small edits

semigroups · Aug 21, 2024 · ae4f45d · ae4f45d
1 parent dfc6a66
commit ae4f45d
Show file tree

Hide file tree

Showing 2 changed files with 27 additions and 23 deletions.
diff --git a/gap/attributes/attr.gd b/gap/attributes/attr.gd
@@ -75,6 +75,7 @@ DeclareAttribute("NambooripadPartialOrder", IsSemigroup);
 DeclareOperation("KernelContainment",
                  [IsTransformation, IsTransformation, IsPosInt]);
 DeclareAttribute("RegularLeqTransformationSemigroupNC", IsTransformationSemigroup);
+DeclareAttribute("MitschLeqSemigroupNC", IsSemigroup);
 DeclareAttribute("MitschLeqSemigroup", IsSemigroup);
 DeclareAttribute("MitschOrderOfTransformationSemigroup",
                  IsFinite and IsTransformationSemigroup);

diff --git a/gap/attributes/attr.gi b/gap/attributes/attr.gi
@@ -1045,10 +1045,10 @@ function(S)
 
   return
     function(x, y)
-      local R;
-      R := RClass(S, x);
-      return IsGreensLessThanOrEqual(R, RClass(S, y))
-        and ForAny(Idempotents(R), e -> e * y = x);
+      local E;
+      E := Idempotents(S);
+      return ForAny(E, e -> e * y = x)
+        and ForAny(E, f -> y * f = x);
     end;
 end);
 
@@ -1089,18 +1089,11 @@ function(S)
         end;
 end);
 
-InstallMethod(MitschLeqSemigroup,
+InstallMethod(MitschLeqSemigroupNC,
 "for a semigroup",
 [IsSemigroup],
 function(S)
-    if IsInverseSemigroup(S) then
-        return NaturalLeqInverseSemigroup(S);
-    elif IsRegularSemigroup(S) and IsTransformationSemigroup(S) then
-        return RegularLeqTransformationSemigroupNC(S);
-    elif IsRegularSemigroup(S) then
-        return NambooripadLeqRegularSemigroup(S);
-    else 
-        return 
+    return 
         function(x, y)
             if x = y then
                 return true;
@@ -1109,6 +1102,20 @@ function(S)
                     ForAny(Elements(S), t -> t * y = x and t * x = x);
             fi;
         end;
+end);
+
+InstallMethod(MitschLeqSemigroup,
+"for a semigroup",
+[IsSemigroup],
+function(S)
+    if IsInverseSemigroup(S) then
+        return NaturalLeqInverseSemigroup(S);
+    elif IsRegularSemigroup(S) and IsTransformationSemigroup(S) then
+        return RegularLeqTransformationSemigroupNC(S);
+    elif IsRegularSemigroup(S) then
+        return NambooripadLeqRegularSemigroup(S);
+    else 
+        return MitschLeqSemigroupNC(S);
     fi;
 end);
 
@@ -1120,19 +1127,15 @@ function(S)
     elts := ShallowCopy(AsListCanonical(S));
     p    := Sortex(elts, {x, y} -> IsGreensDGreaterThanFunc(S)(y, x)) ^ -1;
     func1 := RegularLeqTransformationSemigroupNC(S);
-    func2 := MitschLeqSemigroup(S);
+    func2 := MitschLeqSemigroupNC(S);
     out  := List([1 .. Size(S)], x -> []);
     regular := BlistList([1 .. Size(S)], []);
-    if IsRegularSemigroup(S) then
-        FlipBlist(regular);
-    else
-        for D in RegularDClasses(S) do
-            for a in D do
-                i := PositionCanonical(S, a) ^ (p ^ -1);
-                regular[i] := true;
-            od;
+    for D in RegularDClasses(S) do
+        for a in D do
+            i := PositionCanonical(S, a) ^ (p ^ -1);
+            regular[i] := true;
         od;
-    fi;
+    od;
     for j in [Size(S), Size(S) - 1 .. 1] do
         if regular[j] then
             for i in [j - 1, j - 2 .. 1] do