% 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}