Final tweaks

gap/attributes/isomorph.gi

@@ -105,13 +105,18 @@ end);
 
 InstallMethod(IsIsomorphicSemigroup, "for semigroups",
 [IsSemigroup, IsSemigroup],
-{S, T} -> IsomorphismSemigroups(S, T) <> fail);
-
-InstallMethod(IsIsomorphicSemigroup, "for finite simple semigroups",
-[IsSimpleSemigroup and IsFinite, IsSimpleSemigroup and IsFinite],
 function(R, S)
   local uR, uS, map, mat, next, row, entry, isoR, rmsR, isoS, rmsS;
 
+  if not (IsFinite(R) and IsSimpleSemigroup(R)
+          and IsFinite(S) and IsSimpleSemigroup(S)) then
+    return IsomorphismSemigroups(R, S) <> fail;
+  fi;
+
+  # Note that when experimenting the method for IsomorphismSemigroups for Rees
+  # 0-matrix semigroups is faster than the analogue of the below code, and so
+  # we do not special case finite 0-simple semigroups.
+
   # Take an isomorphism of R to an RMS if appropriate
   if not (IsReesMatrixSemigroup(R) and IsWholeFamily(R)
       and IsPermGroup(UnderlyingSemigroup(R))) then
@@ -129,30 +134,22 @@ function(R, S)
     rmsS := S;
   fi;
 
-  uR := UnderlyingSemigroup(rmsR);
-  uS := UnderlyingSemigroup(rmsS);
-
-  if Length(Rows(rmsR)) <> Length(Rows(rmsS)) then
-    return false;
-  fi;
-  if Length(Columns(rmsR)) <> Length(Columns(rmsS)) then
-    return false;
-  fi;
-  if Size(uR) <> Size(uS) then
-    return false;
-  fi;
-  if not IsGroup(uR) then
-    return false;
-  fi;
-  if not IsGroup(uS) then
+  if Length(Rows(rmsR)) <> Length(Rows(rmsS))
+      or (Length(Columns(rmsR)) <> Length(Columns(rmsS))) then
     return false;
   fi;
 
+  uR := UnderlyingSemigroup(rmsR);
+  uS := UnderlyingSemigroup(rmsS);
+
+  # uS and uR must be groups because we made them so above.
   map := IsomorphismGroups(uS, uR);
   if map = fail then
     return false;
   fi;
 
+  # Make sure underlying groups are the same, and then compare
+  # canonical Rees matrix semigroups of both R and S
   mat := [];
   for row in Matrix(rmsS) do
     next := [];
@@ -162,8 +159,6 @@ function(R, S)
     Add(mat, next);
   od;
 
-  # Make sure underlying groups are the same, and then compare
-  # canonical Rees matrix semigroups of both R and S
   rmsR := CanonicalReesMatrixSemigroup(rmsR);
   rmsS := ReesMatrixSemigroup(uR, mat);
   rmsS := CanonicalReesMatrixSemigroup(rmsS);

tst/standard/attributes/isomorph.tst

@@ -141,6 +141,20 @@ gap> IsIsomorphicSemigroup(S, T);
 false
 gap> IsIsomorphicSemigroup(T, T);
 true
+gap> M := [[(1, 2, 3), ()], [(), ()], [(), ()]];
+[ [ (1,2,3), () ], [ (), () ], [ (), () ] ]
+gap> N := [[(1, 3, 2), ()], [(), (1, 2, 3)]];
+[ [ (1,3,2), () ], [ (), (1,2,3) ] ]
+gap> R := ReesMatrixSemigroup(AlternatingGroup([1 .. 3]), M);;
+gap> S := ReesMatrixSemigroup(AlternatingGroup([1 .. 3]), N);;
+gap> IsIsomorphicSemigroup(R, S);
+false
+gap> R := ReesMatrixSemigroup(AlternatingGroup([1 .. 5]),
+> [[(), ()], [(), (1, 3, 2, 4, 5)]]);;
+gap> S := ReesMatrixSemigroup(AlternatingGroup([1 .. 5]),
+> [[(1, 5, 4, 3, 2), ()], [(1, 4, 5), (1, 4)(3, 5)]]);;
+gap> IsIsomorphicSemigroup(R, S);
+false
 
 # isomorph: IsomorphismSemigroups, for infinite semigroup(s)
 gap> S := FreeSemigroup(1);;