TMP

Author: james-d-mitchell

gap/tools/display.gd

@@ -20,5 +20,7 @@ DeclareOperation("TikzRightCayleyDigraph", [IsSemigroup]);
 
 DeclareOperation("DotLeftCayleyDigraph", [IsSemigroup]);
 DeclareOperation("DotRightCayleyDigraph", [IsSemigroup]);
+DeclareOperation("DotWordGraph", [IsDigraph]);
+DeclareOperation("DotWordGraph", [IsDigraph, IsList, IsList]);
 
 DeclareAttribute("DotSemilatticeOfIdempotents", IsInverseSemigroup);

gap/tools/display.gi

@@ -727,23 +727,166 @@ function(digraph)
 end);
 
 InstallMethod(DotString, "for a Cayley digraph", [IsCayleyDigraph],
-function(digraph)
-  local S, li, label, i;
-  S  := SemigroupOfCayleyDigraph(digraph);
-  if not CanUseFroidurePin(S) or Size(S) > 26 then
+function(D)
+  local S, edge_colors, N, msg, legend, node_labels, offset, en, label, next,
+  edge_func, node_func, result, i;
+
+  S := SemigroupOfCayleyDigraph(D);
+  edge_colors := ["\"#00ff00\"", "\"#ff00ff\"", "\"#007fff\"", "\"#ff7f00\"",
+                  "\"#7fbf7f\"", "\"#4604ac\"", "\"#de0328\"", "\"#19801d\"",
+                  "\"#d881f5\"", "\"#00ffff\"", "\"#ffff00\"", "\"#00ff7f\"",
+                  "\"#ad5867\"", "\"#85f610\"", "\"#84e9f5\"", "\"#f5c778\"",
+                  "\"#207090\"", "\"#764ef3\"", "\"#7b4c00\"", "\"#0000ff\"",
+                  "\"#b80c9a\"", "\"#601045\"", "\"#29b7c0\"", "\"#839f12"];
+  N := Length(GeneratorsOfSemigroup(S));
+  if not CanUseFroidurePin(S) then
     TryNextMethod();
   fi;
-  li := AsListCanonical(S);
+
+  if IsMonoidAsSemigroup(S) and One(GeneratorsOfSemigroup(S)) in S then
+    offset := -1;
+  else
+    offset := 1;
+  fi;
+
+  node_labels := [];
+  en := EnumeratorCanonical(S);
   for i in [1 .. Size(S)] do
-    label := SEMIGROUPS.WordToExtRepObj(MinimalFactorization(S, li[i]));
-    label := SEMIGROUPS.ExtRepObjToString(label);
-    SetDigraphVertexLabel(digraph, i, label);
+    if IsOne(en[i]) then
+      label := "ε";
+    else
+      label := SEMIGROUPS.WordToExtRepObj(MinimalFactorization(S, i) + offset);
+      label := SEMIGROUPS.ExtRepObjToString(label);
+    fi;
+    node_labels[i] := label;
   od;
-  return DotVertexLabelledDigraph(digraph);
+
+  legend := "node [shape=plaintext]\nsubgraph cluster_01 {\nlabel=\"Legend\"\n";
+  Append(legend, "key2 [label=<<table border=\"0\" cellpadding=\"2\"");
+  Append(legend, " cellspacing=\"0\" cellborder=\"0\">\n");
+
+  for i in [1 .. N] do
+    Append(legend,
+           StringFormatted("  <tr><td port=\"i{}\">&nbsp;</td></tr>\n",
+                           i));
+  od;
+  Append(legend, "</table>>]\n");
+  Append(legend, "key [label=<<table border=\"0\" cellpadding=\"2\"");
+  Append(legend, " cellspacing=\"0\" cellborder=\"0\">\n");
+
+  for i in [1 .. N] do
+    label := node_labels[i];
+    next := "<tr><td align=\"right\" ";
+    Append(next, StringFormatted("port=\"i{}\">{}&nbsp;</td></tr>\n", i, label));
+    Append(legend, next);
+  od;
+
+  Append(legend, "</table>>]\n\n");
+
+  for i in [1 .. N] do
+    next := StringFormatted("key:i{1}:e -> key2:i{1}:w [color={2},",
+                            i,
+                            edge_colors[i]);
+    Append(next, "constraint=false]\n");
+    Append(legend, next);
+  od;
+  Append(legend, "}\n");
+
+  node_func := i -> StringFormatted(" [label=\"{}\"]", node_labels[i]);
+  edge_func := {i, j} -> StringFormatted("[color={}]", edge_colors[j]);
+
+  result := DIGRAPHS_DotDigraph(D, [node_func], [edge_func]);
+  result := SplitString(result, "\n");
+  result[3] := "subgraph 00 {";
+  Add(result, "node [shape=box]", 3);
+  Add(result, legend);
+  Add(result, "}");
+  return JoinStringsWithSeparator(result, "\n");
 end);
 
 InstallMethod(DotLeftCayleyDigraph, "for a semigroup", [IsSemigroup],
 S -> DotString(LeftCayleyDigraph(S)));
 
 InstallMethod(DotRightCayleyDigraph, "for a semigroup", [IsSemigroup],
 S -> DotString(RightCayleyDigraph(S)));
+
+InstallMethod(DotWordGraph, "for a word graph and list of edge labels",
+[IsDigraph, IsList, IsList],
+function(D, node_labels, edge_labels)
+  local M, N, edge_colors, msg, legend, label, next, node_func, edge_func, result, v, i;
+
+  if IsNullDigraph(D) then
+    # Word graphs must have at least one node . . .
+    ErrorNoReturn("TODO3");
+  fi;
+
+  M := DigraphNrVertices(D);
+  N := Length(OutNeighboursOfVertex(D, 1));
+
+  if not IsOutRegularDigraph(D) then
+    ErrorNoReturn("TODO1");
+  elif Length(edge_labels) <> N then
+    ErrorNoReturn("TODO2");
+  fi;
+
+  edge_colors := ["\"#00ff00\"", "\"#ff00ff\"", "\"#007fff\"", "\"#ff7f00\"",
+                  "\"#7fbf7f\"", "\"#4604ac\"", "\"#de0328\"", "\"#19801d\"",
+                  "\"#d881f5\"", "\"#00ffff\"", "\"#ffff00\"", "\"#00ff7f\"",
+                  "\"#ad5867\"", "\"#85f610\"", "\"#84e9f5\"", "\"#f5c778\"",
+                  "\"#207090\"", "\"#764ef3\"", "\"#7b4c00\"", "\"#0000ff\"",
+                  "\"#b80c9a\"", "\"#601045\"", "\"#29b7c0\"", "\"#839f12"];
+
+  if N > Length(edge_colors) then
+    msg := Concatenation("the out-degree of every vertex in the 1st argument (a digraph) ",
+                         "must have at most {}, found {}");
+    ErrorNoReturn(StringFormatted(msg, Length(edge_colors), N));
+  fi;
+
+  # node_labels := ["&#949;"];
+
+  # for v in [2 .. M] do
+  #   Add(node_labels, edge_labels{DigraphPath(D, 1, v)[2]});
+  # od;
+
+  legend := "node [shape=plaintext]\nsubgraph cluster_01 {\nlabel=\"Legend\"\n";
+  Append(legend, "key2 [label=<<table border=\"0\" cellpadding=\"2\"");
+  Append(legend, " cellspacing=\"0\" cellborder=\"0\">\n");
+
+  for i in [1 .. N] do
+    Append(legend,
+           StringFormatted("  <tr><td port=\"i{}\">&nbsp;</td></tr>\n",
+                           i));
+  od;
+  Append(legend, "</table>>]\n");
+  Append(legend, "key [label=<<table border=\"0\" cellpadding=\"2\"");
+  Append(legend, " cellspacing=\"0\" cellborder=\"0\">\n");
+
+  for i in [1 .. N] do
+    label := [edge_labels[i]];
+    next := "<tr><td align=\"right\" ";
+    Append(next, StringFormatted("port=\"i{}\">{}&nbsp;</td></tr>\n", i, label));
+    Append(legend, next);
+  od;
+
+  Append(legend, "</table>>]\n\n");
+
+  for i in [1 .. N] do
+    next := StringFormatted("key:i{1}:e -> key2:i{1}:w [color={2},",
+                            i,
+                            edge_colors[i]);
+    Append(next, "constraint=false]\n");
+    Append(legend, next);
+  od;
+  Append(legend, "}\n");
+
+  node_func := i -> StringFormatted(" [label=\"{}\"]", node_labels[i]);
+  edge_func := {i, j} -> StringFormatted("[color={}]", edge_colors[j]);
+
+  result := DIGRAPHS_DotDigraph(D, [node_func], [edge_func]);
+  result := SplitString(result, "\n");
+  result[3] := "subgraph 00 {";
+  Add(result, "node [shape=box]", 3);
+  Add(result, legend);
+  Add(result, "}");
+  return JoinStringsWithSeparator(result, "\n");
+end);