%% DC-PiCTeX
%% Copyright (c) 1990-2013 Pedro Quaresma, University of Coimbra, Portugal
%% 11/1990 (version 1.0); 
%%   10/1991 (version 1.1);
%%    9/1993 (version 1.2);  
%%    3/1995 (version 1.3);
%%  7/1996 (version 2.1);
%%  5/2001 (version 3.0); 
%%   11/2001 (version 3.1);
%%    1/2002 (version 3.2)
%%  5/2002 (version 4.0); 
%%    3/2003 (version 4.1); 
%%      12/2004 (version 4.1.1)
%%    3/2007 (version 4.2)
%%       5/2008 (version 4.2.1)
%%    8/2008 (version 4.3)
%%      12/2008 (version 4.3.1)
%%      12/2009 (version 4.3.2)
%%    4/2013 (version 4.4.0) 
%%    5/2013 (version 5.0)

\immediate\write10{Package DCpic 2013/05/01 v5.0}

\ProvidesPackage{dcpic}[2013/05/01 v5.0]

%% Version X.Y.Z
%%   X - major versions
%%   Y - minor versions
%%   Z - bug corrections
%%
%% Copyright (c) 1990-2013 Pedro Quaresma <pedro@mat.uc.pt>
%%
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either version 1.3
% of this license or (at your option) any later version.
% The latest version of this license is in
%   http://www.latex-project.org/lppl.txt
% and version 1.3 or later is part of all distributions of LaTeX
% version 2005/12/01 or later.
%
% This work has the LPPL maintenance status `maintained'.
% 
% The Current Maintainer of this work is Pedro Quaresma (pedro@mat.uc.pt).
%
% This work consists of the files dcpic.sty.
%%
%% Coimbra, 1st of May, 2013 (2013/05/01)
%% Pedro Quaresma
%%
%%  DCpic is a package of \TeX\ macros for graph modelling in a
%%  (La)\TeX\ or Con\TeX t document. Its distinguishing features are:
%%  the use of \PiCTeX\ a powerful graphical engine, and a simple
%%  specification syntax. A graph is described in terms of its objects
%%  and its edges. The objects are textual elements and the edges can
%%  have various straight or curved forms. 
%%
%%
%%  A graph in DCpic is a "picture" in \PiCTeX, in which we place our
%%  {\em objects} and {\em morphisms} (edges). The user's commands in
%%  DCpic are: {\tt begindc} and {\tt enddc} which establishe the
%%  coordinate system where the objects will by placed; {\tt obj}, the
%%  command which defines the place and the contents of each object;
%%  {\tt mor}, and {\tt cmor}, the commands which define the
%%  morphisms, linear and curved edges, and its labels. 
%%
%%  Example:
%%   \begindc{\commdiag}[30]
%%    \obj(10,15){$A$}
%%    \obj(25,15){$B$}
%%    \obj(40,15){$C$}
%%    \mor{$A$}{$B$}{$f$}
%%    \mor{$B$}{$C$}{$g$}
%%    \cmor((10,11)(11,7)(15,6)(25,6)(35,6)(39,7)(40,11))
%%     \pup(25,3){$g\circ f$}
%%   \enddc
%%
%% NOTES: 
%%    all the numeric values should be integer values.
%% 
%% Available commands:
%%
%% The environment:
%%   \begindc{#1}[#2]
%%        #1 - Graph type
%%          0 = "commdiag" (commutative diagram)
%%          1 = "digraph" (direct graph)
%%          2 = "undigraph" (undirect graph)
%%          3 = "cdigraph" with incircled objects
%%          4 = "cundigraph" with incircled objects
%%        (optional) #2 - magnification factor (default value, 300)
%%
%%   \enddc
%%
%% Objects:
%%   \obj(#1,#2)[#3]{#4}[#5]
%%            #1 and #2 - coordenates
%% (optional) #3 - Label, to be used in the morphims command, if not
%%                 present the #4 will be used to that purpose
%%            #4 - Object contents
%% (optional) #5 - placement of the object (default value \north)
%%                   0="\pcent", center
%%                   1="\north", north
%%                   2="\northeast", northeast
%%                   3="\east", east
%%                   4="\southeast", southeast
%%                   5="\south", south
%%                   6="\southwest", southwest
%%                   7="\west", west
%%                   8="\northwest", northwest
%%  !!! Note !!!
%%  if you omit the #3 argument (label) and the #4 argument is a
%%  complex LaTeX command this can cause this command to crash. In
%%  this case you must specify a label (the empty label [], if you do
%%  needed it it for nothing).
%%
%% Morphims (linear edges). This commando has to two major variants
%% i) Starting and Ending objects specification
%%   \mor{#1}{#2}[#5,#6]{#7}[#8,#9]
%%
%% As you can see this first form is (intencionaly) badly formed, the
%% arguments #3 and #4 are missing (the actual command is correctly
%% formed). 
%% 
%%        #1 - The starting object reference
%%        #2 - The ending object reference
%%
%% from this two we will obtain the objects coordinates, and also the
%% dimensions of the enclosing box. 
%%
%% The objects box dimensions are used to do an automatic adjustment of
%% the edge width.
%%
%% from #1 we obtain (x,y), (#1,#2) in the second form
%% from #2 we obtain (x',y'), (#3,#4) in the second form
%%
%% this values will be passed to the command second form
%%
%%ii) Two points coordinates specification
%%   \mor(#1,#2)(#3,#4)[#5,#6]{#7}[#8,#9]
%%
%% Now we can describe all the arguments
%%
%%          #1 and #2 - coordinates (beginning)
%%          #3 and #4 - coordinates (ending)
%%(optional)#5,#6 - correction factors (defaul values, 100 and 100 (10pt))
%%          #5 - actual beginning of the edge 
%%          #6 - actual ending of the edge 
%%          #7 - text (morphism label)
%%(optional)#8,#9
%%          #8 - label placement
%%               1 = "\atright", at right, default value
%%              -1 = "\atleft", at left
%%          #9 - edge type 
%%               0 = "\solidarrow", default edge
%%               1 = "\dashArrow"
%%               2 = "\dotArrow (thanks to Xingliang Liang <jkl9543@gmail.com>)
%%               3 = "\solidline"
%%               4 = "\dashline"
%%               5 = "\dotline"
%%               6 = "\injectionarrow"  
%%               7 = "\aplicationarrow" 
%%               8 = "\surjectivearrow" 
%%               9 = "\equalline" (thanks to Ruben Debeerst <debeerst@mathematik.uni-kassel.de>)
%%              10 = "\doublearrow" 
%%              11 = "\doubleopposite" 
%%              12 = "\nullarrow" (to allow adding labels to existing arrows)
%%
%% Notes: the equalline "arrow" does not provide a second label.
%%
%% Curved Morphisms (quadratic edges):
%%   \cmor(#1) #2(#3,#4){#5}[#6]
%%          #1 - list of points (odd number)
%%          #2 - tip direction
%%              0 = "\pup", pointing up
%%              1 = "\pdown", pointing down
%%              2 = "\pright", pointing right
%%              3 = "\pleft",  pointing left
%%          #3 and #4 - coordenates of the label
%%          #5 - morphism label
%%(optional)#6 - edge type
%%              0 ="\solidarrow", default value
%%              1 = "\dashArrow"
%%              2 = "\solidline"
%%
%% Notes: insert a space after the command.
%%        the space after the list of points is mandatory
%%
%% Examples:
%% \documentclass[a4paper,11pt]{article}
%% \usepackage{dcpic,pictexwd}
%%
%% \begin{document}
%% \begindc[3]
%% \obj(14,11){$A$}
%% \obj(39,11){$B$}
%% \mor(14,12)(39,12){$f$}%[\atright,\solidarrow]
%% \mor(39,10)(14,10){$g$}%[\atright,\solidarrow]
%% \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
%%
%% \begindc{\commdiag}[3]
%% \obj(10,15)[A]{$A$}
%% \obj(40,15)[Aa]{$A$}
%% \obj(25,15)[B]{$B$}
%% \mor{A}{B}{$f$}%[\atright,\solidarrow]
%% \mor{B}{Aa}{$g$}%[\atright,\solidarrow]
%% \cmor((10,11)(11,7)(15,6)(25,6)(35,6)(39,7)(40,11)) 
%%   \pup(25,3){$id_A$}
%% \enddc
%%
%% \newcommand{\barraA}{\vrule height2em width0em depth0em}
%% \newcommand{\barraB}{\vrule height1.6em width0em depth0em}
%% \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{document}
%%-----------------//-------------
%% Modifications (9/1993)
%%       argument "distance" between de tip of the arrow and the objects
%%       became optional; a new option for the "arrows" (option 3)
%%
%% 2/3/1995 (version 1.3) 
%%       adds "the aplication arrow" (option 4); the distance between
%%       the label and the "arrow" is now a fixed value (100 units).
%% 15/7/1996 (version 2.1)
%%       The comand "\mor" has a new sintax. The 5th and 6th
%%       parameters are now the distance between the two objects and
%%       the arrow tips. The 7th parameter is the label. The 8th e 9th
%%       parameters (label position and type of arrow) are now optional
%%
%% 5/2001 (version 3.0)
%%       Implementation of the comand "\cmor" based on the quadratic
%%       curver comand of PiCTeX
%%
%% 11/2001 (version 3.1)
%%       Changes on the tips of the arrow to became more LaTeX style
%%       (after a conversation on EuroTeX 2001).
%%
%% 1/2002  (version 3.2)
%%       Modification of the commands "obj" and "mor" in such a way
%%       that allows the logical specification of the morphisms, that
%%       is, it is now possible to specify the starting object and the
%%       ending object instead of specify the coordinates.
%%
%%       The length of the arrows is automatically trimmed to the
%%       objects' size.
%%
%% 5/2002 (version 4.0)
%%       New syntax for the commands "begindc" e "obj"
%% !!! New syntax !!!
%%       The command "begindc" now have an obligatory argument, this
%%       argument allows the specification of the graph type
%%         "commdiag" (0), commutative diagrams
%%         "digraph" (1), directed graphs
%%         "undigraph" (2), undirected graphs
%%       The command "obj" has a new syntax: after the coordinates
%%       specification, an optional argument specifying a label, an
%%       obligatory argument given the "value" of the object and the
%%       final optional argument used in the graphs to set the
%%       relative position of the "value" to the "dot" defining the
%%       objects position, the default value is "north".
%%
%% 3/2003 (version 4.1)
%%       Responding to a request of Jon Barker <jeb1@soton.ac.uk> I
%%       create a new type of arrow, the surjective arrow.
%%       For now only horizontal and vertical versions, other angles
%%       are poorly rendered.
%% 12/2004 (version 4.1.1)
%%       New version for the surjective arrows, solve the problems
%%       with the first implementation of this option.
%% 3/2007 (version 4.2)
%%       Adds the "providespackage" directive that was missing.
%%       Adds dashed lines, and dotted lines.
%% 5/2008 (version 4.2.1)
%%       Deleting some counters, trying to avoid the problem "running
%%       out of counters", that occurs because of the use of PiCTeX
%%       and DCpic (only two...)
%% 8/2008 (version 4.3)
%%       Thanks to Ruben Debeerst (debeerst@mathematik.uni-kassel.de),
%%       he added a new arrow "equalline". After that I
%%       decided to add: the doublearrow; the doublearrow with
%%       opposite directions; the null arrow. This last can be used as
%%       a simple form of adding new labels.
%%12/2008 (version 4.3.1)
%%       The comand \id is internalised (\!id), it should be that way
%%       from the begining because it is not to be used from the
%%       outside.
%%       The comand \dasharrow was changed to \dashArrow to avoid a
%%       clash with the AMS command with the same name.
%%12/2009 (version 4.3.2)
%%       There is a conflict between dcpic.sty and hyperref in current
%%        texlive-2009 due to the one letter macro \d (thanks Thorsten
%%        S <thorsten.schwander@gmail.com>).
%%        The \d changed to \deuc (Euclidian Distance). The \x and \y
%%        changed to \xO \yO
%% 4/2013 (version 4.4.0)
%%       Thanks to Xingliang Liang <jkl9543@gmail.com>. He added a new
%%       arrow "dotarrow". 
%% 5/2013 (version 5.0)
%%       The base scale of the graph has changed from 1pt to .1pt to
%%       solve a problem with the implementation of the oblique
%%       equalline (Thanks to Antonio de Nicola).
%%       The LaTeX circle and oval commands where replaced by the
%%       PiCTeX circulararc and ellipticalarc commands to avoid
%%       differences in scales.
%%-----------------//-------------

\catcode`!=11 %  ***** THIS MUST NEVER BE OMITTED (See PiCTeX)

\newcount\aux%
\newcount\auxa%
\newcount\auxb%
\newcount\xO%
\newcount\yO%
\newcount\xl%
\newcount\yl%
\newcount\deuc%
\newcount\dnm%
\newcount\xa%
\newcount\xb%
\newcount\xmed%
\newcount\xc%
\newcount\xd%
\newcount\xe
\newcount\xf
\newcount\ya%
\newcount\yb%
\newcount\ymed%
\newcount\yc%
\newcount\yd
\newcount\ye
\newcount\yf
%% "global variables"
\newcount\expansao%
\newcount\tipografo%       version 4.0
\newcount\distanciaobjmor% version 4.0
\newcount\tipoarco%        version 4.0
\newif\ifpara%
%% version 3.2
\newbox\caixa%
\newbox\caixaaux%
\newif\ifnvazia%
\newif\ifvazia%
\newif\ifcompara%
\newif\ifdiferentes%
\newcount\xaux%
\newcount\yaux%
\newcount\guardaauxa%
\newcount\alt%
\newcount\larg%
\newcount\prof%
%% for the triming 
\newcount\auxqx
\newcount\auxqy
\newif\ifajusta%
\newif\ifajustadist
\def\objPartida{}%
\def\objChegada{}%
\def\objNulo{}%

%% 
%% Stack specification
%%

%%
%% Emtpy stack
%%
\def\!vazia{:}

%%
%% Is Empty? : Stack -> Bool
%%
%% nvazia - True if Not Empy
%% vazia  - True if Empty
\def\!pilhanvazia#1{\let\arg=#1%
\if:\arg\ \nvaziafalse\vaziatrue \else \nvaziatrue\vaziafalse\fi}

%%
%% Push : Elems x Stack -> Stack
%%
\def\!coloca#1#2{\edef\pilha{#1.#2}}

%%
%% Top : Stack -> Elems
%%
%% the empty stack is not taken care
%% the element is "kept" ("guardado") 
\def\!guarda(#1)(#2,#3)(#4,#5,#6){\def\!id{#1}%
\xaux=#2%
\yaux=#3%
\alt=#4%
\larg=#5%
\prof=#6%
}

\def\!topaux#1.#2:{\!guarda#1}
\def\!topo#1{\expandafter\!topaux#1}

%%
%% Pop : Stack -> Stack
%%
%% the empty stack is not taken care
\def\!popaux#1.#2:{\def\pilha{#2:}}
\def\!retira#1{\expandafter\!popaux#1}

%%
%% Compares words : Word x Word -> Bool
%%
%% compara - True if equal
%% diferentes - True if not equal
\def\!comparaaux#1#2{\let\argA=#1\let\argB=#2%
\ifx\argA\argB\comparatrue\diferentesfalse\else\comparafalse\diferentestrue\fi}

\def\!compara#1#2{\!comparaaux{#1}{#2}}

%% Private Macro
%% Absolute Value)
%% \absoluto{n}{absn}
%% input
%%  n - integer
%% output
%%  absn - |n|
\def\!absoluto#1#2{\aux=#1%
  \ifnum \aux > 0
    #2=\aux
  \else
    \multiply \aux by -1
    #2=\aux
  \fi}

%% Name definitions for edge types and directions
\def\solidarrow{0}
\def\dashArrow{1}
\def\dotArrow{2}
\def\solidline{3}
\def\dashline{4}
\def\dotline{5}
\def\injectionarrow{6}
\def\aplicationarrow{7}
\def\surjectivearrow{8}
\def\equalline{9}
\def\doublearrow{10}
\def\doubleopposite{11}
\def\nullarrow{12}

%% Name definitions for edge label placement
\def\atright{-1}
\def\atleft{1}
%% Tip direction for curved edges
\def\pup{0}
\def\pdown{1}
\def\pright{2}
\def\pleft{3}
%% Type of graph
\def\commdiag{0}
\def\digraph{1}
\def\undigraph{2}
\def\cdigraph{3}
\def\cundigraph{4}
%% Positioning of labels in graphs
\def\pcent{0}
\def\north{1}
\def\northeast{2}
\def\east{3}
\def\southeast{4}
\def\south{5}
\def\southwest{6}
\def\west{7}
\def\northwest{8}

%%Private Macro 
%% Adjust the distance between the arrows and the objects regarding
%% the dimensions of the objects.
%% 
%% \ajusta{x}{xl}{y}{yl}{d}{Object} (ajusta = adjust)
%%
%% Input
%%  (x,y) e (xl,yl) -  start, end coordinates of arrow
%%  d - distance specified by the user (default value, 100)
%%  Objecto - reference of the object pointed by the arrow 
%% Output
%%  d - adjusted distance
%% 
%% The adjusted distance is the greatest value between 100 and the
%% object's box dimensions. If the user specify a value this is not
%% altered. 
%%
%% If the arrow is horizontal the length is used.
%% If the arrow is vertical the height is used for arrows in the 1st
%% or 2nd quadrante, or the depth if the arrow is in the 3rd or 4th
%% quadrante. If the arrow is oblique the value is chosen accordingly: 
%%  from 315 to  45 degrees length is used
%%  from  45 to 135 degrees height is used
%%  from 135 to 225 degrees length is used
%%  from 225 to 315 degrees depth is used
\def\!ajusta#1#2#3#4#5#6{\aux=#5%
  \let\auxobj=#6%
  \ifcase \tipografo    % commutative diagrams
    \ifnum\number\aux=100 
      \ajustadisttrue % if needed, adjust
    \else
      \ajustadistfalse  % if not, keeps unchanged
    \fi
  \else  % graphs (directed, undirected, with frames)
   \ajustadistfalse
  \fi
  \ifajustadist
   \let\pilhaaux=\pilha%
   \loop%
     \!topo{\pilha}%
     \!retira{\pilha}%
     \!compara{\!id}{\auxobj}%
     \ifcompara\nvaziafalse \else\!pilhanvazia\pilha \fi%
     \ifnvazia%
   \repeat%
%% push the values into the stack
   \let\pilha=\pilhaaux%
   \ifvazia%
    \ifdiferentes%
%%
%% It is not possible to make de adjustment given the fact that the
%% user did not provide a label for the object in question. We set a
%% value equal to the default value (100)
%%
     \larg=131072% these values are for unit of .1pt
     \prof=65536%
     \alt=65536%
    \fi%
   \fi%
   \divide\larg by 13107% these values are for unit of .1pt
   \divide\prof by 6553%
   \divide\alt by 6553%
   \ifnum\number\yO=\number\yl
%% Case 1 -- horizontal arrow
%%
%% with the division by 13107 we get half the size of the box, for a
%% centered text, the adding of 30 is an empirical adjustment.
    \advance\larg by 30
    \ifnum\number\larg>\aux
     #5=\larg
    \fi
   \else
    \ifnum\number\xO=\number\xl
     \ifnum\number\yl>\number\yO
%% Case 2.1 -- vertical arrow, down direction
%%
      \ifnum\number\alt>\aux
       #5=\alt
      \fi
     \else
%% Case 2.2 -- vertical arrow, up direction
%%
%% with the division by 6553 we get the box height. The adjustment
%% of 50 is an empirical adjustment.
      \advance\prof by 50
      \ifnum\number\prof>\aux
       #5=\prof
      \fi
     \fi
    \else
%% Case 3 -- oblique arrow
%% Case 3.1 --- from 315o to 45o; |x-xl|>|y-yl| 
%% Case 3.3 --- from 135o to 225o; |x-xl|>|y-yl|; Length
     \auxqx=\xO
     \advance\auxqx by -\xl
     \!absoluto{\auxqx}{\auxqx}%
     \auxqy=\yO
     \advance\auxqy by -\yl
     \!absoluto{\auxqy}{\auxqy}%
     \ifnum\auxqx>\auxqy
      \ifnum\larg<100
       \larg=100
      \fi
      \advance\larg by 30
      #5=\larg
     \else
%% Case 3.2 --- from  45o to 135o; |x-xl|<|y-yl| e y>0; Length
      \ifnum\yl>\yO
       \ifnum\larg<100
        \larg=100
       \fi
      \advance\alt by 60
       #5=\alt
      \else
%% Case 3.4 -- from 225o to 315o; |x-xl|<|y-yl| e y<0; Depth
      \advance\prof by 110
       #5=\prof
      \fi
     \fi
    \fi
   \fi
\fi} % the branch else is missing

%%Private Macro 
%% Square root 
%% raiz{n}{m} (raiz = root)
%% ->
%%   n - natural number
%% <-
%%   n - natural number
%%   m - greatest natural number less then the square root of n
\def\!raiz#1#2{\auxa=#1%
  \auxb=1%
  \loop
    \aux=\auxb%
    \advance \aux by 1%
    \multiply \aux by \aux%
    \ifnum \aux < \auxa%
      \advance \auxb by 1%
      \paratrue%
    \else\ifnum \aux=\auxa%
      \advance \auxb by 1%
      \paratrue%
       \else\parafalse%
       \fi
    \fi
  \ifpara%
  \repeat
#2=\auxb}

%%Private Macro 
%% Find the starting and ending points of the "arrow" and also the
%% label position (one coordinate at a time)
%% 
%% ucoord{x1}{x2}{x3}{x4}{x5}{x6}{+|- 1}
%% Input
%%   x1,x2,x3,x4,x5
%% Output
%%   x6
%%  
%%              x2 - x1
%%  x6 = x3 +|- ------- x4
%%                 x5
\def\!ucoord#1#2#3#4#5#6#7{\aux=#2%
  \advance \aux by -#1%
  \multiply \aux by #4%
  \divide \aux by #5%
  \ifnum #7 = -1 \multiply \aux by -1 \fi%
  \advance \aux by #3%
#6=\aux}

%%Private Macro
%% Euclidean distance between two points
%%
%% quadrado = square
%% 
%% quadrado{n}{m}{l}
%% Input
%%   n - natural number
%%   m - natural number
%% Output
%%   l = (n-m)*(n-m)
\def\!quadrado#1#2#3{\aux=#1%
  \advance \aux by -#2%
  \multiply \aux by \aux%
#3=\aux}

%%Private Macro
%% Euclidean distance between arrows and its tags
%%
%% Input
%%     (x,y), (x',y') morphism's name (tag)
%% Output
%%     dnm - distance between an arrow and its tags
%%     (with a trim given by the tag's size
%% Observations
%%     The trimming is for horizontal and vertical arrows
%%     only. Oblique arrows are dealt in a different way
%%
%% Algorithm
%%  caixa0 <- morfism name 
%%  if x-xl = 0 then                   {vertical arrow}
%%     aux <- caixa0 width
%%     dnm <- converstion-sp-pt(aux)/2+3
%%  else                               {non-vertical arrow}
%%     if y-yl = 0 then                {horizontal arrow}
%%        aux <- caixa0 height+depth 
%%        dnm <- converstion-sp-pt(aux)/2+3
%%     else                            {oblique arrow}
%%        dnm <- 3
%%     endif
%%  endif
%% endalgorithm
\def\!distnomemor#1#2#3#4#5#6{\setbox0=\hbox{#5}%
  \aux=#1
  \advance \aux by -#3
  \ifnum \aux=0
     \aux=\wd0 \divide \aux by 13107%2
     \advance \aux by 30
     #6=\aux
  \else
     \aux=#2
     \advance \aux by -#4
     \ifnum \aux=0
        \aux=\ht0 \advance \aux by \dp0 \divide \aux by 13107%2
        \advance \aux by 30
        #6=\aux%
     \else
     #6=30
     \fi
   \fi
}

%%
%% The environment "begindc...enddc"
%%
\def\begindc#1{\!ifnextchar[{\!begindc{#1}}{\!begindc{#1}[30]}}
\def\!begindc#1[#2]{\beginpicture 
  \let\pilha=\!vazia
  \setcoordinatesystem units <.1pt,.1pt>
  \expansao=#2
  \ifcase #1
    \distanciaobjmor=100
    \tipoarco=0         % arrow
    \tipografo=0        % commutative diagram
  \or
    \distanciaobjmor=20
    \tipoarco=0         % arrow
    \tipografo=1        % directed graph
  \or
    \distanciaobjmor=10
    \tipoarco=3         % line
    \tipografo=2        % undirected graph
  \or
    \distanciaobjmor=80
    \tipoarco=0         % arrow 
    \tipografo=3        % directed graph
  \or
    \distanciaobjmor=80
    \tipoarco=3         % line
    \tipografo=4        % undirected graph
  \fi}

\def\enddc{\endpicture}

\def\drawarrowhead <#1> [#2,#3]{%
  \!ifnextchar<{\!drawarrowhead{#1}{#2}{#3}}{\!drawarrowhead{#1}{#2}{#3}<\!zpt,\!zpt> }}

% Xingliang Liang <jkl9543@gmail.com>
%  **  \!ljoin (XCOORD,YCOORD)
%  **  Draws a straight line starting at the last point specified
%  **    by the most recent \!start, \!ljoin, or \!qjoin, and
%  **    ending at (XCOORD,YCOORD).
\def\!ljoindummy (#1,#2){%
  \advance\!intervalno by 1
  \!xE=\!M{#1}\!xunit \!yE=\!M{#2}\!yunit
  \!rotateaboutpivot\!xE\!yE
  \!xdiff=\!xE \advance \!xdiff by -\!xS%**  xdiff = xE - xS
  \!ydiff=\!yE \advance \!ydiff by -\!yS%**  ydiff = yE - yS
  \!Pythag\!xdiff\!ydiff\!arclength%     **  arclength = sqrt(xdiff**2+ydiff**2)
  \global\advance \totalarclength by \!arclength%
  %\!drawlinearsegment%   ** set by dashpat to \!linearsolid or \!lineardashed
  \!xS=\!xE \!yS=\!yE%   ** shift ending points to starting points
  \ignorespaces}

%%
%%	\!drawarrowhead{4pt}{DimC}{DimD} <xshift,yshift> from {\xa} {\ya} to {\xb} {\yb}
%%
\def\!drawarrowhead#1#2#3<#4,#5> from #6 #7 to #8 #9 {%
%
% ** convert to dimensions
  \!xloc=\!M{#8}\!xunit
  \!yloc=\!M{#9}\!yunit
  \!dxpos=\!xloc  \!dimenA=\!M{#6}\!xunit  \advance \!dxpos -\!dimenA
  \!dypos=\!yloc  \!dimenA=\!M{#7}\!yunit  \advance \!dypos -\!dimenA
  \let\!MAH=\!M%                         ** save current c/d mode
  \!setdimenmode%                        ** go into dimension mode
%
  \!xshift=#4\relax  \!yshift=#5\relax%  ** pick up shift
  \!reverserotateonly\!xshift\!yshift%   ** back rotate shift
  \advance\!xshift\!xloc  \advance\!yshift\!yloc
%
% **  draw shaft of arrow
  \!xS=-\!dxpos  \advance\!xS\!xshift
  \!yS=-\!dypos  \advance\!yS\!yshift
  \!start (\!xS,\!yS)
  \!ljoindummy (\!xshift,\!yshift)
%
% ** find 32*cosine and 32*sine of angle of rotation
  \!Pythag\!dxpos\!dypos\!arclength
  \!divide\!dxpos\!arclength\!dxpos
  \!dxpos=32\!dxpos  \!removept\!dxpos\!!cos
  \!divide\!dypos\!arclength\!dypos
  \!dypos=32\!dypos  \!removept\!dypos\!!sin
%
% ** construct arrowhead
  \!halfhead{#1}{#2}{#3}%                ** draw half of arrow head
  \!halfhead{#1}{-#2}{-#3}%              ** draw other half
%
  \let\!M=\!MAH%                         ** restore old c/d mode
  \ignorespaces}

%% Public macro: "mor"
%%
%% Funtion to built the "arrow" between two points
%%
%% The points that are uses to built all the elements of the "arrows"
%% are:
%% 
%%                (xc,yc)
%%                   o
%%                   |
%%  o------o---------o---------o------o
%%(x,y) (xa,ya)   (xm,ym)   (xb,yb)(xl,yl)
%%
%% auxa - distance between (x,y) and (xa,ya), 10pt by default
%% auxb - distance between (xl,yl) and (xb,yb), 10pt by default
%%
\def\mor{%
  \!ifnextchar({\!morxy}{\!morObjA}}
\def\!morxy(#1,#2){%
  \!ifnextchar({\!morxyl{#1}{#2}}{\!morObjB{#1}{#2}}}
\def\!morxyl#1#2(#3,#4){%
  \!ifnextchar[{\!mora{#1}{#2}{#3}{#4}}{\!mora{#1}{#2}{#3}{#4}[\number\distanciaobjmor,\number\distanciaobjmor]}}%
\def\!morObjA#1{%
 \let\pilhaaux=\pilha%
 \def\objPartida{#1}%
 \loop%
    \!topo\pilha%
    \!retira\pilha%
    \!compara{\!id}{\objPartida}%
    \ifcompara \nvaziafalse \else \!pilhanvazia\pilha \fi%
   \ifnvazia%
 \repeat%
 \ifvazia%
  \ifdiferentes%
%%
%% error message and ficticious parameters
%%
   Error: Incorrect label specification%
   \xaux=1%
   \yaux=1%
  \fi%
 \fi% 
 \let\pilha=\pilhaaux%
 \!ifnextchar({\!morxyl{\number\xaux}{\number\yaux}}{\!morObjB{\number\xaux}{\number\yaux}}}
\def\!morObjB#1#2#3{%
  \xO=#1
  \yO=#2
 \def\objChegada{#3}%
 \let\pilhaaux=\pilha%
 \loop
    \!topo\pilha %
    \!retira\pilha%
    \!compara{\!id}{\objChegada}%
    \ifcompara \nvaziafalse \else \!pilhanvazia\pilha \fi
   \ifnvazia
 \repeat
 \ifvazia
  \ifdiferentes%
%%
%% error message and ficticious parameters
%%
   Error: Incorrect label specification
   \xaux=\xO%
   \advance\xaux by \xO%
   \yaux=\yO%
   \advance\yaux by \yO%
  \fi
 \fi
 \let\pilha=\pilhaaux
 \!ifnextchar[{\!mora{\number\xO}{\number\yO}{\number\xaux}{\number\yaux}}{\!mora{\number\xO}{\number\yO}{\number\xaux}{\number\yaux}[\number\distanciaobjmor,\number\distanciaobjmor]}}
\def\!mora#1#2#3#4[#5,#6]#7{%
  \!ifnextchar[{\!morb{#1}{#2}{#3}{#4}{#5}{#6}{#7}}{\!morb{#1}{#2}{#3}{#4}{#5}{#6}{#7}[1,\number\tipoarco] }}
\def\!morb#1#2#3#4#5#6#7[#8,#9]{\xO=#1%
  \yO=#2%
  \xl=#3%
  \yl=#4%
  \multiply \xO by \expansao%
  \multiply \yO by \expansao%
  \multiply \xl by \expansao%
  \multiply \yl by \expansao%
%%
%% Euclidean distance between two points
%% d = \sqrt((x-xl)^2+(y-yl)^2)
%%
  \!quadrado{\number\xO}{\number\xl}{\auxa}%
  \!quadrado{\number\yO}{\number\yl}{\auxb}%
  \deuc=\auxa%
  \advance \deuc by \auxb%
  \!raiz{\deuc}{\deuc}%
%%
%% the point (xa,ya) is at a distance #5 (default value 100) from the
%% point (x,y)
%%
%% given the fact that we have two points (start,end) we need to
%% recover their value searching the stack
  \auxa=#5
  \!compara{\objNulo}{\objPartida}%
  \ifdiferentes% adjusting only when needed
   \!ajusta{\xO}{\xl}{\yO}{\yl}{\auxa}{\objPartida}%
   \ajustatrue
   \def\objPartida{}% reset the value of the starting object
  \fi
%% save the value of aux (after adjustment) to be used in the case of
%% an injective morphism
  \guardaauxa=\auxa
%%
  \!ucoord{\number\xO}{\number\xl}{\number\xO}{\auxa}{\number\deuc}{\xa}{1}%
  \!ucoord{\number\yO}{\number\yl}{\number\yO}{\auxa}{\number\deuc}{\ya}{1}%
%% auxa has the value of the distance between the objects minus the
%% distance between the arrow and the objects (100 default value)
  \auxa=\deuc%
%%
%% the point (xb,yb) is at a distance #6 (default value 100) from the
%% point (xl,yl)
%%
  \auxb=#6
  \!compara{\objNulo}{\objChegada}%
  \ifdiferentes% adjusting only when needed
%  adjustment
   \!ajusta{\xO}{\xl}{\yO}{\yl}{\auxb}{\objChegada}%
   \def\objChegada{}% reset the value of the end object
  \fi
  \advance \auxa by -\auxb%
  \!ucoord{\number\xO}{\number\xl}{\number\xO}{\number\auxa}{\number\deuc}{\xb}{1}%
  \!ucoord{\number\yO}{\number\yl}{\number\yO}{\number\auxa}{\number\deuc}{\yb}{1}%
  \xmed=\xa%
  \advance \xmed by \xb%
  \divide \xmed by 2
  \ymed=\ya%
  \advance \ymed by \yb%
  \divide \ymed by 2
%%
%% find the coordinates of the label position: (xc,yc)
%%
%% after this the values of xmed and ymed are no longer important
%%
  \!distnomemor{\number\xO}{\number\yO}{\number\xl}{\number\yl}{#7}{\dnm}%
  \!ucoord{\number\yO}{\number\yl}{\number\xmed}{\number\dnm}{\number\deuc}{\xc}{-#8}% 
  \!ucoord{\number\xO}{\number\xl}{\number\ymed}{\number\dnm}{\number\deuc}{\yc}{#8}%
%% 
%% draw the "arrow"
%%
\ifcase #9            % 0=solid arrow
  \arrow <4pt> [.2,1.1] from {\xa} {\ya} to {\xb} {\yb}
\or                   % 1=dashed arrow
  \setdashes <2pt>
  \plot {\xa} {\ya}  {\xb} {\yb} /
  \setsolid%
  \drawarrowhead <4pt> [.2,1.1] from {\xa} {\ya} to {\xb} {\yb}
\or                   % 2=dotted arrow (Xingliang Liang <jkl9543@gmail.com> - 4.4.0)
  \setdots <2pt>
  \plot {\xa} {\ya}  {\xb} {\yb} /
  \setsolid%
  \drawarrowhead <4pt> [.2,1.1] from {\xa} {\ya} to {\xb} {\yb}
\or                   % 3=solid line
  \setlinear
  \plot {\xa} {\ya}  {\xb} {\yb} /
\or                   % 4=dashed line
  \setdashes <2pt>
  \setlinear
  \plot {\xa} {\ya}  {\xb} {\yb} /
  \setsolid
\or                   % 5=dotted line
  \setdots <2pt>
  \setlinear
  \plot {\xa} {\ya}  {\xb} {\yb} /
  \setsolid
\or                   % 6=injective arrow
%%
%% 30 units, the radius for the tail of the arrow
%%
%% recover the value of auxa
  \auxa=\guardaauxa
%% makes an adjustment to cope with the tail of the arrow, giving
%% space to the semi-circle
  \advance \auxa by 30% 
%%
%% Note: the values of (xa,ya) will be modified, they will be
%% "pushed" further away from (x,y) in order to acomodate the tail
%% of the "arrow"
%%
%% find the point (xd,yd), the center of a 2pt (20*0.1) circle
%%
 \!ucoord{\number\xO}{\number\xl}{\number\xO}{\number\auxa}{\number\deuc}{\xa}{1}%
 \!ucoord{\number\yO}{\number\yl}{\number\yO}{\number\auxa}{\number\deuc}{\ya}{1}%
 \!ucoord{\number\yO}{\number\yl}{\number\xa}{20}{\number\deuc}{\xd}{-1}%
 \!ucoord{\number\xO}{\number\xl}{\number\ya}{20}{\number\deuc}{\yd}{1}%
%% building the "arrow"
  \arrow <4pt> [.2,1.1] from {\xa} {\ya} to {\xb} {\yb}
%% and its "tail"
  \circulararc -180 degrees from {\xa} {\ya} center at {\xd} {\yd}
\or                   % 7=maps "arrow" ("|-->")
  \auxa=20 %
%%
%% Note: the values of xmed and ymed will be modified
%% 
%% find the two points that defines the tail of the arrow (segment
%% (xmed,ymed)(xd,yd))
 \!ucoord{\number\yO}{\number\yl}{\number\xa}{\number\auxa}{\number\deuc}{\xmed}{-1}%
 \!ucoord{\number\xO}{\number\xl}{\number\ya}{\number\auxa}{\number\deuc}{\ymed}{1}%
 \!ucoord{\number\yO}{\number\yl}{\number\xa}{\number\auxa}{\number\deuc}{\xd}{1}%
 \!ucoord{\number\xO}{\number\xl}{\number\ya}{\number\auxa}{\number\deuc}{\yd}{-1}%
%% building the "arrow"
  \arrow <4pt> [.2,1.1] from {\xa} {\ya} to {\xb} {\yb}
%% and its "tail"
  \setlinear
  \plot {\xmed} {\ymed}  {\xd} {\yd} /
\or                   % 8=surjective arrow ("-->>")
%% building arrow with the first tip
  \arrow <4pt> [.2,1.1] from {\xa} {\ya} to {\xb} {\yb}
%% and the second tip
  \setlinear
  \arrow <6pt> [0,.72] from {\xa} {\ya} to {\xb} {\yb}
\or                   % 9=equalline
%% by Ruben Debeerst: equal-line
%%
%% sets the separation (distance) between the two parallel lines, if
%% horizontal or vertical 1pt (10*0.1) is enough, if not 1.1pt (11*0.1)
\auxa=11
\ifnum\number\yO=\number\yl
\auxa=10
\fi
\ifnum\number\xO=\number\xl
\auxa=10
\fi
%% the two parallel lines will be given by (xmed,ymed)(xd,yd), and
%% (xe,ye)(xf,yf)
  \!ucoord{\number\yO}{\number\yl}{\number\xa}{\number\auxa}{\number\deuc}{\xmed}{-1}%
  \!ucoord{\number\xO}{\number\xl}{\number\ya}{\number\auxa}{\number\deuc}{\ymed}{1}%
  \!ucoord{\number\yO}{\number\yl}{\number\xa}{\number\auxa}{\number\deuc}{\xd}{1}%
  \!ucoord{\number\xO}{\number\xl}{\number\ya}{\number\auxa}{\number\deuc}{\yd}{-1}%
  
  \!ucoord{\number\yO}{\number\yl}{\number\xb}{\number\auxa}{\number\deuc}{\xe}{-1}%
  \!ucoord{\number\xO}{\number\xl}{\number\yb}{\number\auxa}{\number\deuc}{\ye}{1}%
  \!ucoord{\number\yO}{\number\yl}{\number\xb}{\number\auxa}{\number\deuc}{\xf}{1}%
  \!ucoord{\number\xO}{\number\xl}{\number\yb}{\number\auxa}{\number\deuc}{\yf}{-1}%
  \setlinear
  \plot {\xmed} {\ymed}  {\xe} {\ye} /
  \plot {\xd} {\yd}  {\xf} {\yf} /
\or                   % 10=double arrow
%%
%% sets the separation (distance) between the two parallel lines, if
%% horizontal or vertical 2pt is enough, if not 2.5pt. The extra space
%% is needed because of the arrow tip.
\auxa=25
\ifnum\number\yO=\number\yl
\auxa=20
\fi
\ifnum\number\xO=\number\xl
\auxa=20
\fi
%% the two parallel lines will be given by (xmed,ymed)(xd,yd), and
%% (xe,ye)(xf,yf)
  \!ucoord{\number\yO}{\number\yl}{\number\xa}{\number\auxa}{\number\deuc}{\xmed}{-1}%
  \!ucoord{\number\xO}{\number\xl}{\number\ya}{\number\auxa}{\number\deuc}{\ymed}{1}%
  \!ucoord{\number\yO}{\number\yl}{\number\xa}{\number\auxa}{\number\deuc}{\xd}{1}%
  \!ucoord{\number\xO}{\number\xl}{\number\ya}{\number\auxa}{\number\deuc}{\yd}{-1}%
  
  \!ucoord{\number\yO}{\number\yl}{\number\xb}{\number\auxa}{\number\deuc}{\xe}{-1}%
  \!ucoord{\number\xO}{\number\xl}{\number\yb}{\number\auxa}{\number\deuc}{\ye}{1}%
  \!ucoord{\number\yO}{\number\yl}{\number\xb}{\number\auxa}{\number\deuc}{\xf}{1}%
  \!ucoord{\number\xO}{\number\xl}{\number\yb}{\number\auxa}{\number\deuc}{\yf}{-1}%
  \arrow <4pt> [.2,1.1] from {\xmed} {\ymed} to {\xe} {\ye}
  \arrow <4pt> [.2,1.1] from {\xd} {\yd} to {\xf} {\yf}
\or                   % 10=double arrow, opposite directions
%% 
%% sets the separation (distance) between the two parallel lines, if
%% horizontal or vertical 2pt is enough, if not 2.5pt. The extra space
%% is needed because of the arrow tip.
\auxa=22
\ifnum\number\yO=\number\yl
\auxa=20
\fi
\ifnum\number\xO=\number\xl
\auxa=20
\fi
%% the two parallel lines will be given by (xmed,ymed)(xd,yd), and
%% (xe,ye)(xf,yf)
  \!ucoord{\number\yO}{\number\yl}{\number\xa}{\number\auxa}{\number\deuc}{\xmed}{-1}%
  \!ucoord{\number\xO}{\number\xl}{\number\ya}{\number\auxa}{\number\deuc}{\ymed}{1}%
  \!ucoord{\number\yO}{\number\yl}{\number\xa}{\number\auxa}{\number\deuc}{\xd}{1}%
  \!ucoord{\number\xO}{\number\xl}{\number\ya}{\number\auxa}{\number\deuc}{\yd}{-1}%
  
  \!ucoord{\number\yO}{\number\yl}{\number\xb}{\number\auxa}{\number\deuc}{\xe}{-1}%
  \!ucoord{\number\xO}{\number\xl}{\number\yb}{\number\auxa}{\number\deuc}{\ye}{1}%
  \!ucoord{\number\yO}{\number\yl}{\number\xb}{\number\auxa}{\number\deuc}{\xf}{1}%
  \!ucoord{\number\xO}{\number\xl}{\number\yb}{\number\auxa}{\number\deuc}{\yf}{-1}%
  \arrow <4pt> [.2,1.1] from {\xmed} {\ymed} to {\xe} {\ye}
  \arrow <4pt> [.2,1.1] from {\xf} {\yf} to {\xd} {\yd}
\or                   % 11=null arrow (no arrow, only a label)
%%
%% does not draw the arrow, it allows to put two labels in one "arrow"
%%
\fi
%% The label positioning.
%% If the arrows are horizontal or verticals the box is built centered
%% in the object center. If the arrows are oblique the box is built in
%% such a way to avoid the arrow label, having in account the
%% quadrante and the relative position of the arrow and the
%% corresponding label
\auxa=\xl
\advance \auxa by -\xO%
\ifnum \auxa=0 
  \put {#7} at {\xc} {\yc}
\else
  \auxb=\yl
  \advance \auxb by -\yO%
  \ifnum \auxb=0 \put {#7} at {\xc} {\yc}
  \else 
    \ifnum \auxa > 0 
      \ifnum \auxb > 0
        \ifnum #8=1
          \put {#7} [rb] at {\xc} {\yc}
        \else 
          \put {#7} [lt] at {\xc} {\yc}
        \fi
      \else
        \ifnum #8=1
          \put {#7} [lb] at {\xc} {\yc}
        \else 
          \put {#7} [rt] at {\xc} {\yc}
        \fi
      \fi
    \else
      \ifnum \auxb > 0 
        \ifnum #8=1
          \put {#7} [rt] at {\xc} {\yc}
        \else 
          \put {#7} [lb] at {\xc} {\yc}
        \fi
      \else
        \ifnum #8=1
          \put {#7} [lt] at {\xc} {\yc}
        \else 
          \put {#7} [rb] at {\xc} {\yc}
        \fi
      \fi
    \fi
  \fi
\fi
}

%%
%% Curved arrow command
%%
%% \cmor(<list of points (n. odd)>){<label>}
%%
%% The plot must be changed in such a way that its syntax is coherent
%% with the other commands
%%
\def\modifplot(#1{\!modifqcurve #1}
\def\!modifqcurve(#1,#2){\xO=#1%
  \yO=#2%
  \multiply \xO by \expansao%
  \multiply \yO by \expansao%
  \!start (\xO,\yO)
  \!modifQjoin}
\def\!modifQjoin(#1,#2)(#3,#4){\xO=#1%
  \yO=#2%
  \xl=#3%
  \yl=#4%
  \multiply \xO by \expansao%
  \multiply \yO by \expansao%
  \multiply \xl by \expansao%
  \multiply \yl by \expansao%
  \!qjoin (\xO,\yO) (\xl,\yl)       % \!qjoin  is defined in QUADRATIC
  \!ifnextchar){\!fim}{\!modifQjoin}}
\def\!fim){\ignorespaces}

%%
%% The command to draw the arrow tip receives the list of points, get
%% from it the last pair of points and depending of the user choice
%% the arrow tip is drawn.
%%
\def\setaxy(#1{\!pontosxy #1}
\def\!pontosxy(#1,#2){%
  \!maispontosxy}
\def\!maispontosxy(#1,#2)(#3,#4){%
  \!ifnextchar){\!fimxy#3,#4}{\!maispontosxy}}
\def\!fimxy#1,#2){\xO=#1%
  \yO=#2
  \multiply \xO by \expansao
  \multiply \yO by \expansao
  \xl=\xO%
  \yl=\yO%
  \aux=1%
  \multiply \aux by \auxa%
  \advance\xl by \aux%
  \aux=1%
  \multiply \aux by \auxb%
  \advance\yl by \aux%
  \arrow <4pt> [.2,1.1] from {\xO} {\yO} to {\xl} {\yl}}


%%
%% The definition of the command "cmor"
%%
\def\cmor#1 #2(#3,#4)#5{%
  \!ifnextchar[{\!cmora{#1}{#2}{#3}{#4}{#5}}{\!cmora{#1}{#2}{#3}{#4}{#5}[0] }}
\def\!cmora#1#2#3#4#5[#6]{%
  \ifcase #2% "\pup" (pointing up)
      \auxa=0% x do not change
      \auxb=1% y "up" 
    \or% \pdown" (pointing down)
      \auxa=0% x do not change
      \auxb=-1% y "down" 
    \or%  "\pright" (pointing right)
      \auxa=1% x "right"
      \auxb=0% y do not change
    \or% "\pleft" (pointing left)
      \auxa=-1% x "left"
      \auxb=0% y do not change
    \fi  % the line
  \ifcase #6  % arrow solid
    \modifplot#1% draw the line
    % and the arrow tip
    \setaxy#1
  \or  % arrow (with tip) dashed
    \setdashes
    \modifplot#1% draw the line
    \setaxy#1
    \setsolid
  \or  % arrow (without tip)
    \modifplot#1% draw the line
  \fi  % injection morphism
%% label
  \xO=#3%  
  \yO=#4%
  \multiply \xO by \expansao%
  \multiply \yO by \expansao%
  \put {#5} at {\xO} {\yO}}

%%
%% Command to build the objects
%%  \obj(x,y){<text>}[<label>]
%% 
\def\obj(#1,#2){%
  \!ifnextchar[{\!obja{#1}{#2}}{\!obja{#1}{#2}[Nulo]}}
\def\!obja#1#2[#3]#4{%
  \!ifnextchar[{\!objb{#1}{#2}{#3}{#4}}{\!objb{#1}{#2}{#3}{#4}[1]}}
\def\!objb#1#2#3#4[#5]{%
  \xO=#1%
  \yO=#2%
  \def\!pinta{\normalsize$\bullet$}% sets the normal size of the bullet
  \def\!nulo{Nulo}%
  \def\!arg{#3}%
  \!compara{\!arg}{\!nulo}%
  \ifcompara\def\!arg{#4}\fi%
  \multiply \xO by \expansao%
  \multiply \yO by \expansao%
  \setbox\caixa=\hbox{#4}%
  \!coloca{(\!arg)(#1,#2)(\number\ht\caixa,\number\wd\caixa,\number\dp\caixa)}{\pilha}%
  \auxa=\wd\caixa \divide \auxa by 13107%2 
  \advance \auxa by 50
  \auxb=\ht\caixa
  \advance \auxb by \number\dp\caixa
  \divide \auxb by 13107%2 
  \advance \auxb by 50
  \ifcase \tipografo    % commutative diagrams
    \put{#4} at {\xO} {\yO}
  \or                   % directed graphs
    \ifcase #5 % c=0, placement of the object (c=center)
      \put{#4} at {\xO} {\yO}
    \or        % n=1
      \put{\!pinta} at {\xO} {\yO}
      \advance \yO by \number\auxb  % height+depth+5
      \put{#4} at {\xO} {\yO}
    \or        % ne=2
      \put{\!pinta} at {\xO} {\yO}
      \advance \auxa by -2  % para fazer o ajuste (imperfeito)
      \advance \auxb by -2  % ao raio da circunferencia de centro (x,y)
      \advance \xO by \number\auxa  % width+5
      \advance \yO by \number\auxb  % height+depth+5
      \put{#4} at {\xO} {\yO}   
    \or        % e=3
      \put{\!pinta} at {\xO} {\yO}
      \advance \xO by \number\auxa  % width+5
      \put{#4} at {\xO} {\yO}   
    \or        % se=4
      \put{\!pinta} at {\xO} {\yO}
      \advance \auxa by -2  % para fazer o ajuste (imperfeito)
      \advance \auxb by -2  % ao raio da circunferencia de centro (x,y)
      \advance \xO by \number\auxa  % width+5
      \advance \yO by -\number\auxb  % height+depth+5
      \put{#4} at {\xO} {\yO}   
    \or        % s=5
      \put{\!pinta} at {\xO} {\yO}
      \advance \yO by -\number\auxb  % height+depth+5
      \put{#4} at {\xO} {\yO}   
    \or        % sw=6
      \put{\!pinta} at {\xO} {\yO}
      \advance \auxa by -20  % adjusting to the radius of the circle
      \advance \auxb by -20  % with center in (x,y)
      \advance \xO by -\number\auxa  % width+5
      \advance \yO by -\number\auxb  % height+depth+5
      \put{#4} at {\xO} {\yO}   
    \or        % w=7
      \put{\!pinta} at {\xO} {\yO}
      \advance \xO by -\number\auxa  % width+5
      \put{#4} at {\xO} {\yO}   
    \or        % nw=8
      \put{\!pinta} at {\xO} {\yO}
      \advance \auxa by -20  % adjusting to the radius of the circle
      \advance \auxb by -20  % with center in (x,y)
      \advance \xO by -\number\auxa  % width+5
      \advance \yO by \number\auxb  % height+depth+5
      \put{#4} at {\xO} {\yO}   
    \fi
  \or                   % undirect graphs
    \ifcase #5 % c=0
      \put{#4} at {\xO} {\yO}
    \or        % n=1
      \put{\!pinta} at {\xO} {\yO}
      \advance \yO by \number\auxb  % height+depth+5
      \put{#4} at {\xO} {\yO}
    \or        % ne=2
      \put{\!pinta} at {\xO} {\yO}
      \advance \auxa by -20  % adjusting to the radius of the circle
      \advance \auxb by -20  % with center in (x,y)
      \advance \xO by \number\auxa  % width+5
      \advance \yO by \number\auxb  % height+depth+5
      \put{#4} at {\xO} {\yO}   
    \or        % e=3
      \put{\!pinta} at {\xO} {\yO}
      \advance \xO by \number\auxa  % width+5
      \put{#4} at {\xO} {\yO}   
    \or        % se=4
      \put{\!pinta} at {\xO} {\yO}
      \advance \auxa by -20  % see above
      \advance \auxb by -20
      \advance \xO by \number\auxa  % width+5
      \advance \yO by -\number\auxb % height+depth+5
      \put{#4} at {\xO} {\yO}   
    \or        % s=5
      \put{\!pinta} at {\xO} {\yO}
      \advance \yO by -\number\auxb % height+depth+5
      \put{#4} at {\xO} {\yO}   
    \or        % sw=6
      \put{\!pinta} at {\xO} {\yO}
      \advance \auxa by -20  % see above
      \advance \auxb by -20
      \advance \xO by -\number\auxa % width+5
      \advance \yO by -\number\auxb % height+depth+5
      \put{#4} at {\xO} {\yO}   
    \or        % w=7
      \put{\!pinta} at {\xO} {\yO}
      \advance \xO by -\number\auxa % width+5
      \put{#4} at {\xO} {\yO}   
    \or        % nw=8
      \put{\!pinta} at {\xO} {\yO}
      \advance \auxa by -20  % see above
      \advance \auxb by -20
      \advance \xO by -\number\auxa % width+5
      \advance \yO by \number\auxb  % height+depth+5
      \put{#4} at {\xO} {\yO}   
    \fi
   \else % graphs with circular frames
     \ifnum\auxa<\auxb % set aux to be the greatest dimension
       \aux=\auxb
     \else
       \aux=\auxa
     \fi
% if the length of the box is less then 1em, the size of the circle is
% adjust in order not to be less then 10pt
     \ifdim\wd\caixa<1em
       \dimen99 = 10pt
       \aux=\dimen99 
       \divide \aux by 13107
       \advance \aux by 50
     \fi    
     \advance\aux by -20
     \xl=\xO
     \advance\xl by \aux
     \ifnum\aux<120 % gives (more or less) three digits
       \circulararc 360 degrees from {\xl} {\yO} center at {\xO} {\yO}
     \else
       \ellipticalarc axes ratio {\auxa}:{\auxb} 360 degrees from  {\xl} {\yO} center at {\xO} {\yO}
     \fi
     \put{#4} at {\xO} {\yO}
   \fi   
}


\catcode`!=12 %  *****  THIS MUST NEVER BE OMITTED (see PiCTeX)