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\documentclass[a4paper,article]{memoir}
\usepackage[T1]{fontenc}
\usepackage{amsmath,enumitem,showexpl}
%\usepackage[scaled]{beramono}
\title{The \textsf{interval} package}
\author{Lars Madsen\thanks{Email: daleif@imf.au.dk, version: \INTVversion}\\ \small (on behalf of By the Danish \TeX\ collective)}
\setsecnumdepth{none}
%\setlength\overfullrule{5pt}
\usepackage{interval}
\begin{document}
\maketitle
\section{Motivation}
\label{sec:motivation}
In mathematics there are two syntax' when it comes to specifying open
and closed intervals.
The first use parantheses to mark an open end
\begin{align*}
[a,b] \qquad (a,b] \qquad [a,b)\qquad (a,b),
\end{align*}
while the other use brackets throughout
\begin{align*}
[a,b] \qquad ]a,b] \qquad [a,b[\qquad ]a,b[,
\end{align*}
The former poses no problem in \TeX, but the later does, as, e.g., a
closing bracket is being used in place of an opening fence, and thus
have the wrong category when it comes to spacing:
\begin{align*}
]-a,b[+c \qquad\text{versus}\qquad \mathopen{]}-a,b\mathclose{[}+c.
\end{align*}
One could use
\begin{verbatim}
\mathopen{]}-a,b\mathclose{[}+c
\end{verbatim}
to solve the problem, but then \cs{left}\dots\cs{right} can no longer
be used to auto scale the fences.
\section{The \cs{interval} command}
\label{sec:csinterval-command}
The following is the result of a discussion on the Danish \TeX\ Users
groups mailing list. Kudos to Martin Heller, for proposing the
original version using \textsf{pgfkeys}.
We provide a macro and a way to globally configure it
\begin{quote}
\cs{interval}\oarg{options}\marg{start}\marg{end}\\
\cs{intervalconfig}\marg{options}
\end{quote}
We note that the interval separator symbol is hidden inside the
\cs{interval} macro and can be changed using an option.
\subsection{Configuration options}
\label{sec:options}
\begin{description}[style=nextline,font=\sffamily\bfseries]
\item[separator symbol]
symbol that separates the start and end of the interval. Default:
\texttt{\{,\}}, note that as comma is the separating character in the
options specification, the symbol is enclosed in braces, these are
automatically removed.
\item[left open fence]
Default: \texttt{]}
\item[left closed fence]
Default: \texttt{[}
\item[right open fence]
Default: \texttt{[}
\item[right closed fence]
Default: \texttt{]}
\item[soft open fences]
This is just a fast way of saying
\begin{quote}
\ttfamily\obeylines
left open fence=(,
right open fence=)
\end{quote}
\item[colorize]
Default: \meta{empty}. When rewriting an existing document into
using the \textsf{interval} package, it turns out to be \emph{very}
handy to color the result of the \cs{interval} macro to keep track
of which have been rewritten and which has not.
This can be done using
\begin{lstlisting}[basicstyle=\ttfamily,columns=flexible]
\usepackage{xcolor}
\intervalconfig{ colorize=\color{red} }
\end{lstlisting}
It will colorize the entire interval including the fences.
\end{description}
\subsection{Usage options}
By default \cs{interval}\marg{start}\marg{end} will produce a closed
interval. Other types are provided via options:
\begin{description}[style=nextline,font=\sffamily\bfseries]
\item[open]
an open interval
\item[open left]
interval open on the left side
\item[open right]
interval open on the right side
\item[scaled]
auto scale interval fences
\item[scaled=\meta{scaler}]
scale fences using \meta{scaler}, i.e.\ using \texttt{scaled=\cs{Big}}
\end{description}
\fancybreak{}
As some might be guessed, the \texttt{interval} package depends on the
\textsf{pgfkeys} package to handle its key-value configuration.
\newpage
\section{Examples}
\label{sec:examples}
% used for showexpl
\lstset{
explpreset={
xleftmargin=0em,
columns=fixed,
},
pos=r,
width=-99pt,
overhang=0pt,
hsep=2\columnsep,
vsep=\bigskipamount,
rframe=x,
basicstyle=\footnotesize\ttfamily,
}
\begin{LTXexample}
\begin{align*}
&A\in\interval{a}{b}\\
&A\in\interval[open]{a}{b}\\
&A\in\interval[open left]{a}{b}\\
&A\in\interval[open right,
scaled]{a}{\frac12b}=B\\
&A\in\interval[scaled=\big]{a}{b}
\end{align*}
\end{LTXexample}
And using soft open fences:
\begin{LTXexample}
\intervalconfig{
soft open fences,
separator symbol=;,
}
\begin{align*}
&A\in\interval{a}{b}\\
&A\in\interval[open]{a}{b}\\
&A\in\interval[open left]{a}{b}\\
&A\in\interval[open right,
scaled]{a}{\frac12b}=B\\
&A\in\interval[scaled=\big]{a}{b}
\end{align*}
\end{LTXexample}
\end{document}
%%% Local Variables:
%%% mode: latex
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