% \iffalse -*- LaTeX -*-
%
% This is file `cjw-latex.dtx'. You can run this file through
% LaTeX2e to produce a DVI file of documentation. The file
% `cjw-latex.ins' should have come with this file. Run it through
% (La)TeX to extract the bundled macro files.
%
% \fi
\def\RCSinfo{$Id: cjw-latex.dtx,v 0.13 1998/09/01 15:54:20 cwynne Exp $}
\def\RCSsplit $#1: #2,v #3 #4 #5 #6 #7${
\gdef\filename {#2}
\gdef\fileversion{#3}
\gdef\filedate {#4}
\gdef\filetime {#5}
\gdef\fileauthor {#6}
\gdef\filelocker {#7}}
\expandafter\RCSsplit\RCSinfo
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%% Digits \0\1\2\3\4\5\6\7\8\9
%% Exclamation \! Double quote \" Hash (number) \#
%% Dollar \$ Percent \% Ampersand \&
%% Acute accent \' Left paren \( Right paren \)
%% Asterisk \* Plus \+ Comma \,
%% Minus \- Point \. Solidus \/
%% Colon \: Semicolon \; Less than \<
%% Equals \= Greater than \> Question mark \?
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% \iffalse
%<*driver>
\NeedsTeXFormat{LaTeX2e}
\ProvidesFile{cjw-latex.dtx}
[\filedate\space v\fileversion\space
Personal macros for LaTeX2e---CJW]
\documentclass{ltxdoc}
\usepackage{cjwmacro}
% We need math---call it with all options to make sure they work.
\usepackage[derivs,integrals,physics]{cjwmath}
\GetFileInfo{cjw-ltr.dtx}
\EnableCrossrefs
% \DisableCrossrefs % Say \DisableCrossrefs if index is ready
% \OnlyDescription % Comment out for implementation details
\RecordChanges
\begin{document}
\DocInput{cjw-latex.dtx}
\end{document}
%</driver>
% \fi
%
% \DeclareRobustCommand{\cseq}[1]{\texttt{\bslash#1}}
% \DeclareRobustCommand{\pkg} [1]{\textsf{#1}}
% \DeclareRobustCommand{\env} [1]{\textsf{#1}}
%
% \renewcommand{\thefootnote}{\fnsymbol{footnote}}
%
% \title{The \pkg{cjw-latex} Macro Collection\thanks{%
% This file has version \fileversion{} as of \filedate.}}
% \author{Colin J.~Wynne\thanks{E-Mail at:
% \texttt{cwynne@mts.jhu.edu}, \texttt{cwynne@jhu.edu}\,.}}
% \date{\filedate}
%
% \maketitle
%
% \setcounter{StandardModuleDepth}{1}
%
% {\parskip 0pt ^^A % This is the hack used by |doc.dtx|.
% ^^A % (bug in \LaTeX?)
% \tableofcontents
% }
%
% \section*{Introduction}
%
% I have been a \TeX{} user for quite a long time now. It was in my
% junior year in college, in 1992, that one of my friends and one of
% my math professors decided to warp my perception of reality and
% introduce me to Dr.~Knuth's wonderful creation. In those days,
% Plain-\TeX{} was the tool of choice, we coded everything ourselves
% from primitives on up, logical markup was unknown, and \LaTeX{} was
% known as Lame-\TeX. During my senior year I wrote an honors thesis
% in mathematics which required quite a lot of things not present in
% standard Plain-\TeX. My macro files grew, and grew, and\dots
%
% In the year following my graduation, I converted myself to \LaTeX{},
% mostly because of the convergence my own personal modified
% ePlain/NFSS1/Plain format was having towards \LaTeX{} in terms of
% logical markup. Most of macros were easily converted into
% \LaTeX{}-ese. They got more complicated from there.
%
% So now I regularly write up papers, letters, mathematical problem
% sets, and just about anything else that uses the English language,
% in \LaTeX. The macros have evolved quite a bit. More has been
% added. I took to using the |dtx| format for most of my input files,
% and finally decided to wrap my big three up into a single documented
% source file.
%
% I hope that these macros will prove useful to somebody out there,
% and if they do, feel free to buy me a beer next time you see me. I
% have other |dtx| files available, including a modified \pkg{letter}
% class which also does German formal letters, and a package for doing
% outlines. Any package of mine should be identifiable on your
% friendly neighborhood CTAN site with a name like
% \verb+cjw*.(dtx|ins)+.
%
% \section{General macros}
%
% \iffalse
%
\NeedsTeXFormat{LaTeX2e}
%<general>\ProvidesPackage{cjwmacro}
%<math>\ProvidesPackage{cjwmath}
%<deriv>\ProvidesFile{cjwderiv.tex}
%<integ>\ProvidesFile{cjwinteg.tex}
%<phys>\ProvidesFile{cjwphys.tex}
%<units>\ProvidesFile{cjwunits}
[\filedate\space v\fileversion\space
%<general> Personal macros for LaTeX2e---CJW]
%<math> Math macros for LaTeX2e---CJW]
%<deriv> Derivative macros for cjwmath.sty---CJW]
%<integ> Integration macros for cjwmath.sty---CJW]
%<phys> Physics macros for cjwmath.sty---CJW]
%<units> Typesetting units in LaTeX2e---CJW]
%
%<*general>
%
%\fi
%
% I tend to organize my package files as follows---first come flow
% control structures for the package itself, usually in the form of
% new conditionals; then come the options; then comes the meat of the
% package in some sort of vaguely thought out order. This package is
% no exception.
%
% \subsection{Package initialization}
%
% Conditionals are usually used in conjunction with package options to
% provide conditional inclusion of certain code, either \emph{via} an
% \cseq{if}\dots{}\cseq{endif} block or using class options. For this
% package, the subsystem in question is the inclusion of verbatim
% typeset files.
% \begin{macrocode}
\newif\if@verbext \@verbextfalse
% \end{macrocode}
% Not surprisingly, this conditional is used directly by an option.
% \begin{macrocode}
\DeclareOption{verbext}{\@verbexttrue}
% \end{macrocode}
% I used to use options for the loading of additional packages. In
% particular, when I used \pkg{psfig.new} which could not be handled
% as a \LaTeXe{} package, I did this. Now that I use the \pkg{epsfig}
% package that comes with \LaTeXe, I simply issue a warning to
% include the package separately.
% \begin{macrocode}
\DeclareOption{psfig}{%
\PackageWarning{cjwmacro}%
{Obsolete option \CurrentOption. Use package `epsfig' instead.}}
% \end{macrocode}
% Since, however, using \pkg{pstricks} requires several files, I still
% use a package option to take care of all of that. This option
% checks for the existence of \emph{both} files before including
% either, hence the nested calls to \cseq{InputIfFileExists}. A
% similar option is used for \pkg{pst-plot.tex}, since is not
% implemented as a package file.
% \begin{macrocode}
\DeclareOption{pstricks}{%
\InputIfFileExists{pstricks.sty}{%
\InputIfFileExists{pst-node.tex}{}{%
\PackageError{cjwmacro}{File `pst-node.sty' not found.}{}}}%
{\PackageError{cjwmacro}{File `pstricks.sty' not found.}{}}}
\DeclareOption{psplot}{\InputIfFileExists{pst-plot.tex}{}{%
\PackageError{cjwmacro}{File `pst-plot.tex' not found.}{}}}
% \end{macrocode}
%
% The next two options are used to change behavior of some macros on
% draft as opposed to final copies. Currently, only \cseq{ssbreak}
% has such a dependency, and in final form it uses the PS-Tricks
% package to typeset a nice section delimiter. Note the use of
% \cseq{ExecuteOption} by the \pkg{final} option to make sure that
% PS-Tricks is, indeed, available.
% \begin{macrocode}
% What to do for draft vs. final copy.
\DeclareOption{draft}{%
\def\ssbreakbar{\hbox to 2in{\hrulefill}}}
\DeclareOption{final}{%
\ExecuteOptions{pstricks}
\def\ssbreakbar{%
\psset{linewidth=0.4pt,unit=1in}%
\pspicture(-2.5,-0.15)(2.5,0.15)%
\qdisk(0,0){0.04}%
\qdisk(0.33,0){0.02}%
\qdisk(-0.33,0){0.02}%
\pspolygon*(0.33,-0.02)(0.33,0.02)(1.75,0)%
\pspolygon*(-0.33,-0.02)(-0.33,0.02)(-1.75,0)%
\endpspicture}}
% \end{macrocode}
%
% To finish off option handling, we declare a default (warn about
% unknown options), execute defaults, and process the passed option
% list.
% \begin{macrocode}
\DeclareOption*{%
\PackageWarning{cjwmacro}{Unknown option `\CurrentOption'}}
\ExecuteOptions{draft}
\ProcessOptions
% \end{macrocode}
%
% \subsection{General definitions}
%
% These general definitions set up some `meta-macros', to be used by
% other commands.
%
% One of the things I liked a lot about \TeX{} was the use of
% \cseq{let} to make aliases for existing commands without
% sacrificing much of the control sequence space. In the spirit of
% \LaTeXe, however, I have implemented this thrice with name
% checking. Analogously to the \cseq{newcommand}-like macros, we
% offer the following three:
% \begin{macrocode}
\newcommand{\alias} [2]{\@ifdefinable #1{\let #1 #2}}
\alias\realias\let
\newcommand{\providealias}[2]{\@ifundefined #1{\let #1 #2}}
% \end{macrocode}
% Usage is, for example,
% \begin{display}{l}
% \cseq{alias}\cseq{foo}\cseq{bar}
% \end{display}
% which makes \cseq{foo} an alias for \cseq{bar}. As expected,
% \cseq{alias} only works if the new name is currently undefined and
% \cseq{providealias} does nothing if its first argument is already
% defined. Somewhat more lax than its counterpart
% \cseq{renewcommand}, \cseq{realias} does not care if its first
% argument is defined or not. In essence, that command is used to
% unconditionally alias a command. This is why, oddly enough,
% \cseq{realias} is itself just an alias of \cseq{let}. Is this
% getting confusing yet?
%
% Next we input wholesale a few useful packages. These are still in
% the spirit of meta-macros which define this section. The first
% package, \pkg{amstext}, provides the \cseq{text} command, which
% basically puts its argument in text mode inside a box, but in the
% current style (textstyle, scriptstyle, etc.). This is used later
% on. The \pkg{xspace} package is used for control sequences which
% would encounter `the space problem' when expanded as is.
% \begin{macrocode}
\RequirePackage{amstext}
\RequirePackage{xspace}
% \end{macrocode}
% The command \cseq{intertext} from the \pkg{amsmath} package is quite
% useful, but I do not want to include that entire package unless it
% is necessary. Therefore, I make sure that command is defined one
% way or another. I also give it the alias \cseq{rem} since I am
% somewhat nostalgic about ancient forms of \textsf{\small BASIC}\dots{}
% \begin{macrocode}
\providecommand{\intertext}[1]{\noalign{%
\penalty\postdisplaypenalty\addvspace{ 0.5\belowdisplayskip}
\vbox{\normalbaselines\noindent#1}%
\penalty\predisplaypenalty\addvspace{0.5\abovedisplayskip}}}
\alias\rem\intertext
% \end{macrocode}
%
% Next we define some font style names which will be used in some
% contexts later. This is done to avoid hard-coding of certain styles
% and to allow as much customization as possible.
% \begin{macrocode}
\providecommand{\pagenofont} {\normalfont}
\providecommand{\declarefont} {\normalfont\bfseries\mathversion{bold}}
\providecommand{\altdeclarefont}{\normalfont\itshape}
\providecommand{\captionfont} {\normalfont\itshape}
\providecommand{\examplefont} {\normalfont}
\providecommand{\altexamplefont}{\normalfont\itshape}
\providecommand{\labelfont} {\normalfont\bfseries\mathversion{bold}}
\providecommand{\timelinefont} {\normalfont}
\providecommand{\titlefont} {\normalfont\bfseries\Large\mathversion{bold}}
\providecommand{\verbatimfont} {\normalfont\ttfamily}
% \end{macrocode}
%
% The next few commands are for programming convenience. First we
% want to be able to swap the definitions of two control sequences.
% \begin{macrocode}
\newcommand{\swapdef}[2]{{%
\let \@tempa #1\relax
\global\let #1 #2\relax
\global\let #2 \@tempa}}
% \end{macrocode}
% We also want to be able to do the same for lengths (or glue or
% whathaveyou).
% \begin{macrocode}
\newcommand{\swapdim}[2]{{%
\@tempdima #1\relax
\global #1 #2\relax
\global #2 \@tempdima}}
% \end{macrocode}
% Next is a macro constructed from an exercise in \emph{The
% \TeX{}book}, which takes three control sequences and expands them in
% reverse order.
% \begin{macrocode}
\newcommand{\expandthree}[2]{%
\expandafter\expandafter\expandafter #1\expandafter #2}
% \end{macrocode}
%
% This next macro is modified from code I received in the
% |comp.text.tex| newsgroup. According to the e-mail in which I
% received it, the original source is a set of macros for
% \emph{TUGboat}. It turns a number into an ordinal, finding the
% correct ordinal label which is set as a superscript.
% \begin{macrocode}
\newcommand{\nth}[1]{{%
\@tempcnta = #1\relax
\ifnum \@tempcnta < 0\relax % Make sure our number is
\@tempcnta = -\@tempcnta % non-negative.
\fi
\ifnum \@tempcnta < 14\relax % Deal first with the
\ifnum \@tempcnta > 10\relax % exceptions for
\def\@tempa{th} % 11, 12, and 13.
\fi
\else
\loop \ifnum\@tempcnta > 9\relax % Loop until the recursive
\@tempcntb = \@tempcnta % remainder (mod 10) is
\divide \@tempcntb by 10\relax % a single digit in order
\multiply\@tempcntb by 10\relax % to successfully satisfy
\advance \@tempcnta by -\@tempcntb% the ordinality test.
\repeat
\def\@tempa{\ifcase\@tempcnta % Figure the proper label:
th% % 0th
\or st% % 1st
\or nd% % 2nd
\or rd% % 3rd
\else th% % nth
\fi}
\fi
#1\ensuremath{^{\text{\@tempa}}}}} % Superscript the label in
% math mode.
% \end{macrocode}
%
% Continuing in the vein of superscripts, we define two macros which
% put their arguments as sub- and superscripts in script-script
% style. This was motivated by such things as derivative indices
% which look just plain ugly in script style.
% \begin{macrocode}
\alias\sst\scriptscriptstyle
\newcommand{\ssp}[1]{^{\sst#1}}
\newcommand{\ssb}[1]{_{\sst#1}}
% \end{macrocode}
%
% We now come to some very important and necessary macros, namely the
% creation of typeset sideways \textsf{\small ASCII} smiley
% faces. \smiley Since I like to be as general as possible, I have
% also written an \cseq{emote} macro for indicating
% emotions. \emote{smirk}
% \begin{macrocode}
\newcommand{\smiley}[1][\@smiley]{%
\edef\@sf{\spacefactor=\the\spacefactor}%
\unskip\spacefactor=1000\relax\space #1\@sf\xspace}
\newcommand{\@smiley}{%
{\ttfamily\raise 0.078em\hbox{:}\kern-0.1em{-}\kern-0.1em{)}}}
\newcommand{\emote}[1]{%
\smiley[\ensuremath{\langle}\emph{#1}\ensuremath{\rangle}]}
% \end{macrocode}
%
% Since I learned the good habit of doing so at Washington and Lee, I
% often append pledges to my assignments. The generic pledge is
% implemented as an environment. It formerly took an argument, the
% date, but I decided that was superfluous, seeing as how the
% assignment headers set the date once. Why risk inconsistency? Much
% to my surprise, I found out that \LaTeXe's \cseq{maketitle} command
% unsets not only the date holder, but also the command which is used
% to set the date in the first place. Anyhow, this means that the
% date \emph{does} need to be set, but I have left that to be done by
% the headers. The \env{pledge} environment issues a warning if the
% date is not set.
% \begin{macrocode}
\newenvironment{pledge}%
{\ifx\@empty\@date
\PackageWarning{cjwmacro}{Date is not set.}
\fi
\parskip=2pt \parindent=0pt\relax
\null\vfill\begin{flushright}
\itshape\small}
{\\[5ex]\normalfont\footnotesize
\makebox[2in]{\hrulefill}\quad\@date\\
\makebox[2in]{Colin J.~Wynne}\quad{\hphantom{\@date}}\\
\end{flushright}}
% \end{macrocode}
% The old Washington and Lee pledge lives on in my macros\dots{} It
% requires one argument, namely the type of assignment being pledged.
% The argument is optional, though, and a paper is assumed by default.
% \begin{macrocode}
\newcommand{\wnlpledge}[1][paper]{%
\ifx\@empty\@date
\PackageWarning{cjwmacro}{Date is not set.}
\fi
\parskip=2pt \parindent=0pt\relax
\null\vfill\begin{flushright}
\itshape\small
On my honour, I have neither given nor received\\
any unacknowledged aid on this #1.\\[5ex]
\normalfont\footnotesize
\makebox[2in]{\hrulefill}\quad\@date\\
\makebox[2in]{Colin J.~Wynne,~'94}\quad{\hphantom{\@date}}\\
\end{flushright}}
% \end{macrocode}
%
% As mentioned in the option section, there is a macro used to put
% fancy section delimiters into, say, a story. The \cseq{ssbreak}
% command expects the type of delimiter, the \cseq{ssbreakbar}, to be
% defined. Since either \pkg{draft} or \pkg{final} must be chosen as
% an option, this should be fine, but I have put a hopefully redundant
% command in just in case.
% \begin{macrocode}
\newcommand{\ssbreak}{\bigskip
\centerline{\ssbreakbar}\bigbreak}
\providecommand{\ssbreakbar}{}
% \end{macrocode}
%
% \subsection{Box formatting}
%
% I have written some of my own commands for handling boxes. The
% first thing I wanted was an analog of \cseq{mbox} or \cseq{hbox} for
% math mode. The simple version---\cseq{mathbox} puts its argument into an
% \cseq{hbox}, in math mode, in the current style. The second version
% is \cseq{Mathbox}, which takes two arguments, the first of which is
% put in the box and evaluated \emph{before} math mode is entered.
% This was done for a specific application where I needed to get the
% contents of the \cseq{mathbox} itself into boldface. Of course,
% \cseq{boldmath} cannot be evaluated within math mode. Note that the
% style is chosen by the \cseq{mathpalette} macro, and that the
% command \cseq{@mathbox} is essentially just a dummy to allow the
% proper expansion of \cseq{mathpalette}.
% \begin{macrocode}
% \mathbox puts its argument into an \hbox, in math mode, with the
% current \...style.
\def\mathbox #1{\hbox{$\mathpalette\@mathbox{#1}$}}
\def\Mathbox #1#2{\hbox{#1$\mathpalette\@mathbox{#2}$}}
\def\@mathbox#1#2{#1#2}
% \end{macrocode}
% Now, there is a reason why these are defined with \cseq{def} and not
% \cseq{newcommand}. You see, what I really wanted to do was
% something like
% \begin{verbatim}
% \newcommand{\mathbox}[2][]{%
% \hbox{#1$\mathpalette\@mathbox{#1}$}}
% \newcommand{\@mathbox}[2]{#1#2}
% \end{verbatim}
% in order to get optional arguments to my \cseq{mathbox}es. The
% problem, though, is that I want to use this command in the context
% of |\box|$N$|=\mathbox{|\dots{}|}|, and for that to work, the first
% token in the expansion of \cseq{mathbox} \emph{must} be a
% |\|$?$|box| command. The overhead imposed by \cseq{newcommand}
% precludes this. So, I use the cheap hack until I figure out a more
% workable way of implementing what I really want.
%
% A more generically applicable box command is one which does unto
% width what \cseq{smash} does to height. Hence \cseq{smush}:
% \begin{macrocode}
\newcommand{\smush}{\relax
\ifmmode
\def\next{\mathpalette\math@smush}
\else
\let\next\make@smush
\fi \next}
\newcommand{\make@smush}[1]{\setbox0=\hbox{#1}\fin@smush}
\newcommand{\math@smush}[2]{\setbox0=\hbox{$\m@th#1{#2}$}\fin@smush}
\newcommand{\fin@smush}{\wd0=0pt \box0 }
% \end{macrocode}
%
% And finally, vaguely in the realm of boxes, we have struts. Here I
% have defined some math struts of various sizes (corresponding to the
% various delimiter sizes on which they are based).
% \begin{macrocode}
\newcommand{\bigmathstrut} {\vphantom{\big()}}
\newcommand{\biggmathstrut}{\vphantom{\bigg()}}
\newcommand{\Bigmathstrut} {\vphantom{\Big()}}
\newcommand{\Biggmathstrut}{\vphantom{\Bigg()}}
% \end{macrocode}
%
% \subsection{Abbreviations, etc.}
%
% I have found myself using particular types of abbreviations quite
% often---often enough that I wanted control sequences for them,
% whence these first few specimens.
% \begin{macrocode}
\newcommand{\ie} {\emph{i.e.}\xspace}
\newcommand{\eg} {\emph{e.g.}\xspace}
\newcommand{\heisst}{d.h\null.\xspace} % \dh is taken.
% \end{macrocode}
% Note the use of \cseq{xspace} so that explicit space need not be
% given afterward. I did this mostly because I have never decided
% whether or not I want to use a comma after either of this.
%
% The second type of abbreviation is the initial, or should I say
% initials. I finally settled on a style I like---two initials should
% be separated by a thinspace, and will of course need to have the
% spacefactor adjusted if at the end of a sentence (followed by a
% period, in particular). Here is the implementation:
% \begin{macrocode}
\newcommand{\initials}[2]{%
\break@init #2
\@ifdefinable #1{%
\global\edef#1{%
\noexpand\hbox{\@tempa.\noexpand\,\@tempb}%
\noexpand\@ifnextchar.{\noexpand\@}{.\noexpand\xspace}}}}
\def\break@init #1.#2.{%
\def\@tempa{#1}\def\@tempb{#2}}
% \end{macrocode}
% What happens is this. The \cseq{initials} command is given a
% control sequence name and the initials to be used. The initials are
% broken on the periods and returned in the specified tokens. Then,
% if the control sequence is available for definition, it is defined
% in such a way to make all the spacing and punctuation work out.
% Since the tokens need to be expanded back to the separate initials,
% an \cseq{edef} is required---at the same time, use of
% \cseq{noexpand} is made to keep things from going kablooie at
% definition time. Here are some standard initials by way of usage
% example.
% \begin{macrocode}
\initials{\UN}{U.N.}
\initials{\US}{U.S.}
\initials{\AI}{A.I.}
% \end{macrocode}
%
% \subsection{Dates}
%
% I have had call to do a fair amount of \TeX{} in both English and
% German. Therefore, in implementing the examples of date macros from
% \emph{The \TeX{}book}, I have provided for both languages.
%
% \begin{macrocode}
% LaTeX style commands for date-parts, both English and German.
\providecommand{\theday}{\number\day\relax}
\providecommand{\themonth}{%
\ifcase\month\or January\or February\or%
March\or April\or May\or June\or July\or August\or%
September\or October\or November\or December\fi}
\providecommand{\themonat}{%
\ifcase\month\or Januar\or Februar\or%
M\"arz\or April\or Mai\or Juni\or Juli\or August\or%
September\or Oktober\or November\or Dezember\fi}
\providecommand{\theyear}{\number\year\relax}
% \end{macrocode}
% Note that \cseq{today} is unconditionally defined by the following
% underhandedness.
% \begin{macrocode}
\providecommand{\today}{}
\renewcommand{\today}{\theday~\themonth, \theyear\xspace}
\providecommand{\heute}{}
\renewcommand{\heute}{den~\theday.\ \themonat\ \theyear\xspace}
\alias\gdate\heute
% \end{macrocode}
%
% \subsection{Page styles and titles}
%
% We are finally into the realm of more traditional package macros,
% namely creating some general page appearances. Here I have
% redefined the \pkg{plain} pagestyle to take advantage of the
% \cseq{pagenofont} defined above.
% \begin{macrocode}
\renewcommand{\ps@plain}{%
\let\@mkboth \@gobbletwo
\let\@oddhead \@empty
\let\@evenhead\@empty
\def\@oddfoot{\pagenofont\hfil\thepage\hfil}
\let\@evenfoot\@oddfoot}
% \end{macrocode}
% The \pkg{topright} pagestyle has page numbers (strangely enough) at the top
% right of the page.
% \begin{macrocode}
\newcommand{\ps@topright}{%
\let\@mkboth \@gobbletwo
\def\@oddhead{\pagenofont\hfil\thepage}
\let\@evenhead\@oddhead
\let\@oddfoot \@empty
\let\@evenfoot\@empty}
% \end{macrocode}
%
% \subsection{Text formatting}
%
% \subsubsection{Timelines}
%
% A timeline is a long, running, two-column format used, for example,
% to do r\'esum\'es or vit\ae (or, if you are in Germany, a
% \emph{Lebenslauf}). The idea is that a date (or some identifying
% information) appears at the left, and the content is given in the
% righthand column. The usage is
% \begin{display}{l}
% |\timeline[|\meta{pos}|]{|\meta{date}|}|
% \end{display}
% where \meta{pos} is exactly the argument to \cseq{makebox}, the
% justification of the \meta{date} entry within the lefthand column.
% That column has length \cseq{timelineskip}, which can off course be
% set as desired.
% \begin{macrocode}
\newlength{\timelineskip}
\setlength{\timelineskip}{1.75in}
% \end{macrocode}
% The actual entries are not considered to be two separate columns.
% Rather, the first line is padded out to \cseq{timelineskip} with
% makebox, and following lines use a hanging indentation. The control
% sequence \cseq{endtimeline} is defined trivially so that a timeline
% entry may be used as a \env{timeline} environment.
% \begin{macrocode}
\newcommand{\timeline}[2][l]{%
\noindent\hangindent=\timelineskip
\makebox[\timelineskip][#1]{\timelinefont{#2}}\ignorespaces}
\let\endtimeline\relax
% \end{macrocode}
%
% \subsubsection{Mathematical declarations}
%
% In writing up mathematics, one often wishes to declare definitions,
% theorems, and so forth. I have written generic declaration macros
% which can be customized for these uses. Since I prefer to have all
% such things numbered seuqentially, they use a common counter, called
% \cseq{declare}, strangely enough. They are numbered within sections
% if sections are being numbered.
% \begin{macrocode}
\@ifundefined{c@section}
{\newcounter{declare}}
{\newcounter{declare}[section]
\renewcommand{\thedeclare}{\thesection.\arabic{declare}}}
% \end{macrocode}
% When declarations are numbered, it is sometime nice to have the
% declaration type and number appear uniformly wide throughout. This
% is done by forcing the declaration to appear in a box of width
% \cseq{declareindent}.
% \begin{macrocode}
\newlength{\declareindent}
\setlength{\declareindent}{0pt}
% \end{macrocode}
% We use some internal commands to specify exactly how the declaration
% is typeset. In fact, we will be defining not only declaration, but
% an alternate declaration form so that two different methods may be
% used simultaneously in a document---\eg, when theorems and major
% results are to be italicized, but definitions and so forth are not.
% \begin{macrocode}
\newcommand{\@declare} [1]{{\declarefont#1:}\quad}
\newcommand{\@altdeclare}[1]{{\altdeclarefont#1:}\quad}
% \end{macrocode}
% The generic declarations are environments, and are provided in both
% numbered (normal) and unnumbered (starred) forms. The latter are
% more simple.
% \begin{macrocode}
\newenvironment{declaration*}[1]%
{\medbreak\noindent\ignorespaces
\@declare{#1}\ignorespaces}%
{\kern0pt\nobreak\smallskip}
\newenvironment{altdeclaration*}[1]%
{\medbreak\noindent\ignorespaces
\@altdeclare{#1}\ignorespaces}%
{\kern0pt\nobreak\smallskip}
% \end{macrocode}
% The numbered versions introduce nothing surprising, but are a tad
% more involved.
% \begin{macrocode}
\newenvironment{declaration}[1]%
{\medbreak\refstepcounter{declare}
\noindent\ignorespaces
\ifnum\declareindent = 0\relax%
\@declare{\thedeclare\quad #1}
\else
\makebox[\declareindent]{\@declare{\thedeclare\hss #1}}
\fi\ignorespaces}
{\kern0pt\nobreak\smallskip}
\newenvironment{altdeclaration}[1]%
{\medbreak\noindent\ignorespaces
\refstepcounter{declare}
\ifnum\declareindent = 0\relax
\@altdeclare{\thedeclare\quad #1}
\else
\makebox[\declareindent]{\@altdeclare{\thedeclare\hss #1}}
\fi\ignorespaces}
{\kern0pt\nobreak\smallskip}
% \end{macrocode}
% Now, because I am essentially lazy and do not want the extra typing
% needed for an environment, I have shortcuts, \cseq{declare} and
% \cseq{altdeclare}, as well as numbered versions \cseq{ndeclare} and
% \cseq{altndeclare}. The first argument is passed to the
% corresponding environment, and the following paragraph is the body
% of the environment.
% \begin{macrocode}
\def\declare #1#2\par{%
\begin{declaration*}{#1}#2\end{declaration*}\par}
\def\altdeclare #1#2\par{%
\begin{altdeclaration*}{#1}#2\end{altdeclaration*}\par}
\def\ndeclare #1#2\par{%
\begin{declaration}{#1}#2\end{declaration}\par}
\def\altndeclare#1#2\par{%
\begin{altdeclaration}{#1}#2\end{altdeclaration}\par}
% \end{macrocode}
% Genreality is all well and good, but there are some stock
% declarations, given here in both numbered and unnumbered versions.
% \begin{macrocode}
\providecommand{\corollary} {\declare{Corollary}}
\providecommand{\definition} {\declare{Definition}}
\providecommand{\lemma} {\declare{Lemma}}
\providecommand{\proposition} {\declare{Proposition}}
\providecommand{\theorem} {\declare{Theorem}}
\providecommand{\note} {\altdeclare{Note}}
\providecommand{\ncorollary} {\ndeclare{Corollary}}
\providecommand{\ndefinition} {\ndeclare{Definition}}
\providecommand{\nlemma} {\ndeclare{Lemma}}
\providecommand{\nproposition}{\ndeclare{Proposition}}
\providecommand{\ntheorem} {\ndeclare{Theorem}}
\providecommand{\nnote} {\altndeclare{Note}}
% \end{macrocode}
% In addition, the following German declaration (meaning a claim) is
% also defined.
% \begin{macrocode}
\providecommand{\behaupt} {\declare{Behauptung}}
\providecommand{\nbehaupt} {\ndeclare{Behauptung}}
% \end{macrocode}
% Finally, since one is not likely to mix numbered and unnumbered,
% here is a control sequence that will make sure everything is
% numbered.
% \begin{macrocode}
\newcommand{\allndeclares}{%
\let\declare \ndeclare
\let\altdeclare \altndeclare}
% \end{macrocode}
%
% Now that we have propositions, claims, and theorems (oh my!), we
% want to be able to prove them. The first step is to define a proof
% environment. The environment simply sets up a label and some
% spacing. The label is in |\altdeclarefont|. The label is an
% optional argument which defaults to `Proof', oddly enough.
% \begin{macrocode}
\newenvironment{proof}[1][Proof]%
{\smallbreak\noindent{\altdeclarefont#1:}%
\quad\ignorespaces}%
{\qed}
% \end{macrocode}
% Just in case you are prooving in German, we also have the following:
% \begin{macrocode}
\newenvironment{beweis}[1][Beweis]%
{\smallbreak\noindent{\altdeclarefont#1:}%
\quad\ignorespaces}%
{\qed}
% \end{macrocode}
% Note that the end of a proof has the command |\qed|, which we will
% unconditionally define here. This is adapted from \emph{The
% \TeX{}book}. The idea is to right justify |\qedsymbol| on the line
% where |\qed| is invoked, unless there is not a comfortable amount of
% room. That amount is given as 2\,em. When this happens, the line
% is broken and the |\qedsymbol| appears flush right on the following
% line.
% \begin{macrocode}
\providecommand{\qed}{}
\renewcommand{\qed}{%
{\unskip\nobreak\hfil\penalty 50%
\hskip 2em\hbox{}\nobreak\hfil\qedsymbol%
\parfillskip=0pt \finalhyphendemerits=0 \par}}
% \end{macrocode}
% The standard end-of-proof symbol is a box, but I prefer somewhat
% less ink. I use \TeX's hollow diamond suit symbol (again
% unconditionally defined).
% \begin{macrocode}
\providecommand{\qedsymbol}{}
\renewcommand{\qedsymbol}{\lower 0.35ex\hbox{$\diamondsuit$}}
% \end{macrocode}
% In case it is desired, the box symbol is defined as |\qedbox|, and
% then with a simple alias this can be used to end all proofs.
% \begin{macrocode}
\newcommand{\qedbox}{\vrule height4pt width3pt depth2pt}
% \end{macrocode}
% Now we wish to define control sequences for some constructions
% commonly found in proofs. I often find myself writing out proofs
% which require cases. There are two types of cases. Often I will
% want to have two cases, one for each definition of an equivalence
% for example. In this case, the case delimiters will be something
% like |\then| and |\when| commands, and should be set in parentheses
% to mark them clearly. The other type is the more general `Case
% $n$:' (where $n$, one hopes, will not be \emph{too} large). To
% cover both of these, we use a fairly typical \LaTeX{} conceit:
% \begin{display}{l}
% |\Case*{|\meta{case}|}|
% \end{display}
% where the unstarred argument sets \meta{case} inside parentheses and
% the star supresses the parentheses. A German alias is given.
% \begin{macrocode}
\newcommand{\Case}{\@ifstar{\@starCase}{\@Case}}
\newcommand{\@starCase}[1]{\@@Case{#1}}
\newcommand{\@Case}[1]{\@@Case{(#1)}}
\newcommand{\@@Case}[1]{%
\noindent{\declarefont#1}\quad\ignorespaces}
\alias\Fall\Case
% \end{macrocode}
% And finally, just in case the proof is by contradiction, we have the
% following.
% \begin{macrocode}
\newcommand{\contra}{\ensuremath{\Rightarrow\Leftarrow}}
% \end{macrocode}
%
%
% \subsubsection{Problems and examples}
%
% In addition to declarations, and for subjects other than
% mathematics, one might want to provide examples and worked
% problems. I implement examples as a separate environment (well,
% \emph{four} separate environments) so that they may have fonts
% distinct from declarations.
% \begin{macrocode}
\newenvironment{example*}%
{\@nameuse{declaration*}{Example}\examplefont}
{\medbreak}
\newenvironment{altexample*}%
{\@nameuse{declaration*}{Example}\examplefont}
{\medbreak}
\newenvironment{example}%
{\declaration{Example}\examplefont}
{\medbreak}
\newenvironment{altexample}%
{\declaration{Example}\examplefont}
{\medbreak}
% \end{macrocode}
%
% Problems are handled differently. In my experience, problems do not
% appear in longwinded documents using sectioning, and so the counter
% need not be embedded.
% \begin{macrocode}
\newcounter{problem}
\setcounter{problem}{0}
\renewcommand{\theproblem}{\arabic{problem}}
\renewcommand{\p@problem}{}
% \end{macrocode}
% Often when working a problem, one wishes to include a reference to
% the source. This is accomplished via the \cseq{Page} macro. Usage
% is
% \begin{display}{l}
% |\Page*[|\meta{author}|]{|\meta{pp}|}{|\meta{problem}|}|
% \end{display}
% In the \LaTeX{} tradition, the standard command tries to outguess
% you by prepending a hash `\#' to the problem number, whereas the
% starred version omits this. Thus, the standard version produces
% \begin{display}{l}
% ([\meta{author},~]p.\,\meta{pp}, \#\meta{problem})
% \end{display}
% and \cseq{Page*} leaves off the hash. Notice that the space between
% author and page number is inserted by the macro. The macro is
% defined robustly so that it can be used in moving arguments.
% \begin{macrocode}
\DeclareRobustCommand{\Page}{%
\@ifstar{\@Page{}}{\@Page{\#}}}
\def\@Page#1{%
\@ifnextchar [{\@@Page{#1}}{\@@Page{#1}[]}}
\def\@@Page#1[#2]#3#4{%
\def\@tempa{#2}%
\ifx\@empty\@tempa%
\let\@tempb\@tempa%
\else%
\edef\@tempb{\@tempa,~}%
\fi%
(\@tempb p.\,#3, #1{#4})}
% \end{macrocode}
%
% The statement of a problem is given in an environment, again so that
% font customization can be easily done. The \env{statement}
% environment takes a single optional argument, which is typeset at
% the beginning of the statement in \cseq{altdeclarefont}. The rest
% of the statement is in \cseq{declarefont}. I use the optional
% argument to pass a \cseq{Page} reference most often---note, though,
% that if the optional argument to \cseq{Page} is used, the whole
% \cseq{Page} command should be put in braces sp that the square
% brackets of optional arguments do not get confused.
% \begin{macrocode}
\newenvironment{statement}[1][\null]%
{\def\@tempa{#1}\def\@tempb{\null}%
\ifx\@tempa\@tempb%
\def\@tempc{\null}%
\else%
\def\@tempc{\altdeclarefont\@tempa\quad}%
\fi%
\declarefont{\@tempc}\ignorespaces}
{\removelastskip\nopagebreak\smallskip}
% \end{macrocode}
% A problem, now, is basically just a wrapper for the statement. It
% generates and sets the problem number, does some spacing, and the
% body of the \env{problem} environment becomes the body of the
% \env{statement}. In essence, a \env{problem} is a numbered
% \env{statement}. There is a starred version which does not do
% numbers and references---this just does the correct spacing and
% calls \env{statement}. Note that the problem number is set using a
% macro from the \pkg{cjw-outl} package.
% \begin{macrocode}
\newenvironment{problem}%
{\setcounter{equation}{0}%
\gdef\theequation{\theproblem.\arabic{equation}}%
\removelastskip\medbreak%
\refstepcounter{problem}%
\noindent\theoutlabel{\theproblem.}%
\statement}
{\endstatement}
\newenvironment{problem*}%
{\removelastskip\medbreak%
\noindent\statement}
{\endstatement}
% \end{macrocode}
% Since I have been known to write assignments in German, we provide
% the aliases to make an \env{aufgabe} environment.
% \begin{macrocode}
\alias \aufgabe \problem
\realias\endaufgabe\endproblem
% \end{macrocode}
% For parts and subparts of problems, the aliases are English and the
% main definitions are German because I wrote these while I was in
% Germany. So, parts (\emph{Teile}) are numbered within problems and
% subparts (\emph{Subteile}) within parts. The defaults for
% cross-referencing (the \cseq{p@} forms) are set, too.
% \begin{macrocode}
\newcounter{teil} [problem]
\newcounter{steil}[teil]
\renewcommand{\theteil} {(\alph{teil})}
\renewcommand{\p@teil} {\theproblem}
\renewcommand{\thesteil} {(\roman{steil})}
\renewcommand{\p@steil}{\p@teil\theteil}
% \end{macrocode}
% The environment \env{part}/\env{teil} used to be implemented
% entirely in terms of the \pkg{cjw-outl} package, but that was a
% little bit of overkill, and made the numbering more difficult to
% implement. I ought to one day implement problems/parts/subparts
% entirely in terms of the outline macros. We'll see.
%
% Anyway, the current implementations still rely on some of the
% definitions from the \pkg{cjw-outl} package. The
% \env{part}/\env{teil} environments take a single optional argument,
% namely the outline depth. Level one starts the text flush left at
% the margin, which is usually where the \env{problem} is, hence a
% \env{part} should be at level two, and this is the default. A more
% detailed explanation of the goings-on here can be found in
% \pkg{cjw-outl.dtx}.
% \begin{macrocode}
\newenvironment{teil}[1][2]%
{\@tempcnta=#1\advance\@tempcnta by -1\relax
\ifnum\@tempcnta < 1\relax
\leftskip=0pt\relax
\else
\leftskip=\@tempcnta\outlindent
\fi
\refstepcounter{teil}
\addvspace{\medskipamount}%
\noindent\theoutlabel{\theteil}%
\ignorespaces}
{\par\smallbreak}
% \end{macrocode}
% The default level for \env{ppart} or \env{steil}, the subpart
% environments, is three.
% \begin{macrocode}
\newenvironment{steil}[1][3]%
{\@tempcnta=#1\advance\@tempcnta by -1\relax
\ifnum\@tempcnta < 1\relax
\leftskip=0pt\relax
\else
\leftskip=\@tempcnta\outlindent
\fi
\refstepcounter{steil}
\addvspace{\medskipamount}%
\noindent\theoutlabel{\thesteil}%
\ignorespaces}
{\par\smallbreak}
% \end{macrocode}
% English aliases are, of course, given.
% \begin{macrocode}
\realias\part \teil
\realias\endpart \endteil
\alias \ppart \steil
\realias\endppart\endsteil
% \end{macrocode}
%
% \subsubsection{Footnotes}
%
% This is a simple modification to a standard \LaTeXe{} internal
% macro, because I prefer hanging indentation on my footnote text.
% \begin{macrocode}
\long\def\@makefntext#1{%
\parindent 1em\noindent\hangindent=\parindent%
\hb@xt@ 1em{\hss \llap{\@makefnmark} }#1}
% \end{macrocode}
%
% \subsubsection{Text displays}
%
% I have turned the \cseq{begindisplay} and \cseq{enddisplay} macro
% pair from \emph{The \TeX{}book} (page~421) into a \LaTeX{}
% environment. As with Knuth's macros, local definitions for use
% within the display can be given, in this case via the
% \env{display}'s optional argument. Since the environment is
% implemented through the standard \env{tabular} environment, there is
% a mandatory argument specifying column layout. Overall, usage is
% \begin{display}{l}
% \cseq{begin}|{display}[|\meta{local}|]{|\meta{cols}|}|
% \end{display}
% with local definitions \meta{local} and column descriptol
% \meta{col}. (By the way, the previous display was created with the
% \env{display} environment\dots)
%
% The display's offset from the left margin is specified by
% \cseq{textdisplay indent}. Default value is equal to
% \cseq{parindent}, and is therefore set below, after
% \cseq{parindent}.
% \begin{macrocode}
\newlength{\textdisplayindent}
% \end{macrocode}
% The actual \env{display} environment uses the spacing and penalties
% of mathematical displays.
% \begin{macrocode}
\newenvironment{display}[2][]
{\vadjust{\penalty\predisplaypenalty}
\@newline[\abovedisplayskip]%
\begingroup%
#1%
\begin{tabular}{@{\null\hspace{\textdisplayindent}\null}#2}}
{\end{tabular}\endgroup
\vadjust{\penalty\postdisplaypenalty}
\@newline[\belowdisplayskip]\ignorespaces}
% \end{macrocode}
%
% \subsection{Verbatim inclusions}
%
% Since I only occassionally need to include verbatim files, the
% following macros need to be specifically included by a package
% option, as was mentioned above.
% \begin{macrocode}
\if@verbext
% \end{macrocode}
% For numbered inclusions, we need a line number counter.
% \begin{macrocode}
\newcounter{vfline}
\renewcommand{\thevfline}{\arabic{vfline}}
% \end{macrocode}
% We need the following command from \emph{The \TeX{}book}.
% \begin{macrocode}
\providecommand{\uncatcodespecials}{%
\def\do##1{\catcode`##1=12 }\dospecials}
% \end{macrocode}
% The basic command is \cseq{verbfile} which takes an optional
% argument specifying the starting line number (default is one), and a
% mandatory argument which is, of course, the name of the file to
% include. There is also \cseq{verbfilenolines} which does not number
% lines, and needs only the one mandatory argument.
% \begin{macrocode}
\providecommand{\verbfile}[2][1]{%
\par\begingroup\@vf@lines{#1}\input{#2}\relax\endgroup}
\providecommand{\verbfilenolines}[1]{%
\par\begingroup\@vf@nolines\input{#1}\relax\endgroup}
% \end{macrocode}
% In the manner of command which need to do \cseq{catcode} trickery,
% the above are primarily wrappers for the real commands. The one
% problem with these as currently implemented is that they do not
% handle leading space in the included file. Oh, well.
% \begin{macrocode}
\newcommand{\@vf@lines}[1]{%
\verbatimfont
\setcounter{vfline}{#1}
\addtocounter{vfline}{-1}
\setlength{\parindent}{0pt}
\setlength{\parskip}{0pt}
\def\par{\leavevmode\endgraf}
\obeylines \uncatcodespecials \obeyspaces
\everypar{\null\stepcounter{vfline}%
\llap{\scriptsize\thevfline\quad}\null}}
\newcommand{\@vf@nolines}{%
\verbatimfont
\setlength{\parindent}{0pt}
\setlength{\parskip}{0pt}
\def\par{\leavevmode\endgraf}
\obeylines \uncatcodespecials \obeyspaces
\everypar{\null}}
% \end{macrocode}
% Now we end the inclusion conditional.
% \begin{macrocode}
\fi
% \end{macrocode}
%
% \subsection{Initialization}
%
% We use the \cseq{AtBeginDocument} command to set up some default
% values when the document is actually started.
% \begin{macrocode}
\AtBeginDocument{%
\setlength{\parindent} {20pt}
\setlength{\parskip} { 2pt plus 1pt}
\setlength{\textdisplayindent}{\parindent}}
% \end{macrocode}
%
% \iffalse
%
%</general>
%
% \fi
%
%
% \section{Math macros}
%
% \iffalse
%
%<*math>
%
% \fi
%
% While some macros useful for typesetting mathematics have already
% been covered, none of them had to do with mathematical equations or
% symbols---they were macros for logical flow and delineation. In
% this package, \pkg{cjwmath}, I have written macros which are
% specifically for typesetting the actual math---the vast majority of
% these macros, if not actually all of them, are meant to be used in
% math mode.
%
% \subsection{Package initialization}
%
% Since different papers require different types of math, I have again
% used the introduction of conditionals and package options to control
% what code is actually loaded. The important one concerns use of the
% AMS math packages in AMS-\LaTeX. This is included as an option to
% my package because some of my definitions depend upon whether the
% AMS macros are being used. There are conditionals for including
% code for calculus (both derivatives and integrals) and some code for
% physics.
% \begin{macrocode}
\newif \if@amsmath
\newif \if@derivatives
\newif \if@integrals
\newif \if@physics
% \end{macrocode}
% There are options corresponding to each conditional.
% \begin{macrocode}
\DeclareOption{amsmath} {\@amsmathtrue}
\DeclareOption{derivs} {\@derivativestrue}
\DeclareOption{integrals}{\@integralstrue}
\DeclareOption{physics} {\@physicstrue}
% \end{macrocode}
% There used to be another option for typesetting units. While I
% originally included that code in this package directly, I found
% several occasions where I wanted units but not the rest of the math
% code. Therefore, units are in a separate package, and the option
% now just reminds the user to input that package by itself.
% \begin{macrocode}
\DeclareOption{units}{%
\PackageWarning{cjwmath}%
{Obsolete option \CurrentOption. Use package `cjwunits' instead.}}
% \end{macrocode}
% Finally, there is a default option, to warn about unknown options,
% and the passed option list is processed.
% \begin{macrocode}
\DeclareOption*{%
\PackageWarning{cjwmath}{Unknown option `\CurrentOption'}}
\ProcessOptions
% \end{macrocode}
%
% This package depends upon the previous one.
% \begin{macrocode}
\RequirePackage{cjwmacro}
% \end{macrocode}
% It also uses the AMS fonts, for which we require \pkg{amssymb},
% which itself requires \pkg{amsfonts}.
% \begin{macrocode}
\RequirePackage{amssymb}
% \end{macrocode}
% Just in case things get screwy in \pkg{cjwmacro}---which they
% shouldn't, we explicitly require \pkg{amstext} here, too, for the
% \cseq{text} command.
% \begin{macrocode}
\RequirePackage{amstext}
% \end{macrocode}
% I much prefer the following package to AMS's own blackboard bold
% font.
% \begin{macrocode}
\RequirePackage{bbm}
% \end{macrocode}
% If the \pkg{amsmath} option is specified, we load the package (which
% itself brings in a lot of other stuff).
% \begin{macrocode}
\if@amsmath
\RequirePackage{amsmath}
\fi
% \end{macrocode}
%
% \subsection{Miscellaneous macros}
%
% Here is a package command which I have written to cover the
% shortcomings of AMS-\LaTeX's |\DeclareNewMathOperator| command. In
% particular, I would like to be able to set different fonts for some
% operators. The syntax is
% \begin{display}{l}
% |\NewMathOp*[|\meta{font}|]{\cs}{|\meta{text}|}|
% \end{display}
% The optional star makes an operator with limits. The \meta{font}
% is, by default, |\operator@font|. |\cs| is the name of the new
% mathop. \meta{text} should be the printed version of the operator,
% but may also include, for example, extra kerning information, as in
% \begin{display}{l}
% |\NewMathOp[\mathfrak]{\so}{o\kern 0pt}|
% \end{display}
% The command should produce something robust.
% \begin{macrocode}
\DeclareRobustCommand{\NewMathOp}{%
\@ifstar{\@makenewop{\displaylimits}}
{\@makenewop{\nolimits}}}
% \end{macrocode}
% The first iteration applies a font if the optional argument is not
% given.
% \begin{macrocode}
\def\@makenewop#1{%
\@ifnextchar [{\@@makenewop{#1}}
{\@@makenewop{#1}[\operator@font]}}
% \end{macrocode}
% Finally, the net operator itself is declared robustly. The
% arguments are, in order, either |\displaylimits| or |\nolimits|, the
% font, the control sequence, and the operator text.
% \begin{macrocode}
\def\@@makenewop#1[#2]#3#4{%
\DeclareRobustCommand{#3}{%
\mathop{\kern\z@{#2{#4}}}#1}}
% \end{macrocode}
%
% The next few macros have to do with things not specific to any
% particular flavor of mathematics. For example, I like some of the
% alternate Greek characters more than the originals---notice how we
% cleverly required the \pkg{cjwmacro} package which gives us the
% \cseq{swapdef} command.
% \begin{macrocode}
\swapdef{\epsilon}{\varepsilon}
% \swapdef{\theta}{\vartheta}
\swapdef{\rho}{\varrho}
% \end{macrocode}
% I also like the empty set symbol from AMS, to which I also assign a
% German alias.
% \begin{macrocode}
\swapdef{\nothing}{\varnothing}
\alias\leer\nothing
% \end{macrocode}
% The standard symbols `$\exists$' and `$\forall$' do not have
% satisfactory spacing, in my opinion, so I redefine them as
% relations. Notice the aliasing so that the symbols' redefinition
% can be carried out regardless of current math fonts.
% \begin{macrocode}
\alias\@@exists\exists
\renewcommand{\exists}{\mathrel{\@@exists}}
\alias\@@forall\forall
\renewcommand{\forall}{\mathrel{\@@forall}}
% \end{macrocode}
% What \LaTeX{} cleverly calls \cseq{ni} (a backwards `$\in$') really
% ought to mean `such that,' hence I rename it:
% \begin{macrocode}
\newcommand{\st}{\mathrel{\ni}}
% \end{macrocode}
% Being essentially lazy, I also prefer to make a nice control
% sequence for some standard abbreviations. One happens to be
% German (since in German it is more acceptable to use abbreviations
% of long phrases even in a more formal setting).
% \begin{macrocode}
\newcommand{\WLOG}{Without loss of generality\xspace}
\newcommand{\Wlog}{without loss of generality\xspace}
\newcommand{\obda}{o.B.d.A.\xspace}
\newcommand{\fp}{floating-point\xspace}
% \end{macrocode}
% The following two commands are simply for phantoms I often find
% myself using, for example to make alignments in arrays and matrices
% come out right. The mnemonic is `phantom negative' or `phantom equals'.
% \begin{macrocode}
\newcommand{\pneg}{\phantom{-}}
\newcommand{\peq}{\phantom{=}}
% \end{macrocode}
% Going probably too far into the realm of generalization, here are
% some macros to set their arguments inside matching scaled delimiters
% of various sorts.
% \begin{macrocode}
\newcommand{\anglebrackets}[1]{%
\left\langle #1 \right\rangle}
\newcommand{\curlybrackets}[1]{%
\left\{ #1 \right\}}
\newcommand{\squarebrackets}[1]{%
\left[ #1 \right]}
\newcommand{\vertbrackets}[1]{%
\left| #1 \right|}
\newcommand{\Vertbrackets}[1]{%
\left\| #1 \right\|}
% \end{macrocode}
% And now for something completely different---sometimes an operand
% should be left generic, but not in terms of a variable. The usual
% way of accomplishing this is to place a small dot where the argument
% would otherwise go. As I consider this to imply `no argument', the
% command is |\noarg|.
% \begin{macrocode}
\newcommand{\noarg}{\,\cdot\,}
% \end{macrocode}
% We end with a few things that should be fairly obvious.
% \begin{macrocode}
\newcommand{\ee}[1]{\times10^{#1}}
\newcommand{\half}{\sfrac12}
\newcommand{\ninfty}{-\infty}
% \end{macrocode}
% This is shorthand for function definitions, including an extra
% control sequence for some backwards compatibility and an alias to
% German.
% \begin{macrocode}
\newcommand{\fcn}[2]{\colon{#1}\rightarrow{#2}}
\newcommand{\mapping}[3]{{#1}\fkt{#2}{#3}}
\alias\fkt\fcn
% \end{macrocode}
% Restrictions of functions:
% \begin{macrocode}
\newcommand{\restr}[2][\big]{\kern -.1em #1|_{#2}}
% \end{macrocode}
%
%
% \subsection{Combinatorics}
%
% The binomial coefficient $\choose{n}{k}$ is defined, depending on
% whether or not AMS-\LaTeX{} is being used.
% \begin{macrocode}
\if@amsmath
\realias\choose\binom
\else
\renewcommand{\choose}[2]{{{#1}\atopwithdelims(){#2}}}
\fi
% \end{macrocode}
% And lastly, we have the combinatorial doohickie which is read as
% `$n$ multichoose $k$', using doubled parentheses as delimiters. I
% think this comes out looking right.
% \begin{macrocode}
\newcommand{\mchoose}[2]{%
\mathchoice%
{\left(\kern-0.48em\choose{#1}{#2}\kern-0.48em\right)}
{\left(\kern-0.30em
\choose{\smash{#1}}{\smash{#2}}\kern-0.30em\right)}
{\left(\kern-0.30em
\choose{\smash{#1}}{\smash{#2}}\kern-0.30em\right)}
{\left(\kern-0.30em
\choose{\smash{#1}}{\smash{#2}}\kern-0.30em\right)}
}
% \end{macrocode}
% There is also the old-fashioned $\Comb{n}{k}$-type notation, as used
% both in English and in German.
% \begin{macrocode}
\newcommand{\Comb}[2]{% % C
{}_{#1}{\operator@font C}_{#2}} % #1 #2
\newcommand{\Komb}[2]{% % #2
{\operator@font Ko}_{#1}^{#2}} % Ko
\newcommand{\Kombun}[2]{\Komb{#1,\neq}{#2}} % #1
\newcommand{\Perm}[2]{% % #2
{\operator@font Pe}_{#1}^{#2}} % Pe
\newcommand{\Permun}[2]{\Perm{#1,\neq}{#2}} % #1
% \end{macrocode}
%
% \subsection{Sets}
%
% The most important macro in this section is named, of course,
% |\set|. The idea is to make sets which look like
% \begin{displaymath}
% \set{x \in \R^2}{\norm{x}_p = 1 \forall p = 1,2,3,\ldots}.
% \end{displaymath}
% That is, there should be scaled braces around two halves separated
% by a scaled logical delimiter, the vertical bar. The problem with
% this is getting everything the same height, since the $\mid$
% specifier does not scale and there is no middle-counterpart to
% |\left|\dots|\right|.
%
% So, the command has the form:
% \begin{display}{l}
% |\set[|\meta{mid}|]{|\meta{left}|}{|\meta{right}|}|
% \end{display}
% The optional \meta{mid} specifies an alternate delimiter to use
% between the two definition halves of the set. If it is left
% \emph{empty}, the null delimiter `.' will be assumed. If anything
% at all appears in the optional argument, though, the first token
% \emph{must} be a delimiter, as it will immediately be preceded by a
% sizing macro. For example, if you wish to use a colon to separate
% the definitions, use `|[.:]|' as the optional argument. The
% mandatory \meta{left} and \meta{right} are simply the halves of the
% set definition.
% \begin{macrocode}
\newcommand{\set}[3][|]{{%
\newdimen\@tempdimd%
% \end{macrocode}
% Each half is set in its own box, then the larger of the respective
% heights and depths are determined.
% \begin{macrocode}
\setbox0=\mathbox{#2}\@tempdima=\ht0 \@tempdimb=\dp0%
\setbox0=\mathbox{#3}\@tempdimc=\ht0 \@tempdimd=\dp0%
\ifdim\@tempdimc > \@tempdima
\@tempdima=\@tempdimc
\fi
\ifdim\@tempdimd > \@tempdimb
\@tempdimb=\@tempdimb
\fi
% \end{macrocode}
% We create an invisible rule with that height and depth, and make
% sure we have a valid delimiter if the optional argument is empty.
% \begin{macrocode}
\def\@tempa{\vrule width0pt height\@tempdima depth\@tempdimb}
\def\@tempb{#1}
\ifx\@empty\@tempb
\def\@tempb{.}
\fi
% \end{macrocode}
% Finally, we use a null left delimiter to balance the middle
% delimiter, and then a left brace to balance the right brace. The
% rule is set inside both pairs so that they scale identically. Note
% the use of |\expandafter| so that when the first |\right| is
% expanded, it can grab the delimiter in |\@tempb|.
% \begin{macrocode}
\left.\left\{ \@tempa{#2} \,\expandafter\right\@tempb\,{#3} \right\} }}
% \end{macrocode}
% For backwards compatibility, I make two aliases for |\set|; the old
% commands required the user to specify the larger side of the set
% definition in order to get sizing correct.
% \begin{macrocode}
\alias\setl\set
\alias\setr\set
% \end{macrocode}
%
% Here are some macros for typesetting sets symbolically. First off,
% we might want to know how to typeset a level set.
% \begin{macrocode}
\newcommand{\lvl}[2][\alpha]{\Gamma\ssb{#2}\ssp{(#1)}}
% \end{macrocode}
% There are also fuzzy sets, and their corresponding level sets.
% \begin{macrocode}
\if@amsmath
\newcommand{\fset}[1]{\Tilde{#1}}
\else
\newcommand{\fset}[1]{\tilde{#1}}
\fi
\newcommand{\flvl}[2][\alpha]{\lvl[#1]{\fset{#2}}}
% \end{macrocode}
% For want of a better font, I will typeset set collections
% in |\mathcal|.
% \begin{macrocode}
\alias\coll\mathcal
% \end{macrocode}
%
% Finally, we deal with some set operators.
% \emph{The \TeX{}book} points out the difference between |\setminus|
% and |\backslash|. I prefer to think of them as `set
% complementation' and `coset', respectively.
% \begin{macrocode}
\alias\scomp\setminus
\alias\coset\backslash
% \end{macrocode}
% The next macro attempts to create a symmetric difference operator.
% I don't like it, but I probably won't do better until I learn to
% make my own \textsf{M{\small ETAFONT}} characters\ldots
% \begin{macrocode}
\newcommand{\symmdiff}{%
\mathbin{\text{\footnotesize$\bigtriangleup$}}}
% \end{macrocode}
%
%
% \subsection{Sequences and series}
%
% Just a few macros are required for various sequences and series,
% mostly for indexing. The best explanation is simply an example.
% The code
% \begin{display}{l}
% |$y \in \seq{x_{ij}}$, where $i\inset{n}$, $j\inrange[0]{m}$|
% \end{display}
% produces
% \begin{display}{l}
% $y \in \seq{x_{ij}}$, where $i\inset{n}$, $j\inrange[0]{m}$.
% \end{display}
%
% \begin{macrocode}
\newcommand{\seq} [1] {\curlybrackets{#1}}
\newcommand{\inset} [2][1]{\in\{ #1,\ldots,#2 \}}
\newcommand{\inrange}[2][1]{ = #1,\ldots,#2}
% \end{macrocode}
%
%
% \subsection{Calculus}
%
% The calculus macros are relegated to auxiliary files, as I rarely
% need them.
%
% \subsubsection{Derivatives}
%
% We load the derivatives in if they are requested.
% \begin{macrocode}
\if@derivatives
\InputIfFileExists{cjwderiv.tex}{}{%
\PackageWarning{cjwmath}{Option `cjwderiv.tex' not found.}
\@@derivativesfalse}
\fi
% \end{macrocode}
% This loads both simple and partial derivative macros.
%\iffalse
%</math>
%<*deriv>
%\fi
%
% The derivatives are all variations on the basic |\dd| macro, which
% should be fairly self explanatory.
% \begin{macrocode}
\newcommand{\dd} [2]{\frac{d#1}{d#2}}
\newcommand{\ddt}[1]{\dd{#1}{t}}
\newcommand{\ddu}[1]{\dd{#1}{u}}
\newcommand{\ddv}[1]{\dd{#1}{v}}
\newcommand{\ddx}[1]{\dd{#1}{x}}
\newcommand{\ddy}[1]{\dd{#1}{y}}
\newcommand{\sdd} [2]{\frac{d^2#1}{d#2^2}}
\newcommand{\sddx}[1]{\sdd{#1}{x}}
\newcommand{\sddy}[1]{\sdd{#1}{y}}
\newcommand{\sddt}[1]{\sdd{#1}{t}}
\newcommand{\sddu}[1]{\sdd{#1}{u}}
\newcommand{\sddv}[1]{\sdd{#1}{v}}
% \end{macrocode}
%
% \subsubsection{Partial derivatives}
%
% The partial derivatives are all variations on the theme of |\pard|,
% which is as |\dd|, replacing the $d$ with $\partial$.
% \begin{macrocode}
\newcommand{\pard} [2]{\frac{\partial#1}{\partial#2}}
\newcommand{\pardx}[1]{\pard{#1}{x}}
\newcommand{\pardy}[1]{\pard{#1}{y}}
\newcommand{\pardz}[1]{\pard{#1}{z}}
\newcommand{\pardu}[1]{\pard{#1}{u}}
\newcommand{\pardv}[1]{\pard{#1}{v}}
\newcommand{\pardt}[1]{\pard{#1}{t}}
\newcommand{\spard} [2]{\frac{\partial^2#1}{\partial#2^2}}
\newcommand{\spardx}[1]{\spard{#1}{x}}
\newcommand{\spardy}[1]{\spard{#1}{y}}
\newcommand{\spardz}[1]{\spard{#1}{z}}
\newcommand{\spardu}[1]{\spard{#1}{u}}
\newcommand{\spardv}[1]{\spard{#1}{v}}
\newcommand{\spardt}[1]{\spard{#1}{t}}
\newcommand{\spardxy}[1]{\frac{\partial^2#1}{\partial x\partial y}}
\newcommand{\spardyx}[1]{\frac{\partial^2#1}{\partial y\partial x}}
\newcommand{\spardxz}[1]{\frac{\partial^2#1}{\partial x\partial z}}
\newcommand{\spardzx}[1]{\frac{\partial^2#1}{\partial z\partial x}}
\newcommand{\spardyz}[1]{\frac{\partial^2#1}{\partial y\partial z}}
\newcommand{\spardzy}[1]{\frac{\partial^2#1}{\partial z\partial y}}
% \end{macrocode}
%\iffalse
%</deriv>
%<*math>
%\fi
%
% \subsubsection{Integrals}
%
% We load the integrals in if they are requested.
% \begin{macrocode}
\if@integrals
\InputIfFileExists{cjwinteg.tex}{}{%
\PackageWarning{cjwmath}{Option `cjwinteg.tex' not found.}
\@@integralsfalse}
\fi
% \end{macrocode}
%\iffalse
%</math>
%<*integ>
%\fi
%
% The first macro is simply a variation of |\int| using the |\limits|
% macro.
% \begin{macrocode}
\def\integ{\mathop{\int}\limits}
% \end{macrocode}
% Next we have a small shortcut for the differential at the end of an
% integral. We work around \LaTeX's font encoding macro.
% \begin{macrocode}
\alias\latex@d\d
\renewcommand{\d}{\,d}
% \end{macrocode}
% We have macros for double and triple integrals, with and without
% |\limits|.
% \begin{macrocode}
\newcommand{\dint}{\int\!\!\!\int}
\newcommand{\dinteg}{\mathop{\int\!\!\!\int}\limits}
\newcommand{\tint}{\int\!\!\!\int\!\!\!\int}
\newcommand{\tinteg}{\mathop{\int\!\!\!\int\!\!\!\int}\limits}
% \end{macrocode}
% To be honest, I have no idea why I wrote this one. It is probably
% buried in a homework file of mine somewhere, but I'll be a fiddler
% crab if I can remember where\dots
% \begin{macrocode}
\newcommand{\flushintlim}[1]{{\phantom{#1} #1}}
% \end{macrocode}
%\iffalse
%</integ>
%<*math>
%\fi
%
% \subsection{Algebra}
%
% We define how to typeset an algebra.
% \begin{macrocode}
\alias\alg\mathbbm
% \end{macrocode}
%
% \subsubsection{Fields}
%
% A field will also be done in blackboard bold.
% \begin{macrocode}
\alias\field\mathbbm
% \end{macrocode}
% The following fields are defined.
% \begin{macrocode}
\newcommand{\C}{\field{C}} % Complex
\newcommand{\E}{\field{E}} % Euclidean (also Evens)
% \end{macrocode}
% Note that $\H$ is a \LaTeX{} accent, so we save it away before
% redefining it as a field.
% \begin{macrocode}
\alias\latex@H\H % Quaternions
\renewcommand{\H}{\field{H}} % (Hamiltonian field)
\newcommand{\N}{\field{N}} % Natural numbers
\newcommand{\Q}{\field{Q}} % Rationals
\newcommand{\R}{\field{R}} % Reals
% \newcommand{\Rn}[1][n]{\R^{#1}}
\newcommand{\Z}{\field{Z}} % Integers
\newcommand{\pr}{\field{P}} % Primes
% \end{macrocode}
%
% \subsubsection{Groups}
%
% Remember |\NewMathOp|? One use for it is in defining mathematical
% groups. Here are a bunch.
% \begin{macrocode}
% Groups are typeset as operators.
\NewMathOp {\Aut}{Aut} % Automorphisms
\NewMathOp {\End}{End} % Endomorphisms
\NewMathOp {\GL}{GL} % General Linear
\NewMathOp {\Inn}{Inn} % Inner products
\NewMathOp {\Pin}{Pin} % Pin
\NewMathOp {\SL}{SL} % Special Linear
\NewMathOp {\SO}{SO} % Special Orthogonal
\NewMathOp {\SU}{SU} % Special Unitary
\NewMathOp[\mathfrak]{\Sn}{S} % Symmetric
\NewMathOp {\Spin}{Spin} % Spin
\NewMathOp {\Sp}{Sp} % Symplectic
\NewMathOp {\Unit}{U\kern 0pt}% Unitary
\NewMathOp {\Orth}{O\kern 0pt}% Orthogonal
\NewMathOp[\mathfrak]{\slin}{sl} % Tangent group to SL
\NewMathOp[\mathfrak]{\so}{o\kern 0pt} % skew orthogonal
\NewMathOp[\mathfrak]{\sp}{sp} % skew symplectic
\NewMathOp[\mathfrak]{\su}{u\kern 0pt} % skew hermitian
% \end{macrocode}
%
% \subsubsection{Linear algebra}
%
% If matrices are to be typeset specially, we will use the |\mathcal| font.
% \begin{macrocode}
\alias\mtx\mathcal
% \end{macrocode}
% I have often seen the letter $\Theta$ used for the matrix of zeros.
% I like it that way.
% \begin{macrocode}
\newcommand{\nullmtx}{\mtx\Theta}
% \end{macrocode}
% Taken from Horn and Johnson, a matrix norm can be represented with a
% triple-bar delimiter.
% \begin{macrocode}
\newcommand{\mnorm}[1]{%
\left\vert\kern-0.9pt\left\vert\kern-0.9pt\left\vert #1
\right\vert\kern-0.9pt\right\vert\kern-0.9pt\right\vert}
% \end{macrocode}
% We define the Lie product of two matrices.
% \begin{macrocode}
\newcommand{\lie}[1]{\squarebrackets{#1}}
% \end{macrocode}
% There is an for the trace (Spur, auf Deutsch) of a matrix\dots
% \begin{macrocode}
\NewMathOp{\Spur}{Spur}
\NewMathOp{\Tr}{Tr}
% \end{macrocode}
% \dots as well as for diagonal matrices.
% \begin{macrocode}
\NewMathOp{\Diag}{Diag}
% \end{macrocode}
%
% This is a shortcut for putting delimiters around matrices. With
% AMS-\LaTeX, we use an environment, taking as its two mandatory
% arguments the left and right delimiters, respectively.
% \begin{macrocode}
\if@amsmath
\newenvironment{arbmatrix}[2]%
{\def\@tempa{#2}\left#1 \matrix}{\endmatrix \right\@tempa}
% \end{macrocode}
% Without AMS, we use a command as does standard \LaTeX, and define
% some basic types.
% \begin{macrocode}
\else
\newcommand{\arbmatrix}[3]{\left#1 \matrix{#2} \right#3}
\providecommand{\bmatrix}[1]{\arbmatrix[{#1}]}
\providecommand{\vmatrix}[1]{\arbmatrix|{#1}|}
\fi
% \end{macrocode}
%
% The next bit of code is used to enter sparse matrices which are
% often represented in the literature with an oversized zero marking
% the region of zeros. This takes more than a bit of trickery in
% \LaTeX. The oversized digit will be put in a box, which in most
% cases needs horizontal and/or vertical adjustment from the position
% where it is placed in the matrix by default. The default vertical
% offset will be called |\numoffset|, and is set by default to the
% height of a |\Bigmathstrut|.
% \begin{macrocode}
\newlength{\numoffset}
{\setbox0=\hbox{$\Bigmathstrut$}
\@tempdima=0.8\ht0\relax
\global\numoffset\@tempdima}
% \end{macrocode}
% Occasionally, one might wish to use something other than a zero as
% the oversized digit. We define a generic |\Number| macro to be
% used. The usage is
% \begin{display}{l}
% |\Number|\oarg{raise}\marg{num}
% \end{display}
% where \meta{raise} is the amount by which the number is raised and
% \meta{num} is the number to be used.
% \begin{macrocode}
\newcommand{\Number}[2][-\numoffset]{%
\@tempdima=#1\relax
\smash{\hbox{\raise\@tempdima\@bignumber{#2}}}}
% \end{macrocode}
% The macros |\@bignumber| is called to do the dirty work of
% typesetting the number.
% \begin{macrocode}
\newcommand{\@bignumber}[1]{\hbox{\LARGE$#1$}}
% \end{macrocode}
% Now, the horizontal adjustment mentioned earlier usually refers to
% the need to have the large digit straddle two columns in a matrix.
% This is easily accomplished with |\multicolumn|. Here things start
% to get ugly, though; |\multicolumn| must be the first thing after
% the |&| in the array. But the reasonable way to include an optional
% argument to be passed through to |\Number| is to use the
% |\newcommand| feature, which ends up putting junk in the way---this
% is exactly the same problem which arose in writing |\mathbox|
% earlier. Therefore, there are currently two separate commands, one
% which takes the optional argument, and one which doesn't. I would
% really like to remedy this if I ever figure out how.
% \begin{macrocode}
\def\bignumber #1{\multicolumn{2}{c}{\Number{#1}}}
\def\Bignumber[#1]#2{\multicolumn{2}{c}{\Number[#1]{#2}}}
% \end{macrocode}
% Here are some specific cases for using zero, as is most commonly the
% case.
% \begin{macrocode}
\newcommand{\Zero}[1][-\numoffset]{\Number[#1]{0}}
\def\bigzero {\bignumber{0}}
\def\Bigzero[#1]{\Bignumber[#1]{0}}
% \end{macrocode}
%
% From this we wish to construct various types of matrices. Each
% variation will have two versions, depending on whether or not
% AMS-\LaTeX{} has been invoked. Each version, though, has an
% optional argument which is what will be passed through as
% \meta{raise} to |\Bigzero|. The names of each matrix are an attempt
% to indicate the layout. For example, the command |\iidiagi| takes
% three mandatory arguments which will be the diagonal entries, the
% first two in the upper left, and the third in the lower right with
% |\ddots| separating them. Likewise, we have |\idiagii| and
% |\idiagi|.
% \begin{macrocode}
\if@amsmath
\newcommand{\iidiagi}[4][-\numoffset]{% % 2 0
\begin{bmatrix} % 3
#2 & & \Bigzero[#1] \\ % .
& #3 & & \\ % .
\Bigzero[#1] & \ddots & \\ % 0 4
& & & #4
\end{bmatrix}}
\newcommand{\idiagii}[4][-\numoffset]{% % 2 0
\begin{bmatrix} % .
#2 & & \Bigzero[#1] \\ % .
& \ddots & & \\ % 3
\Bigzero[#1] & #3 & \\ % 0 4
& & & #4
\end{bmatrix}}
\newcommand{\idiagi}[3][-1.2pt]{% % 2 0
\begin{bmatrix} % .
#2 & \Bigzero[#1] \\ % .
& \ddots & \\ % .
\Bigzero[#1] & #3 % 0 3
\end{bmatrix}}
\else
\newcommand{\iidiagi}[4][-\numoffset]{% % 2 0
\matrix{% % 3
#2 & & \Bigzero[#1] \\ % .
& #3 & & \\ % .
\Bigzero[#1] & \ddots & \\ % 0 4
& & & #4}}
\newcommand{\idiagii}[4][-\numoffset]{%
\pmatrix{% % 2 0
#2 & & \Bigzero[#1] \\ % .
& \ddots & & \\ % .
\Bigzero[#1] & #3 & \\ % 3
& & & #4}} % 0 4
%
\newcommand{\idiagi}[3][-1.2pt]{% % 2 0
\pmatrix{% % .
#2 & \Bigzero[#1] \\ % .
& \ddots & \\ % .
\Bigzero[#1] & #3}} % 0 3
\fi
% \end{macrocode}
%
% We now wish to typeset the transpose of a matrix. The most general
% form is
% \begin{display}{l}
% |\@trans|\oarg{pre}\marg{post}
% \end{display}
% which expands to `|^{|\meta{pre}|t|\meta{post}|}|'. Next is
% |\trans| which takes a single optional argument for \meta{post} (no
% \meta{pre}).
% \begin{macrocode}
\newcommand{\@trans}[2][]{^{#1\text{\normalfont\textsf{t}}#2}}
\newcommand{\trans} [1][]{\@trans[]{#1}}
% \end{macrocode}
% Why? I don't know---I needed |\trinv|, below, and decided to
% generalize.
% \begin{macrocode}
\newcommand{\trinv} {\@trans[-]{}}
% \end{macrocode}
% For backwards compatibility, I have |\ct|\marg{mtx} to represent
% matrix \meta{mtx} as conjugated and transposed.
% \begin{macrocode}
\newcommand{\ct}[1]{\conj{#1}\trans}
% \end{macrocode}
%
% The next topic is vectors. I prefer |\vec| to be logical markup as
% opposed to a specific accent. Thus, I create an alias |\sarvec|
% (short arrow vector) for the original |\vec|, and another alias
% |\arvec| for a long arrow, which is just |\overrightarrow|.
% \begin{macrocode}
\alias\sarvec\vec
\alias\arvec \overrightarrow
% \end{macrocode}
% The actual typesetting I prefer for vectors (when I use anything at
% all) is boldface. This requires the |\Mathbox| command defined
% earlier so that the argument can be set in a bold math version.
% \begin{macrocode}
\renewcommand{\vec}[1]{\Mathbox{\boldmath}{#1}}
% \end{macrocode}
% To typeset vectors in long form simply uses the |\matrix|
% command---but this depends, again, on whether AMS-\LaTeX{} is being
% used. In either case, a single argument---the contents of the
% vector---is required. Simply delimit with |\\| for column vectors
% and |&| for rows.
% \begin{macrocode}
\if@amsmath
\newcommand{\bvec}[1]{%
\begin{bmatrix}#1\end{bmatrix}}
\newcommand{\pvec}[1]{%
\begin{pmatrix}#1\end{pmatrix}}
% \end{macrocode}
% There are also two aliases for row vectors for backwards
% compatibility.
% \begin{macrocode}
\alias\brvec\bvec
\alias\prvec\pvec
\else
\newcommand{\bvec}[1]{\bmatrix{#1}}
\newcommand{\pvec}[1]{\pmatrix{#1}}
% \newcommand{\bvec}[2][r]{%
% \left[ \begin{array}{#1}#2\end{array} \right]}
% \newcommand{\pvec}[2][r]{%
% \left( \begin{array}{#1}#2\end{array} \right)}
\fi
% \end{macrocode}
% The null vector, like the null matrix, is given with $\theta$.
% \begin{macrocode}
\newcommand{\nullvec}{\vec{0}}
% \end{macrocode}
% Once we have vectors, we need dot products. The simple version just
% puts its argument inside angled brackets.
% \begin{macrocode}
\newcommand{\dotp}[1]{\anglebrackets{#1}}
% \end{macrocode}
% If special vector notation is required, the two arguments should be
% separated by a comma (which should be the case anyway), and then
% each half is passed to |\vec|.
% \begin{macrocode}
\newcommand{\vdotp}[1]{\@vdotp#1@@@}
\def\@vdotp #1,#2@@@{\dotp{\vec #1,\vec #2}}
% \end{macrocode}
%
% We define some other vector operators to go with the dot product.
% These are the curl, the divergence, and the Laplacian. These are
% usually read as `del dot', `del cross', and `del squared', so the
% first thing to do is rename the |\nabla|(?).
% \begin{macrocode}
\newcommand{\del} {\vec\nabla}
% \end{macrocode}
% \LaTeX{} defines |\div|, so we rename that and renew the command.
% \begin{macrocode}
\alias\@@div\div
\renewcommand{\div}{\del\dot}
% \end{macrocode}
% Finally, we have the other two.
% \begin{macrocode}
\newcommand{\curl} {\del\cross}
\newcommand{\lapl} {\del^2}
% \end{macrocode}
%
% In German texts, the linear hull is usually represented as a list of
% vectors in square brackets.
% \begin{macrocode}
\alias\huelle\squarebrackets
% \end{macrocode}
%
% \subsection{Operators}
%
% This section is simply a gathering point for all sorts of
% mathematical operators---not in the |\NewMathOp| sense, like various
% groups defined above, but in the sense of mathematical doohickies
% which take one or two operands and give you something new.
%
% \subsubsection{Binary operators}
%
% What we have first is a whole bunch of names for the large, `x'-like
% times symbol. In the case of specifying dimension (as in, a 4-by-3
% matrix), we declare it a |\mathord| so as not to invoke binary
% spacing. Then |\mal| is simply German for `times', and |\cross| is
% the vector space (or group) product using the same symbol.
% \begin{macrocode}
\newcommand{\by}{\mathord{\times}}
\alias\mal \times
\alias\cross \times
% \end{macrocode}
% To indicate isomorphism, I have most often used an equals sign with
% a tilde above it.
% \begin{macrocode}
\alias\iso \simeq
% \end{macrocode}
% This next one stretches the usefulness of aliasing by defining an
% operator for normal subgroups.
% \begin{macrocode}
\alias\nsubgrp \trianglelefteq
% \end{macrocode}
% Next we specify a congruence symbol.
% \begin{macrocode}
\realias\cong \equiv
% \end{macrocode}
% In graph theory, we want a symbol for adjacency of nodes.
% \begin{macrocode}
\alias\adj\leftrightarrow
% \end{macrocode}
% We unconditionally define |\Box| to be a square operator symbol.
% \begin{macrocode}
\providecommand{\Box}{}
\renewcommand{\Box}{\mathbin{\square}}
% \end{macrocode}
% We give a number theoretic division relation, in English and
% German.
% \begin{macrocode}
\newcommand{\teilt}{\mathbin{|}}
\alias\divides\teilt
% \end{macrocode}
% Once upon a time I wanted a `big dot' operator.
% \begin{macrocode}
% \newcommand{\bdot}{\mathop{\lower0.33ex\hbox{\LARGE$\cdot$}}}
% \end{macrocode}
% We can use \LaTeX's built-in |\stackrel| to create a definition
% relation.
% \begin{macrocode}
\newcommand{\defeq}{\stackrel{\text{def}}{=}}
% \end{macrocode}
% The symbol I first saw used to indicate disjoint union was a union
% `cup' with a bar through the middle. Using a naming convention
% similar to AMS-\LaTeX's |\Uplus| we get text and display versions.
% \begin{macrocode}
\newcommand{\uminus}{%
\,\,{\mathbin{\cup\kern-.6em{\raise.05em%
\hbox{-\negthinspace-\kern-.25em-}}}}\,\,}
\newcommand{\Uminus}{%
\mathop{\bigcup\kern-0.9em{\raise.05em%
\hbox{-\negthinspace-\kern-.25em-}}}}
% \end{macrocode}
% We define some handy names for various arrows.
% \begin{macrocode}
\providecommand{\implies}{\;\Longrightarrow\;}
\alias\then\implies
\if@amsmath
\newcommand{\when}{\DOTSB \;\Longleftarrow \;}
\else
\newcommand{\when}{\;\Longleftarrow \;}
\fi
% \end{macrocode}
% The following can be used when tracing a series of implications
% through a multiline equation environment, for example.
% \begin{macrocode}
\newcommand{\limplies}{\llap{$\implies$}\quad}
% \end{macrocode}
% Based on \emph{The \TeX{}book}, I have written a `skewed' fraction,
% which uses a diagonal separator.
% \begin{macrocode}
\newcommand{\sfrac}[2]{%
\hbox{\kern 0.1em%
\raise 0.5ex\hbox {\scriptsize$#1$}%
\kern -0.1em $/$%
\kern -0.15em%
\lower 0.25ex\hbox {\scriptsize$#2$}}%
\kern 0.2em}
% \end{macrocode}
% If we are not using AMS-\LaTeX, the following well not yet be
% defined.
% \begin{macrocode}
\providecommand{\tfrac}{\sfrac}
\providecommand{\dfrac}[2]{{{#1}\over{#2}}}
% \end{macrocode}
%
%
% \subsubsection{Unary operators}
%
% I most often use the longer versions of various math accents, so I
% redefine them by default to be long. The short ones are saved in a
% macro with identical name save for a prepended `s' (as we have
% already seen for |\arvec| and |\sarvec|). The simple ones are bars,
% tildes, and hats.
% \begin{macrocode}
\alias\sbar\bar
\renewcommand{\bar}[1]{\overline{#1}}
\alias\stilde\tilde
\alias\retilde\widetilde
\alias\shat\hat
\realias\hat\widehat
% \end{macrocode}
% We need something better than the default real- and imaginary-part
% macros.
% \begin{macrocode}
\renewcommand{\Im}{%
\mathop{\mathfrak{Im}}}
\renewcommand{\Re}{%
\mathop{\mathfrak{Re}}}
% \end{macrocode}
% Complex conjugation is usually denoted by a bar.
% \begin{macrocode}
\alias\conj \bar
% \end{macrocode}
% Inversion of various types is used often enough to warrant a control
% sequence.
% \begin{macrocode}
\newcommand{\inv}{^{-1}}
% \end{macrocode}
% To denote power sets, I have used to different alternatives. The
% default is the standard |\wp| symbol---I don't know what it is
% supposed to be used for, but it can be modified for the task. On
% the other hand, if we have a real math script font (as one might
% have if using my \pkg{callig} style\dots) we will certainly use
% that.
% \begin{macrocode}
\@ifundefined{mathscript}
{\newcommand{\Pow}{\raise 0.4ex\Mathbox{\Large}{\wp}}}
{\NewMathOp[\mathscript]{\Pow}{P}}
% \end{macrocode}
% And what macro would be complete without a German alias? (Auf
% Deutsch, die Potenzmenge.)
% \begin{macrocode}
\alias\Pot\Pow
% \end{macrocode}
% We can leave the letter `\/I\/' to computer scientists who don't
% know how to write an indicator function. For our purposes, we want
% the neat-o-keen blackboard bold font.
% \begin{macrocode}
\newcommand{\1}{\mathbbm{1}}
% \end{macrocode}
%
% Next we have some trigonometric shortcuts.
% \begin{macrocode}
\alias\acos\arccos
\alias\asin\arcsin
\alias\atan\arctan
% \end{macrocode}
% Using our generic bracketing macros from earlier, we have absolute
% value, cardinality (order of a set), cyclic generators, and norms.
% \begin{macrocode}
\alias\abs \vertbrackets
\alias\ord \abs
\alias\cyc \anglebrackets
\alias\norm\Vertbrackets
% \end{macrocode}
%
% Multiple sums are recurrent enough (no pun intended \smiley) to get
% macros. We have double sums, triple sums, and $n$-fold sums.
% \begin{macrocode}
\newcommand{\dsum}{\mathop{\sum\sum}\limits}
\newcommand{\tsum}{\mathop{\sum\sum\sum}\limits}
\newcommand{\nsum}{\mathop{\sum\sum\cdots\sum}\limits}
% \end{macrocode}
%
% The next two macros indicate monotone limits, respectively ascending
% (mnemonic `limit up') and descending (you guessed it---`limit
% down').
% \begin{macrocode}
\NewMathOp*{\ulim}{lim\raise0.4ex\mathbox{\mathord{\smash{\uparrow}}}}
\NewMathOp*{\dlim}{lim\raise0.4ex\mathbox{\mathord{\smash{\downarrow}}}}
% \end{macrocode}
%
%
% Finally we have the miscellany, where we can really go to town with
% |\NewMathOp|! These should be pretty clear, unless you don't do
% math in German, in which case some will be pretty odd.
% \begin{macrocode}
\NewMathOp*{\argmax}{arg\,max} % arg min
\NewMathOp*{\argmin}{arg\,min} % arg min
\NewMathOp {\Aff} {Aff} % Affine hull
\NewMathOp {\Bild} {Bild} % Bild
\NewMathOp {\Cone} {Cone} % Cone
\NewMathOp {\Conv} {Conv} % Convex hull
\NewMathOp {\Core} {Core} % Fuzzy set core
\NewMathOp {\diam} {diam} % diameter
\NewMathOp {\dom} {dom} % Domain
\NewMathOp {\Epi} {Epi} % Epigraph
\NewMathOp*{\esssup}{ess\,sup} % Essential supremum
\NewMathOp {\fl} {fl} % float-point
\NewMathOp {\ggT} {ggT} % ggT
\NewMathOp {\Grad} {Grad} % Grad
\NewMathOp {\Hypo} {Hypo} % Hypograph
\NewMathOp {\Int} {Int} % Interior
\NewMathOp {\Kern} {Kern} % Kernel
\NewMathOp {\kgV} {kgV} % kgV
\NewMathOp {\Lin} {Lin} % Linear hull
\NewMathOp {\lcm} {lcm} % LCM
\NewMathOp {\Ord} {Ord} % order
\NewMathOp {\proj} {proj} % Projection
\NewMathOp {\Rang} {Rang} % Rang
\NewMathOp {\range} {range} % Range
\NewMathOp {\Rank} {Rank} % Rank
\NewMathOp {\rot} {rot} % Rotation
\NewMathOp {\Span} {Span} % Span
\NewMathOp {\val} {val} % value
% \end{macrocode}
%
%
% \subsection{Physics}
%
% Now, since physics is a subset of mathematics, physics macros are
% invoked from within the math macro file.
% \begin{macrocode}
\if@physics
\InputIfFileExists{cjwphys.tex}{}{%
\PackageWarning{cjwmath}{Option `cjwphys.tex' not found.}
\@@physicsfalse}
\fi
% \end{macrocode}
%\iffalse
%</math>
%<*phys>
%\fi
%
% The only thing really specific to physics that I ever used---meaning
% not applicable in any more general mathematical setting---was the
% bra/ket notation. Here we have bras (br\ae?), kets, and brakets,
% the latter of which bear uncoincidental resemblance to the |\set|
% macro.
% \begin{macrocode}
\newcommand{\bra}[1]{\left\langle #1 \right|\,}
\newcommand{\ket}[1]{\,\left| #1 \right\rangle}
\newcommand{\braket}[2]{%
\newdimen\@tempdimd%
\setbox0=\mathbox{#1}\@tempdima=\ht0 \@tempdimb=\dp0%
\setbox0=\mathbox{#2}\@tempdimc=\ht0 \@tempdimd=\dp0%
\ifdim\@tempdimc > \@tempdima
\@tempdima=\@tempdimc
\fi
\ifdim\@tempdimd > \@tempdimb
\@tempdimb=\@tempdimb
\fi
\def\@tempa{\vrule width0pt height\@tempdima depth\@tempdimb}
\left.\left\langle \@tempa{#1} \,\right|\,{#2} \right\rangle }
% \end{macrocode}
%\iffalse
%</phys>
%<*math>
%\fi
%
%
% \subsection{Probability}
%
% Here comes that |\NewMathOp| thingie again. First thing is to
% define some standard probabilistic operators, which really need to
% be typeset in an operator font in order not to look horrible.
% \begin{macrocode}
\NewMathOp{\Prob} {P} % Probability operator
\NewMathOp{\Corr} {Corr} % Correlation
\NewMathOp{\Cov} {Cov} % Covariance
\NewMathOp{\Expct}{E} % Expectation
\NewMathOp{\SD} {SD} % Standard Deviation.
\NewMathOp{\Var} {Var} % Variance
% \end{macrocode}
% Here is a macro to put inside of some of those operators where
% conditional events are being considered.
% \begin{macrocode}
\newcommand{\given}{\,|\,}
% \end{macrocode}
% Usually a single tilde, which as an operator bears the name of
% |\sim| in \LaTeX, indicates a distribution. Hence, we make an
% alias.
% \begin{macrocode}
\alias\distrib\sim
% \end{macrocode}
% And coming back to |\NewMathOp|, we define some standard
% distributions\dots
% \begin{macrocode}
\NewMathOp{\Bin} {Bin} % Binary dist.
\newcommand{\Nbin}{-\!\Bin} % Negative Binom.
\NewMathOp{\Exp} {Exp} % Exponential dist.
\NewMathOp{\Geom}{Geom} % Geometric dist.
\NewMathOp{\Norm}{Norm} % Normal dist.
\NewMathOp{\Poi} {Poi} % Poisson dist.
\NewMathOp{\Unif}{Unif} % Uniform dist.
% \end{macrocode}
% \dots and the normal density and distribution functions (which might
% also be represented as $\Phi$ and $\phi$).
% \begin{macrocode}
\NewMathOp[\mathfrak]{\Ndens}{N}
\NewMathOp[\mathfrak]{\Ndist}{n}
% \end{macrocode}
% The last thing to do is create some macros for probabilistic modes
% of convergence. We go, again, from the general to the specific.
% \begin{macrocode}
\NewMathOp*{\@mapsto}{\mapstochar\rightarrow}
\newcommand{\@probconv}[1]{\mathrel{\@mapsto\limits^{1}}}
\newcommand{\asconv}{\@probconv{a.s.}} % Almost sure conv.
\newcommand{\inprob}{\@probconv{P}} % Conv. in probability
\newcommand{\inlaw} {\@probconv{L}} % Conv. in law
\newcommand{\vague} {\@probconv{v}} % Vague conv.
% \end{macrocode}
%
% \iffalse
%
%</math>
%
% \fi
%
%
% \section{Units}
%
% \iffalse
%
%<*units>
%
% \fi
%
% The package \pkg{cjwunits} simply standardizes how to typeset units
% (or dimensions---things such as seconds, meters, and so forth).
% Most of the work is done by defining a pretty simple macro,
% |\unit|. The rest is just a collection of standard units which may
% be invoked (meaning ones I have used, and therefore stuck into the
% file).
%
% \subsection{Package initialization}
%
% The initialization does most everything. We first specify a font
% for the unit types.
% \begin{macrocode}
\newcommand{\unitfont}{\operator@font}
% \end{macrocode}
% Now the workhorse of the package is defined. It is pretty
% foolproof, in that it can be invoked in or out of math, may or may
% not be followed by explicit space, and the font as defined above is
% pretty customizable.
% \begin{macrocode}
\newcommand{\unit}[1]{\ensuremath{\,{\unitfont{#1}\kern\z@}}\xspace}
% \end{macrocode}
%
% Now come the examples.
%
% \subsection{Distance}
% \begin{macrocode}
\newcommand{\ang} {\unit{\AA}} % angstroms
\alias\Ao\ang
\newcommand{\cm} {\unit{cm}} % centimetres
\newcommand{\inch}{\unit{in}} % inches
\newcommand{\km} {\unit{km}} % kilometres
\newcommand{\mi} {\unit{mi}} % miles
\newcommand{\m} {\unit{m}} % metres
% \end{macrocode}
%
% \subsection{Electricity and magnetism}
%
% \begin{macrocode}
\newcommand{\Hz} {\unit{Hz}} % herz
\newcommand{\J} {\unit{J}} % joules
\newcommand{\V} {\unit{V}} % volts
\newcommand{\eV} {\unit{eV}} % electron volts
\newcommand{\erg} {\unit{erg}} % ergs
% \end{macrocode}
%
% \subsection{Mass}
%
% \begin{macrocode}
\newcommand{\amu} {\unit{amu}} % atomic mass units
\newcommand{\gram}{\unit{g}} % grams
\newcommand{\kg} {\unit{kg}} % kilograms
\newcommand{\Ton} {\unit{T}} % tons
\newcommand{\kT} {\unit{kT}} % kilotons
\newcommand{\MT} {\unit{MT}} % megatons
% \end{macrocode}
%
% \subsection{Thermodynamics}
%
% \begin{macrocode}
\newcommand{\kelv}{\unit{K}} % kelvins
% \end{macrocode}
%
% \subsection{Time}
%
% It seems that |\sec| already means secant, so we need a preservation
% and renewal here.
% \begin{macrocode}
\alias\secant\sec
\renewcommand{\sec} {\unit{s}} % seconds
% \end{macrocode}
%
% \subsection{Velocity}
%
% \begin{macrocode}
\newcommand{\cee} {\unit{c}} % speed o' light
% \end{macrocode}
%
% \iffalse
%
%</units>
%
% \fi