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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} |