3 Drawings of semigroups
  
  There  are  some  pictures  that  may  give  a  lot  of  information about a
  semigroup.  This  is  the  case of the egg-box picture of the D-classes, the
  right  Cayley  graph  of  a finite monoid and the Schutzenberger graphs of a
  finite inverse monoid.
  
  
  3.1 Drawing the D-class of an element of a semigroup
  
  3.1-1 DrawDClassOfElement
  
  > DrawDClassOfElement( arg ) _______________________________________function
  
  This  function  takes  as arguments a semigroup followed by a transformation
  which  is  the  element  whose D-class will be drawn. Optionally we can then
  specify  n  lists of elements and the elements of each list will be drawn in
  different  colours. Finally, we may specify a string name the file that will
  be  used to write the drawing of the class (in PostScript format) and if the
  last   argument   is  the  integer  1  then  the  elements  will  appear  as
  transformations,  otherwise  they will appear as words. The idempotents will
  be marked with a * before them.
  
  This  last  optional argument may also be the integer 2 and in this case the
  elements   will   appear   as  integers,  where  i  represents  the  element
  Elements(S)[i].
  
  ---------------------------  Example  ----------------------------
    gap> DrawDClassOfElement(poi3, Transformation([1,4,3,4]));
    gap> DrawDClassOfElement(poi3, Transformation([1,4,3,4]),1);
    gap> DrawDClassOfElement(poi3, Transformation([1,4,3,4]),
     [Transformation( [ 2, 3, 4, 4 ] )],1);
    gap> DrawDClassOfElement(poi3, Transformation([1,4,3,4]),
     [Transformation( [ 2, 3, 4, 4 ] ), Transformation( [ 2, 4, 3, 4 ] )],
     [Transformation( [ 2, 4, 3, 4 ] )],1);
    gap> DrawDClassOfElement(poi3, Transformation([1,4,3,4]), 
     [Transformation( [ 2, 4, 3, 4 ] )],"Dclass",1);
          
  ------------------------------------------------------------------
  
  
  3.2 Drawing the D-classes of a semigroup
  
  3.2-1 DrawDClasses
  
  > DrawDClasses( arg ) ______________________________________________function
  
  This function is similar to the previous one, except that this one draws all
  the  D-classes  of  the semigroup given as the first argument. It then takes
  optionally  n  lists of elements and the elements of each list will be drawn
  in  different  colours.  It also accepts a string specifying the name of the
  file  in which the drawing will be written and the last, optional, argument,
  the  integer  1,  to specify whether the elements will appear as words or as
  transformations  as in the previous function. The idempotents will be marked
  with a * before them.
  
  This  last  optional argument may also be the integer 2 and in this case the
  elements   will   appear   as  integers,  where  i  represents  the  element
  Elements(S)[i].
  
  ---------------------------  Example  ----------------------------
    gap> DrawDClasses(poi3,"DClasses");
    gap> DrawDClasses(poi3, [Transformation( [ 2, 3, 4, 4 ] ),
      Transformation( [ 2, 4, 3, 4 ] )],
      [Transformation( [ 2, 4, 3, 4 ] )],1);
          
  ------------------------------------------------------------------
  
  
  3.3 Cayley graphs
  
  3.3-1 DrawRightCayleyGraph
  
  > DrawRightCayleyGraph( S ) ________________________________________function
  
  Draws the right Cayley graph of a finite monoid or semigroup S.
  
  3.3-2 DrawCayleyGraph
  
  > DrawCayleyGraph( S ) _____________________________________________function
  
  This function is a synonym of DrawRightCayleyGraph (3.3-1).
  
  For  example,  the command DrawCayleyGraph(b21); would produce the following
  image  (where  state  i  represents  the element Elements(S)[i], the neutral
  element  is colored in "light blue" and all other idempotents are colored in
  "light coral"):
  
  
  3.4 Schutzenberger graphs
  
  3.4-1 DrawSchutzenbergerGraphs
  
  > DrawSchutzenbergerGraphs( S ) ____________________________________function
  
  Draws the Schutzenberger graphs of the inverse semigroup S.
  
  For example, DrawSchutzenbergerGraphs(poi3); would produce the following:
  
  
  3.5 Drawings output formats
  
  By  default,  when  a  drawing  is  requested, it is outputted in PostScript
  format.    Since    graphviz    allows    other    output    formats    (see
  http://www.graphviz.org/doc/info/output.html),   it   is  possible  to  also
  request a drawing in a format other than PostScript.
  
  3.5-1 DrawingsListOfExtraFormats
  
  > DrawingsListOfExtraFormats_________________________________global variable
  
  This  is  a  global  variable  which  holds  the  valid output formats for a
  drawing.  It  currently  has  the  value: ["dia", "fig", "gd", "gd2", "gif",
  "hpgl", "jpg", "mif", "mp", "pcl", "pic", "plain", "plain-ext", "png", "ps",
  "ps2",    "svg",    "svgz",    "vrml",    "vtx",    "wbmp",   "none"]   (see
  http://www.graphviz.org/doc/info/output.html for their description).
  
  3.5-2 DrawingsExtraFormat
  
  > DrawingsExtraFormat________________________________________global variable
  
  This  is  a  global variable which holds the alternative output format for a
  drawing. By default its value is "none" which indicates that just PostScript
  will be used as the output format.
  
  If  its  value  becomes  one of those in DrawingsListOfExtraFormats (3.5-1),
  then  besides  the  PostScript  file,  it will also be created a file in the
  alternative format.
  
  To change this variable's value, please use SetDrawingsExtraFormat (3.5-3).
  
  3.5-3 SetDrawingsExtraFormat
  
  > SetDrawingsExtraFormat( f ) ______________________________________function
  
  This function is used to set the value of DrawingsExtraFormat (3.5-2) to the
  format f which is one of DrawingsListOfExtraFormats (3.5-1).
  
  ---------------------------  Example  ----------------------------
    gap> DrawingsExtraFormat;
    "none"
    gap> SetDrawingsExtraFormat("jpg");
    gap> DrawingsExtraFormat;
    "jpg"
    
    gap> DrawRightCayleyGraph(poi3);
    Displaying file: /tmp/tmp.tpJqvI/cayleygraph.dot.ps
    The extra output format file: /tmp/tmp.tpJqvI/cayleygraph.dot.jpg
    has also been created.
    
  ------------------------------------------------------------------
  
  
  3.6 Drawings extra graph attributes
  
  The  functions  described in this subsection are intended to give the user a
  finer  control  over  the  final  drawing.  They  allow  to define the graph
  attributes  described in http://graphviz.org/doc/info/attrs.html. (Note that
  only  graph  attributes  are  allowed  to  be  defined,  not  edge  nor node
  attributes are supported yet.)
  
  3.6-1 DrawingsExtraGraphAttributes
  
  > DrawingsExtraGraphAttributes_______________________________global variable
  
  This  is  a  global  variable  which  holds a list of strings, each of which
  defines  a dot graph attribute. This variable is not intended to be modified
  by  the  user  directly, but can be used to check which extra attributes are
  currently     defined.     To     set    the    attributes,    please    use
  SetDrawingsExtraGraphAttributes   (3.6-2).  If  DrawingsExtraGraphAttributes
  holds  the  value  "none"  then  the  default dot settings will be used. Use
  ClearDrawingsExtraGraphAttributes (3.6-3) to set it to "none".
  
  3.6-2 SetDrawingsExtraGraphAttributes
  
  > SetDrawingsExtraGraphAttributes( L ) _____________________________function
  
  This  is  the  function  to  define  the  drawing's  graph  attributes  (see
  http://graphviz.org/doc/info/attrs.html for a list and explanation of them).
  the  argument  L  is  a  list  of strings, each of which defines a dot graph
  attribute.  For example, if we wanted to define the graph size to be 7x9 (in
  inches), we would call SetDrawingsExtraGraphAttributes(["size=7,9"]);.
  
  If  we  also wanted to define the graph to be displayed in landscape mode we
  would  call SetDrawingsExtraGraphAttributes(["size=7,9", "rotate=90"]);. If,
  in  addition  we  wanted  to define the background color to be, for example,
  pink,    we    would    call    SetDrawingsExtraGraphAttributes(["size=7,9",
  "rotate=90", "bgcolor=pink"]);.
  
  After  defining  the attributes, any command that creates a drawing will use
  the  last  defined  attributes. To set them back to the defaults, please use
  ClearDrawingsExtraGraphAttributes (3.6-3).
  
  ---------------------------  Example  ----------------------------
    gap> DrawingsExtraGraphAttributes;
    "none"
    
    
    gap> SetDrawingsExtraGraphAttributes(["size=7,9"]);
    
    gap> DrawingsExtraGraphAttributes;
    [ "size=7,9" ]
    
    
    gap> SetDrawingsExtraGraphAttributes(["size=7,9", "rotate=90"]);
    
    gap> DrawingsExtraGraphAttributes;
    [ "size=7,9", "rotate=90" ]
    
    
    gap> SetDrawingsExtraGraphAttributes(["size=7,9", "rotate=90", "bgcolor=pink"]);
    
    gap> DrawingsExtraGraphAttributes;
    [ "size=7,9", "rotate=90", "bgcolor=pink" ]
    
    
    gap> ClearDrawingsExtraGraphAttributes();
    
    gap> DrawingsExtraGraphAttributes;
    "none"
  ------------------------------------------------------------------
  
  3.6-3 ClearDrawingsExtraGraphAttributes
  
  > ClearDrawingsExtraGraphAttributes(  ) ____________________________function
  
  This function sets the graph drawing attributes back to dot's defaults.