Add SubdigraphsMonomorphisms

doc/z-chap6.xml

@@ -20,7 +20,7 @@ from} $E_a$ \emph{to} $E_b$. In this case we say that $E_a$ and $E_b$ are
     &nauty; (via &NautyTracesInterface;) to calculate canonical labellings and
     automorphism groups of digraphs; see <Cite Key="JK07"/> and <Cite
       Key="MP14"/> for more details about &bliss; and &nauty;,
-    respectively. 
+    respectively.
 
     <#Include Label="DigraphsUseNauty">
     <#Include Label="AutomorphismGroupDigraph">
@@ -65,6 +65,7 @@ from} $E_a$ \emph{to} $E_b$. In this case we say that $E_a$ and $E_b$ are
     <#Include Label="EmbeddingsDigraphs">
     <#Include Label="IsDigraphHomomorphism">
     <#Include Label="IsDigraphEmbedding">
+    <#Include Label="SubdigraphsMonomorphisms">
     <#Include Label="DigraphsRespectsColouring">
     <#Include Label="GeneratorsOfEndomorphismMonoid">
     <#Include Label="DigraphColouring">

gap/cliques.gi

@@ -10,26 +10,6 @@
 #############################################################################
 ##
 
-BindGlobal("AddOrbitToHashMap",
-function(G, set, hashmap)
-  local gens, o, im, pt, g;
-
-  gens := GeneratorsOfGroup(G);
-  o    := [set];
-  Assert(1, not set in hashmap);
-  hashmap[set] := true;
-  for pt in o do
-    for g in gens do
-      im := OnSets(pt, g);
-      if not im in hashmap then
-        hashmap[im] := true;
-        Add(o, im);
-      fi;
-    od;
-  od;
-  return o;
-end);
-
 InstallMethod(CliqueNumber, "for a digraph", [IsDigraph],
 D -> Maximum(List(DigraphMaximalCliquesReps(D), Length)));
 
@@ -570,7 +550,7 @@ function(arg...)
       orbits := HashMap();
       for c in cliques do
         if not c in orbits then
-          AddOrbitToHashMap(G, c, orbits);
+          DIGRAPHS_AddOrbitToHashMap(G, c, orbits);
         fi;
       od;
       out := Keys(orbits);
@@ -729,7 +709,7 @@ function(digraph, hook, user_param, limit, include, exclude, max, size, reps)
 
         new_found := 0;
         if not clique in found_orbits then
-          orbit := AddOrbitToHashMap(group, clique, found_orbits);
+          orbit := DIGRAPHS_AddOrbitToHashMap(group, clique, found_orbits);
           n := Length(orbit);
 
           if invariant_include and invariant_exclude then
@@ -915,7 +895,7 @@ 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 := AddOrbitToHashMap(grp, c, found_orbits);
+      orb := DIGRAPHS_AddOrbitToHashMap(grp, c, found_orbits);
       n := Length(orb);
 
       if invariant then  # we're not just looking for orbit reps, but inc and

gap/grahom.gd

@@ -21,6 +21,11 @@ DeclareOperation("MonomorphismsDigraphs", [IsDigraph, IsDigraph]);
 DeclareOperation("MonomorphismsDigraphsRepresentatives",
                  [IsDigraph, IsDigraph]);
 
+DeclareOperation("SubdigraphsMonomorphismsRepresentatives",
+                 [IsDigraph, IsDigraph]);
+DeclareOperation("SubdigraphsMonomorphisms",
+                 [IsDigraph, IsDigraph]);
+
 DeclareOperation("DigraphEpimorphism", [IsDigraph, IsDigraph]);
 DeclareOperation("EpimorphismsDigraphs", [IsDigraph, IsDigraph]);
 DeclareOperation("EpimorphismsDigraphsRepresentatives", [IsDigraph, IsDigraph]);

gap/grahom.gi

@@ -330,6 +330,79 @@ function(D1, D2)
   return Union(List(aut, x -> hom * x));
 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);
+
+  map := HashMap();
+  reps := [];
+
+  for set in Combinations(GV, HN) do
+    if not set in map then
+      Add(reps, set);
+      DIGRAPHS_AddOrbitToHashMap(AutomorphismGroup(G), set, 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));
+    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));
+    od;
+    return DigraphNC(new);
+  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;
+  od;
+  return result;
+end);
+
 ################################################################################
 # SURJECTIVE HOMOMORPHISMS
 

gap/orbits.gd

@@ -12,6 +12,7 @@ DeclareGlobalFunction("DIGRAPHS_Orbits");
 DeclareGlobalFunction("DIGRAPHS_TraceSchreierVector");
 DeclareGlobalFunction("DIGRAPHS_EvaluateWord");
 DeclareAttribute("DIGRAPHS_Stabilizers", IsDigraph, "mutable");
+DeclareGlobalFunction("DIGRAPHS_AddOrbitToHashMap");
 
 DeclareAttribute("DigraphGroup", IsDigraph);
 DeclareAttribute("DigraphOrbits", IsDigraph);

gap/orbits.gi

@@ -68,6 +68,26 @@ function(G, domain)
   return rec(orbits := orbs, schreier := sch, lookup := lookup);
 end);
 
+InstallGlobalFunction(DIGRAPHS_AddOrbitToHashMap,
+function(G, set, hashmap)
+  local gens, o, im, pt, g;
+
+  gens := GeneratorsOfGroup(G);
+  o    := [set];
+  Assert(1, not set in hashmap);
+  hashmap[set] := true;
+  for pt in o do
+    for g in gens do
+      im := OnSets(pt, g);
+      if not im in hashmap then
+        hashmap[im] := true;
+        Add(o, im);
+      fi;
+    od;
+  od;
+  return o;
+end);
+
 InstallMethod(RepresentativeOutNeighbours, "for a digraph by out-neighbours",
 [IsDigraphByOutNeighboursRep],
 function(D)

gap/utils.gi

@@ -262,7 +262,8 @@ function(arg...)
       s := InputTextString(ex[1]);
 
       start_time := IO_gettimeofday();
-      test := Test(s, rec(ignoreComments := false,
+      test := Test(s, rec(compareFunction := "uptowhitespace",
+                          ignoreComments := false,
                           width := 72,
                           EQ := EQ,
                           reportDiff := Ignore,

tst/standard/grahom.tst

@@ -2739,6 +2739,26 @@ false
 gap> IsLatticeEpimorphism(D, D, (2, 3));
 true
 
+# SubdigraphsMonomorphisms
+gap> SubdigraphsMonomorphisms(CompleteBipartiteDigraph(2, 2),
+> CompleteDigraph(4));
+[ Transformation( [ 1, 3, 2 ] ), Transformation( [ 2, 3, 1 ] ), 
+  Transformation( [ 3, 4, 2, 1 ] ) ]
+gap> D := DigraphFromGraph6String("D^{");
+<immutable symmetric digraph with 5 vertices, 18 edges>
+gap> SubdigraphsMonomorphisms(CompleteDigraph(4), D);
+[ Transformation( [ 1, 3, 4, 5, 5 ] ), Transformation( [ 2, 3, 4, 5, 5 ] ) ]
+gap> Length(SubdigraphsMonomorphisms(CompleteDigraph(4), CompleteDigraph(12)));
+495
+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
+
 #  DIGRAPHS_UnbindVariables
 gap> Unbind(D);
 gap> Unbind(D1);