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authorNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
committerNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
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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@math.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.
+
+
+\subsection{Short hands}
+\label{sec:shorthands}
+
+For convenience the following short hands are provided as of version 0.4.
+\begin{description}[style=nextline,font=\normalfont]
+\item[\cs{ointerval}\oarg{options}\marg{start}\marg{end}]
+ is short for \cs{interval}\texttt{[open,}\meta{options}\texttt{]}\marg{start}\marg{end}
+\item[\cs{linterval}\oarg{options}\marg{start}\marg{end}]
+ is short for \cs{interval}\texttt{[open left,}\meta{options}\texttt{]}\marg{start}\marg{end}
+\item[\cs{rinterval}\oarg{options}\marg{start}\marg{end}]
+ is short for \cs{interval}\texttt{[open right,}\meta{options}\texttt{]}\marg{start}\marg{end}
+\end{description}
+
+%\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}[varwidth=true]
+\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}{\frac{1}{2}b}=B \\
+& A\in\interval[scaled=\big]{a}{b} \\
+& A\in\ointerval[scaled]{%
+ \tfrac{1}{3}}{\tfrac{1}{2}}
+\end{align*}
+\end{LTXexample}
+And using soft open fences:
+\begin{LTXexample}[varwidth=true]
+\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}{\frac{1}{2}b}=B \\
+& A\in\interval[scaled=\big]{a}{b} \\
+& A\in\rinterval{a}{b}
+\end{align*}
+\end{LTXexample}
+
+
+
+\end{document}
+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: t
+%%% End: