\bBigg@choice{\textstyle}{1}{#1}{#2}}%
  {\bBigg@choice{\scriptstyle}{0.7}{#1}{#2}}%
  {\bBigg@choice{\scriptscriptstyle}{0.5}{#1}{#2}}}}
\fi
%    \end{macrocode}

% Define punctuation marks (|\bigp|, etc.)
% and binary operators (|\bigb|, etc.).
%
%    \begin{macrocode}
\newcommand{\bigp}{\mathpunct\big}
\newcommand{\Bigp}{\mathpunct\Big}
\newcommand{\biggp}{\mathpunct\bigg}
\newcommand{\Biggp}{\mathpunct\Bigg}
\newcommand{\bigb}{\mathbin\big}
\newcommand{\Bigb}{\mathbin\Big}
\newcommand{\biggb}{\mathbin\bigg}
\newcommand{\Biggb}{\mathbin\Bigg}
%    \end{macrocode}

% Define size selectors for standard size (|dlm@norm|),
% variable size (|dlm@var|).
%
%    \begin{macrocode}
\newcommand{\dlm@class}[1]{\csname dlm@class@#1\endcsname}
\newcommand{\dlm@class@}{}
\newcommand{\dlm@class@l}{\mathopen}
\newcommand{\dlm@class@r}{\mathclose}
\newcommand{\dlm@class@o}{\mathopen}
\newcommand{\dlm@class@c}{\mathclose}
\newcommand{\dlm@class@m}{\mathrel}
\newcommand{\dlm@class@p}{\mathpunct}
\newcommand{\dlm@class@b}{\mathbin}
\newcommand{\dlm@norm}[1]{\dlm@class{#1}\bBigg@{0.0}}
\newcommand{\dlm@big}[1]{\dlm@class{#1}\big}
\newcommand{\dlm@Big}[1]{\dlm@class{#1}\Big}
\newcommand{\dlm@bigg}[1]{\dlm@class{#1}\bigg}
\newcommand{\dlm@Bigg}[1]{\dlm@class{#1}\Bigg}
\newcommand{\dlm@var}[1]{\csname dlm@var@#1\endcsname}
\newcommand{\dlm@var@}[1]{\middle#1}
\newcommand{\dlm@var@l}[1]{\mathopen{}\mathclose\bgroup\left#1}
\newcommand{\dlm@var@r}[1]{\right#1\egroup}
\newcommand{\dlm@var@o}[1]{\mathopen{}\middle#1\mathopen{}}
\newcommand{\dlm@var@c}[1]{\mathclose{}\middle#1\mathclose{}}
\newcommand{\dlm@var@m}[1]{\mathrel{}\middle#1\mathrel{}}
\newcommand{\dlm@var@p}[1]{\middle#1\mathpunct{}}
\newcommand{\dlm@var@b}[1]{\mathbin{}{}\mkern-\medmuskip%
  \middle#1\mkern-\medmuskip{}\mathbin{}}
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Optional Size Argument Processing.}
%
% Parse the optional argument following |\delim|\ldots\
% commands to specify the size of delimiters.
% If the next character in line begins a group (`|{|') it is assumed that
% there is no optional argument.
% Otherwise the selected size is written to |\dlm@arg|.
% Unspecified or unknown sizes default to normal size.
% Finally, execute the code passed as an explicit argument to |\dlm@parsesize|.
%
%    \begin{macrocode}
\newcommand{\dlm@parsesize}[1]{\@ifnextchar\bgroup%
  {\dlm@parsesize@{#1}{0}}{\dlm@parsesize@{#1}}}
\newcommand{\dlm@parsesize@}[2]{\let\dlm@arg\dlm@norm%
  \if0#2\let\dlm@arg\dlm@norm\fi%
  \if1#2\let\dlm@arg\dlm@big\fi%
  \if+#2\let\dlm@arg\dlm@big\fi%
  \if!#2\let\dlm@arg\dlm@big\fi%
  \if2#2\let\dlm@arg\dlm@Big\fi%
  \if3#2\let\dlm@arg\dlm@bigg\fi%
  \if4#2\let\dlm@arg\dlm@Bigg\fi%
  \if*#2\let\dlm@arg\dlm@var\fi%
  #1}
%    \end{macrocode}
% Note that the delimited expression should be contained within a group
% such that nested delimiters will not overwrite the outer size definition.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Size Selection.}
%
% The command |\selectdelim| reproduces the delimiter in the second argument
% using the math class given in the first argument
% using the previously selected size stored in |\dlm@arg|.
% It appends the class identifier to the command stored in |\dlm@arg|
% and calls the latter with the delimiter as the argument.
% If the class identifier is `|.|', just return the delimiter argument as is.
%    \begin{macrocode}
\newcommand{\selectdelim}[2][]{\if.#1#2\else\dlm@arg{#1}#2\fi}
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Declaration of New Delimiter Commands.}
%
% Declares a new set of delimiters as the macro `|\|\emph{name}'.
% This macro checks for an optional size argument and stores it in |\dlm@arg|.
% It then passes on to a second macro `|\dlm@dcl@|\emph{name}',
% which takes the actual code.
%    \begin{macrocode}
\newcommand{\DeclareMathDelimiterSet}[1]{\expandafter\dlm@declare%
  \csname dlm@dcl@\expandafter\@gobble\string#1\endcsname{#1}}
\def\dlm@declare#1#2{\newcommand{#2}{\dlm@parsesize{#1}}\newcommand{#1}}
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Inline Delimiter Declarations.}
%
% Inline declaration for delimiters via |\delim...|.
% The following code is similar to the one produced by
% |\DeclareMathDelimiterSet|, but the delimiter arguments
% are processed \emph{before} the optional size modifier.
%
% |\delim| is used for a single delimited expression.
%    \begin{macrocode}
\newcommand{\delim}[2]
  {\dlm@parsesize{\dlm@dcl@delim{#1}{#2}}}
\newcommand{\dlm@dcl@delim}[3]
  {\selectdelim[l]#1{#3}\selectdelim[r]#2}
%    \end{macrocode}

% |\delimpair| is used for two delimited expressions separated
% by an intermediate delimiter.
%    \begin{macrocode}
\newcommand{\delimpair}[3]
  {\dlm@parsesize{\dlm@dcl@delimpair{#1}{#2}{#3}}}
\newcommand{\dlm@dcl@delimpair}[5]
  {\selectdelim[l]#1{#4}\selectdelim#2{#5}\selectdelim[r]#3}
%    \end{macrocode}

% |\delimtriple| is used for three delimited expressions separated
% by two intermediate delimiters.
%    \begin{macrocode}
\newcommand{\delimtriple}[4]
  {\dlm@parsesize{\dlm@dcl@delimtriple{#1}{#2}{#3}{#4}}}
\newcommand{\dlm@dcl@delimtriple}[7]
  {\selectdelim[l]#1{#5}\selectdelim#2{#6}\selectdelim#3{#7}\selectdelim[r]#4}
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Standard Definitions.}
%
% Define some common delimiters (by |providecommand| so as not to
% overwrite previously existing commands).
% This code is activated only if the package option |stddef| is set to |true|.
%    \begin{macrocode}
\ifdlm@std
\providecommand{\brk}[1][r]{\begingroup\def\dlm@use{\delim()}%
  \if r#1 \def\dlm@use{\delim()}\fi%
  \if s#1 \def\dlm@use{\delim[]}\fi%
  \if c#1 \def\dlm@use{\delim\{\}}\fi%
  \if a#1 \def\dlm@use{\delim<>}\fi%
  \expandafter\endgroup\dlm@use}
\providecommand{\eval}[1][v]{\begingroup\def\dlm@use{\delim.\rvert}%
  \if v#1 \def\dlm@use{\delim.\rvert}\fi%
  \if s#1 \def\dlm@use{\delim[]}\fi%
  \expandafter\endgroup\dlm@use}
\providecommand{\abs}{\delim\lvert\rvert}
\providecommand{\norm}{\delim\lVert\rVert}
\fi
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Extended Definitions.}
%
% Define some extended delimiters.
% This code is activated only if the package option |extdef| is set to |true|.
%    \begin{macrocode}
\ifdlm@ext
\providecommand{\pair}{\delimpair({[.],})}
\providecommand{\set}{\delim\{\}}
\providecommand{\setcond}{\delimpair\{|\}}
\providecommand{\intv}[1][c]{\begingroup\def\dlm@use{\delimpair[{[.],}]}%
  \if c#1 \def\dlm@use{\delimpair[{[.],}]}\fi%
  \if l#1 \def\dlm@use{\delimpair]{[.],}]}\fi%
  \if r#1 \def\dlm@use{\delimpair[{[.],}[}\fi%
  \if o#1 \def\dlm@use{\delimpair]{[.],}[}\fi%
  \expandafter\endgroup\dlm@use}
\providecommand{\avg}{\delim<>}
\providecommand{\corr}{\delim<>}
\providecommand{\comm}{\delimpair[{[.],}]}
\providecommand{\acomm}{\delimpair\{{[.],}\}}
\providecommand{\bra}{\delim<|}
\providecommand{\ket}{\delim|>}
\providecommand{\braket}{\delimpair<|>}
\fi
%    \end{macrocode}

%\iffalse
%</package>
%\fi
%
\endinput