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+% $Id: qsymbols.tex,v 1.8 1996/12/05 04:27:20 krisrose Exp $
+%
+% `Quoted math symbol abbreviations' package for LaTeX2e.
+% Copyright © 1994  Kristoffer H. Rose  <kris@diku.dk>
+%
+% This package is free software; you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by the
+% Free Software Foundation; either version 2 of the License, or (at your
+% option) any later version.
+%
+% This package is distributed in the hope that it will be useful, but
+% WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+% or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+% for more details.
+%
+% You should have received a copy of the GNU General Public License along
+% with this package; if not, write to the Free Software Foundation, Inc.,
+% 675 Mass Ave, Cambridge, MA 02139, USA.
+%
+\NeedsTeXFormat{LaTeX2e}
+\documentclass[a4paper]{article}
+\usepackage{shortvrb} \let\|=| \MakeShortVerb\|
+\usepackage{amsmath}
+
+%\usepackage[debug]{qsymbols}
+\usepackage[xy,curve,matrix,oldcm,debug]{qsymbols}
+%\usepackage[purexy,curve,matrix,debug]{qsymbols}
+
+\newcommand\QSYMBOLS{\texttt{qsymbols}}
+\newcommand\AMS{{\the\textfont2 A\kern-.1667em\lower.5ex\hbox{M}\kern-.125emS}}
+
+\ifx\Xy\undefined
+ \newcommand{\Xy}{\leavevmode
+   \hbox{\kern-.1em X\kern-.3em\lower.4ex\hbox{Y\kern-.15em}}}
+ \newcommand{\xymatrix}[1]{}
+\fi
+
+\begin{document}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\title{ Summary of \QSYMBOLS }
+
+\author{Kristoffer H.~Rose%
+  \thanks{E-mail: \texttt{kris\@diku.dk},
+    W3~URL: \texttt{http://www.diku.dk/users/kris/}.}}
+
+\date{Version \qsymbolsversion\ $\langle$\qsymbolsdate$\rangle$}
+
+\maketitle
+
+\begin{abstract}\noindent
+  \QSYMBOLS\ is a \LaTeX~\cite{L94:LaTeX} package defining systematic
+  mnemonic abbreviations, starting with a single open quote |`| for symbols,
+  and in double quotes |"|\dots|"| for arrows, for characters from the
+  |amssymb| and |stmaryrd| fonts.  Optionally a very large class of arrows
+  can be typeset using the \Xy-pic package.
+\end{abstract}
+
+\tableofcontents
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\section{Introduction}
+
+\QSYMBOLS\ sets up a number of mnemonic and compact abbreviations for math
+symbols from \LaTeX\ and the packages \texttt{amssymb} and \texttt{stmaryrd},
+which it loads.  The abbreviations all start with the backquote character |`|
+except for arrows that are of the form |"->"|.  Some are a single characters,
+some a more complicated pattern, but always the idea is to use abbreviations
+that hint at the \textit{visual} appearance of the symbol.  Finally it is
+possible for the user to add more abbreviations of the simpler categories.
+
+You can retrieve \QSYMBOLS\ as well as the \texttt{amssymb} and
+\texttt{stmaryrd} packages by anonymous ftp from all CTAN archives in
+directory \texttt{/tex-archive\slash macros\slash latex\slash contrib\slash
+  supported/}\footnote{The `home' of \QSYMBOLS\ is \texttt{ftp.diku.dk} in
+  directory \texttt{/diku/users/kris/TeX/qsymbols/}.} (each package has its
+own subdirectory).
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\section{Simple symbols}
+
+\subsection{Greek letters}
+
+All the standard greek letters used in math are available as |`| followed by
+a letter: either lowercase:
+\[
+\begin{array}{\|r\|*{25}{@{\hspace{1ex}}c}\|}
+  \hline
+  x    &|a|&|b|&|c|&|d|&|e|&|f|&|g|&|h|&|i|&|j|&|k|&|l|&|m|&|n|&|p|&|q|
+       &|r|&|s|&|t|&|u|&|v|&|w|&|x|&|y|&|z|\\
+  \hline
+  |`|x &`a &`b &`c &`d &`e &`f &`g &`h &`i &`j &`k &`l &`m &`n &`p &`q
+       &`r &`s &`t &`u &`v &`w &`x &`y &`z \\
+\hline
+\end{array}
+\]
+or uppercase:
+\[
+\begin{array}{\|r\|*{11}c\|}
+  \hline
+  X    &|D|&|F|&|G|&|J|&|L|&|P|&|Q|&|S|&|W|&|X|&|Y|\\
+  \hline
+  |`|X &`D &`F &`G &`J &`L &`P &`Q &`S &`W &`X &`Y \\
+  \hline
+\end{array}
+\]
+
+\subsection{Common symbols}
+
+Simple symbols are available using |`| followed by a symbolic representation
+of the symbol.  The most common have single character representations:
+\[
+\begin{array}{\|r\|*{18}{@{\hspace{.5pc}}c}\|}
+  \hline
+  x
+&|+|&|*|&|:|&|;|&|/|&|U|&|C|&|_|&|T|&|o|&|.|&|=|&|~|&|E|&|A|&|!|&|^|&|V|\\
+  \hline
+  |`|x
+&`+ &`* &`: &`; &`/ &`U &`C &`_ &`T &`o &`. &`= &`~ &`E &`A &`! &`^ &`V \\
+  \hline
+\end{array}
+\]
+
+\subsection{Circled and Boxed Symbols}
+
+These are represented using round and square brackets, respectively:
+\[
+\begin{array}{\|r\|*{20}{@{\hspace{.5pc}}c}\|}
+\hline
+    x| |&   & |+|& |-|& |`*|& |/|&   \|   & |`/|&|`.|& |*|& |`o|
+        & |`^|& |`V|& |<|& |>|& |?|& |!|& |:-|& |R|& |C|& |a| \\
+\hline
+|`(|x|)|&`()&`(+)&`(-)&`(`*)&`(/)&\varobar&`(`/)&`(`.)&`(*)&`(`o)
+        &`(`^)&`(`V)&`(<)&`(>)&`(?)&`(!)&`(:-)&`(R)&`(C)&`(a) \\
+\hline
+|`[|x|]|&`[]&`[+]&`[-]&`[`*]&`[/]&\boxbar &`[`/]&`[`.]&`[*]&`[`o]
+        &`[`^]&`[`V]&`[<]&`[>]&`[?]&`[!]&`[:-]&`[R]&`[C]&`[a] \\
+\hline
+|`<|x|>|&`<>&`<+>&`<->&`<`*>&`</>&        &`<`/>&`<`.>&`<*>&`<`o>
+        &`<`^>&`<`V>&    &    &`<?>&`<!>&`<:->&`<R>&`<C>&`<a> \\
+\hline
+|`{|x|}|&`{}&`{+}&`{-}&`{`*}&`{/}&        &`{`/}&`{`.}&`{*}&`{`o}
+        &`{`^}&`{`V}&    &    &`{?}&`{!}&`{:-}&`{R}&`{C}&`{a} \\
+\hline
+\end{array}
+\]
+As it can be seen, `undefined' codes of the forms |`(a)| and |`[a]| result in
+the contents being circled and boxed, respectively.
+
+\subsection{Bold symbols}
+
+The \AMS-\LaTeX\ |\boldsymbol| command is available by using the special
+abbreviation |`@|$x$ for the bold version $`@x$ of $x$ as well as |`@`|$x$
+where $x$ is on one of the forms described in this section, i.e., |`@`a|
+gives~$`@`a$.
+
+\subsection{Adding new symbols}
+
+Symbols of all the above forms can be added using the form
+$$
+|\newqsymbol|~|{`|\mbox{\it code}|}|~|{|\mbox{\it expansion}|}|
+$$ which makes |`|\textit{code} behave as \textit{expansion} in math mode.
+\textit{code} should be either a single character or some characters enclosed
+in |()|, |[]|, |<>|, or |{}|.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\section{Orderings}
+
+Two to four consecutive |`|s indicate an ordering relation:
+\[
+\def\e{\epsilon}
+\def\be{{\backepsilon}}
+\begin{array}{\|c\|*6{@{\hspace{\jot}}c}\|*6{@{\hspace{\jot}}c}\|}
+  \hline
+  \e,\be &|``|\e  &|``/|\e  &|``|\e|=|  &|``/|\e|=|  &|```|\e  &|````|\e
+         &|``|\be &|``/|\be &|``|\be|=| &|``/|\be|=| &|```|\be &|````|\be \\
+  \hline
+  |<|,|>| & ``< & ``/< & ``<= & ``/<= & ```< & ````<
+          & ``> & ``/> & ``>= & ``/>= & ```> & ````> \\
+  |(|,|)| & ``( & ``/( & ``(= & ``/(= & ```( & ````(
+          & ``) & ``/) & ``)= & ``/)= & ```) & ````) \\
+  |[|,|]| & ``[ & ``/[ & ``[= & ``/[= & ```[ & ````[
+          & ``] & ``/] & ``]= & ``/]= & ```] & ````] \\
+  |\{|,|\}| & ``\{ & ``/\{ & ``\{= & ``/\{= & ```\{ & ````\{
+            & ``\} & ``/\} & ``\}= & ``/\}= & ```\} & ````\} \\
+  |\<|,|\>| & ``\< & ``/\< & ``\<= & ``/\<= & ```\< & ````\<
+            & ``\> & ``/\> & ``\>= & ``/\>= & ```\> & ````\> \\
+  | ~|,|\~| & ``~ & ``/~ & ``~= & ``/~= & ```~ & ````~
+            & ``\~ & ``/\~ & ``\~= & ``/\~= & ```\~ & ````\~ \\
+  |(-|,|-)| & ``(- & ``/(- & ``(-= & ``/(-= & ```(- & ````(-
+          & ``-) & ``/-) & ``-)= & ``/-)= & ```-) & ````-) \\
+  |(+|,|+)| & ``(+ & ``/(+ & ``(+= & ``/(+= & ```(+ & ````(+
+          & ``+) & ``/+) & ``+)= & ``/+)= & ```+) & ````+) \\
+  \hline
+\end{array}
+\]
+Some abbreviations are provided for convenience:
+\[
+\begin{array}{\|r\|*{4}c\|}
+\hline
+x     & |U|& |V|& |S|& |P|\\
+\hline
+|``|x &``U &``V &``S &``P \\
+\hline
+\end{array}
+\]
+There is no simple way to add more orderings.
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\section{Arrows}
+
+Double quotes |"|\dots|"| make it possible to typeset arrows.  On some
+systems |"| is reserved for other uses, in that case you can use |`"|\dots|"|
+instead.
+
+\subsection{Canned arrows}
+
+The available arrows are shown in figure~\ref{f.canned-arrows} where $!$
+means that the arrow is available in a long version by adding a |!| just
+after the stem character (one of |-=|), and |?| means that it stretches to
+accomodate labels (when no |!|s are given, see below).
+
+\begin{figure*}[ht]
+$$
+\begin{array}{\|ccl\|ccl\|ccl\|}
+\hline
+\verb;"<-"; &`"<-" &!@&\verb;"<->";&`"<->"&!&\verb;"->";&`"->"&!@ \\
+\verb;"<="; &`"<=" &!@&\verb;"<=>";&`"<=>"&!&\verb;"=>";&`"=>"&!@ \\
+\verb;"<3"; &`"<3" &@ &&&                   &\verb;"3>";&`"3>"&@ \\
+\verb;"</-";&`"</-"&  &\verb;"</->";&`"</->"& &\verb;"-/>";&`"-/>"& \\
+\verb;"</=";&`"</="&  &\verb;"</=>";&`"</=>"& &\verb;"=/>";&`"=/>"& \\
+\hline
+\verb;"^<-";&`"^<-"&  &&&                   &\verb;"^->";&`"^->"& \\
+\verb;"_<-";&`"_<-"&  &&&                   &\verb;"_->";&`"_->"& \\
+\hline
+\verb;"<-|";&`"<-|"&!@&&&                   &\verb;"|->";&`"|->"&!@\\
+\verb;"<=|";&`"<=|"&!@&&&                   &\verb;"|=>";&`"|=>"&!@\\
+\hline
+\verb;"<-'";&`"<-'"&@&&&                   &\verb;"`->";&`"`->"&@\\
+\verb;"<-<";&`"<-<"& &&&                   &\verb;">->";&`">->"& \\
+\hline
+\verb;"<|-";&`"<|-"&@&\verb;"<|-|>";&`"<|-|>"&@&\verb;"-|>";&`"-|>"&@\\
+&&                   &&&                       &\verb;"-o";&`"-o"  &@\\
+\hline
+\verb;"<--";&`"<--"& &&&                   &\verb;"-->";&`"-->"& \\
+&&                   &\verb;"<~>";&`"<~>"& &\verb;"~>";&`"~>"& \\
+\hline
+\verb;"<<-";&`"<<-"&@&&&                   &\verb;"->>";&`"->>"&@\\
+\verb;"<<=";&`"<<="&@&&&                   &\verb;"=>>";&`"=>>"&@\\
+\hline
+\hline
+\verb;"|-";&`"|-"&  &\verb;"|/-";&`"|/-"& &\verb;"-|";&`"-|"&  \\
+\verb;"|=";&`"|="&   &\verb;"|/=";&`"|/="&  &&& \\
+\verb;"||-";&`"||-"& &\verb;"||/-";&`"||/-"&&&& \\
+\hline
+\end{array}
+$$
+\caption{Standard `canned' arrow symbols.}
+\label{f.canned-arrows}
+\end{figure*}
+
+\subsection{Labelling arrows}
+
+Inserting |{^|$s$|}| or |{_|$s$|}|, where $s$ is a legal super- or subscript,
+respectively, will typeset these as limits, and even grows it in those cases
+where the arrow is marked with a ``@'' in the table.
+\[
+\begin{array}{\|c\|*3c\|}
+  \hline
+     x    &|-{_1}>|&|3>{^{`a`.`b}}|&{\verb,<|-|>{_{\mbox{push}}},}\\
+  \hline
+  |"|x|"| &"-{_1}>"&"3>{^{`a`.`b}}"&      "<|-|>{_{\mbox{push}}}"\\
+  \hline
+\end{array}
+\]
+
+\subsection{Adding new arrows}
+
+You can add more `canned' arrows of this kind with commands
+$$
+|\newqsymbol|~|{"|\mbox{\it arrow}|"}|~|{|\mbox{\it expansion}|}|
+$$
+which makes |"|\textit{arrow}|"| behave as \textit{expansion} in math mode.
+
+Similarly, you can add stretchable arrows using commands of the form
+$$
+|\newqsymbol|~|{"|\mbox{\it arrow}|@"}|~|{|\mbox{\it filler}|}|
+$$ which makes |"|\textit{arrow}|"| stretch under long labels as
+\textit{filler} dictates: this should behave as the plain \TeX\ command
+|\rightarrowfill| or use the macro
+$$
+|\genericarrowfill{|\textit{tail}|}{|\textit{leader}|}{|\textit{head}|}|
+$$
+\QSYMBOLS\ includes, for example, the declaration
+$$
+|\newqsymbol{"3>@"}{\genericarrowfill\equiv\equiv\Rrightarrow}|
+$$
+
+\subsection{Using \Xy-pic for arrows}
+
+If the option |[xy]| is used in the |\usepackage| command, or if
+\Xy-pic~\cite{R94:Xy-picRM}\footnote{\Xy-pic version~3 is needed for this to
+  work.} is already loaded, then the \Xy-pic arrow feature (with the `cmtip'
+extension) is used to allow a much more general class of arrows.
+
+First, all blank entries in figure~\ref{f.canned-arrows} are filled; if the
+option |[purexy]| is used instead of |[xy]| then all the entries of the table
+are replaces with \Xy-pic generated arrows (this gives a somewhat more
+homogenous look and avoids loading of |ams| and |stmary| arrows).
+
+Second, general arrows can be constructed according to the following rules:
+\begin{itemize}
+
+\item Basic arrows are composed by combining the variants
+  |23^_|, the tips |<>|\verb,|,|xo`'|, and the connectors |-=.:~|.
+
+\item The character |/| `negates' the arrow (once or twice) similar to the
+  way |\not| does for relations:
+  \[
+  \begin{array}{\|c\|*2c\|}
+    \hline
+       x    &|`-/>|&|=//!>| \\
+    \hline
+    \mbox{\tt "}x\mbox{\tt "} &"`-/>"&"=//!>"\\
+    \hline
+  \end{array}
+  \]
+
+\item Each |!| character makes the arrow a bit longer.
+  \[
+  \begin{array}{\|c\|*4c\|}
+    \hline
+       x    &|->|&|-!>|&|-!!>| &|-!!!>| \\
+    \hline
+    \mbox{\tt "}x\mbox{\tt "} &"->"&"-!>"&"-!!>" &"-!!!>" \\
+    \hline
+  \end{array}
+  \]
+  \textit{Note}: Some arrows are automatically made a bit longer, e.g., the
+  |<~>| arrow shown above.
+
+\item The form |*|\emph{object} inserts the \Xy-pic \emph{object} which will
+  be used for the tail, shaft, or tip as indicated by the position.  Here are
+  some examples:
+  \[
+  \begin{array}{\|c\|*2c\|}
+    \hline
+       x    &|*{x}-*{y}!|&\verb+*{}*{*}|!!+\\
+    \hline
+    |"|x|"| &"*{x}-*{y}!"&     "*{}*{*}|!!"\\
+    \hline
+  \end{array}
+  \]
+  as in the examples it is recommended to specify all three of tail, shaft,
+  and head, when using this, in particular an empty tail when the shaft is
+  specified with |*| because otherwise it is taken as the tail.
+
+\item The forms |(|$x$|)| and |[|$x$|]| insert a break with $x$ in a
+  circle and box, respectively:
+  \[
+  \begin{array}{\|c\|*2c\|}
+    \hline
+       x    &|(1)>|&|[1]>>|\\
+    \hline
+    |"|x|"| &"(1)>"&"[1]>>"\\
+    \hline
+  \end{array}
+  \]
+
+\item The special code |{|$\ell$|}| adds the $\ell$ material to the end of
+  the \Xy-pic arrow: All \Xy-pic $\langle$labels$\rangle$ can be used as
+  described in~\cite[\S16]{R94:Xy-picRM}, for example,
+  \[
+  \begin{array}{\|c\|*1c\|}
+    \hline
+       x    &\verb,={|{`b}}!!|>,\\
+    \hline  
+    |"|x|"| &     "={|{`b}}!!|>"\\
+    \hline
+  \end{array}
+  \]
+  Use this with care!
+
+\item Similarly the special code |@{|$\ell$|}| adds the $|@|\ell$ material
+  (note the omission of the braces) to the beginning of the \Xy-pic arrow:
+  all \Xy-pic arrow $\langle$form$\rangle$s can be used <form> to the
+  beginning of the arrow specification; this can be used to as described
+  in~\cite[\S16]{R94:Xy-picRM}, for example,
+  \[
+  \begin{array}{\|c\|*2c\|}
+    \hline
+       x    &\verb;|-@{/^/}!!!>|; &\verb;->!!!!@{(dr,ul)};\\
+    \hline
+    |"|x|"|
+            &     "|-@{/^/}!!!>|" &     "->!!!!@{(dr,ul)}"\\
+    \hline
+  \end{array}
+  \]
+  Use this with care!
+
+\end{itemize}
+
+\subsection{Using \protect\QSYMBOLS\ arrows in \protect\Xy-pic diagrams}
+
+Finally it is possible to some extent to use \QSYMBOLS\ arrows in \Xy-pic
+matrices (as described in the \Xy-pic User's Guide~\cite{R94:Xy-picUG}) and
+graphs (as described in the \Xy-pic Reference
+Manual~\cite[\S19]{R94:Xy-picRM}).  First notice that you should always use
+the |`"|\dots|"| form.  Second, the entire |`"|\dots|"| construction behaves
+as an arrow made with |\ar| for matrices and |:| for graphs, that is, you
+must add a `target address' for the arrow after it.  Further information of
+this can be found
+
+Here is the canonical pull-back example diagram from category theory typeset
+using qsymbols:
+\begin{verbatim}
+    \xymatrix{
+     U `"->"@/_/[ddr]_y `".>"[dr]|-{(x,y)} `"->"@/^/[drr]^x \\
+      & X \times_Z Y `"=>"[d]^q `"=>"[r]_p & X `"=>"[d]_f   \\
+      & Y `"=>"[r]^g                       & Z              }
+\end{verbatim}
+typesets
+\begin{displaymath}
+    \xymatrix{
+     U `"->"@/_/[ddr]_y `".>"[dr]|-{(x,y)} `"->"@/^/[drr]^x \\
+      & X \times_Z Y `"=>"[d]^q `"=>"[r]_p & X `"=>"[d]_f   \\
+      & Y `"=>"[r]^g                       & Z              }
+\end{displaymath}
+As you can see, \Xy-pic is loaded by \QSYMBOLS\ and as a convenience \Xy-pic
+options may be passed to \QSYMBOLS.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{thebibliography}{1}
+
+\bibitem{L94:LaTeX}
+Leslie Lamport.
+\newblock {\em {\LaTeX}---A Document Preparation System}.
+\newblock Addison-Wesley, 2nd edition, 1994.
+
+\bibitem{R94:Xy-picUG}
+Kristoffer~H. Rose.
+\newblock {\Xy}-pic user's guide.
+\newblock Mathematics Report 94--148, MPCE, Macquarie University, NSW 2109,
+  Australia, June 1994.
+\newblock For version 2.10+. Latest version available with URL {\tt
+  ftp://ftp.diku.dk\slash diku\slash users\slash kris\slash TeX\slash xy\slash
+  xyguide.ps}.
+
+\bibitem{R94:Xy-picRM}
+Kristoffer~H. Rose and Ross Moore.
+\newblock {\Xy}-pic reference manual.
+\newblock Mathematics Report 94--155, MPCE, Macquarie University, NSW 2109,
+  Australia, June 1994.
+\newblock For version 2.10+. Latest version available by anonymous ftp in {\tt
+  ftp.diku.dk: /diku\slash users\slash kris\slash TeX\slash xyrefer.ps.Z}.
+
+\end{thebibliography}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\end{document}
+
+% $Log: qsymbols.tex,v $
+% Revision 1.8  1996/12/05 04:27:20  krisrose
+% Handles sub/superscripts without Xy-pic; cleaned up.
+%
+% Revision 1.7  1994/12/12  01:29:28  kris
+% Updates for Xy-pic v3 in progress...
+%
+% Changed `" to `@ and made `" = ".
+%
+% Revision 1.5  1994/10/28  18:19:28  kris
+% Added '{..} and documented "...{...}..." <labels>.
+%
+% Revision 1.4  1994/10/28  15:08:46  kris
+% Added boldsymbol support.
+%
+% Revision 1.3  1994/10/26  16:47:07  kris
+% Fixed a few things :-)
+%
+% Revision 1.2  1994/10/26  02:10:17  kris
+% Integrated qarrow; use of Xy-pic is an option.
+%
+% Revision 1.1  1994/10/24  22:55:12  kris
+% Initial revision
+%
+% From kris-sty.tex 1.4.