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authorNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
committerNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
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tree60335e10d2f4354b0674ec22d7b53f0f8abee672 /macros/latex/contrib/pb-diagram/pb-examples.tex
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+% 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}