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authorKarl Berry <karl@freefriends.org>2006-01-09 00:49:07 +0000
committerKarl Berry <karl@freefriends.org>2006-01-09 00:49:07 +0000
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tree90d17e00e572ecb1e24764b6f29c80e098b08d29 /Master/texmf-dist/doc/latex/pb-diagram
parent950209b26f70aa87ed07c54f82a95b6f03b7c3a0 (diff)
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-rw-r--r--Master/texmf-dist/doc/latex/pb-diagram/COPYING339
-rw-r--r--Master/texmf-dist/doc/latex/pb-diagram/README68
-rw-r--r--Master/texmf-dist/doc/latex/pb-diagram/pb-examples.tex245
-rw-r--r--Master/texmf-dist/doc/latex/pb-diagram/pb-manual.tex574
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diff --git a/Master/texmf-dist/doc/latex/pb-diagram/COPYING b/Master/texmf-dist/doc/latex/pb-diagram/COPYING
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@@ -0,0 +1,339 @@
+ GNU GENERAL PUBLIC LICENSE
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diff --git a/Master/texmf-dist/doc/latex/pb-diagram/README b/Master/texmf-dist/doc/latex/pb-diagram/README
new file mode 100644
index 00000000000..1aca8ff21bd
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/pb-diagram/README
@@ -0,0 +1,68 @@
+This package contains version 5.0 of the "pb-diagram.sty"
+LaTeX macro package by Paul Burchard, along with complete
+documentation and examples. The "diagram" environment provided
+by this package allows the LaTeX user to easily create complex
+commutative diagrams, by placing formula nodes on a conceptual
+grid and attaching arrows to them.
+
+The grid used in these diagrams is not a fixed square grid.
+Instead, the environment automatically generates a correctly scaled
+and shaped rectangular grid which will compactly hold the formulas,
+while leaving room for the arrows between them. Moreover, the
+arrows automatically adapt to the spaces between the formulas
+being connected.
+
+* Improvements from Previous Versions *
+
+version 5.0:
+ - XY-PIC arrow fonts can be used, for even nicer, PostScript-
+ compatible arrows, thanks to Bill Richter <richter@math.nwu.edu>
+ - now distributed under GNU General Public License
+
+version 4.1:
+ - LAMS arrow fonts now compile correctly, thanks to
+ fix from Ingo Hadan <hadan@mathematik.hu-berlin.de>
+ - \arrow command works better outside of diagrams
+
+version 4.0:
+ - makes pb-diagram more compatible with LaTeX2e and AMS-LaTeX
+ - fixes a grid geometry bug that doubled some diagrams
+ - corrects the direction of LAMS-TeX arrow embellishments
+ - adds a double-headed arrow option
+ - leaves many more TeX box nesting levels for arrow labels
+ - produces less verbose output during typesetting
+
+* Upgrading Papers *
+
+In versions 3.6 and earlier, certain uncommon types of diagrams
+came out twice too large; to produce exactly compatible behavior
+in versions 4.0 and later, use the following declaration:
+
+ \let\dggeometry=\dgoldgeometry
+
+In versions 3.4 and earlier, the names of the packages differed;
+here is a dictionary for translating the list of packages to load:
+
+ diagram -> pb-diagram
+ lamsarrow,diagram -> pb-diagram,lamsarrow,pb-lams
+
+* Installation *
+
+ File Name Where to Put It
+ ------------------- -------------------
+ pb-diagram.sty TEXINPUTS
+ pb-xy.sty TEXINPUTS
+ pb-lams.sty TEXINPUTS
+ lamsarrow.sty TEXINPUTS
+ pb-manual.tex documentation area
+ pb-examples.tex documentation area
+ mf/lams*.mf MFINPUTS
+ tfm/lams*.tfm TEXFONTS
+ README
+
+Please let me know if you have any problems with
+this package.
+
+Paul Burchard
+<burchard@pobox.com>
+
diff --git a/Master/texmf-dist/doc/latex/pb-diagram/pb-examples.tex b/Master/texmf-dist/doc/latex/pb-diagram/pb-examples.tex
new file mode 100644
index 00000000000..ed9338e34ab
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/pb-diagram/pb-examples.tex
@@ -0,0 +1,245 @@
+% pb-examples.tex: nifty example using pb-diagram.sty
+% Authors: Bill Richter et al.
+% Version Number: 5.0
+% Version Date: 20 Oct 1998
+%
+\def\tooee{LaTeX2e}
+\ifx\fmtname\tooee
+ \documentclass[12pt]{article}\usepackage{pb-diagram}
+\else
+ \documentstyle[12pt,pb-diagram]{article}
+\fi
+\title{Examples of the Diagram Environment}
+\author{Stolen from Various Sources}
+\begin{document}
+\maketitle
+
+\setlength{\fboxsep}{0pt}
+
+This ridiculous example shows how the package fits
+arrows in between the formulas, taking into account the
+exact size of every formula. (The box around the diagram
+shows how the shape of the entire diagram is made known to
+\LaTeX.) Note that diagonal arrows are fitted to either
+the tops or sides of the formulas, depending individual
+circumstances.
+\begin{center}\fbox{$
+\begin{diagram}
+\node{\left[\begin{array}{cc} A_{00} & A_{01} \\
+ A_{10} & A_{11}\end{array}\right]}
+ \arrow{e,t}{a} \arrow{s,l}{c} \arrow{ese,b,1}{u}
+ \node{B^*} \arrow{e,t}{b^*}
+ \node{C} \arrow{s,r}{d} \arrow{wsw,b,1}{v}
+\\
+\node{D} \arrow[2]{e,b}{e}
+ \node[2]{H^2(X,\, \omega_X \otimes L^{\otimes(-n^2+n)})}
+\end{diagram}
+$}\end{center}
+
+% Catcode hack to get typewriter `\' inside arg of another command
+% where \verb is illegal.
+\begingroup \catcode`|=0 \catcode`\\=12
+ |gdef|bbb{{|tt\}}%
+|endgroup
+%
+\makeatletter
+\@ifundefined{lamsvector}{%
+ (There are some additional diagrams at this point in the file,
+ which you can see if you add
+ \ifx\fmtname\tooee
+ {\tt\bbb usepackage\{lamsarrow\}\bbb usepackage\{pb-lams\}}
+ at the end of the list of included packages.)
+ \else
+ \mbox{\tt lamsarrow,pb-lams} at the end of the
+ document style options.)
+ \fi
+}{%
+\newpage
+This diagram shows off the fancy arrows fonts from LamS-\TeX.
+\[
+\begin{diagram}
+\node{A} \arrow{e,t,V}{a} \arrow{s,l,'}{c} \arrow{ese,b,1,`}{u}
+ \node{B} \arrow{e,t,A}{b}
+ \node{C} \arrow{s,r,J}{d} \arrow{wsw,b,1,L}{v} \\
+\node{D} \arrow[2]{e,b,S}{e}
+ \node[2]{E}
+\end{diagram}
+\]
+
+The two diagrams below differ only in that the second has an extra diagonal
+arrow. Because the first diagram is naturally very long, this diagonal arrow
+could not be drawn into the first diagram even with the LamS-\TeX\ fonts. So
+the diagram automatically compromises the diagram's aspect ratio to make the
+arrow possible.
+\[
+\begin{diagram}
+\node{\rule{80pt}{1pt}} \arrow[3]{e} % remove arrow: \arrow{seee,..}
+ \node[3]{\rule{80pt}{1pt}} \arrow{s}\\
+\node{\rule{80pt}{1pt}} \arrow{e}
+ \node{\rule{80pt}{1pt}} \arrow{e}
+ \node{\rule{80pt}{1pt}} \arrow{e}
+ \node{\rule{80pt}{1pt}}
+\end{diagram}
+\]
+\[
+\begin{diagram}
+\node{\rule{80pt}{1pt}} \arrow[3]{e} \arrow{seee,..}
+ \node[3]{\rule{80pt}{1pt}} \arrow{s}\\
+\node{\rule{80pt}{1pt}} \arrow{e}
+ \node{\rule{80pt}{1pt}} \arrow{e}
+ \node{\rule{80pt}{1pt}} \arrow{e}
+ \node{\rule{80pt}{1pt}}
+\end{diagram}
+\]}
+\makeatother
+
+\newpage
+These examples show how to simulate split arrows by placing the diagram on a finer grid than logically necessary.
+\[
+ \dgARROWLENGTH=0.6\dgARROWLENGTH
+ \begin{diagram}
+ \node[2]{A}\arrow[2]{s}\\
+ \node{B}\arrow{e,-} \node{}\arrow{e,t}{\alpha} \node{C} \\
+ \node[2]{D}\arrow{ne,b}{\beta}
+ \end{diagram}
+\]
+
+\[
+\begin{diagram}
+\node{A} \arrow[2]{e,t}{a} \arrow[2]{s,l}{c} \arrow[2]{ese,t,3}{u}
+ \node[2]{B^*} \arrow[2]{e,t}{b^*}
+ \node[2]{C} \arrow[2]{s,r}{d} \arrow{wsw,-}
+\\
+ \node[3]{} \arrow{wsw,t}{v}
+\\
+\node{D} \arrow[4]{e,b}{e}
+ \node[4]{E}
+\end{diagram}
+\]
+
+
+\newpage
+Here are several ``real life'' examples from Bill Richter's work:
+%%%% Note: for ease of tex-ing we don't assume extra fonts.
+\let\frak\relax
+\let\Bbb=\relax
+%%%%
+%\font\tenfrak=eufm10 scaled \magstep1
+%\font\sevenfrak=eufm7 scaled \magstep1
+%\font\fivefrak=eufm5 scaled \magstep1
+%\newfam\frakfam \def\frak{\fam\frakfam\tenfrak} \textfont\frakfam=\tenfrak
+%\scriptfont\frakfam=\sevenfrak \scriptscriptfont\frakfam=\fivefrak
+%%%%
+%%%%
+\def\a{ \alpha }
+\def\d{ \delta }
+\def\s{ \sigma }
+\def\l{ \lambda }
+\def\p{ \partial }
+\def\st{{\tilde\s}}
+\def\O{ \Omega }
+\def\S{\Sigma}
+\def\Z{{\Bbb Z }}
+\def\@{ \otimes }
+\def\^{ \wedge }
+\def\({ \left( }
+\def\){ \right) }
+\def\K#1{{ K\(\Z/2,#1\) }}
+\def\KZ#1{{K\(\Z/4,#1\) }}
+\def\id{ \mathop{id}\nolimits }
+\def\h{ {\frak h} }
+\def\e{ {\frak e} }
+\def\G{ G }
+\def\pinch{{ \mathop{{\rm pinch}} }}
+\def\tuber{{ \bar\tau }}
+%%%%
+%%%%
+\[
+\begin{diagram}
+\node[4]{ \K{8n+1} }
+\\
+\node[2]{ \KZ{8n-1} } \arrow{e} \arrow{ene,t}{Sq^2}
+ \node{E} \arrow{ne,b}{\Theta} \arrow{s,l}{\pi}
+\\
+\node{ \S\O X \^ \O X } \arrow{e,t}{H_\mu} \arrow{ne,t}{\s(\a\@\a)}
+ \node{ \Sigma \O X } \arrow{e,t}{\sigma} \arrow{ne,t}{\st}
+ \node{ X } \arrow{e,t}{\a^2}
+ \node{ \KZ{8n}. }
+\end{diagram}
+\]
+
+\[
+\begin{diagram}
+\node[3]{\O\S A} \arrow[2]{e,t}{\l_2}
+ \node[2]{\O^2 \( \S A \^ \S A \)}
+\\
+\node[4]{\#}
+\\
+% Note: the next two lines are like
+% \node{\O B} \arrow[2]{e,t,1}{\d} \arrow[2]{ne,t}{\O\(\p\)}
+% but put a gap in first arrow to make room for crossing arrow
+\node{\O B} \arrow{e,t,-}{\d} \arrow[2]{ne,t}{\O\(\p\)}
+ \node{} \arrow{e}
+ \node{F} \arrow[2]{e,t}{\h} \arrow[2]{s,r}{\pi} \arrow[2]{n,r}{J}
+ \node[2]{\O^2 \( B \^ \S A \)} \arrow[2]{n,r}{\O^2\(\p\^\id\)}
+\\
+\\
+\node{A} \arrow[2]{ne,t}{\e} \arrow[2]{e,t}{f} \arrow[2]{nne,t,1}{E}
+ \node[2]{X} \arrow[2]{e,t}{h}
+ \node[2]{B.}
+\end{diagram}
+\]
+
+\[
+\divide\dgARROWLENGTH by3
+\begin{diagram}
+\node[9]{\O S^5}
+\\
+\\
+\\
+\node[8]{\scriptstyle\quad (\beta)}
+\\
+\node{\O\( M^5_{2\iota}\)} \arrow[4]{e,t}{\O\(\pinch\)}
+ \node[4]{\O S^5} \arrow[2]{e,t,-}{\d} \arrow[4]{ne,t}{\O\(2\iota\)}
+ \node[2]{} \arrow[2]{e}
+ \node[2]{\G} \arrow[4]{e,t}{\h_2}
+ \arrow[2]{s,r,-}{\pi} \arrow[4]{n,r}{J}
+ \node[4]{J\(S^4\^S^4\)}
+\\
+\\
+\node[3]{J_2\( M^4_{2\iota}\)} \arrow[3]{e,t,3,-}{\d_2} \arrow[2]{ne,t}{\iota}
+ \node[3]{} \arrow{e}
+ \node{\G_2} \arrow[4]{e,t,3}{\h_2} \arrow[2]{ne,t}{\iota}
+ \node[2]{} \arrow[2]{s}
+ \node[2]{S^8} \arrow[2]{ne,b}{E}
+\\
+\node[4]{\scriptstyle (\alpha)}
+\\
+\node{M^{12}_{2\iota}} \arrow[4]{e,t}{\tuber} \arrow[2]{ne,t}{\tau}
+ \node[4]{S^4} \arrow[4]{e,t}{\iota} \arrow[2]{ne,t}{\e} \arrow[4]{nne,t,3}{E}
+ \node[4]{M^5_{2\iota}} \arrow[4]{e,t}{\pinch}
+ \node[4]{S^5}
+\end{diagram}
+\]
+
+\newpage
+Example by Anders Thorup (thorup@math.ku.dk), originally done with a
+package developed by himself and Steven Kleiman
+(kleiman@math.mit.edu):
+\[
+\begin{diagram}
+\node{H^k(B_G\times N;Q)=H^k_G(N;Q)}
+ \arrow[2]{e,t}{f^*_j} \arrow[2]{s,l}{p^*} \arrow{se,t}{\tilde f^*}
+ \node[2]{H^k_G(F_j;Q)} \arrow[2]{s,r}{q^*_j}
+\\
+\node[2]{H^k_G(M;Q)} \arrow{ne,t}{i^*_j} \arrow[2]{s,l,1}{i^*}
+\\
+\node{H^k(N;Q)}\arrow{e,t,-}{\tilde f^*_j=f^*_j}\arrow{se,b}{\tilde f^*=f^*}
+ \node{} \arrow{e}
+ \node{H^k(F_j;Q)}
+\\
+\node[2]{H^k(M;Q)} \arrow{ne,b}{i^*_j}
+\end{diagram}
+\]
+
+\end{document}
diff --git a/Master/texmf-dist/doc/latex/pb-diagram/pb-manual.tex b/Master/texmf-dist/doc/latex/pb-diagram/pb-manual.tex
new file mode 100644
index 00000000000..d0a25612ccd
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/pb-diagram/pb-manual.tex
@@ -0,0 +1,574 @@
+% pb-manual.tex: user's manual for pb-diagram.sty macros
+% Author: Paul Burchard <burchard@pobox.com>
+% Version Number: 5.0
+% Version Date: 20 Oct 1998
+%
+% Copyright (c) 1990, 1992, 1995, 1998 by Paul Burchard
+%
+% This program 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 program 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 program; if not, write to the Free Software
+% Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
+%
+\def\tooee{LaTeX2e}
+\ifx\fmtname\tooee
+ \documentclass[12pt]{article}\usepackage{pb-diagram}
+\else
+ \documentstyle[12pt,pb-diagram]{article}
+\fi
+\def\diagramversion{5.0}
+\title{User's Guide to the Diagram Environment,
+ Version \diagramversion}
+\author{Paul Burchard (burchard@pobox.com)}
+\def\tfrac#1#2{{\textstyle\frac{#1}{#2}}}
+\begin{document}
+\maketitle
+
+\section{Introduction}
+
+The \verb"diagram" environment allows the
+\ifx\fmtname\tooee\LaTeXe\else\LaTeX\fi{} user to easily
+create complex commutative diagrams, by placing formula nodes
+on a conceptual grid and attaching arrows to them.
+
+The grid used in these diagrams is not a fixed square grid.
+Instead, the environment automatically generates a correctly scaled
+and shaped rectangular grid which will compactly hold the formulas,
+while leaving room for the arrows between them. Moreover, the
+arrows automatically adapt to the spaces between the formulas
+being connected. These features are accomplished with a
+three-pass algorithm that takes into account the width
+and height of every formula.
+
+The arrows in these diagrams are quite flexible.
+Arrows may, in any combination,
+\begin{itemize}
+ \item point in any of a large number of lattice directions;
+ \item span multiple rows and columns of the grid;
+ \item cross other arrows;
+ \item have labels on either or both sides,
+ with adjustable positioning;
+ \item have a variety of head, tail, and shaft styles.
+\end{itemize}
+The fancier arrow styles are made possible by special fonts,
+either from Xy-pic or {\sc LamS}-\TeX, but the package can be used
+without them if necessary.
+
+\pagebreak[3]
+To get a feel for how the package works, here are some examples of
+commands for producing arrows:
+\begin{flushright}
+%
+% Catcode hack to get typewriter `\' `{' `}' inside arg of command
+% where \verb is illegal.
+\begingroup
+ \catcode`|=0 \catcode`[=1 \catcode`]=2
+ \catcode`\{=12 \catcode`\}=12 \catcode`\\=12
+ |gdef|bbb[\]|gdef|lll[{]|gdef|rrr[}]%
+|endgroup
+\def\ttt{\ifx\fmtname\tooee\fontfamily{cmtt}\selectfont\else\tt\fi}%
+%
+% tighten it up a bit to fit on page in 12pt
+\setlength{\dgARROWLENGTH}{1.5em}%
+\noindent
+$\begin{diagram}
+ \node{\makebox[0pt][r]{\ttt\bbb arrow\lll e\rrr \quad}+}
+ \arrow{e} \node{+} \node{+} \node{+} \node{+} \\
+ \node{+} \arrow{s,lr}{\makebox[0pt][r]{\ttt\bbb
+ arrow\lll s,lr\rrr\lll\bbb alpha\rrr\lll\bbb beta\rrr\quad}
+ \alpha}{\beta}
+ \node{+} \node{+} \node{+} \node{+} \\
+ \node{+} \node{+} \node{+} \node{+} \node{+} \\
+ \node{\makebox[0pt][r]{\ttt\bbb
+ arrow[2]\lll ene,t,3,..\rrr\lll f\_0\rrr\quad}+}
+ \arrow[2]{ene,t,3,..}{f_0} \node{+}
+ \node{+} \node{+} \node{+}
+\end{diagram}$
+\end{flushright}
+And here is a simple example diagram:
+\[
+ \begin{diagram}
+ \node{A} \arrow{e,t}{a} \arrow{s,l}{c} \arrow{ese}
+ \node{B^*} \arrow{e,t}{b^*}
+ \node{C} \arrow{s,r}{d} \arrow{wsw} \\
+ \node{D} \arrow[2]{e,b}{e} \node[2]{E}
+ \end{diagram}
+\]
+\begin{verbatim}
+ \[
+ \begin{diagram}
+ \node{A} \arrow{e,t}{a} \arrow{s,l}{c} \arrow{ese}
+ \node{B^*} \arrow{e,t}{b^*}
+ \node{C} \arrow{s,r}{d} \arrow{wsw} \\
+ \node{D} \arrow[2]{e,b}{e} \node[2]{E}
+ \end{diagram}
+ \]
+\end{verbatim}
+
+\pagebreak[4]
+\section{Loading the Diagram Package}
+
+To use the \verb"diagram" environment, begin your
+\ifx\fmtname\tooee\LaTeXe\else\LaTeX2e\fi{} file with:
+\begin{verbatim}
+ \documentclass{DOCSTYLE}\usepackage{pb-diagram}
+\end{verbatim}
+where \verb"DOCSTYLE" is your document style (e.g.,
+\verb"article"). The style file \verb"pb-diagram.sty" needs to
+be placed in one of your system's \TeX{} input directories.
+
+If you are using older versions of \LaTeX{} (2.09 or older), then
+you would begin instead with:
+\begin{verbatim}
+ \documentstyle[pb-diagram]{DOCSTYLE}
+\end{verbatim}
+
+If you have {\em METAFONT\/} available on your system,
+and would like to make use of the additional features
+of the Xy-pic fonts (highly recommended!), then you should
+instead begin your
+\ifx\fmtname\tooee\LaTeXe\else\LaTeX2e\fi{} file with:
+\begin{verbatim}
+ \documentclass{DOCSTYLE}
+ \usepackage[cmtip,arrow]{xy}
+ \usepackage{pb-diagram,pb-xy}
+\end{verbatim}
+This option requires that you have Xy-pic installed on your
+system. Xy-pic is available from your nearest CTAN archive
+(e.g. {\tt http://ctan.tug.org/}) in the CTAN directory
+{\tt macros/generic/diagrams/xypic/}.
+
+An alternative set of fonts which enables some of the
+fancier features is the {\sc LamS}-\TeX{} font set; to
+use it, begin your
+\ifx\fmtname\tooee\LaTeXe\else\LaTeX2e\fi{} file with:
+\begin{verbatim}
+ \documentclass{DOCSTYLE}
+ \usepackage{pb-diagram,lamsarrow,pb-lams}
+\end{verbatim}
+This option requires the {\em METAFONT\/} source files
+\verb"lams1.mf" through \verb"lams5.mf" to be installed.
+
+Installation of additional fonts is system-dependent,
+but will involve moving the \verb".mf" files into the system's
+{\em METAFONT\/} input directory, and then running the
+{\em METAFONT\/} program. This program will generate the
+\verb".tfm" files required for \TeX, and the \verb".pk" or
+\verb".gf" files required for printing and previewing.
+On {\sc unix} systems, the relevant files are typically
+located in \verb"/usr/lib/mf" and \verb"/usr/lib/tex", or
+\verb"/usr/local/lib/mf" and \verb"/usr/local/lib/tex".
+
+If you are having troubling getting \LaTeX{} to properly
+process an older paper which uses this package, check the
+later section, ``Upgrading Papers from Previous Versions.''
+
+\pagebreak[4]
+\section{Using the Diagram Environment}
+\subsection{Overall Structure of the Environment}
+
+The \verb"diagram" environment should be used in
+{\em math mode only}. Its usage is as follows:\footnote{For
+compatibility reasons, the diagram environment accepts and
+optional argument. When this argument is supplied, the grid
+geometry is calculated in exactly the same way as in version~1.0
+of this package. Therefore, manuscripts written with version~1.0
+require no changes to be processed with version~\diagramversion.}
+\begin{verbatim}
+ \begin{diagram}
+ NODE ARROW ARROW ... NODE ARROW ARROW ... .... \\
+ NODE ARROW ARROW ... NODE ARROW ARROW ... .... \\
+ ...
+ NODE ARROW ARROW ... NODE ARROW ARROW ... ....
+ \end{diagram}
+\end{verbatim}
+
+Each \verb"NODE" places a centered formula at a new grid point, and
+each \verb"ARROW" which follows this \verb"NODE" (but precedes the
+next \verb"NODE") will be attached by its tail to the same grid
+point. The diagram will be automatically be given a geometry which
+accomodates these elements, but you can also fine-tune it afterwards
+by hand if it didn't turn out like you imagined
+(see the section on ``Fine-Tuning'' below). We now explain
+how to specify the \verb"NODE"s and \verb"ARROW"s.
+
+\subsection{Formula Nodes}
+
+A \verb"NODE" is specified by the comand:
+\begin{verbatim}
+ \node[NCOLS]{FORMULA}
+\end{verbatim}
+where the optional argument \verb"NCOLS" tells how many grid columns
+to move forward from the previous node (the default is 1). The
+\verb"FORMULA" is the math mode material which you want to place at
+that node in the grid.
+
+The \verb"\\" command moves to the next grid row. As is usual in
+\LaTeX{} arrays, the final row should not end with a \verb"\\", and
+any blank columns at the end of a row need not be entered. More
+generally, it is possible to move \verb"NROWS" rows down at once
+using the command:
+\begin{verbatim}
+ \\[NROWS]
+\end{verbatim}
+
+\subsection{Arrows and their Embellishments}
+
+An \verb"ARROW" is specified by the \verb"\arrow" command, which may
+also be used anywhere in math mode, independent of the
+\verb"diagram" environment. Its usage depends on the number of
+labels desired:
+\begin{verbatim}
+ \arrow[SIZE]{DIRECTION,OPTIONS}
+ \arrow[SIZE]{DIRECTION,ONELABEL,OPTIONS}{LABEL}
+ \arrow[SIZE]{DIRECTION,TWOLABEL,OPTIONS}{LABEL1}{LABEL2}
+\end{verbatim}
+The commas should not have any spaces before or after them, and there
+should not be any extra spaces or commas at the beginning or end of
+the list. The optional integer argument \verb"SIZE" tells how many
+times its normal length the arrow should be made. For example,
+\verb"\arrow[2]{e}" will span two columns, while \verb"\arrow[2]{s}"
+will span two rows.
+
+The arrow \verb"DIRECTION" may be chosen from the compass point
+directions:
+\begin{verbatim}
+ n,e,s,w,ne,nw,se,sw,nne,nnw,sse,ssw,ene,ese,wnw,wsw
+\end{verbatim}
+If the \verb"pb-lams" style has been loaded, the \verb"DIRECTION"
+may also be chosen from this list:
+\begin{verbatim}
+ nee,see,nww,sww,
+ neee,nnne,nnnw,nwww,swww,sssw,ssse,seee,
+ nnnee,nnnww,sssww,sssee,nneee,nnwww,sswww,sseee
+\end{verbatim}
+(For more information about arrow directions, see the sections
+on ``Fine Tuning'' and ``Customizing'' below.)
+
+Any \verb"LABEL"s present are math mode material. The
+\verb"ONELABEL" specifier may be chosen from:
+\begin{tabbing}
+ {\tt xxx}\={\tt x}\qquad\=\kill
+ \>{\tt t}\> top\\
+ \>{\tt b}\> bottom\\
+ \>{\tt l}\> left (only for use with vertical arrows)\\
+ \>{\tt r}\> right (only for use with vertical arrows)
+\end{tabbing}
+The \verb"TWOLABEL" specifier may be chosen from:
+\begin{tabbing}
+ {\tt xxx}\={\tt x}\qquad\=\kill
+ \>{\tt tb}\> top and bottom\\
+ \>{\tt lr}\> left and right (only for use with vertical arrows)
+\end{tabbing}
+
+The \verb"OPTION"s describe the style of the arrow shaft, the symbols
+to be used at the head and tail of the arrow, and the positions of
+the labels. The defaults are: a simple line shaft, a single simple
+arrowhead, no special tail symbol, and labels positioned at the
+midpoint of the arrow shaft. The \verb"OPTION"s may be selected from
+the lists which follow. Most of the options can be combined with
+others; however, not all combinations make sense. In addition,
+options marked with~(*) are only available with
+either \verb"pb-xy" or \verb"pb-lams" loaded;
+and options marked with~(**) are only available with \verb"pb-xy" loaded.
+Shaft options are:
+\begin{tabbing}
+ {\tt xxx}\={\tt x}\qquad\=\kill
+ \>{\tt ..}\> dotted or dashed arrow shaft\\
+ \>{\tt =}\> double line shaft* (``equals sign'')\\
+ \>{\tt !}\> invisible arrow shaft
+\end{tabbing}
+Arrow head options are:
+\begin{tabbing}
+ {\tt xxx}\={\tt x}\qquad\=\kill
+ \>{\tt -}\> no arrow heads\\
+ \>{\tt <>}\> arrow heads on both ends\\
+ \>{\tt A}\> double arrow head*\\
+ \>{\tt '}\> left half of arrow head*\\
+ \>{\tt `}\> right half of arrow head*
+\end{tabbing}
+Arrow tail options are:
+\begin{tabbing}
+ {\tt xxx}\={\tt x}\qquad\=\kill
+ \>{\tt V}\> single arrow tail*\\
+ \>{\tt J}\> left fish hook arrow tail*\\
+ \>{\tt L}\> right fish hook arrow tail*\\
+ \>{\tt S}\> squiggle arrow tail*
+ \>{\tt T}\> ``mapsto'' arrow tail**
+\end{tabbing}
+In the default configuration, the label positioning options are:
+\begin{tabbing}
+ {\tt xxx}\={\tt x}\qquad\=\kill
+ \>{\tt 1}\> 1/4 of way from tail end\\
+ \>{\tt 2}\> 2/4 of way from tail end (the default)\\
+ \>{\tt 3}\> 3/4 of way from tail end
+\end{tabbing}
+However, if more flexibility is needed, there is an
+\verb"ARROWPARTS" parameter which specifies how many pieces the arrow
+will be divided into to determine the meaning of the label
+positioning option. (In general, the positioning option may be any
+single digit.) For example, to position a label 5/6 of the way from
+the tail end of the arrow, you would use commands like these:
+\begin{verbatim}
+ \dgARROWPARTS=6
+ \begin{diagram}
+ ... \arrow{e,t,5}{MYLABEL} ...
+ \end{diagram}
+\end{verbatim}
+\verb"ARROWPARTS" should be even, so that ordinary labels can
+be properly positioned at the half-way point.
+
+
+\section{Fine Tuning the Diagrams}
+
+Many of the parameters used by the \verb"diagram" environment are
+accessible to you and documented here so that the existing features
+can be fine-tuned.
+
+The most important parameter is \verb"\dgARROWLENGTH", which
+specifies the minimum length for all arrows. The \verb"diagram"
+environment will independently adjust the horizontal and vertical
+scales of its rectangular grid until at least that much room is
+available for each arrow. This calculation takes into account
+the room that must be set aside for the each of the two formulas
+being connected by an arrow. The default minimum arrow length is
+\begin{verbatim}
+ \dgARROWLENGTH=2.5em
+\end{verbatim}
+The \verb"\arrow" command may also be used outside of the diagram
+environment; in that case, its length is instead controlled by
+the parameter
+\begin{verbatim}
+ \dgTEXTARROWLENGTH=1.1em
+\end{verbatim}
+
+Some anomalies you may encounter: the collision of formulas is not
+checked unless an arrow connects them. Therefore, if two formulas
+turn out to overlap you can just connect them with an invisible arrow.
+
+Another problem may occur when you simulate ``arrow fragments''
+using a finer grid. The arrow-length checker does not know what
+is a ``fragment'' and so it will force each fragment to be
+\verb"\dgARROWLENGTH" long. The easiest way to fix this is to
+locally divide \verb"\dgARROWLENGTH" by the scale factor between
+the coarse and fine grids. For example:
+{\samepage
+\begin{verbatim}
+ \divide\dgARROWLENGTH by2
+ \begin{diagram}
+ \node[2]{A}\arrow[2]{s}\\
+ \node{B}\arrow{e,-} \node{}\arrow{e,t}{\alpha} \node{C}\\
+ \node[2]{D}
+ \end{diagram}
+\end{verbatim}
+\[
+ \divide\dgARROWLENGTH by2
+ \begin{diagram}
+ \node[2]{A}\arrow[2]{s}\\
+ \node{B}\arrow{e,-} \node{}\arrow{e,t}{\alpha} \node{C}\\
+ \node[2]{D}
+ \end{diagram}
+\]
+}
+
+The space set aside for a formula
+further includes padding to keep the arrows from actually touching the
+formulas. The padding increases the apparent horizontal size of
+each formula by \verb"\dgHORIZPAD" and the apparent vertical size
+by \verb"\dgVERTPAD". The default values of these parameters are:
+\begin{verbatim}
+ \dgHORIZPAD=1em
+ \dgVERTPAD=2ex
+\end{verbatim}
+
+The ratio of the horizontal and vertical scales of the grid,
+known as the {\em aspect ratio\/}, cannot be completely
+arbitrary because of the slope limitations of font-based arrows.
+In order that the full required set of compass-point directions be
+available, the optimal calculated aspect ratio will be approximated
+so as to be compatible with the available fonts. In plain
+\LaTeX{} mode the possibile aspect ratios are half-integers up to~2,
+while in {\sc LamS}-\TeX{} mode they are half-integers up to~3.
+
+\verb"\dgLABELOFFSET" is the (approximate) distance which will
+separate labels from their arrows. An arrow is divided into
+\verb"\dgARROWPARTS" parts for custom positioning of labels along the
+arrow (the only sensible choices for this number are 2,4,6,8,10). By
+default,
+\begin{verbatim}
+ \dgLABELOFFSET=.7ex
+ \dgARROWPARTS=4
+\end{verbatim}
+
+The following two parameters regulate the appearance of dotted arrows
+in plain \LaTeX{} mode:
+\begin{verbatim}
+ \dgDOTSPACING=0.35em
+ \dgDOTSIZE=1.5\fontdimen8\tenln
+\end{verbatim}
+
+By default, nodes are typeset \verb"\displaystyle", and labels
+\verb"\scriptstyle". This is controlled by the commands
+\verb"\dgeverynode" (which is executed prior to the formula of each
+node) and \verb"\dgeverylabel" (which is executed prior to the
+formula of each label). They can be changed with
+\verb"\renewcommand", like this:
+\begin{verbatim}
+ \renewcommand{\dgeverynode}{\displaystyle}
+ \renewcommand{\dgeverylabel}{\scriptstyle}
+\end{verbatim}
+These commands may alternatively be defined to take one argument,
+which will be the content of the node or label.
+
+
+\section{Customizing the Package}
+
+The \verb"diagram" environment was designed in a modular way to make
+it easy to add features.
+
+To add a new option to the \verb"\arrow" command---say
+\verb"**"---you need only define a command named \verb"\dgo@**" which
+sets the desired parameters. Let's say you want the \verb"**" option
+to make \verb"\arrow" use a custom arrow design of yours. Since
+\verb"\dg@VECTOR" is the parameter that governs the arrow-drawing
+code, you would say
+\begin{verbatim}
+ \@namedef{dgo@**}{\let\dg@VECTOR=\myamazingvector}
+\end{verbatim}
+where \verb"\myamazingvector" is your custom arrow code (analogous
+to \LaTeX's \verb"\vector" command). Note that if this definition is
+not in a style file, it needs to be bracketed with
+\verb"\makeatletter...\makeatother". You can then use your custom
+arrow style like any other option:
+\begin{verbatim}
+ \arrow{sw,t,**}{\Gamma}
+\end{verbatim}
+
+Adding new arrow direction codes is done by defining commands of the
+form \verb"\dgt@DIRCODE". These commands set \verb"\vector"-like
+parameters to specify the arrow direction (thinking of the arrow as
+laid out on a grid where the basic rectangle is unit wide and one
+unit high). For example:
+\begin{verbatim}
+ \@namedef{dgt@sse}{\dg@DX=1 \dg@DY=-2 \dg@SIZE=1 }
+\end{verbatim}
+
+You can also customize the way the grid geometry is computed by
+redefining the \verb"\dggeometry" command. It must set
+the integer parameters \verb"\dg@XGRID" and \verb"\dg@YGRID" and
+the length parameter \verb"\unitlength". Each grid rectangle
+will then be 1000\verb"\dg@XGRID" by 1000\verb"\dg@YGRID"
+\verb"\unitlength"s in size. The assigned values of
+\verb"\dg@XGRID" and \verb"\dg@YGRID" should be smallish numbers
+(to avoid arithmetic overflow) with \verb"XGRID":\verb"YGRID"
+as the desired aspect ratio. As inputs,
+you should use the pre-supplied values of \verb"\dg@XGRID" and
+\verb"\dg@YGRID", which are the calculated minimum width and
+height that grid rectangles must have, measured in scaled
+points (sp).
+
+In plain \LaTeX{} mode, the aspect ratio must be a half-integer
+between~$\tfrac12$ and~2 (or the inverse of such) in order to
+support the basic 16 compass directions. In {\sc LamS}-\TeX{} mode,
+the aspect ratio need only be a half-integer between~$\tfrac12$
+and~3 in order to support these same basic directions; and when
+the aspect ratio is chosen from these values, almost all the
+arrow directions $(p,q)$ with $\max(|p|,|q|)\le 3$ are supported.
+The exceptions are that arrows of type $(\pm 3,\,\pm 2)$ are
+only rendered approximately in some aspect ratios, and that
+arrows of type $(\pm 3,\,\pm 1)$ are not supported unless
+the aspect ratio is a half-integer between~$\tfrac12$ and~2.
+The \verb"\dggeometry" macro for {\sc LamS}-\TeX{} mode
+{\em automatically\/} detects when it needs to restrict the
+aspect ratio because of a type $(\pm 3,\,\pm 1)$ arrow in
+the diagram.
+
+
+\section{Upgrading Papers from Previous Versions}
+
+Some slightly incompatible changes have been made during
+the evolution of this package.
+
+Beginning with version~3.5, the files and names of the packages
+were reorganized to simplify electronic publication. Here is a
+dictionary to make the translation:
+\begin{center}
+\begin{tabular}{|l|l|} \hline
+ Old Packages & New Packages \\ \hline
+ \tt diagram & \tt pb-diagram \\
+ \tt lamsarrow,diagram & \tt pb-diagram,lamsarrow,pb-lams \\ \hline
+\end{tabular}
+\end{center}
+The order of the packages must be as shown in the table.
+
+Beginning with version~4.0, a bug which caused occasional diagrams
+to come out twice too large was eliminated. If you have an old paper
+which was tuned for the earlier geometry calculation, you can get
+the previous behavior back by including the command
+\verb"\let\dggeometry=\dgoldgeometry" in the document's preamble.
+
+
+\section{Implementation Notes}
+
+All command names defined in the \verb"pb-diagram.sty" style file
+begin with ``\verb"\dg"'', except \verb"\diagram",
+\verb"\enddiagram", \verb"\node", \verb"\arrow",
+\verb"\\", and the \LaTeX{} enhancements \verb"\newoptcommand",
+\verb"\newoptenvironment", \verb"\renewoptcommand", and
+\verb"\renewoptenvironment". All private commands contain an `@' in
+their names. The commands \verb"\node" and \verb"\\" are only defined
+within the \verb"diagram" environment. Spaces following the
+\verb"\end{diagram}" are ignored.
+
+In all the macro files in this package, lines have been limited to
+less than~70 characters to avoid problems with electronic mailing.
+
+
+\section{Copyright and Acknowledgments}
+
+The \verb"pb-diagram" package is
+copyright \copyright\ 1990, 1992, 1995, 1998 by Paul Burchard.
+
+This program 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 program 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 program; if not, write to the Free Software
+Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
+
+The file \verb"pb-xy.sty" is
+copyright \copyright\ 1998 by Bill Richter,
+and is also distributed under the terms of the GNU General Public License.
+
+The fonts \verb"lams1.mf" through \verb"lams5.mf", as well as the
+macros in \verb"lamsarrow.sty", are copyright \copyright\ 1989,
+1990, 1991 by The Texplorators Corporation, 1572 West Gray \#377,
+Houston, TX 77019--4948. Beginning with version 4.1 of this package,
+the fonts include a patch by Ingo Hadan which makes them compatible
+with recent versions of \verb"cmbase.mf", and in particular, eliminating
+a division-by-zero error that caused certain glyphs to appear wildly deformed.
+
+I would like to acknowledge inspiration from a macro package of
+Marc-Paul van der Hulst. Bill Richter was of major help to me with
+his topological torture-testing of this package, and he provided
+some spectacular example diagrams for distribution with this package.
+Dan Christensen made many good suggestions which were incorporated
+into version 4.0.
+
+\end{document}