\documentclass[a4paper]{article} \usepackage{pictexwd,dcpic} \voffset=-2cm \hoffset=-1cm \addtolength{\textwidth}{2cm} \addtolength{\textheight}{4cm} \newcommand{\barraA}{\vrule height2em width0em depth0em} \newcommand{\barraB}{\vrule height1.6em width0em depth0em} \begin{document} \begin{center} DCpic - Examples \end{center} \paragraph{Commutative Diagrams --- Curved arrows.} A rectangular curve with rounded corners is easy to specify and should cater for most needs. With this in mind we give the following tip to the user: to specify a rectangular, with rounded corners, curve we choose the points which give us the {\em expanded chess-horse movement}, that is, $(x,y)$, $(x\pm4,y\mp1)$, $(x\mp1,y\pm4)$, or $(x,y)$,$(x\pm1,y\mp4)$, $(x\mp4,y\pm1)$, those sets of points will give us the four corners of the rectangle; to form the whole line it is only necessary to add an odd number of points joining the two (or more) corners. {\footnotesize \begin{verbatim} \begindc{\commdiag}[2] \cmor((10,20)(6,21)(5,25)) \pup(5,15){$x$} \enddc \end{verbatim} } $$ \begindc{\commdiag}[3] \cmor((10,20)(6,21)(5,25)) \pup(5,15){$x$} \enddc $$ {\footnotesize \begin{verbatim} \begindc{\commdiag}[3] \obj(10,15){$A$} \obj(40,15)[Al]{$A$} \obj(25,15){$B$} \mor{$A$}{$B$}{$f$} \mor{$B$}{Al}{$g$} \cmor((10,11)(11,7)(15,6)(25,6)(35,6)(39,7)(40,11)) \pup(25,3){$id_A$} \enddc \end{verbatim} } $$ \begindc{\commdiag}[3] \obj(10,15){$A$} \obj(40,15)[Al]{$A$} \obj(25,15){$B$} \mor{$A$}{$B$}{$f$} \mor{$B$}{Al}{$g$} \cmor((10,11)(11,7)(15,6)(25,6)(35,6)(39,7)(40,11)) \pup(25,3){$id_A$} \enddc $$ {\footnotesize \begin{verbatim} \begindc{\commdiag}[3] \obj(14,11){$A$} \obj(39,11){$B$} \mor(14,12)(39,12){$f$} \mor(39,10)(14,10){$g$} \cmor((10,10)(6,11)(5,15)(6,19)(10,20)(14,19)(15,15)) \pdown(2,20){$id_A$} \cmor((40,7)(41,3)(45,2)(49,3)(50,7)(49,11)(45,12)) \pleft(54,3){$id_B$} \enddc \end{verbatim} } $$ \begindc{\commdiag}[3] \obj(14,11){$A$} \obj(39,11){$B$} \mor(14,12)(39,12){$f$} \mor(39,10)(14,10){$g$} \cmor((10,10)(6,11)(5,15)(6,19)(10,20)(14,19)(15,15)) \pdown(2,20){$id_A$} \cmor((40,7)(41,3)(45,2)(49,3)(50,7)(49,11)(45,12)) \pleft(54,3){$id_B$} \enddc $$ {\footnotesize \begin{verbatim} \begindc{\commdiag}[3] \obj(10,18){$A$} \obj(40,18){$B$} \cmor((10,20)(15,25)(20,20)(25,15)(30,20)(35,25)(40,20)) \pdown(25,12){$f$}[2] \cmor((10,15)(15,10)(20,15)(25,20)(30,15)(35,10)(40,15)) \pup(25,22){$g$}[2] \enddc \end{verbatim} } $$ \begindc{\commdiag}[3] \obj(10,18){$A$} \obj(40,18){$B$} \cmor((10,20)(15,25)(20,20)(25,15)(30,20)(35,25)(40,20)) \pdown(25,12){$f$}[2] \cmor((10,15)(15,10)(20,15)(25,20)(30,15)(35,10)(40,15)) \pup(25,22){$g$}[2] \enddc $$ \vfill \pagebreak \paragraph{Commutative Diagrams --- Size Adjusting.} With the new version (v4.0) two new features are introduced, relative specification {\tt $\backslash$mor\{objA\}\{objB\}} instead of {\tt $\backslash$mor(1,3)(4,5)}, and the arrows now automatically adjust their size to the object's box size. {\scriptsize \begin{verbatim} \begindc{\commdiag} \obj(1,3)[objSum]{$\displaystyle \sum_{k=2}^n \left\lfloor\frac{\phi(k)}{k-1}\right\rfloor}$} \obj(4,5)[objB]{$B$} \obj(4,3)[objA]{$A$} \obj(4,1)[objBp]{$B$} \mor{objSum}{objB}{$f$} \mor{objB}{objA}{$g$} \mor{objSum}{objA}{$f\circ g$}[\atright,\solidarrow] \mor{objSum}{objBp}{$f$}[\atright,\solidarrow] \mor{objA}{objBp}{$g$}[\atright,\solidarrow] \enddc \end{verbatim} } $$ \begindc{\commdiag} \obj(1,3)[objSum]{$\displaystyle \sum_{k=2}^n \left\lfloor\frac{\phi(k)}{k-1}\right\rfloor$} \obj(4,5)[objB]{$B$} \obj(4,3)[objA]{$A$} \obj(4,1)[objBp]{$B$} \mor{objSum}{objB}{$f$} \mor{objB}{objA}{$g$} \mor{objSum}{objA}{$f\circ g$}[\atright,\solidarrow] \mor{objSum}{objBp}{$f$}[\atright,\solidarrow] \mor{objA}{objBp}{$g$}[\atright,\solidarrow] \enddc $$ {\scriptsize \begin{verbatim} \begindc{\commdiag} \obj(10,10)[A]{$OOOOOO$}\obj(15,10)[Aa]{$XXXX$}\obj(14,11)[Ab]{$XXXX$} \obj(13,12)[Ac]{$XXXX$}\obj(12,13)[Ad]{$XXXX$}\obj(11,14)[Ae]{$XXXX$} \obj(10,15)[Af]{$XXXX$}\obj(9,14)[Ag]{$BBBB$}\obj(8,13)[Ah]{$XXXX$} \obj(7,12)[Ai]{$XXXX$}\obj(6,11)[Aj]{$XXXX$}\obj(5,10)[Ak]{$XXXX$} \obj(6,9)[Al]{$XXXX$}\obj(7,8)[Am]{$XXXX$}\obj(8,7)[An]{$BBBB$} \obj(9,6)[Ao]{$CCCC$}\obj(10,5)[Ap]{$DDDD$}\obj(11,6)[Aq]{$EEEE$} \obj(12,7)[Ar]{$EEEE$}\obj(13,8)[As]{$EEEE$}\obj(14,9)[At]{$EEEE$} \mor{A}{Aa}{$a1$}\mor{A}{Ab}{$a2$}\mor{A}{Ac}{$a3$}\mor{A}{Ad}{$a4$} \mor{A}{Ae}{$a5$}\mor{A}{Af}{$a6$}\mor{A}{Ag}{$a7$}\mor{A}{Ah}{$a8$} \mor{A}{Ai}{$a9$}\mor{A}{Aj}{$a10$}\mor{A}{Ak}{$a11$}\mor{A}{Al}{$a12$} \mor{A}{Am}{$a13$}\mor{A}{An}{$a14$}\mor{A}{Ao}{$a15$}\mor{A}{Ap}{$a16$} \mor{A}{Aq}{$a17$}\mor{A}{Ar}{$a18$}\mor{A}{As}{$a19$}\mor{A}{At}{$a20$} \enddc \end{verbatim} } $$ \begindc{\commdiag}[29] \obj(10,10)[A]{$OOOOOO$}\obj(15,10)[Aa]{$XXXX$}\obj(14,11)[Ab]{$XXXX$} \obj(13,12)[Ac]{$XXXX$}\obj(12,13)[Ad]{$XXXX$}\obj(11,14)[Ae]{$XXXX$} \obj(10,15)[Af]{$XXXX$}\obj(9,14)[Ag]{$BBBB$}\obj(8,13)[Ah]{$XXXX$} \obj(7,12)[Ai]{$XXXX$}\obj(6,11)[Aj]{$XXXX$}\obj(5,10)[Ak]{$XXXX$} \obj(6,9)[Al]{$XXXX$}\obj(7,8)[Am]{$XXXX$}\obj(8,7)[An]{$BBBB$} \obj(9,6)[Ao]{$CCCC$}\obj(10,5)[Ap]{$DDDD$}\obj(11,6)[Aq]{$EEEE$} \obj(12,7)[Ar]{$EEEE$}\obj(13,8)[As]{$EEEE$}\obj(14,9)[At]{$EEEE$} \mor{A}{Aa}{$a1$}\mor{A}{Ab}{$a2$}\mor{A}{Ac}{$a3$}\mor{A}{Ad}{$a4$} \mor{A}{Ae}{$a5$}\mor{A}{Af}{$a6$}\mor{A}{Ag}{$a7$}\mor{A}{Ah}{$a8$} \mor{A}{Ai}{$a9$}\mor{A}{Aj}{$a10$}\mor{A}{Ak}{$a11$}\mor{A}{Al}{$a12$} \mor{A}{Am}{$a13$}\mor{A}{An}{$a14$}\mor{A}{Ao}{$a15$}\mor{A}{Ap}{$a16$} \mor{A}{Aq}{$a17$}\mor{A}{Ar}{$a18$}\mor{A}{As}{$a19$}\mor{A}{At}{$a20$} \enddc $$ \vfill \pagebreak \paragraph{Commutative Diagrams --- A Complex Diagram} {\scriptsize \begin{verbatim} \begindc{\commdiag}[35] \obj(1,1)[Gr]{$G$} \obj(3,1)[Grstar]{$G_{r^*}$} \obj(5,1)[H]{$H$} \obj(2,2)[SigmaG]{$\Sigma^G$} \obj(6,2)[SigmaH]{$\Sigma^H$} \obj(1,3)[Lm]{$L_m$} \obj(3,3)[Krm]{$K_{r,m}$} \obj(5,3)[Rmstar]{$R_{m^*}$} \obj(1,5)[L]{$L$} \obj(3,5)[Lr]{$L_r$} \obj(5,5)[R]{$R$} \obj(2,6)[SigmaL]{$\Sigma^L$} \obj(6,6)[SigmaR]{$\Sigma^R$} \mor{Gr}{SigmaG}{$\lambda^G$} \mor{Grstar}{Gr}{$i_5$}[\atleft,\aplicationarrow] \mor{Grstar}{H}{$r^*$}[\atright,\solidarrow] \mor{H}{SigmaH}{$\lambda^H$}[\atright,\dashArrow] \mor{SigmaG}{SigmaH}{$\varphi^{r^*}$}[\atright,\solidarrow] \mor{Lm}{Gr}{$m$}[\atright,\solidarrow] \mor{Lm}{L}{$i_2$}[\atleft,\aplicationarrow] \mor{Krm}{Lm}{$i_3\quad$}[\atright,\aplicationarrow] \mor{Krm}{Rmstar}{$r$} \mor{Krm}{Lr}{$i_4$}[\atright,\aplicationarrow] \mor{Krm}{Grstar}{$m$} \mor{Rmstar}{R}{$i_6$}[\atright,\aplicationarrow] \mor{Rmstar}{H}{$m^*$} \mor{L}{SigmaL}{$\lambda^L$} \mor{Lr}{L}{$i_1\quad$}[\atright,\aplicationarrow] \mor{Lr}{R}{$r$} \mor{R}{SigmaR}{$\lambda^R$}[\atright,\solidarrow] \mor{SigmaL}{SigmaG}{$\varphi^m$}[\atright,\solidarrow] \mor{SigmaL}{SigmaR}{$\varphi^r$} \mor{SigmaR}{SigmaH}{$\varphi^{m^*}$} \enddc \end{verbatim} } $$ \begindc{\commdiag}[35] \obj(1,1)[Gr]{$G$} \obj(3,1)[Grstar]{$G_{r^*}$} \obj(5,1)[H]{$H$} \obj(2,2)[SigmaG]{$\Sigma^G$} \obj(6,2)[SigmaH]{$\Sigma^H$} \obj(1,3)[Lm]{$L_m$} \obj(3,3)[Krm]{$K_{r,m}$} \obj(5,3)[Rmstar]{$R_{m^*}$} \obj(1,5)[L]{$L$} \obj(3,5)[Lr]{$L_r$} \obj(5,5)[R]{$R$} \obj(2,6)[SigmaL]{$\Sigma^L$} \obj(6,6)[SigmaR]{$\Sigma^R$} \mor{Gr}{SigmaG}{$\lambda^G$} \mor{Grstar}{Gr}{$i_5$}[\atleft,\aplicationarrow] \mor{Grstar}{H}{$r^*$}[\atright,\solidarrow] \mor{H}{SigmaH}{$\lambda^H$}[\atright,\dashArrow] \mor{SigmaG}{SigmaH}{$\varphi^{r^*}$}[\atright,\solidarrow] \mor{Lm}{Gr}{$m$}[\atright,\solidarrow] \mor{Lm}{L}{$i_2$}[\atleft,\aplicationarrow] \mor{Krm}{Lm}{$i_3\quad$}[\atright,\aplicationarrow] \mor{Krm}{Rmstar}{$r$} \mor{Krm}{Lr}{$i_4$}[\atright,\aplicationarrow] \mor{Krm}{Grstar}{$m$} \mor{Rmstar}{R}{$i_6$}[\atright,\aplicationarrow] \mor{Rmstar}{H}{$m^*$} \mor{L}{SigmaL}{$\lambda^L$} \mor{Lr}{L}{$i_1\quad$}[\atright,\aplicationarrow] \mor{Lr}{R}{$r$} \mor{R}{SigmaR}{$\lambda^R$}[\atright,\solidarrow] \mor{SigmaL}{SigmaG}{$\varphi^m$}[\atright,\solidarrow] \mor{SigmaL}{SigmaR}{$\varphi^r$} \mor{SigmaR}{SigmaH}{$\varphi^{m^*}$} \enddc $$ \vfill \pagebreak \vfill \pagebreak {\scriptsize \begin{verbatim} \begindc{\commdiag}[4] \obj(10,10){$G$}[Gr] \obj(30,10){$G_{r^*}$}[Grstar] \obj(50,10){$H$}[H] \obj(20,20){$\Sigma^G$}[SigmaG] \obj(60,20){$\Sigma^H$}[SigmaH] \obj(10,30){$L_m$}[Lm] \obj(30,30){$K_{r,m}$}[Krm] \obj(50,30){$R_{m^*}$}[Rmstar] \obj(10,50){$L$}[L] \obj(30,50){$L_r$}[Lr] \obj(50,50){$R$}[R] \obj(20,60){$\Sigma^L$}[SigmaL] \obj(60,60){$\Sigma^R$}[SigmaR] \mor{Gr}{SigmaG}{$\lambda^G$} \mor{Grstar}{Gr}{$i_5$}[\atleft,\aplicationarrow] \mor{Grstar}{H}{$r^*$}[\atright,\solidarrow] \mor{H}{SigmaH}{$\lambda^H$}[\atright,\dashArrow] \mor{SigmaG}{SigmaH}{$\varphi^{r^*}$}[\atright,\solidarrow] \mor{Lm}{Gr}{$m$}[\atright,\solidarrow] \mor{Lm}{L}{$i_2$}[\atleft,\aplicationarrow] \mor{Krm}{Lm}{$i_3\quad$}[\atright,\aplicationarrow] \mor{Krm}{Rmstar}{$r$} \mor{Krm}{Lr}{$i_4$}[\atright,\aplicationarrow] \mor{Krm}{Grstar}{$m$} \mor{Rmstar}{R}{$i_6$}[\atright,\aplicationarrow] \mor{Rmstar}{H}{$m^*$} \mor{L}{SigmaL}{$\lambda^L$} \mor{Lr}{L}{$i_1\quad$}[\atright,\aplicationarrow] \mor{Lr}{R}{$r$} \mor{R}{SigmaR}{$\lambda^R$}[\atright,\solidarrow] \mor{SigmaL}{SigmaG}{$\varphi^m$}[\atright,\solidarrow] \mor{SigmaL}{SigmaR}{$\varphi^r$} \mor{SigmaR}{SigmaH}{$\varphi^{m^*}$} \cmor((10,7)(11,3)(15,2)(40,2)(65,2)(69,3)(70,7)(70,10)(70,14)(69,18)(65,19)) \pleft(75,10){$\varphi^{r^*}\lambda^G$} \cmor((10,53)(10,58)(10,63)(11,67)(15,68)(45,68)(65,68)(69,67)(70,63)(70,44)(70,25)(69,21)(65,20)) \pleft(76,40){$\varphi^{m^*}\varphi^r\lambda^L$} \enddc \end{verbatim} } $$ \begindc{\commdiag}[4] \obj(10,10)[Gr]{$G$} \obj(30,10)[Grstar]{$G_{r^*}$} \obj(50,10)[H]{$H$} \obj(20,20)[SigmaG]{$\Sigma^G$} \obj(60,20)[SigmaH]{$\Sigma^H$} \obj(10,30)[Lm]{$L_m$} \obj(30,30)[Krm]{$K_{r,m}$} \obj(50,30)[Rmstar]{$R_{m^*}$} \obj(10,50)[L]{$L$} \obj(30,50)[Lr]{$L_r$} \obj(50,50)[R]{$R$} \obj(20,60)[SigmaL]{$\Sigma^L$} \obj(60,60)[SigmaR]{$\Sigma^R$} \mor{Gr}{SigmaG}{$\lambda^G$} \mor{Grstar}{Gr}{$i_5$}[\atleft,\aplicationarrow] \mor{Grstar}{H}{$r^*$}[\atright,\solidarrow] \mor{H}{SigmaH}{$\lambda^H$}[\atright,\dashArrow] \mor{SigmaG}{SigmaH}{$\varphi^{r^*}$}[\atright,\solidarrow] \mor{Lm}{Gr}{$m$}[\atright,\solidarrow] \mor{Lm}{L}{$i_2$}[\atleft,\aplicationarrow] \mor{Krm}{Lm}{$i_3\quad$}[\atright,\aplicationarrow] \mor{Krm}{Rmstar}{$r$} \mor{Krm}{Lr}{$i_4$}[\atright,\aplicationarrow] \mor{Krm}{Grstar}{$m$} \mor{Rmstar}{R}{$i_6$}[\atright,\aplicationarrow] \mor{Rmstar}{H}{$m^*$} \mor{L}{SigmaL}{$\lambda^L$} \mor{Lr}{L}{$i_1\quad$}[\atright,\aplicationarrow] \mor{Lr}{R}{$r$} \mor{R}{SigmaR}{$\lambda^R$}[\atright,\solidarrow] \mor{SigmaL}{SigmaG}{$\varphi^m$}[\atright,\solidarrow] \mor{SigmaL}{SigmaR}{$\varphi^r$} \mor{SigmaR}{SigmaH}{$\varphi^{m^*}$} \cmor((10,7)(11,3)(15,2)(40,2)(65,2)(69,3)(70,7)(70,10)(70,14)(69,18)(65,19)) \pleft(75,10){$\varphi^{r^*}\lambda^G$} \cmor((10,53)(10,58)(10,63)(11,67)(15,68)(45,68)(65,68)(69,67)(70,63)(70,44)(70,25)(69,21)(65,20)) \pleft(76,40){$\varphi^{m^*}\varphi^r\lambda^L$} \enddc $$ \vfill \pagebreak {\scriptsize \begin{verbatim} \begindc{\commdiag}[4] \obj(10,10)[Gr]{$G$} \obj(30,10)[Grstar]{$G_{r^*}$} \obj(50,10)[H]{$H$} \obj(20,20)[SigmaG]{$\Sigma^G$} \obj(60,20)[SigmaH]{$\Sigma^H$} \obj(10,30)[Lm]{$L_m$} \obj(30,30)[Krm]{$K_{r,m}$} \obj(50,30)[Rmstar]{$R_{m^*}$} \obj(10,50)[L]{$L$} \obj(30,50)[Lr]{$L_r$} \obj(50,50)[R]{$R$} \obj(20,60)[SigmaL]{$\Sigma^L$} \obj(60,60)[SigmaR]{$\Sigma^R$} \mor{Gr}{SigmaG}{$\lambda^G$} \mor{Grstar}{Gr}{$i_5$}[\atleft,\aplicationarrow] \mor{Grstar}{H}{$r^*$}[\atright,\solidarrow] \mor{H}{SigmaH}{$\lambda^H$}[\atright,\dashArrow] \mor{SigmaG}{SigmaH}{$\varphi^{r^*}$}[\atright,\solidarrow] \mor{Lm}{Gr}{$m$}[\atright,\solidarrow] \mor{Lm}{L}{$i_2$}[\atleft,\aplicationarrow] \mor{Krm}{Lm}{$i_3\quad$}[\atright,\aplicationarrow] \mor{Krm}{Rmstar}{$r$} \mor{Krm}{Lr}{$i_4$}[\atright,\aplicationarrow] \mor{Krm}{Grstar}{$m$} \mor{Rmstar}{R}{$i_6$}[\atright,\aplicationarrow] \mor{Rmstar}{H}{$m^*$} \mor{L}{SigmaL}{$\lambda^L$} \mor{Lr}{L}{$i_1\quad$}[\atright,\aplicationarrow] \mor{Lr}{R}{$r$} \mor{R}{SigmaR}{$\lambda^R$}[\atright,\solidarrow] \mor{SigmaL}{SigmaG}{$\varphi^m$}[\atright,\solidarrow] \mor{SigmaL}{SigmaR}{$\varphi^r$} \mor{SigmaR}{SigmaH}{$\varphi^{m^*}$} \cmor((10,7)(11,3)(15,2)(33,2)(53,2)(56,3)(61,8)(66,13)(69,16)(69,18)(65,19)) \pleft(75,10){$\varphi^{r^*}\lambda^G$} \cmor((10,53)(10,54)(10,55)(11,59)(15,64)(19,67)(23,68)(44,68)(65,68)(69,67)(70,63)(70,44)(70,25)(69,21)(65,20)) \pleft(76,40){$\varphi^{m^*}\varphi^r\lambda^L$} \enddc \end{verbatim} } $$ \begindc{\commdiag}[4] \obj(10,10)[Gr]{$G$} \obj(30,10)[Grstar]{$G_{r^*}$} \obj(50,10)[H]{$H$} \obj(20,20)[SigmaG]{$\Sigma^G$} \obj(60,20)[SigmaH]{$\Sigma^H$} \obj(10,30)[Lm]{$L_m$} \obj(30,30)[Krm]{$K_{r,m}$} \obj(50,30)[Rmstar]{$R_{m^*}$} \obj(10,50)[L]{$L$} \obj(30,50)[Lr]{$L_r$} \obj(50,50)[R]{$R$} \obj(20,60)[SigmaL]{$\Sigma^L$} \obj(60,60)[SigmaR]{$\Sigma^R$} \mor{Gr}{SigmaG}{$\lambda^G$} \mor{Grstar}{Gr}{$i_5$}[\atleft,\aplicationarrow] \mor{Grstar}{H}{$r^*$}[\atright,\solidarrow] \mor{H}{SigmaH}{$\lambda^H$}[\atright,\dashArrow] \mor{SigmaG}{SigmaH}{$\varphi^{r^*}$}[\atright,\solidarrow] \mor{Lm}{Gr}{$m$}[\atright,\solidarrow] \mor{Lm}{L}{$i_2$}[\atleft,\aplicationarrow] \mor{Krm}{Lm}{$i_3\quad$}[\atright,\aplicationarrow] \mor{Krm}{Rmstar}{$r$} \mor{Krm}{Lr}{$i_4$}[\atright,\aplicationarrow] \mor{Krm}{Grstar}{$m$} \mor{Rmstar}{R}{$i_6$}[\atright,\aplicationarrow] \mor{Rmstar}{H}{$m^*$} \mor{L}{SigmaL}{$\lambda^L$} \mor{Lr}{L}{$i_1\quad$}[\atright,\aplicationarrow] \mor{Lr}{R}{$r$} \mor{R}{SigmaR}{$\lambda^R$}[\atright,\solidarrow] \mor{SigmaL}{SigmaG}{$\varphi^m$}[\atright,\solidarrow] \mor{SigmaL}{SigmaR}{$\varphi^r$} \mor{SigmaR}{SigmaH}{$\varphi^{m^*}$} \cmor((10,7)(11,3)(15,2)(33,2)(53,2)(56,3)(61,8)(66,13)(69,16)(69,18)(65,19)) \pleft(75,10){$\varphi^{r^*}\lambda^G$} \cmor((10,53)(10,54)(10,55)(11,59)(15,64)(19,67)(23,68)(44,68)(65,68)(69,67)(70,63)(70,44)(70,25)(69,21)(65,20)) \pleft(76,40){$\varphi^{m^*}\varphi^r\lambda^L$} \enddc $$ \vfill \pagebreak \paragraph{Undirected Graphs --- Magnification factor,} the magnification factor gives us the capability of adapting the size of the graph to the available space, without having to redesign the graph, for example the specification of the next two graphs differs only in the magnification factor: 20 for the first; and 16 for the second. \begin{center} \begin{tabular}{cc} \begindc{\undigraph}[20] \obj(1,1)[1]{} \obj(3,2)[2]{} \obj(5,1)[3]{} \obj(3,4)[4]{} \mor{1}{2}{} \mor{1}{3}{} \mor{2}{3}{} \mor{4}{1}{} \mor{4}{3}{} \mor{2}{4}{} \enddc &\qquad \begindc{\undigraph}[16] \obj(1,1)[1]{} \obj(3,2)[2]{} \obj(5,1)[3]{} \obj(3,4)[4]{} \mor{1}{2}{} \mor{1}{3}{} \mor{2}{3}{} \mor{4}{1}{} \mor{4}{3}{} \mor{2}{4}{} \enddc \end{tabular} \end{center} {\scriptsize \begin{verbatim} \begindc{\undigraph}[20] \begindc{\undigraph}[16] \obj(1,1)[1]{} \obj(1,1)[1]{} \obj(3,2)[2]{} \obj(3,2)[2]{} \obj(5,1)[3]{} \obj(5,1)[3]{} \obj(3,4)[4]{} \obj(3,4)[4]{} \mor{1}{2}{} \mor{1}{2}{} \mor{1}{3}{} \mor{1}{3}{} \mor{2}{3}{} \mor{2}{3}{} \mor{4}{1}{} \mor{4}{1}{} \mor{4}{3}{} \mor{4}{3}{} \mor{2}{4}{} \mor{2}{4}{} \enddc \enddc \end{verbatim}} \paragraph{Undirected Graphs --- ``Around the World''} $$ \begindc{\undigraph}[7] \obj(6,4){18}[\south] \obj(18,4){17}[\south] \obj(8,7){11}[\west] \obj(12,8){12}[\south] \obj(16,7){13}[\east] \obj(8,11){10}[\west] \obj(10,12){6}[\northwest] \obj(12,10){5} \obj(14,12){4}[\northeast] \obj(16,11){14}[\east] \obj(2,16){19} \obj(6,15){9} \obj(9,16){8} \obj(11,14){7} \obj(13,14){3} \obj(15,16){2} \obj(18,15){15} \obj(22,16){16} \obj(12,19){1}[\northeast] \obj(12,22){20} \mor{18}{17}{}\mor{18}{11}{}\mor{18}{19}{} \mor{11}{12}{}\mor{11}{10}{}\mor{12}{13}{} \mor{12}{5}{}\mor{10}{6}{}\mor{10}{9}{} \mor{5}{6}{}\mor{5}{4}{}\mor{13}{17}{} \mor{13}{14}{}\mor{9}{19}{}\mor{9}{8}{} \mor{6}{7}{}\mor{4}{3}{}\mor{4}{14}{} \mor{19}{20}{}\mor{8}{1}{}\mor{8}{7}{} \mor{7}{3}{}\mor{3}{2}{}\mor{2}{1}{} \mor{2}{15}{}\mor{14}{15}{}\mor{17}{16}{} \mor{16}{20}{}\mor{1}{20}{}\mor{15}{16}{} \enddc $$ {\scriptsize \begin{verbatim} \begindc{\undigraph}[7] \obj(6,4){18}[\south] \obj(18,4){17}[\south] \obj(8,7){11}[\west] \obj(12,8){12}[\south] \obj(16,7){13}[\east] \obj(8,11){10}[\west] \obj(10,12){6}[\northwest] \obj(12,10){5} \obj(14,12){4}[\northeast] \obj(16,11){14}[\east] \obj(2,16){19} \obj(6,15){9} \obj(9,16){8} \obj(11,14){7} \obj(13,14){3} \obj(15,16){2} \obj(18,15){15} \obj(22,16){16} \obj(12,19){1}[\northeast] \obj(12,22){20} \mor{18}{17}{}\mor{18}{11}{}\mor{18}{19}{} \mor{11}{12}{}\mor{11}{10}{}\mor{12}{13}{} \mor{12}{5}{}\mor{10}{6}{}\mor{10}{9}{} \mor{5}{6}{}\mor{5}{4}{}\mor{13}{17}{} \mor{13}{14}{}\mor{9}{19}{}\mor{9}{8}{} \mor{6}{7}{}\mor{4}{3}{}\mor{4}{14}{} \mor{19}{20}{}\mor{8}{1}{}\mor{8}{7}{} \mor{7}{3}{}\mor{3}{2}{}\mor{2}{1}{} \mor{2}{15}{}\mor{14}{15}{}\mor{17}{16}{} \mor{16}{20}{}\mor{1}{20}{}\mor{15}{16}{} \enddc \end{verbatim}} \vfill \pagebreak \paragraph{Directed Graphs} $$ \begindc{\digraph}[25] \obj(1,5){A}[\west] \obj(1,3){B}[\west] \obj(1,1){C}[\west] \obj(5,5){E}[\east] \obj(5,3){F}[\east] \obj(5,1){G}[\east] \mor{A}{E}{5} \mor{A}{F}{3} \mor{B}{F}{6}[\atright,\solidarrow] \mor{C}{E}{1} \mor{C}{F}{5} \mor{C}{G}{7} \enddc $$ {\scriptsize \begin{verbatim} \begindc{\digraph}[25] \obj(1,5){A}[\west] \obj(1,3){B}[\west] \obj(1,1){C}[\west] \obj(5,5){E}[\east] \obj(5,3){F}[\east] \obj(5,1){G}[\east] \mor{A}{E}{5} \mor{A}{F}{3} \mor{B}{F}{6}[\atright,\solidarrow] \mor{C}{E}{1} \mor{C}{F}{5} \mor{C}{G}{7} \enddc \end{verbatim} } \paragraph{Circled Directed Graphs} $$ \begindc{\cdigraph}[20] \obj(6,6){18}[1] \obj(12,6){17}[1] \mor{18}{17}{} \enddc $$ {\scriptsize \begin{verbatim} \begindc{\cdigraph}[20] \obj(6,6){18}[1] \obj(12,6){17}[1] \mor{18}{17}{} \enddc \end{verbatim} } \paragraph{Circled Undirected Graphs} Some fine adjustment is nedeeded in some lines. $$\small \begindc{\cundigraph}[11] \obj(6,4){18}[\south]\obj(18,4){17}[\south] \obj(8,7){11}[\west]\obj(12,8){12}[\south] \obj(16,7){13}[\east]\obj(8,11){10}[\west] \obj(10,12)[6]{6}[\south]\obj(12,10)[5]{5}[\east] \obj(14,12){4}[\northeast]\obj(16,11){14}[\east] \obj(2,16){19}[\west]\obj(6,15){9} \obj(9,16){8}\obj(11,14){7}[\west] \obj(13,14){3}\obj(15,16){2} \obj(18,15){15}\obj(22,16){16}[\east] \obj(12,19){1}[\west]\obj(12,22){20}[\north] \mor{18}{17}[7,7]{}\mor{18}{11}{}\mor{18}{19}{}\mor{11}{12}{} \mor{11}{10}{}\mor{12}{13}{}\mor{12}{5}{}\mor{10}{6}{} \mor{10}{9}{}\mor{5}{6}{}\mor{5}{4}{}\mor{13}{17}[8,6]{} \mor{13}{14}{}\mor{9}{19}{}\mor{9}{8}{}\mor{6}{7}{} \mor{4}{3}{}\mor{4}{14}{}\mor{19}{20}{}\mor{8}{1}{} \mor{8}{7}{}\mor{7}{3}{}\mor{3}{2}{}\mor{2}{1}{} \mor{2}{15}{}\mor{14}{15}{}\mor{17}{16}{}\mor{16}{20}{} \mor{1}{20}{}\mor{15}{16}{} \enddc $$ {\scriptsize \begin{verbatim} \begindc{\cundigraph}[13] \obj(6,4){18}[\south]\obj(18,4){17}[\south] \obj(8,7){11}[\west]\obj(12,8){12}[\south] \obj(16,7){13}[\east]\obj(8,11){10}[\west] \obj(10,12)[6]{6}[\south]\obj(12,10)[5]{5}[\east] \obj(14,12){4}[\northeast]\obj(16,11){14}[\east] \obj(2,16){19}[\west]\obj(6,15){9} \obj(9,16){8}\obj(11,14){7}[\west] \obj(13,14){3}\obj(15,16){2} \obj(18,15){15}\obj(22,16){16}[\east] \obj(12,19){1}[\west]\obj(12,22){20}[\north] \mor{18}{17}[7,7]{}\mor{18}{11}{}\mor{18}{19}{}\mor{11}{12}{} \mor{11}{10}{}\mor{12}{13}{}\mor{12}{5}{}\mor{10}{6}{} \mor{10}{9}{}\mor{5}{6}{}\mor{5}{4}{}\mor{13}{17}[8,6]{} \mor{13}{14}{}\mor{9}{19}{}\mor{9}{8}{}\mor{6}{7}{} \mor{4}{3}{}\mor{4}{14}{}\mor{19}{20}{}\mor{8}{1}{} \mor{8}{7}{}\mor{7}{3}{}\mor{3}{2}{}\mor{2}{1}{} \mor{2}{15}{}\mor{14}{15}{}\mor{17}{16}{}\mor{16}{20}{} \mor{1}{20}{}\mor{15}{16}{} \enddc \end{verbatim} } \paragraph{New arrows and Lines in v4.1} \paragraph{Surjective arrow} $$ \begindc{\commdiag}[3] \obj(10,15){$A$} \obj(40,15)[Al]{$A$} \obj(25,15){$B$} \obj(40,5){$A^\prime$} \mor{$A$}{$B$}{$f$}[\atleft,\surjectivearrow] \mor{$B$}{Al}{$g$}[\atleft,\surjectivearrow] \mor{$B$}{$A^\prime$}{$g^\prime$}[\atright,\surjectivearrow] \enddc $$ \paragraph{Dashed and Dotted lines} $$ \begindc{\commdiag}[3] \obj(10,20){$A$} \obj(40,30)[Al]{$A$} \obj(25,30){$B$} \obj(40,40){$A^\prime$} \obj(40,10)[Ald]{$A$} \obj(25,10)[Bd]{$B$} \obj(40,0)[Apd]{$A^\prime$} \mor{$A$}{$B$}{}[\atleft,\dashline] \mor{$B$}{Al}{}[\atleft,\dashline] \mor{$B$}{$A^\prime$}{}[\atright,\dashline] \mor{$A$}{Bd}{}[\atleft,\dotline] \mor{Bd}{Ald}{}[\atleft,\dotline] \mor{Bd}{Apd}{}[\atright,\dotline] \enddc $$ \end{document} %%% Local Variables: %%% mode: latex %%% TeX-master: t %%% End: