From 087037d946928765bc5098fe2b706601255ecd3d Mon Sep 17 00:00:00 2001
From: Karl Berry <karl@freefriends.org>
Date: Tue, 28 May 2013 00:19:26 +0000
Subject: interval (24may13)

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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}\\ \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{intervalsetup}\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}
+
+\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
+%%% TeX-master: t
+%%% End: 
-- 
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