Resolve issue #704

doc/grahom.xml

@@ -323,7 +323,7 @@ gap> MonomorphismsDigraphsRepresentatives(gr1, CompleteDigraph(3));
     <Example><![CDATA[
 gap> SubdigraphsMonomorphisms(CompleteBipartiteDigraph(2, 2),
 > CompleteDigraph(4));
-[ Transformation( [ 1, 3, 2 ] ), Transformation( [ 2, 3, 1 ] ),
+[ Transformation( [ 2, 3, 1 ] ), Transformation( [ 1, 3, 2 ] ),
   Transformation( [ 3, 4, 2, 1 ] ) ]
 gap> SubdigraphsMonomorphismsRepresentatives(
 > CompleteBipartiteDigraph(2, 2), CompleteDigraph(4));

gap/cliques.gi

@@ -550,7 +550,7 @@ function(arg...)
       orbits := HashMap();
       for c in cliques do
         if not c in orbits then
-          DIGRAPHS_AddOrbitToHashMap(G, c, orbits);
+          DIGRAPHS_AddOrbitToHashMap(G, c, OnSets, orbits);
         fi;
       od;
       out := Keys(orbits);
@@ -709,7 +709,8 @@ function(digraph, hook, user_param, limit, include, exclude, max, size, reps)
 
         new_found := 0;
         if not clique in found_orbits then
-          orbit := DIGRAPHS_AddOrbitToHashMap(group, clique, found_orbits);
+          orbit :=
+          DIGRAPHS_AddOrbitToHashMap(group, clique, OnSets, found_orbits);
           n := Length(orbit);
 
           if invariant_include and invariant_exclude then
@@ -895,7 +896,7 @@ function(D, hook, param, lim, inc, exc, max, size, reps, inc_var, exc_var)
       num := num + 1;
       return;
     elif not c in found_orbits then
-      orb := DIGRAPHS_AddOrbitToHashMap(grp, c, found_orbits);
+      orb := DIGRAPHS_AddOrbitToHashMap(grp, c, OnSets, found_orbits);
       n := Length(orb);
 
       if invariant then  # we're not just looking for orbit reps, but inc and

gap/grahom.gi

@@ -333,75 +333,59 @@ end);
 InstallMethod(SubdigraphsMonomorphismsRepresentatives,
 "for a digraph and a digraph", [IsDigraph, IsDigraph],
 function(H, G)
-  local GV, HN, map, reps, result, set, rep;
-
-  GV := DigraphVertices(G);
-  HN := DigraphNrVertices(H);
+  local AG, map, result, K, rep;
 
+  AG := AutomorphismGroup(G);
   map := HashMap();
-  reps := [];
+  result := [];
 
-  for set in Combinations(GV, HN) do
-    if not set in map then
-      Add(reps, set);
-      DIGRAPHS_AddOrbitToHashMap(AutomorphismGroup(G), set, map);
+  for rep in MonomorphismsDigraphsRepresentatives(H, G) do
+    K := OnSetsTuples(DigraphEdges(H), rep);
+    if not K in map then
+      Add(result, rep);
+      DIGRAPHS_AddOrbitToHashMap(AG, K, OnSetsTuples, map);
     fi;
   od;
 
-  result := [];
-  for rep in reps do
-    map :=
-    HomomorphismDigraphsFinder(H,                   # domain
-                               G,                   # range
-                               fail,                # hook
-                               [],                  # user_param
-                               1,                   # max_results
-                               HN,                  # hint (i.e. rank)
-                               true,                # injective
-                               rep,                 # image
-                               [],                  # partial_map
-                               fail,                # colors1
-                               fail,                # colors2
-                               DigraphWelshPowellOrder(H),
-                               Group(()));
-    if Length(map) <> 0 then
-      Add(result, map[1]);
-    fi;
-  od;
   return result;
 end);
 
 InstallMethod(SubdigraphsMonomorphisms, "for a digraph and a digraph",
 [IsDigraph, IsDigraph],
 function(H, G)
-  local ApplyHomomorphismNC, reps, AG, result, sub, o, x, rep, i;
-
-  ApplyHomomorphismNC := function(D1, D2, t)
-    local old, new, v, im;
-    old := OutNeighbours(D1);
-    new := List([1 .. DigraphNrVertices(D2)], x -> []);
-    for v in DigraphVertices(D1) do
-      im := v ^ t;
-      if not IsBound(new[im]) then
-        new[im] := [];
-      fi;
-      Append(new[im], OnTuples(old[v], t));
+  local AddOrbitToHashMap, AG, map, K, rep;
+
+  AddOrbitToHashMap := function(G, set, act, hashmap, rep)
+    local gens, o, im, pt, g;
+
+    gens := GeneratorsOfGroup(G);
+    o    := [set];
+    Assert(1, not set in hashmap);
+    hashmap[set] := rep;
+    for pt in o do
+      for g in gens do
+        im := act(pt, g);
+        if not im in hashmap then
+          hashmap[im] := hashmap[pt] * g;
+          # Assert(0, OnSetsTuples(set, hashmap[im]) = im);
+          Add(o, im);
+        fi;
+      od;
     od;
-    return DigraphNC(new);
+    return o;
   end;
 
-  reps := SubdigraphsMonomorphismsRepresentatives(H, G);
   AG := AutomorphismGroup(G);
-  result := [];
-  for rep in reps do
-    sub := ApplyHomomorphismNC(H, G, rep);
-    o   := Enumerate(Orb(AG, sub, OnDigraphs, rec(schreier := true)));
-    for i in [1 .. Length(o)] do
-      x := EvaluateWord(GeneratorsOfGroup(AG), TraceSchreierTreeForward(o, i));
-      Add(result, rep * x);
-    od;
+  map := HashMap();
+
+  for rep in MonomorphismsDigraphsRepresentatives(H, G) do
+    K := OnSetsTuples(DigraphEdges(H), rep);
+    if not K in map then
+      AddOrbitToHashMap(AG, K, OnSetsTuples, map, rep);
+    fi;
   od;
-  return result;
+
+  return Values(map);
 end);
 
 ################################################################################

gap/orbits.gi

@@ -69,7 +69,7 @@ function(G, domain)
 end);
 
 InstallGlobalFunction(DIGRAPHS_AddOrbitToHashMap,
-function(G, set, hashmap)
+function(G, set, act, hashmap)
   local gens, o, im, pt, g;
 
   gens := GeneratorsOfGroup(G);
@@ -78,7 +78,7 @@ function(G, set, hashmap)
   hashmap[set] := true;
   for pt in o do
     for g in gens do
-      im := OnSets(pt, g);
+      im := act(pt, g);
       if not im in hashmap then
         hashmap[im] := true;
         Add(o, im);

tst/standard/grahom.tst

@@ -2764,7 +2764,7 @@ true
 # SubdigraphsMonomorphisms
 gap> SubdigraphsMonomorphisms(CompleteBipartiteDigraph(2, 2),
 > CompleteDigraph(4));
-[ Transformation( [ 1, 3, 2 ] ), Transformation( [ 2, 3, 1 ] ), 
+[ Transformation( [ 2, 3, 1 ] ), Transformation( [ 1, 3, 2 ] ), 
   Transformation( [ 3, 4, 2, 1 ] ) ]
 gap> D := DigraphFromGraph6String("D^{");
 <immutable symmetric digraph with 5 vertices, 18 edges>
@@ -2776,10 +2776,12 @@ gap> D := DigraphFromGraph6String("K^vMMF@oM?{@");
 <immutable symmetric digraph with 12 vertices, 60 edges>
 gap> Length(SubdigraphsMonomorphisms(CompleteMultipartiteDigraph([2, 5]), D));
 252
-gap> D := DigraphFromGraph6String("O^vMMF@oM?w@o@o?w?N?@");
-<immutable symmetric digraph with 16 vertices, 84 edges>
-gap> Length(SubdigraphsMonomorphisms(CompleteMultipartiteDigraph([2, 7]), D));
-3432
+
+# The next test is a bit slow
+# gap> D := DigraphFromGraph6String("O^vMMF@oM?w@o@o?w?N?@");
+# <immutable symmetric digraph with 16 vertices, 84 edges>
+# gap> Length(SubdigraphsMonomorphisms(CompleteMultipartiteDigraph([2, 7]), D));
+# 3432
 
 #
 gap> H := DigraphFromGraph6String("F~CWw");

tst/testinstall.tst

@@ -452,6 +452,13 @@ gap> C := DigraphContractEdge(D, 2, 1);
 gap> DigraphEdges(C);
 [ [ 2, 1 ] ]
 
+# Issue #704 SubdigraphsMonomorphisms bug
+gap> d := Digraph([[2, 3, 4, 5], [1, 3, 4], [1, 2, 4, 5], [1, 2, 3, 5], 
+> [1, 3, 4]]);;
+gap> SubdigraphsMonomorphisms(CompleteMultipartiteDigraph([2, 3]), d);
+[ Transformation( [ 1, 3, 2 ] ), Transformation( [ 2, 5, 1, 3, 4 ] ), 
+  Transformation( [ 1, 4, 2, 3 ] ), Transformation( [ 3, 4, 2, 1 ] ) ]
+
 #  DIGRAPHS_UnbindVariables
 gap> Unbind(C);
 gap> Unbind(D);