display: add methods for drawing Cayley graphs

Using dot or tikz, for digraphs and semigroups.

gap/tools/display.gd

@@ -15,4 +15,12 @@ DeclareOperation("DotString", [IsObject, IsRecord]);
 DeclareOperation("TexString", [IsObject]);
 DeclareOperation("TexString", [IsObject, IsObject]);
 
+DeclareOperation("TikzCayleyDigraph", [IsCayleyDigraph]);
+DeclareOperation("TikzLeftCayleyDigraph", [IsSemigroup]);
+DeclareOperation("TikzRightCayleyDigraph", [IsSemigroup]);
+
+DeclareOperation("DotCayleyDigraph", [IsCayleyDigraph]);
+DeclareOperation("DotLeftCayleyDigraph", [IsSemigroup]);
+DeclareOperation("DotRightCayleyDigraph", [IsSemigroup]);
+
 DeclareAttribute("DotSemilatticeOfIdempotents", IsInverseSemigroup);

gap/tools/display.gi

@@ -735,3 +735,96 @@ function(coll)
  deg := DegreeOfTransformationCollection(coll);
  return JoinStringsWithSeparator(List(coll, x -> TexString(x, deg)), "\n");
 end);
+
+InstallMethod(TikzLeftCayleyDigraph, "for a semigroup", [IsSemigroup],
+function(S)
+ return TikzCayleyDigraph(LeftCayleyDigraph(S));
+end);
+
+InstallMethod(TikzRightCayleyDigraph, "for a semigroup", [IsSemigroup],
+function(S)
+ return TikzCayleyDigraph(RightCayleyDigraph(S));
+end);
+
+InstallMethod(TikzCayleyDigraph, "for a Cayley digraph", [IsCayleyDigraph],
+function(digraph)
+ local S, vertex, edge, str, nbs, x, from, gen;
+
+ # TODO add checks that there aren't more than 26 vertices
+ S := SemigroupOfCayleyDigraph(digraph);
+
+ vertex := function(x)
+ local word, name, label;
+ word := MinimalFactorization(S, x);
+ name := SEMIGROUPS.WordToString(word);
+ label := SEMIGROUPS.ExtRepObjToString(SEMIGROUPS.WordToExtRepObj(word));
+ return Concatenation(" \\node [vertex] (", name, ") at (0, 0) {};\n",
+ " \\node at (0, 0) {$", label, "$};\n\n");
+ end;
+
+ edge := function(from, to, gen)
+ local word;
+ word := MinimalFactorization(S, AsListCanonical(S)[from]);
+ from := SEMIGROUPS.WordToString(word);
+ word := MinimalFactorization(S, AsListCanonical(S)[to]);
+ to := SEMIGROUPS.WordToString(word);
+ gen := SEMIGROUPS.WordToString([gen]);
+ if from <> to then
+ return Concatenation(" \\path[->] (", from,
+ ") edge [edge] node {$", gen, "$} (",
+ to, ");\n");
+ else
+ return Concatenation(" \\path[->] (", from,
+ ") edge [loop]\n",
+ " node {$", gen, "$} (", to, ");\n");
+ fi;
+ end;
+
+ str := "";
+
+ Append(str, "\\begin{tikzpicture}[scale=1, auto, \n");
+ Append(str, " vertex/.style={circle, draw, thick, fill=white, minimum");
+ Append(str, " size=0.65cm},\n");
+ Append(str, " edge/.style={arrows={-angle 90}, thick},\n");
+ Append(str, " loop/.style={min distance=5mm,looseness=5,");
+ Append(str, "arrows={-angle 90},thick}]\n\n");
+
+ Append(str, " % Vertices . . .\n");
+ for x in AsListCanonical(S) do
+ Append(str, vertex(x));
+ od;
+
+ Append(str, " % Edges . . .\n");
+ nbs := OutNeighbours(digraph);
+ for from in [1 .. Size(S)] do
+ for gen in [1 .. Size(nbs[from])] do
+ Append(str, edge(from, nbs[from][gen], gen));
+ od;
+ od;
+
+ Append(str, "\\end{tikzpicture}");
+ return str;
+end);
+
+InstallMethod(DotCayleyDigraph, "for a Cayley digraph", [IsCayleyDigraph],
+function(digraph)
+ local S, li, label, i;
+ S := SemigroupOfCayleyDigraph(digraph);
+ li := AsListCanonical(S);
+ for i in [1 .. Size(S)] do
+ label := SEMIGROUPS.WordToExtRepObj(MinimalFactorization(S, li[i]));
+ label := SEMIGROUPS.ExtRepObjToString(label);
+ SetDigraphVertexLabel(digraph, i, label);
+ od;
+ return DotVertexLabelledDigraph(digraph);
+end);
+
+InstallMethod(DotLeftCayleyDigraph, "for a semigroup", [IsSemigroup],
+function(S)
+ return DotCayleyDigraph(LeftCayleyDigraph(S));
+end);
+
+InstallMethod(DotRightCayleyDigraph, "for a semigroup", [IsSemigroup],
+function(S)
+ return DotCayleyDigraph(RightCayleyDigraph(S));
+end);