fropin: add Left/RightCayleyDigraph

These essentially just wrap the value previously returned by
Left/RightCayleyGraphSemigroup in a Digraph object. Methods for
Left/RightCayleyGraphSemigroup continue to exist (just calling
OutNeighbours(Left/RightCayleyDigraph) since they are defined in the
library. All other occurrences of Left/RightCayleyGraphSemigroup are
replaced with Left/RightCayleyDigraph.

PackageInfo.g

@@ -236,7 +236,7 @@ Dependencies := rec(
   GAP := ">=4.9.0",
   NeededOtherPackages := [["orb", ">=4.7.5"],
                           ["io", ">=4.4.4"],
-                          ["digraphs", ">=0.10.0"],
+                          ["digraphs", ">=0.9.0"],
                           ["genss", ">=1.5"]],
   SuggestedOtherPackages := [["gapdoc", ">=1.5.1"]],
 

doc/fropin.xml

@@ -50,8 +50,8 @@ false
       returns a list of the elements of <A>S</A> in the order they are
       enumerated by the Froidure-Pin Algorithm. This is the same as the order
       used to index the elements of <A>S</A> in <Ref
-        Attr="RightCayleyGraphSemigroup"/> and <Ref
-        Attr="LeftCayleyGraphSemigroup"/>. <P/>
+        Attr="RightCayleyDigraph"/> and <Ref
+        Attr="LeftCayleyDigraph"/>. <P/>
 
       <C>EnumeratorCanonical</C> and <C>IteratorCanonical</C> return an
       enumerator and an iterator where the elements are
@@ -67,8 +67,8 @@ false
       <C>AsList</C> may not equal the value returned by <C>AsListCanonical</C>.
       <C>AsListCanonical</C> exists so that there is a method for obtaining the
       elements of <A>S</A> in the particular order used by 
-      <Ref Attr="RightCayleyGraphSemigroup"/> and 
-      <Ref Attr="LeftCayleyGraphSemigroup"/>.<P/>
+      <Ref Attr="RightCayleyDigraph"/> and 
+      <Ref Attr="LeftCayleyDigraph"/>.<P/>
 
       See also <Ref Oper="PositionCanonical"/>.
 
@@ -183,27 +183,34 @@ true]]></Example>
   </ManSection>
 <#/GAPDoc>
 
-<#GAPDoc Label="RightCayleyGraphSemigroup">
+<#GAPDoc Label="RightCayleyDigraph">
   <ManSection>
-    <Attr Name="RightCayleyGraphSemigroup" Arg="S"/> 
-    <Attr Name="LeftCayleyGraphSemigroup" Arg="S"/> 
+    <Attr Name="RightCayleyDigraph" Arg="S"/> 
+    <Attr Name="LeftCayleyDigraph" Arg="S"/> 
     <Returns>A list of lists of positive integers.</Returns>
     <Description>
       When the argument <A>S</A> is a semigroup in the representation 
       <Ref Filt="IsEnumerableSemigroupRep"/>, 
-      <C>RightCayleyGraphSemigroup</C> returns the right
-      Cayley graphs of <A>S</A>, as a list <C>graph</C> where 
-      <C>graph[i][j]</C> is equal to 
+      <C>RightCayleyDigraph</C> returns the right
+      Cayley graphs of <A>S</A>, as a <Ref Oper="Digraph" BookName="digraphs"/>
+      <C>digraph</C> where vertex <C>OutNeighbours(digraph)[i][j]</C> is 
       <C>PositionCanonical(<A>S</A>, AsListCanonical(<A>S</A>)[i] *
         GeneratorsOfSemigroup(<A>S</A>)[j])</C>.
-      The list returned by <C>LeftCayleyGraphSemigroup</C> is defined analogously.
+      The list returned by <C>LeftCayleyDigraph</C> is defined analogously.<P/>
+
+      The digraph returned by this attribute belongs to the category 
+      <Ref Filt="IsCayleyDigraph" BookName="digraphs"/>, the semigroup <A>S</A>
+      and the generators used to create the digraph can be recovered from the
+      digraph using  <Ref Attr="SemigroupOfCayleyDigraph" BookName="digraphs"/>
+      and <Ref Attr="GeneratorsOfCayleyDigraph" BookName="digraphs"/>.
+
       <Example><![CDATA[
 gap> S := FullTransformationMonoid(2);
 <full transformation monoid of degree 2>
-gap> RightCayleyGraphSemigroup(S);
-[ [ 1, 2, 3 ], [ 2, 1, 3 ], [ 3, 4, 3 ], [ 4, 3, 3 ] ]
-gap> LeftCayleyGraphSemigroup(S);
-[ [ 1, 2, 3 ], [ 2, 1, 4 ], [ 3, 3, 3 ], [ 4, 4, 4 ] ]]]></Example>
+gap> RightCayleyDigraph(S);
+<multidigraph with 4 vertices, 12 edges>
+gap> LeftCayleyDigraph(S);
+<multidigraph with 4 vertices, 12 edges>]]></Example>
     </Description>
   </ManSection>
 <#/GAPDoc>

doc/z-chap13.xml

@@ -27,7 +27,7 @@
     <Heading>
        Cayley graphs
      </Heading>
-     <#Include Label = "RightCayleyGraphSemigroup">
+     <#Include Label = "RightCayleyDigraph">
    </Section>
 
   <!--**********************************************************************-->

gap/congruences/conginv.gi

@@ -507,7 +507,7 @@ SEMIGROUPS.KernelTraceClosure := function(S, kernel, traceBlocks, pairstoapply)
   hashlen := SEMIGROUPS.OptionsRec(S).hashlen.L;
   ht := HTCreate([1, 1], rec(forflatplainlists := true,
                              treehashsize := hashlen));
-  right := RightCayleyGraphSemigroup(idsmgp);
+  right := OutNeighbours(RightCayleyDigraph(idsmgp));
   genstoapply := [1 .. Length(right[1])];
 
   #

gap/greens/gree.gi

@@ -391,8 +391,6 @@ function(S)
 
   l  := LeftCayleyGraphSemigroup(S);
   r  := RightCayleyGraphSemigroup(S);
-  # WW: in the future, when l and r are digraphs, gr can be created
-  #     by using DigraphEdgeUnion(l, r)
   gr := Digraph(List([1 .. Length(l)], i -> Concatenation(l[i], r[i])));
   gr := QuotientDigraph(gr, DigraphStronglyConnectedComponents(gr).comps);
   return List(OutNeighbours(gr), Set);

gap/greens/gren.gi

@@ -225,19 +225,19 @@ end);
 InstallMethod(GreensRRelation, "for an enumerable semigroup",
 [IsEnumerableSemigroupRep],
 function(S)
-  local fam, rel;
+  local fam, data, rel;
   if IsActingSemigroup(S) then
     TryNextMethod();
   fi;
   fam := GeneralMappingsFamily(ElementsFamily(FamilyObj(S)),
                                ElementsFamily(FamilyObj(S)));
-
+  data := DigraphStronglyConnectedComponents(RightCayleyDigraph(S));
   rel := Objectify(NewType(fam,
                            IsEquivalenceRelation
                              and IsEquivalenceRelationDefaultRep
                              and IsGreensRRelation
                              and IsEnumerableSemigroupGreensRelationRep),
-                   rec(data := GABOW_SCC(RightCayleyGraphSemigroup(S))));
+                   rec(data := data));
   SetSource(rel, S);
   SetRange(rel, S);
   SetIsLeftSemigroupCongruence(rel, true);
@@ -250,19 +250,19 @@ end);
 InstallMethod(GreensLRelation, "for an enumerable semigroup",
 [IsEnumerableSemigroupRep],
 function(S)
-  local fam, rel;
+  local fam, data, rel;
   if IsActingSemigroup(S) then
     TryNextMethod();
   fi;
   fam := GeneralMappingsFamily(ElementsFamily(FamilyObj(S)),
                                ElementsFamily(FamilyObj(S)));
-
+  data := DigraphStronglyConnectedComponents(LeftCayleyDigraph(S));
   rel := Objectify(NewType(fam,
                            IsEquivalenceRelation
                              and IsEquivalenceRelationDefaultRep
                              and IsGreensLRelation
                              and IsEnumerableSemigroupGreensRelationRep),
-                   rec(data := GABOW_SCC(LeftCayleyGraphSemigroup(S))));
+                   rec(data := data));
   SetSource(rel, S);
   SetRange(rel, S);
   SetIsRightSemigroupCongruence(rel, true);
@@ -514,19 +514,20 @@ InstallMethod(HClassReps, "for a Green's class of an enumerable semigroup",
 [IsGreensClass and IsEnumerableSemigroupGreensClassRep],
 C -> SEMIGROUPS.XClassRepsOfClass(C, GreensHRelation));
 
-## Partial order of D-classes
-# There is duplicate code in here and in maximal D-classes
+# There is duplicate code in here and in maximal D-classes.
+#
+# This cannot be replaced with the method for IsSemigroup and IsFinite since
+# the value of GreensDRelation(S)!.data.comps is not the same as the output of
+# DigraphStronglyConnectedComponents.
 
 InstallMethod(PartialOrderOfDClasses, "for a finite enumerable semigroup",
 [IsEnumerableSemigroupRep and IsFinite],
 function(S)
   local l, r, gr;
-
-  l  := LeftCayleyGraphSemigroup(S);
-  r  := RightCayleyGraphSemigroup(S);
-  gr := Digraph(List([1 .. Length(l)], i -> Concatenation(l[i], r[i])));
+  l  := LeftCayleyDigraph(S);
+  r  := RightCayleyDigraph(S);
+  gr := DigraphEdgeUnion(l, r);
   gr := QuotientDigraph(gr, GreensDRelation(S)!.data.comps);
-
   return List(OutNeighbours(gr), Set);
 end);
 

gap/ideals/idealenum.gi

@@ -53,8 +53,8 @@ SEMIGROUPS.EnumerateIdeal := function(enum, limit, lookfunc)
   indices := enum!.indices;
 
   S := SupersemigroupOfIdeal(UnderlyingCollection(enum));
-  left := LeftCayleyGraphSemigroup(S);
-  right := RightCayleyGraphSemigroup(S);
+  left := OutNeighbours(LeftCayleyDigraph(S));
+  right := OutNeighbours(RightCayleyDigraph(S));
   # FIXME Once the left and right Cayley graphs have been calculated, the
   # entire data structure of S is known and from this it is relatively easy to
   # find the entire data structure for I, so there is no point to what follows,

gap/main/fropin.gd

@@ -48,3 +48,6 @@ DeclareOperation("Enumerate", [IsEnumerableSemigroupRep]);
 DeclareOperation("IsFullyEnumerated", [IsEnumerableSemigroupRep]);
 
 DeclareProperty("IsSemigroupEnumerator", IsEnumeratorByFunctions);
+
+DeclareAttribute("LeftCayleyDigraph", IsEnumerableSemigroupRep);
+DeclareAttribute("RightCayleyDigraph", IsEnumerableSemigroupRep);

gap/main/fropin.gi

@@ -565,11 +565,23 @@ end);
 InstallMethod(RightCayleyGraphSemigroup, "for an enumerable semigroup rep",
 [IsEnumerableSemigroupRep], 3,
 function(S)
+  return OutNeighbours(RightCayleyDigraph(S));
+end);
+
+InstallMethod(RightCayleyDigraph,
+"for an enumerable semigroup rep",
+[IsEnumerableSemigroupRep],
+function(S)
+  local digraph;
   if not IsFinite(S) then
-    ErrorNoReturn("Semigroups: RightCayleyGraphSemigroup: usage,\n",
+    ErrorNoReturn("Semigroups: RightCayleyDigraph: usage,\n",
                   "the first argument (a semigroup) must be finite,");
   fi;
-  return EN_SEMI_RIGHT_CAYLEY_GRAPH(S);
+  digraph := Digraph(EN_SEMI_RIGHT_CAYLEY_GRAPH(S));
+  SetFilterObj(digraph, IsCayleyDigraph);
+  SetSemigroupOfCayleyDigraph(digraph, S);
+  SetGeneratorsOfCayleyDigraph(digraph, GeneratorsOfSemigroup(S));
+  return digraph;
 end);
 
 # same method for ideals
@@ -578,11 +590,23 @@ InstallMethod(LeftCayleyGraphSemigroup,
 "for an enumerable semigroup rep",
 [IsEnumerableSemigroupRep], 3,
 function(S)
+  return OutNeighbours(LeftCayleyDigraph(S));
+end);
+
+InstallMethod(LeftCayleyDigraph,
+"for an enumerable semigroup rep",
+[IsEnumerableSemigroupRep],
+function(S)
+  local digraph;
   if not IsFinite(S) then
-    ErrorNoReturn("Semigroups: LeftCayleyGraphSemigroup: usage,\n",
+    ErrorNoReturn("Semigroups: LeftCayleyDigraph: usage,\n",
                   "the first argument (a semigroup) must be finite,");
   fi;
-  return EN_SEMI_LEFT_CAYLEY_GRAPH(S);
+  digraph := Digraph(EN_SEMI_LEFT_CAYLEY_GRAPH(S));
+  SetFilterObj(digraph, IsCayleyDigraph);
+  SetSemigroupOfCayleyDigraph(digraph, S);
+  SetGeneratorsOfCayleyDigraph(digraph, GeneratorsOfSemigroup(S));
+  return digraph;
 end);
 
 InstallMethod(MultiplicationTable, "for an enumerable semigroup",

gap/semigroups/grpperm.gi

@@ -156,7 +156,7 @@ function(S)
                   "IsGroupAsSemigroup,");
   fi;
 
-  cay := RightCayleyGraphSemigroup(S);
+  cay := OutNeighbours(RightCayleyDigraph(S));
   deg := Size(S);
   gen := [];
 

gap/semigroups/semifp.gi

@@ -92,7 +92,7 @@ function(x1, x2)
   return x1 ^ map < x2 ^ map;
 end);
 
-#TODO AsSSortedList, RightCayleyGraph, any more?
+#TODO AsSSortedList, RightCayleyDigraph, any more?
 
 InstallMethod(ViewString, "for an f.p. semigroup element",
 [IsElementOfFpSemigroup], String);

gap/semigroups/semitrans.gi

@@ -782,12 +782,12 @@ function(S)
   local cay, deg, gen, next, T, iso, inv, i;
 
   if not IsFinite(S) then
-    # This is unreachable in tests, since there is not other method that
+    # This is unreachable in tests, since there is no other method that
     # terminates
     TryNextMethod();
   fi;
 
-  cay := RightCayleyGraphSemigroup(S);
+  cay := OutNeighbours(RightCayleyDigraph(S));
   deg := Size(S);
   gen := [];
 
@@ -826,7 +826,7 @@ function(S)
     TryNextMethod();
   fi;
 
-  cay := RightCayleyGraphSemigroup(S);
+  cay := OutNeighbours(RightCayleyDigraph(S));
   deg := Size(S);
   gen := EmptyPlist(Length(cay[1]));
 

src/fropin.cc

@@ -338,9 +338,9 @@ Obj fropin(Obj obj, Obj limit, Obj lookfunc, Obj looking) {
   return data;
 }
 
-// Using the output of GABOW_SCC on the right and left Cayley graphs of a
-// semigroup, the following function calculates the strongly connected
-// components of the union of these two graphs.
+// Using the output of DigraphStronglyConnectedComponents on the right and left
+// Cayley graphs of a semigroup, the following function calculates the strongly
+// connected components of the union of these two graphs.
 
 Obj SCC_UNION_LEFT_RIGHT_CAYLEY_GRAPHS(Obj self, Obj scc1, Obj scc2) {
   UInt* ptr;
@@ -416,9 +416,9 @@ Obj SCC_UNION_LEFT_RIGHT_CAYLEY_GRAPHS(Obj self, Obj scc1, Obj scc2) {
 }
 
 // <right> and <left> should be scc data structures for the right and left
-// Cayley graphs of a semigroup, as produced by GABOW_SCC. This function find
-// the H-classes of the semigroup from <right> and <left>. The method used is
-// that described in:
+// Cayley graphs of a semigroup, as produced by
+// DigraphStronglyConnectedComponents. This function find the H-classes of the
+// semigroup from <right> and <left>. The method used is that described in:
 // http://www.liafa.jussieu.fr/~jep/PDF/Exposes/StAndrews.pdf
 
 Obj FIND_HCLASSES(Obj self, Obj right, Obj left) {

tst/standard/attr.tst

@@ -342,22 +342,23 @@ gap> Size(MinimalDClass(s));
 gap> MultiplicativeZero(s);
 Transformation( [ 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 ] )
 
-#T# attr: RightCayleyGraphSemigroup
+#T# attr: RightCayleyDigraph
 gap> S := Semigroup(PartialPerm([1, 2, 3], [1, 3, 4]),
 >                   PartialPerm([1, 2, 3], [2, 5, 3]),
 >                   PartialPerm([1, 2, 3], [4, 1, 2]),
 >                   PartialPerm([1, 2, 3, 4], [2, 4, 1, 5]),
 >                   PartialPerm([1, 3, 5], [5, 1, 3]));;
-gap> RightCayleyGraphSemigroup(S);;
-gap> Length(STRONGLY_CONNECTED_COMPONENTS_DIGRAPH(last)) = NrRClasses(S);
+gap> digraph := RightCayleyDigraph(S);;
+gap> Length(DigraphStronglyConnectedComponents(digraph).comps) 
+> = NrRClasses(S);
 true
 
-#T# attr: RightCayleyGraphSemigroup, infinite
-gap> RightCayleyGraphSemigroup(FreeSemigroup(2));
+#T# attr: RightCayleyDigraph, infinite
+gap> RightCayleyDigraph(FreeSemigroup(2));
 Error, no method found! For debugging hints type ?Recovery from NoMethodFound
-Error, no 2nd choice method found for `CayleyGraphSemigroup' on 1 arguments
+Error, no 1st choice method found for `RightCayleyDigraph' on 1 arguments
 
-#T# attr: LeftCayleyGraphSemigroup
+#T# attr: LeftCayleyDigraph
 gap> S := Monoid(BooleanMat([[1, 1, 1, 1, 1], [1, 0, 1, 0, 0],
 >                              [1, 1, 0, 1, 0], [1, 1, 1, 1, 1],
 >                              [1, 1, 0, 0, 0]]),
@@ -373,15 +374,15 @@ gap> S := Monoid(BooleanMat([[1, 1, 1, 1, 1], [1, 0, 1, 0, 0],
 >                BooleanMat([[1, 0, 0, 0, 1], [1, 0, 0, 0, 1],
 >                              [0, 0, 0, 0, 1], [0, 1, 1, 0, 1],
 >                              [1, 1, 1, 0, 1]]));;
-gap> LeftCayleyGraphSemigroup(S);;
-gap> Length(STRONGLY_CONNECTED_COMPONENTS_DIGRAPH(last)) = NrLClasses(S);
+gap> digraph := LeftCayleyDigraph(S);;
+gap> Length(DigraphStronglyConnectedComponents(digraph).comps) 
+> = NrLClasses(S);
 true
 
-#T# attr: RightCayleyGraphSemigroup, infinite
-gap> LeftCayleyGraphSemigroup(FreeInverseSemigroup(2));
+#T# attr: RightCayleyDigraph, infinite
+gap> LeftCayleyDigraph(FreeInverseSemigroup(2));
 Error, no method found! For debugging hints type ?Recovery from NoMethodFound
-Error, no 2nd choice method found for `CayleyGraphDualSemigroup' on 1 argument\
-s
+Error, no 1st choice method found for `LeftCayleyDigraph' on 1 arguments
 
 #T# attr: IsomorphismReesMatrixSemigroup
 gap> D := GreensDClassOfElement(Semigroup(