  
  [1X3 [33X[0;0YDrawings of semigroups[133X[101X
  
  [33X[0;0YThere  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 Schützenberger graphs of a
  finite inverse monoid.[133X
  
  
  [1X3.1 [33X[0;0YDrawing the D-class of an element of a semigroup[133X[101X
  
  [1X3.1-1 DrawDClassOfElement[101X
  
  [29X[2XDrawDClassOfElement[102X( [3Xarg[103X ) [32X function
  
  [33X[0;0YThis  function  uses [2XDotForDrawingDClassOfElement[102X ([14X3.1-2[114X) to compute the dot
  code  to  produce  the image that is then displayed. It 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, if the
  last   argument   is  the  integer  [10X1[110X  then  the  elements  will  appear  as
  transformations,  otherwise  they will appear as words. The idempotents will
  be marked with a * before them.[133X
  
  [33X[0;0YThis  last  optional argument may also be the integer [10X2[110X and in this case the
  elements   will   appear   as  integers,  where  [10Xi[110X  represents  the  element
  [10XElements(S)[i][110X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XDrawDClassOfElement(poi3, Transformation([1,4,3,4]));[127X[104X
    [4X[25Xgap>[125X [27XDrawDClassOfElement(poi3, Transformation([1,4,3,4]),1);[127X[104X
    [4X[25Xgap>[125X [27XDrawDClassOfElement(poi3, Transformation([1,4,3,4]),[127X[104X
    [4X[28X [Transformation( [ 2, 3, 4, 4 ] )],1);[128X[104X
    [4X[25Xgap>[125X [27XDrawDClassOfElement(poi3, Transformation([1,4,3,4]),[127X[104X
    [4X[28X [Transformation( [ 2, 3, 4, 4 ] ), Transformation( [ 2, 4, 3, 4 ] )],[128X[104X
    [4X[28X [Transformation( [ 2, 4, 3, 4 ] )],1);[128X[104X
    [4X[25Xgap>[125X [27XDrawDClassOfElement(poi3, Transformation([1,4,3,4]), [127X[104X
    [4X[28X [Transformation( [ 2, 4, 3, 4 ] )],"Dclass",1);[128X[104X
    [4X[28X      [128X[104X
  [4X[32X[104X
  
  [33X[0;0YThis  is  the  image  produced by the first command in the previous example:
  This  is  the  image produced by the fourth command in the previous example:
  This is the image produced by the last command in the previous example:[133X
  
  [1X3.1-2 DotForDrawingDClassOfElement[101X
  
  [29X[2XDotForDrawingDClassOfElement[102X( [3Xarg[103X ) [32X function
  
  [33X[0;0YThis  function  computes  the dot code that can be used to produce a drawing
  for  the D-class of an element of a semigroup. This can be done by using the
  function  [2XDrawDClassOfElement[102X ([14X3.1-1[114X) (if the system is properly configured)
  or  by  the  user in some independent way. The arguments and options are the
  same than those of [2XDrawDClassOfElement[102X ([14X3.1-1[114X).[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X      gap> DotForDrawingDClassOfElement(poi3,Transformation([1,4,3,4]));[128X[104X
    [4X[28X"digraph  DClassOfElement {\ngraph [center=yes,ordering=out];\nnode [shape=pla\[128X[104X
    [4X[28Xintext];\nedge [color=cornflowerblue,arrowhead=none];\n1 [label=<\n<TABLE BORD\[128X[104X
    [4X[28XER=\"0\" CELLBORDER=\"0\" CELLPADDING=\"0\" CELLSPACING=\"0\" PORT=\"1\">\n<TR\[128X[104X
    [4X[28X><TD BORDER=\"0\"><TABLE CELLSPACING=\"0\"><TR><TD BGCOLOR=\"white\" BORDER=\"\[128X[104X
    [4X[28X0\">*abc</TD></TR>\n</TABLE></TD><TD BORDER=\"0\"><TABLE CELLSPACING=\"0\"><TR\[128X[104X
    [4X[28X><TD BGCOLOR=\"white\" BORDER=\"0\">a</TD></TR>\n</TABLE></TD><TD BORDER=\"0\"\[128X[104X
    [4X[28X><TABLE CELLSPACING=\"0\"><TR><TD BGCOLOR=\"white\" BORDER=\"0\">ab</TD></TR>\[128X[104X
    [4X[28X\n</TABLE></TD></TR>\n<TR><TD BORDER=\"0\"><TABLE CELLSPACING=\"0\"><TR><TD BG\[128X[104X
    [4X[28XCOLOR=\"white\" BORDER=\"0\">bc</TD></TR>\n</TABLE></TD><TD BORDER=\"0\"><TABL\[128X[104X
    [4X[28XE CELLSPACING=\"0\"><TR><TD BGCOLOR=\"white\" BORDER=\"0\">*bca</TD></TR>\n</T\[128X[104X
    [4X[28XABLE></TD><TD BORDER=\"0\"><TABLE CELLSPACING=\"0\"><TR><TD BGCOLOR=\"white\" \[128X[104X
    [4X[28XBORDER=\"0\">b</TD></TR>\n</TABLE></TD></TR>\n<TR><TD BORDER=\"0\"><TABLE CELL\[128X[104X
    [4X[28XSPACING=\"0\"><TR><TD BGCOLOR=\"white\" BORDER=\"0\">c</TD></TR>\n</TABLE></TD\[128X[104X
    [4X[28X><TD BORDER=\"0\"><TABLE CELLSPACING=\"0\"><TR><TD BGCOLOR=\"white\" BORDER=\"\[128X[104X
    [4X[28X0\">ca</TD></TR>\n</TABLE></TD><TD BORDER=\"0\"><TABLE CELLSPACING=\"0\"><TR><\[128X[104X
    [4X[28XTD BGCOLOR=\"white\" BORDER=\"0\">*cab</TD></TR>\n</TABLE></TD></TR>\n</TABLE>\[128X[104X
    [4X[28X>];\n}\n"[128X[104X
    [4X[28X      [128X[104X
  [4X[32X[104X
  
  [33X[0;0YBy  using  Print  (or PrinTo, if one wants to print to a file) the string is
  displayed as follows:[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XPrint(last);[127X[104X
    [4X[28Xdigraph  DClassOfElement {[128X[104X
    [4X[28Xgraph [center=yes,ordering=out];[128X[104X
    [4X[28Xnode [shape=plaintext];[128X[104X
    [4X[28Xedge [color=cornflowerblue,arrowhead=none];[128X[104X
    [4X[28X1 [label=<[128X[104X
    [4X[28X<TABLE BORDER="0" CELLBORDER="0" CELLPADDING="0" CELLSPACING="0" PORT="1">[128X[104X
    [4X[28X<TR><TD BORDER="0"><TABLE CELLSPACING="0"><TR><TD BGCOLOR="white" BORDER="0">*\[128X[104X
    [4X[28Xabc</TD></TR>[128X[104X
    [4X[28X</TABLE></TD><TD BORDER="0"><TABLE CELLSPACING="0"><TR><TD BGCOLOR="white" BOR\[128X[104X
    [4X[28XDER="0">a</TD></TR>[128X[104X
    [4X[28X</TABLE></TD><TD BORDER="0"><TABLE CELLSPACING="0"><TR><TD BGCOLOR="white" BOR\[128X[104X
    [4X[28XDER="0">ab</TD></TR>[128X[104X
    [4X[28X</TABLE></TD></TR>[128X[104X
    [4X[28X<TR><TD BORDER="0"><TABLE CELLSPACING="0"><TR><TD BGCOLOR="white" BORDER="0">b\[128X[104X
    [4X[28Xc</TD></TR>[128X[104X
    [4X[28X</TABLE></TD><TD BORDER="0"><TABLE CELLSPACING="0"><TR><TD BGCOLOR="white" BOR\[128X[104X
    [4X[28XDER="0">*bca</TD></TR>[128X[104X
    [4X[28X</TABLE></TD><TD BORDER="0"><TABLE CELLSPACING="0"><TR><TD BGCOLOR="white" BOR\[128X[104X
    [4X[28XDER="0">b</TD></TR>[128X[104X
    [4X[28X</TABLE></TD></TR>[128X[104X
    [4X[28X<TR><TD BORDER="0"><TABLE CELLSPACING="0"><TR><TD BGCOLOR="white" BORDER="0">c\[128X[104X
    [4X[28X</TD></TR>[128X[104X
    [4X[28X</TABLE></TD><TD BORDER="0"><TABLE CELLSPACING="0"><TR><TD BGCOLOR="white" BOR\[128X[104X
    [4X[28XDER="0">ca</TD></TR>[128X[104X
    [4X[28X</TABLE></TD><TD BORDER="0"><TABLE CELLSPACING="0"><TR><TD BGCOLOR="white" BOR\[128X[104X
    [4X[28XDER="0">*cab</TD></TR>[128X[104X
    [4X[28X</TABLE></TD></TR>[128X[104X
    [4X[28X</TABLE>>];[128X[104X
    [4X[28X}[128X[104X
  [4X[32X[104X
  
  
  [1X3.2 [33X[0;0YDrawing the D-classes of a semigroup[133X[101X
  
  [1X3.2-1 DrawDClasses[101X
  
  [29X[2XDrawDClasses[102X( [3Xarg[103X ) [32X function
  
  [33X[0;0YThis 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, as an optional argument, the integer
  [10X1[110X,   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.[133X
  
  [33X[0;0YThe dot code is computed by [2XDotForDrawingDClasses[102X ([14X3.2-2[114X).[133X
  
  [33X[0;0YThis  last  optional argument may also be the integer [10X2[110X and in this case the
  elements   will   appear   as  integers,  where  [10Xi[110X  represents  the  element
  [10XElements(S)[i][110X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XDrawDClasses(poi3);[127X[104X
    [4X[25Xgap>[125X [27XDrawDClasses(poi3, [Transformation( [ 2, 3, 4, 4 ] ),[127X[104X
    [4X[28X  Transformation( [ 2, 4, 3, 4 ] )],[128X[104X
    [4X[28X  [Transformation( [ 2, 4, 3, 4 ] )],1);[128X[104X
    [4X[28X      [128X[104X
  [4X[32X[104X
  
  [33X[0;0YThis  is  the  image  produced by the first command in the previous example:
  This is the image produced by the second command in the previous example:[133X
  
  [1X3.2-2 DotForDrawingDClasses[101X
  
  [29X[2XDotForDrawingDClasses[102X( [3Xarg[103X ) [32X function
  
  [33X[0;0YThis  function  computes  the dot code that can be used to produce a drawing
  for  the D-class of an element of a semigroup. This can be done by using the
  function  [2XDrawDClasses[102X  ([14X3.2-1[114X) (if the system is properly configured) or by
  the  user  in  some  independent way. The arguments and options are the same
  than those of [2XDrawDClasses[102X ([14X3.2-1[114X).[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XPrint(DotForDrawingDClasses(poi3));[127X[104X
    [4X[28Xdigraph  DClasses {[128X[104X
    [4X[28Xgraph [center=yes,ordering=out];[128X[104X
    [4X[28Xnode [shape=plaintext];[128X[104X
    [4X[28Xedge [color=cornflowerblue,arrowhead=none];[128X[104X
    [4X[28X## ... many more lines ...[128X[104X
    [4X[28X</TABLE></TD></TR>[128X[104X
    [4X[28X</TABLE>>];[128X[104X
    [4X[28X4:4 -> 3:3;[128X[104X
    [4X[28X3:3 -> 2:2;[128X[104X
    [4X[28X2:2 -> 1:1;[128X[104X
    [4X[28X}[128X[104X
    [4X[28X      [128X[104X
  [4X[32X[104X
  
  
  [1X3.3 [33X[0;0YCayley graphs[133X[101X
  
  [1X3.3-1 DrawRightCayleyGraph[101X
  
  [29X[2XDrawRightCayleyGraph[102X( [3XS[103X ) [32X function
  
  [33X[0;0YDraws the right Cayley graph of a finite monoid or semigroup [3XS[103X.[133X
  
  [1X3.3-2 DrawCayleyGraph[101X
  
  [29X[2XDrawCayleyGraph[102X( [3XS[103X ) [32X function
  
  [33X[0;0YThis function is a synonym of [2XDrawRightCayleyGraph[102X ([14X3.3-1[114X).[133X
  
  [33X[0;0YFor  example,  the command [10XDrawCayleyGraph(b21);[110X would produce the following
  image  (where  state  [10Xi[110X  represents  the element [10XElements(S)[i][110X, the neutral
  element  is  coloured in "light blue" and all other idempotents are coloured
  in "light coral"):[133X
  
  [1X3.3-3 DotForDrawingRightCayleyGraph[101X
  
  [29X[2XDotForDrawingRightCayleyGraph[102X( [3XS[103X ) [32X function
  
  [33X[0;0YThis  function  computes  the dot code that is used by the previous function
  and can also be used by the reader in some independent way.[133X
  
  
  [1X3.4 [33X[0;0YSchützenberger graphs[133X[101X
  
  [1X3.4-1 DrawSchutzenbergerGraphs[101X
  
  [29X[2XDrawSchutzenbergerGraphs[102X( [3XS[103X ) [32X function
  
  [33X[0;0YDraws the Schützenberger graphs of the inverse semigroup [3XS[103X.[133X
  
  [33X[0;0YFor example, [10XDrawSchutzenbergerGraphs(poi3);[110X would produce the following:[133X
  
  
  [1X3.5 [33X[0;0YDrawings output formats[133X[101X
  
  [33X[0;0YBy  default,  when  a  drawing  is requested, it is outputted in pdf format.
  Since      [10Xgraphviz[110X      allows      other      output      formats     (see
  [7Xhttp://www.graphviz.org/doc/info/output.html[107X),   it   is  possible  to  also
  request a drawing in a format other than pdf.[133X
  
  [1X3.5-1 DrawingsListOfExtraFormats[101X
  
  [29X[2XDrawingsListOfExtraFormats[102X[32X global variable
  
  [33X[0;0YThis  is  a  global  variable  which  holds  the  valid output formats for a
  drawing.  It  currently  has  the  value: [10X["dia", "fig", "gd", "gd2", "gif",
  "hpgl", "jpg", "mif", "mp", "pcl", "pic", "plain", "plain-ext", "png", "ps",
  "ps2",    "svg",    "svgz",    "vrml",    "vtx",    "wbmp",   "none"][110X   (see
  [7Xhttp://www.graphviz.org/doc/info/output.html[107X for their description).[133X
  
  [1X3.5-2 DrawingsExtraFormat[101X
  
  [29X[2XDrawingsExtraFormat[102X[32X global variable
  
  [33X[0;0YThis  is  a  global variable which holds the alternative output format for a
  drawing.  By  default its value is [10X"none"[110X which indicates that just pdf will
  be used as the output format.[133X
  
  [33X[0;0YIf  its  value  becomes  one of those in [2XDrawingsListOfExtraFormats[102X ([14X3.5-1[114X),
  then besides the pdf file, it will also be created a file in the alternative
  format.[133X
  
  [33X[0;0YTo change this variable's value, please use [2XSetDrawingsExtraFormat[102X ([14X3.5-3[114X).[133X
  
  [1X3.5-3 SetDrawingsExtraFormat[101X
  
  [29X[2XSetDrawingsExtraFormat[102X( [3Xf[103X ) [32X function
  
  [33X[0;0YThis function is used to set the value of [2XDrawingsExtraFormat[102X ([14X3.5-2[114X) to the
  format [3Xf[103X which is one of [2XDrawingsListOfExtraFormats[102X ([14X3.5-1[114X).[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XDrawingsExtraFormat;[127X[104X
    [4X[28X"none"[128X[104X
    [4X[25Xgap>[125X [27XSetDrawingsExtraFormat("jpg");[127X[104X
    [4X[25Xgap>[125X [27XDrawingsExtraFormat;[127X[104X
    [4X[28X"jpg"[128X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XDrawRightCayleyGraph(poi3);[127X[104X
    [4X[28XDisplaying file: /tmp/tmp.tpJqvI/cayleygraph.dot.ps[128X[104X
    [4X[28XThe extra output format file: /tmp/tmp.tpJqvI/cayleygraph.dot.jpg[128X[104X
    [4X[28Xhas also been created.[128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  
  [1X3.6 [33X[0;0YDrawings extra graph attributes[133X[101X
  
  [33X[0;0YThe  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 [7Xhttp://graphviz.org/doc/info/attrs.html[107X. (Note that
  only  graph  attributes  are  allowed  to  be  defined,  not  edge  nor node
  attributes are supported yet.)[133X
  
  [1X3.6-1 DrawingsExtraGraphAttributes[101X
  
  [29X[2XDrawingsExtraGraphAttributes[102X[32X global variable
  
  [33X[0;0YThis  is  a  global  variable  which  holds a list of strings, each of which
  defines  a [13Xdot[113X graph attribute. This variable is [13Xnot[113X 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
  [2XSetDrawingsExtraGraphAttributes[102X   ([14X3.6-2[114X).  If  [10XDrawingsExtraGraphAttributes[110X
  holds  the  value  [10X"none"[110X  then  the  default [13Xdot[113X settings will be used. Use
  [2XClearDrawingsExtraGraphAttributes[102X ([14X3.6-3[114X) to set it to [10X"none"[110X.[133X
  
  [1X3.6-2 SetDrawingsExtraGraphAttributes[101X
  
  [29X[2XSetDrawingsExtraGraphAttributes[102X( [3XL[103X ) [32X function
  
  [33X[0;0YThis  is  the  function  to  define  the  drawing's  graph  attributes  (see
  [7Xhttp://graphviz.org/doc/info/attrs.html[107X for a list and explanation of them).
  the  argument  [3XL[103X  is  a  list  of strings, each of which defines a [13Xdot[113X graph
  attribute.  For example, if we wanted to define the graph size to be 7x9 (in
  inches), we would call [10XSetDrawingsExtraGraphAttributes(["size=7,9"]);[110X.[133X
  
  [33X[0;0YIf  we  also wanted to define the graph to be displayed in landscape mode we
  would  call [10XSetDrawingsExtraGraphAttributes(["size=7,9", "rotate=90"]);[110X. If,
  in  addition  we  wanted to define the background colour to be, for example,
  pink,    we    would    call    [10XSetDrawingsExtraGraphAttributes(["size=7,9",
  "rotate=90", "bgcolor=pink"]);[110X.[133X
  
  [33X[0;0YAfter  defining  the attributes, any command that creates a drawing will use
  the  last  defined  attributes. To set them back to the defaults, please use
  [2XClearDrawingsExtraGraphAttributes[102X ([14X3.6-3[114X).[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XDrawingsExtraGraphAttributes;[127X[104X
    [4X[28X"none"[128X[104X
    [4X[28X[128X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XSetDrawingsExtraGraphAttributes(["size=7,9"]);[127X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XDrawingsExtraGraphAttributes;[127X[104X
    [4X[28X[ "size=7,9" ][128X[104X
    [4X[28X[128X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XSetDrawingsExtraGraphAttributes(["size=7,9", "rotate=90"]);[127X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XDrawingsExtraGraphAttributes;[127X[104X
    [4X[28X[ "size=7,9", "rotate=90" ][128X[104X
    [4X[28X[128X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XSetDrawingsExtraGraphAttributes(["size=7,9", "rotate=90", "bgcolor=pink"]);[127X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XDrawingsExtraGraphAttributes;[127X[104X
    [4X[28X[ "size=7,9", "rotate=90", "bgcolor=pink" ][128X[104X
    [4X[28X[128X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XClearDrawingsExtraGraphAttributes();[127X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XDrawingsExtraGraphAttributes;[127X[104X
    [4X[28X"none"[128X[104X
  [4X[32X[104X
  
  [1X3.6-3 ClearDrawingsExtraGraphAttributes[101X
  
  [29X[2XClearDrawingsExtraGraphAttributes[102X(  ) [32X function
  
  [33X[0;0YThis function sets the graph drawing attributes back to [13Xdot[113X's defaults.[133X
  
