congsemigraph: add meet method

semigroups · Jun 15, 2022 · b961e22 · b961e22
1 parent 256410a
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diff --git a/gap/congruences/congsemigraph.gi b/gap/congruences/congsemigraph.gi
@@ -237,6 +237,30 @@ function(cong1, cong2)
   return CongruenceByWangPair(S, Union(H, X), Difference(W, Union(H, X)));
 end);
 
+InstallMethod(MeetSemigroupCongruences,
+"for two congruences by Wang pair",
+[IsCongruenceByWangPair, IsCongruenceByWangPair],
+function(cong1, cong2)
+  local out, H1, H2, W1, W2, H, V0, v;
+  out := OutNeighbours(GraphOfGraphInverseSemigroup(Source(cong1)));
+  H1 := cong1!.H;
+  H2 := cong2!.H;
+  W1 := cong1!.W;
+  W2 := cong2!.W;
+  H := Union(H1, H2);
+  V0 := [];
+  for v in Difference(Union(W1, W2), H) do
+    if ForAll(out[v], w -> w in H) then
+      Add(V0, v);
+    fi;
+  od;
+  return CongruenceByWangPair(Source(cong1),
+                              Intersection(H1, H2),
+                              Union(Intersection(W1, H2),
+                                    Intersection(W2, H1),
+                                    Difference(Intersection(W1, W2), V0)));
+end);
+
 InstallMethod(IsSubrelation,
 "for two congruences by Wang pair",
 [IsCongruenceByWangPair, IsCongruenceByWangPair],

diff --git a/tst/standard/congruences/congsemigraph.tst b/tst/standard/congruences/congsemigraph.tst
@@ -317,6 +317,104 @@ gap> LatticeOfCongruences(S);
 <lattice of 12 two-sided congruences over 
  <finite graph inverse semigroup with 4 vertices, 4 edges>>
 
+# Meet and join
+gap> D := Digraph([[3, 4], [3, 4], [4], []]);
+<immutable digraph with 4 vertices, 5 edges>
+gap> S := GraphInverseSemigroup(D);
+<finite graph inverse semigroup with 4 vertices, 5 edges>
+gap> L := LatticeOfCongruences(S);
+<lattice of 10 two-sided congruences over 
+ <finite graph inverse semigroup with 4 vertices, 5 edges>>
+gap> C := CongruencesOfSemigroup(S);
+[ <graph inverse semigroup congruence with H = [ 1, 2, 3, 4 ] and W = [  ]>, 
+  <graph inverse semigroup congruence with H = [ 4 ] and W = [ 1, 2 ]>, 
+  <graph inverse semigroup congruence with H = [ 1, 3, 4 ] and W = [  ]>, 
+  <graph inverse semigroup congruence with H = [ 4 ] and W = [ 1 ]>, 
+  <graph inverse semigroup congruence with H = [ 2, 3, 4 ] and W = [  ]>, 
+  <graph inverse semigroup congruence with H = [ 4 ] and W = [ 2 ]>, 
+  <graph inverse semigroup congruence with H = [ 3, 4 ] and W = [  ]>, 
+  <graph inverse semigroup congruence with H = [  ] and W = [ 3 ]>, 
+  <graph inverse semigroup congruence with H = [ 4 ] and W = [  ]>, 
+  <graph inverse semigroup congruence with H = [  ] and W = [  ]> ]
+gap> val := true;;
+> for i in [1 .. Length(C)] do
+> for j in [1 .. Length(C)] do
+> pos := Position(C, JoinSemigroupCongruences(C[i], C[j]));
+> join := PartialOrderDigraphJoinOfVertices(L, i, j);
+> if pos <> join then
+> Error(StringFormatted("the join of congruences {} and {} is {} but should be {}", 
+>                       i, j, pos, join));
+> val := false;
+> fi;
+> od;
+> od;
+> val;
+true
+gap> val := true;;
+> for i in [1 .. Length(C)] do
+> for j in [1 .. Length(C)] do
+> pos := Position(C, MeetSemigroupCongruences(C[i], C[j]));
+> meet := PartialOrderDigraphMeetOfVertices(L, i, j);
+> if pos <> meet then
+> Error(StringFormatted("the meet of congruences {} and {} is {} but should be {}", 
+>                       i, j, pos, meet));
+> val := false;
+> fi;
+> od;
+> od;
+> val;
+true
+
+# More meet and join
+gap> D := Digraph([[2], [3, 4], [4], []]);
+<immutable digraph with 4 vertices, 4 edges>
+gap> S := GraphInverseSemigroup(D);
+<finite graph inverse semigroup with 4 vertices, 4 edges>
+gap> L := LatticeOfCongruences(S);
+<lattice of 12 two-sided congruences over 
+ <finite graph inverse semigroup with 4 vertices, 4 edges>>
+gap> C := CongruencesOfSemigroup(S);
+[ <graph inverse semigroup congruence with H = [ 1, 2, 3, 4 ] and W = [  ]>, 
+  <graph inverse semigroup congruence with H = [ 4 ] and W = [ 1, 2 ]>, 
+  <graph inverse semigroup congruence with H = [ 3, 4 ] and W = [ 1 ]>, 
+  <graph inverse semigroup congruence with H = [  ] and W = [ 1, 3 ]>, 
+  <graph inverse semigroup congruence with H = [ 4 ] and W = [ 1 ]>, 
+  <graph inverse semigroup congruence with H = [  ] and W = [ 1 ]>, 
+  <graph inverse semigroup congruence with H = [ 2, 3, 4 ] and W = [  ]>, 
+  <graph inverse semigroup congruence with H = [ 4 ] and W = [ 2 ]>, 
+  <graph inverse semigroup congruence with H = [ 3, 4 ] and W = [  ]>, 
+  <graph inverse semigroup congruence with H = [  ] and W = [ 3 ]>, 
+  <graph inverse semigroup congruence with H = [ 4 ] and W = [  ]>, 
+  <graph inverse semigroup congruence with H = [  ] and W = [  ]> ]
+gap> val := true;;
+> for i in [1 .. Length(C)] do
+> for j in [1 .. Length(C)] do
+> pos := Position(C, JoinSemigroupCongruences(C[i], C[j]));
+> join := PartialOrderDigraphJoinOfVertices(L, i, j);
+> if pos <> join then
+> Error(StringFormatted("the join of congruences {} and {} is {} but should be {}", 
+>                       i, j, pos, join));
+> val := false;
+> fi;
+> od;
+> od;
+> val;
+true
+gap> val := true;;
+> for i in [1 .. Length(C)] do
+> for j in [1 .. Length(C)] do
+> pos := Position(C, MeetSemigroupCongruences(C[i], C[j]));
+> meet := PartialOrderDigraphMeetOfVertices(L, i, j);
+> if pos <> meet then
+> Error(StringFormatted("the meet of congruences {} and {} is {} but should be {}", 
+>                       i, j, pos, meet));
+> val := false;
+> fi;
+> od;
+> od;
+> val;
+true
+
 #
 gap> SEMIGROUPS.StopTest();
 gap> STOP_TEST("Semigroups package: standard/congruences/cong.tst");