From c31b830137ad889fb93502dca3b37224c3d93672 Mon Sep 17 00:00:00 2001
From: "James D. Mitchell" <jdm3@st-andrews.ac.uk>
Date: Tue, 25 Jun 2024 13:29:44 +0100
Subject: [PATCH 01/23] Some template improvements

---
 gap/attributes/isomorph.gi | 19 ++++++++++++++-----
 gap/attributes/isorms.gi   |  2 +-
 2 files changed, 15 insertions(+), 6 deletions(-)

diff --git a/gap/attributes/isomorph.gi b/gap/attributes/isomorph.gi
index 5d28954a8..266516c5a 100644
--- a/gap/attributes/isomorph.gi
+++ b/gap/attributes/isomorph.gi
@@ -107,6 +107,16 @@ InstallMethod(IsIsomorphicSemigroup, "for semigroups",
 [IsSemigroup, IsSemigroup],
 {S, T} -> IsomorphismSemigroups(S, T) <> fail);
 
+InstallMethod(IsIsomorphicSemigroup, "for semigroups",
+[IsSimpleSemigroup, IsSimpleSemigroup],
+function(S, T)
+  if not IsReesMatrixSemigroup(S) then
+    SS := Range(IsomorphismReesMatrixSemigroupOverPermGroup(S);
+  fi;
+  # Same for T
+  return CanonicalReesMatrixSemigroup(S) = CanonicalReesMatrixSemigroup(T);
+end);
+
 InstallMethod(IsomorphismSemigroups, "for finite simple semigroups",
 [IsSimpleSemigroup and IsFinite, IsSimpleSemigroup and IsFinite],
 function(S, T)
@@ -279,13 +289,12 @@ function(S, T)
     return fail;
   fi;
 
-  DS := SEMIGROUPS.CanonicalDigraph(S);
-  DT := SEMIGROUPS.CanonicalDigraph(T);
-  p := IsomorphismDigraphs(DS[1], DT[1], DS[2], DT[2]);
-  if p = fail then
+  if CanonicalMultiplicationTable(S) <> CanonicalMultiplicationTable(T) then
     return fail;
   fi;
-  p := RestrictedPerm(p, [1 .. Size(S)]);
+  p := CanonicalMultiplicationTablePerm(S)
+       * CanonicalMultiplicationTablePerm(T) ^ -1;
+
   map := x -> AsSSortedList(T)[PositionSorted(S, x) ^ p];
   inv := x -> AsSSortedList(S)[PositionSorted(T, x) ^ (p ^ -1)];
   return SemigroupIsomorphismByFunctionNC(S, T, map, inv);
diff --git a/gap/attributes/isorms.gi b/gap/attributes/isorms.gi
index 60e6e75b9..16eb327f8 100644
--- a/gap/attributes/isorms.gi
+++ b/gap/attributes/isorms.gi
@@ -1368,7 +1368,7 @@ function(S)
 end);
 
 InstallMethod(CanonicalReesMatrixSemigroup,
-"for a Rees 0-matrix semigroup",
+"for a Rees matrix semigroup",
 [IsReesMatrixSemigroup],
 function(S)
   local G, mat;

From 43f85035967445e5c9ed8916f00a95629ad53d41 Mon Sep 17 00:00:00 2001
From: "James D. Mitchell" <jdm3@st-andrews.ac.uk>
Date: Thu, 27 Jun 2024 13:45:05 +0100
Subject: [PATCH 02/23] More example isomorph code

---
 gap/attributes/isomorph.gi | 11 ++++++++++-
 1 file changed, 10 insertions(+), 1 deletion(-)

diff --git a/gap/attributes/isomorph.gi b/gap/attributes/isomorph.gi
index 266516c5a..2f39ec9cc 100644
--- a/gap/attributes/isomorph.gi
+++ b/gap/attributes/isomorph.gi
@@ -105,7 +105,16 @@ end);
 
 InstallMethod(IsIsomorphicSemigroup, "for semigroups",
 [IsSemigroup, IsSemigroup],
-{S, T} -> IsomorphismSemigroups(S, T) <> fail);
+function(S, T)
+  if IsSimpleSemigroup(S) and IsSimpleSemigroup(T) then
+    return IsIsomorphicSemigroup(Range(IsomorphismReesMatrixSemigroup(S)), ...);
+  fi;
+  return IsomorphismSemigroups(S, T) <> fail;
+end);
+
+InstallMethod(IsIsomorphicSemigroup, "for Rees matrix semigroups",
+[IsReesMatrixSemigroup, IsReesMatrixSemigroup],
+IsIsomorphicRMS);
 
 InstallMethod(IsIsomorphicSemigroup, "for semigroups",
 [IsSimpleSemigroup, IsSimpleSemigroup],

From 90aafa27b5d63cc547dea673cd63fbdf2215869d Mon Sep 17 00:00:00 2001
From: Tillman Froehlich <tillmanfroehlich@gmail.com>
Date: Fri, 28 Jun 2024 12:39:23 +0100
Subject: [PATCH 03/23] Added the isomtest file created in the meeting
 yesterday

---
 gap/attributes/isomtest.g | 39 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 39 insertions(+)
 create mode 100644 gap/attributes/isomtest.g

diff --git a/gap/attributes/isomtest.g b/gap/attributes/isomtest.g
new file mode 100644
index 000000000..757143164
--- /dev/null
+++ b/gap/attributes/isomtest.g
@@ -0,0 +1,39 @@
+RandomIsomorphicRMS := function(R)
+  local table, p, S;
+  if Size(R) > 384 then
+    ErrorNoReturn("Tillman what were thinking???");
+  fi;
+  table := MultiplicationTable(R);
+  p := Random(SymmetricGroup(Size(R)));
+  S := SemigroupByMultiplicationTableNC(OnMultiplicationTable(table, p));
+  return Range(IsomorphismReesMatrixSemigroup(S));
+end;
+
+# TODO check that this is faster than computing CanonicalMultiplicationTable
+
+IsIsomorphicRMS := function(R, S)
+  local uR, uS, map;
+  # TODO check that R and S have the same dimensions, and same size underlying group
+  R := CanonicalReesMatrixSemigroup(R);
+  uR := UnderlyingSemigroup(R);
+  uS := UnderlyingSemigroup(S);
+  # TODO check if uR, uS is a group
+  map := IsomorphismGroups(uS, uR);
+  if map = fail then
+    return false;
+  fi;
+
+  mat := [];
+  for row in Matrix(S) do
+    next := [];
+    for entry in row do
+      Add(next, entry ^ map);
+    od;
+    Add(mat, next);
+  od;
+  S := ReesMatrixSemigroup(uR, mat);
+  S := CanonicalReesMatrixSemigroup(S);
+  return Matrix(R) = Matrix(S);
+end;
+
+# TODO similar thing for RZMS

From da909422cca7bcb1d40f6c813cb19a0110529ac3 Mon Sep 17 00:00:00 2001
From: Tillman Froehlich <tillmanfroehlich@gmail.com>
Date: Fri, 28 Jun 2024 12:55:52 +0100
Subject: [PATCH 04/23] Fixed some (but not all) syntax errors

---
 gap/attributes/isomorph.gi | 6 ++++--
 gap/attributes/isomtest.g  | 4 ++--
 2 files changed, 6 insertions(+), 4 deletions(-)

diff --git a/gap/attributes/isomorph.gi b/gap/attributes/isomorph.gi
index 2f39ec9cc..5f0fbd02e 100644
--- a/gap/attributes/isomorph.gi
+++ b/gap/attributes/isomorph.gi
@@ -107,7 +107,8 @@ InstallMethod(IsIsomorphicSemigroup, "for semigroups",
 [IsSemigroup, IsSemigroup],
 function(S, T)
   if IsSimpleSemigroup(S) and IsSimpleSemigroup(T) then
-    return IsIsomorphicSemigroup(Range(IsomorphismReesMatrixSemigroup(S)), ...);
+    return IsIsomorphicSemigroup(Range(IsomorphismReesMatrixSemigroup(S)), 
+                                 Range(IsomorphismReesMatrixSemigroups(T)));
   fi;
   return IsomorphismSemigroups(S, T) <> fail;
 end);
@@ -119,8 +120,9 @@ IsIsomorphicRMS);
 InstallMethod(IsIsomorphicSemigroup, "for semigroups",
 [IsSimpleSemigroup, IsSimpleSemigroup],
 function(S, T)
+  local SS;
   if not IsReesMatrixSemigroup(S) then
-    SS := Range(IsomorphismReesMatrixSemigroupOverPermGroup(S);
+    SS := Range(IsomorphismReesMatrixSemigroupOverPermGroup(S));
   fi;
   # Same for T
   return CanonicalReesMatrixSemigroup(S) = CanonicalReesMatrixSemigroup(T);
diff --git a/gap/attributes/isomtest.g b/gap/attributes/isomtest.g
index 757143164..7d90e8d43 100644
--- a/gap/attributes/isomtest.g
+++ b/gap/attributes/isomtest.g
@@ -1,7 +1,7 @@
 RandomIsomorphicRMS := function(R)
   local table, p, S;
   if Size(R) > 384 then
-    ErrorNoReturn("Tillman what were thinking???");
+    ErrorNoReturn("Tillman what were you thinking???");
   fi;
   table := MultiplicationTable(R);
   p := Random(SymmetricGroup(Size(R)));
@@ -12,7 +12,7 @@ end;
 # TODO check that this is faster than computing CanonicalMultiplicationTable
 
 IsIsomorphicRMS := function(R, S)
-  local uR, uS, map;
+  local uR, uS, map, mat, next, row, entry;
   # TODO check that R and S have the same dimensions, and same size underlying group
   R := CanonicalReesMatrixSemigroup(R);
   uR := UnderlyingSemigroup(R);

From ac959811def54e73c87067634a3d042b8ce6d137 Mon Sep 17 00:00:00 2001
From: Tillman Froehlich <tillmanfroehlich@gmail.com>
Date: Tue, 2 Jul 2024 10:22:19 +0100
Subject: [PATCH 05/23] Added reminder of which packages to load

---
 gap/attributes/isomtest.g | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/gap/attributes/isomtest.g b/gap/attributes/isomtest.g
index 7d90e8d43..a38ee8d3b 100644
--- a/gap/attributes/isomtest.g
+++ b/gap/attributes/isomtest.g
@@ -1,3 +1,6 @@
+# LoadPackage("Semigroups");
+# LoadPackage("smallsemi");
+
 RandomIsomorphicRMS := function(R)
   local table, p, S;
   if Size(R) > 384 then

From 6bc39003ff8c7386e712034791b9d2d9dbf76a50 Mon Sep 17 00:00:00 2001
From: Tillman Froehlich <tillmanfroehlich@gmail.com>
Date: Tue, 2 Jul 2024 10:46:37 +0100
Subject: [PATCH 06/23] Removed useless comments

---
 gap/attributes/isomtest.g | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/gap/attributes/isomtest.g b/gap/attributes/isomtest.g
index a38ee8d3b..7d90e8d43 100644
--- a/gap/attributes/isomtest.g
+++ b/gap/attributes/isomtest.g
@@ -1,6 +1,3 @@
-# LoadPackage("Semigroups");
-# LoadPackage("smallsemi");
-
 RandomIsomorphicRMS := function(R)
   local table, p, S;
   if Size(R) > 384 then

From 98f816f8b41ed1eaaa792d149409b85c415e2fb3 Mon Sep 17 00:00:00 2001
From: Tillman Froehlich <tillmanfroehlich@gmail.com>
Date: Tue, 2 Jul 2024 11:54:46 +0100
Subject: [PATCH 07/23] Commented out code that doesn't work yet

---
 gap/attributes/isomorph.gi | 36 ++++++++++++++++++------------------
 1 file changed, 18 insertions(+), 18 deletions(-)

diff --git a/gap/attributes/isomorph.gi b/gap/attributes/isomorph.gi
index 5f0fbd02e..c43fe624f 100644
--- a/gap/attributes/isomorph.gi
+++ b/gap/attributes/isomorph.gi
@@ -106,27 +106,27 @@ end);
 InstallMethod(IsIsomorphicSemigroup, "for semigroups",
 [IsSemigroup, IsSemigroup],
 function(S, T)
-  if IsSimpleSemigroup(S) and IsSimpleSemigroup(T) then
-    return IsIsomorphicSemigroup(Range(IsomorphismReesMatrixSemigroup(S)), 
-                                 Range(IsomorphismReesMatrixSemigroups(T)));
-  fi;
+  #if IsSimpleSemigroup(S) and IsSimpleSemigroup(T) then
+  #  return IsIsomorphicSemigroup(Range(IsomorphismReesMatrixSemigroup(S)), 
+  #                               Range(IsomorphismReesMatrixSemigroup(T)));
+  #fi;
   return IsomorphismSemigroups(S, T) <> fail;
 end);
 
-InstallMethod(IsIsomorphicSemigroup, "for Rees matrix semigroups",
-[IsReesMatrixSemigroup, IsReesMatrixSemigroup],
-IsIsomorphicRMS);
-
-InstallMethod(IsIsomorphicSemigroup, "for semigroups",
-[IsSimpleSemigroup, IsSimpleSemigroup],
-function(S, T)
-  local SS;
-  if not IsReesMatrixSemigroup(S) then
-    SS := Range(IsomorphismReesMatrixSemigroupOverPermGroup(S));
-  fi;
-  # Same for T
-  return CanonicalReesMatrixSemigroup(S) = CanonicalReesMatrixSemigroup(T);
-end);
+#InstallMethod(IsIsomorphicSemigroup, "for Rees matrix semigroups",
+#[IsReesMatrixSemigroup, IsReesMatrixSemigroup],
+#IsIsomorphicRMS);
+
+#InstallMethod(IsIsomorphicSemigroup, "for semigroups",
+#[IsSimpleSemigroup, IsSimpleSemigroup],
+#function(S, T)
+#  local SS;
+#  if not IsReesMatrixSemigroup(S) then
+#    SS := Range(IsomorphismReesMatrixSemigroupOverPermGroup(S));
+#  fi;
+#  # Same for T
+#  return CanonicalReesMatrixSemigroup(S) = CanonicalReesMatrixSemigroup(T);
+#end);
 
 InstallMethod(IsomorphismSemigroups, "for finite simple semigroups",
 [IsSimpleSemigroup and IsFinite, IsSimpleSemigroup and IsFinite],

From cfa3fc2fe25d23c1b7e9a7247ce8b2194f66d204 Mon Sep 17 00:00:00 2001
From: awesometillman <tillmanfroehlich@gmail.com>
Date: Wed, 3 Jul 2024 15:58:49 +0100
Subject: [PATCH 08/23] Added function to make some random Rees matrix
 semigroups.

---
 gap/attributes/isomtest.g | 14 ++++++++++++++
 1 file changed, 14 insertions(+)

diff --git a/gap/attributes/isomtest.g b/gap/attributes/isomtest.g
index 7d90e8d43..c4f49f6c8 100644
--- a/gap/attributes/isomtest.g
+++ b/gap/attributes/isomtest.g
@@ -37,3 +37,17 @@ IsIsomorphicRMS := function(R, S)
 end;
 
 # TODO similar thing for RZMS
+
+MakeSomeRMS := function(n)
+  local semigroups_list, S;
+
+  semigroups_list := [];
+  while Length(semigroups_list) < n do
+    S := RandomSemigroup(IsReesMatrixSemigroup, 2, 2);
+    if Size(S) < 384 then
+      Append(semigroups_list, [S]);
+    fi;
+  od;
+
+  return semigroups_list;
+end;

From caef41114d5b2e26dbfbb34a17b8e96fa0716387 Mon Sep 17 00:00:00 2001
From: awesometillman <tillmanfroehlich@gmail.com>
Date: Wed, 3 Jul 2024 16:54:24 +0100
Subject: [PATCH 09/23] Added testing function to compare isomorphism
 functions.

---
 gap/attributes/isomtest.g | 28 +++++++++++++++++++++++++---
 1 file changed, 25 insertions(+), 3 deletions(-)

diff --git a/gap/attributes/isomtest.g b/gap/attributes/isomtest.g
index c4f49f6c8..fb44f2a27 100644
--- a/gap/attributes/isomtest.g
+++ b/gap/attributes/isomtest.g
@@ -1,6 +1,6 @@
 RandomIsomorphicRMS := function(R)
   local table, p, S;
-  if Size(R) > 384 then
+  if Size(R) > 1000 then
     ErrorNoReturn("Tillman what were you thinking???");
   fi;
   table := MultiplicationTable(R);
@@ -39,15 +39,37 @@ end;
 # TODO similar thing for RZMS
 
 MakeSomeRMS := function(n)
+  # Returns a list of n small Rees matrix semigroups
   local semigroups_list, S;
 
   semigroups_list := [];
   while Length(semigroups_list) < n do
-    S := RandomSemigroup(IsReesMatrixSemigroup, 2, 2);
-    if Size(S) < 384 then
+    S := RandomSemigroup(IsReesMatrixSemigroup, 4, 5, AlternatingGroup(4));
+    if Size(S) < 1000 then
       Append(semigroups_list, [S]);
     fi;
   od;
 
   return semigroups_list;
 end;
+
+TestRMS := function(S, n)
+  # Tests isomorphism algorithms on given semigroup S
+  # by comparing it to n random isomorphic RMS
+  local T, i, runtime;
+
+  for i in [1 .. n] do
+    T := RandomIsomorphicRMS(S);
+    Print("Semigroup ", i, "\n");
+
+    Print("using IsIsomorphicRMS\n");
+    runtime := Runtime();
+    Print(IsIsomorphicRMS(S, T), "\n");
+    Print(Runtime() - runtime, "\n");
+
+    Print("using IsIsomorphicSemigroup\n");
+    runtime := Runtime();
+    Print(IsIsomorphicSemigroup(S, T), "\n");
+    Print(Runtime() - runtime, "\n");
+  od;
+end;
\ No newline at end of file

From dc79b2540783f8c722be2b3ca30c710765227ccd Mon Sep 17 00:00:00 2001
From: awesometillman <tillmanfroehlich@gmail.com>
Date: Wed, 3 Jul 2024 17:06:59 +0100
Subject: [PATCH 10/23] Improved testing function

---
 gap/attributes/isomtest.g | 28 ++++++++++++++++++++--------
 1 file changed, 20 insertions(+), 8 deletions(-)

diff --git a/gap/attributes/isomtest.g b/gap/attributes/isomtest.g
index fb44f2a27..cefb05317 100644
--- a/gap/attributes/isomtest.g
+++ b/gap/attributes/isomtest.g
@@ -56,20 +56,32 @@ end;
 TestRMS := function(S, n)
   # Tests isomorphism algorithms on given semigroup S
   # by comparing it to n random isomorphic RMS
-  local T, i, runtime;
+  local T, i, runtime, oldres, oldtime, newres, newtime, score, mismatches;
 
+  score := [0, 0];
+  mismatches := 0;
   for i in [1 .. n] do
     T := RandomIsomorphicRMS(S);
-    Print("Semigroup ", i, "\n");
 
-    Print("using IsIsomorphicRMS\n");
     runtime := Runtime();
-    Print(IsIsomorphicRMS(S, T), "\n");
-    Print(Runtime() - runtime, "\n");
+    newres := IsIsomorphicRMS(S, T);
+    newtime := Runtime() - runtime;
 
-    Print("using IsIsomorphicSemigroup\n");
     runtime := Runtime();
-    Print(IsIsomorphicSemigroup(S, T), "\n");
-    Print(Runtime() - runtime, "\n");
+    oldres := IsIsomorphicSemigroup(S, T);
+    oldtime := Runtime() - runtime;
+
+    if not newres = oldres then
+      mismatches := mismatches + 1;
+    fi;
+
+    if newtime < oldtime then
+      score[1] := score[1] + 1;
+    else
+      score[2] := score[2] + 1;
+    fi;
   od;
+
+  Print("Score: ", score, "\n");
+  Print("Mismatches: ", mismatches);
 end;
\ No newline at end of file

From e2f8ec98f67b07985d8e0f9b495e9ae3029c1285 Mon Sep 17 00:00:00 2001
From: awesometillman <tillmanfroehlich@gmail.com>
Date: Thu, 4 Jul 2024 15:06:39 +0100
Subject: [PATCH 11/23] Made testing function compare both isomorphic and
 non-isomorphic semigroups.

---
 gap/attributes/isomtest.g | 24 ++++++++++++++++++------
 1 file changed, 18 insertions(+), 6 deletions(-)

diff --git a/gap/attributes/isomtest.g b/gap/attributes/isomtest.g
index cefb05317..35934c456 100644
--- a/gap/attributes/isomtest.g
+++ b/gap/attributes/isomtest.g
@@ -39,7 +39,7 @@ end;
 # TODO similar thing for RZMS
 
 MakeSomeRMS := function(n)
-  # Returns a list of n small Rees matrix semigroups
+  # Makes n random Rees matrix semigroups which aren't too large
   local semigroups_list, S;
 
   semigroups_list := [];
@@ -54,21 +54,30 @@ MakeSomeRMS := function(n)
 end;
 
 TestRMS := function(S, n)
-  # Tests isomorphism algorithms on given semigroup S
-  # by comparing it to n random isomorphic RMS
-  local T, i, runtime, oldres, oldtime, newres, newtime, score, mismatches;
+  # Runs both the new and old isomorphism algorithms on
+  # n semigroups isomorphic to S and n randomly generated
+  # Rees matrix semigroups, then compares times and answers
+  local T, i, runtime, oldres, oldtime, newres, newtime, score, mismatches, testlist;
 
   score := [0, 0];
   mismatches := 0;
+
+  testlist := MakeSomeRMS(n);
   for i in [1 .. n] do
     T := RandomIsomorphicRMS(S);
+    Append(testlist, [T]);
+  od;
+
+  Print("Finished making test list \n");
+
+  for i in [1 .. (2*n)] do
 
     runtime := Runtime();
-    newres := IsIsomorphicRMS(S, T);
+    newres := IsIsomorphicRMS(S, testlist[i]);
     newtime := Runtime() - runtime;
 
     runtime := Runtime();
-    oldres := IsIsomorphicSemigroup(S, T);
+    oldres := IsIsomorphicSemigroup(S, testlist[i]);
     oldtime := Runtime() - runtime;
 
     if not newres = oldres then
@@ -80,6 +89,9 @@ TestRMS := function(S, n)
     else
       score[2] := score[2] + 1;
     fi;
+
+    Print("Finished test ", i, "\n");
+
   od;
 
   Print("Score: ", score, "\n");

From 1a745389c11ffdf8b2b2bb8846d9d8dfffce48d5 Mon Sep 17 00:00:00 2001
From: awesometillman <tillmanfroehlich@gmail.com>
Date: Thu, 4 Jul 2024 15:19:14 +0100
Subject: [PATCH 12/23] Added testing both isomorphism methods against
 comparing canonical multiplication tables

---
 gap/attributes/isomtest.g | 29 +++++++++++++++++++++++------
 1 file changed, 23 insertions(+), 6 deletions(-)

diff --git a/gap/attributes/isomtest.g b/gap/attributes/isomtest.g
index 35934c456..2fb5b1682 100644
--- a/gap/attributes/isomtest.g
+++ b/gap/attributes/isomtest.g
@@ -9,7 +9,12 @@ RandomIsomorphicRMS := function(R)
   return Range(IsomorphismReesMatrixSemigroup(S));
 end;
 
-# TODO check that this is faster than computing CanonicalMultiplicationTable
+# TODO check that this is faster than computing CanonicalMultiplicationTable (CMT)
+
+IsIsomorphicByCMT := function(S, T)
+  # Checks if the canonical multiplication tables of S and T are the same
+  return CanonicalMultiplicationTable(S) = CanonicalMultiplicationTable(T);
+end;
 
 IsIsomorphicRMS := function(R, S)
   local uR, uS, map, mat, next, row, entry;
@@ -57,9 +62,9 @@ TestRMS := function(S, n)
   # Runs both the new and old isomorphism algorithms on
   # n semigroups isomorphic to S and n randomly generated
   # Rees matrix semigroups, then compares times and answers
-  local T, i, runtime, oldres, oldtime, newres, newtime, score, mismatches, testlist;
+  local T, i, runtime, oldres, oldtime, newres, newtime, badres, badtime, score, mismatches, testlist;
 
-  score := [0, 0];
+  score := [0, 0, 0];
   mismatches := 0;
 
   testlist := MakeSomeRMS(n);
@@ -80,14 +85,26 @@ TestRMS := function(S, n)
     oldres := IsIsomorphicSemigroup(S, testlist[i]);
     oldtime := Runtime() - runtime;
 
-    if not newres = oldres then
+    runtime := Runtime();
+    badres := IsIsomorphicByCMT(S, testlist[i]);
+    badtime := Runtime() - runtime;
+
+    if not ((newres = oldres) and (newres = badres)) then
       mismatches := mismatches + 1;
     fi;
 
     if newtime < oldtime then
-      score[1] := score[1] + 1;
+      if newtime < badtime then
+        score[1] := score[1] + 1;
+      else;
+        score[3] := score[3] + 1;
+      fi;
     else
-      score[2] := score[2] + 1;
+      if oldtime < badtime then
+        score[2] := score[2] + 1;
+      else
+        score[3] := score[3] + 1;
+      fi;
     fi;
 
     Print("Finished test ", i, "\n");

From 3f672034b9c829dfff90dd6392c2eb00fb6f90c0 Mon Sep 17 00:00:00 2001
From: awesometillman <tillmanfroehlich@gmail.com>
Date: Fri, 5 Jul 2024 11:48:19 +0100
Subject: [PATCH 13/23] Finished writing IsIsomorphicRMS function, ready to add
 it to isomorph.gi

---
 gap/attributes/isomtest.g | 20 ++++++++++++++++++--
 1 file changed, 18 insertions(+), 2 deletions(-)

diff --git a/gap/attributes/isomtest.g b/gap/attributes/isomtest.g
index 2fb5b1682..60fabe39c 100644
--- a/gap/attributes/isomtest.g
+++ b/gap/attributes/isomtest.g
@@ -18,11 +18,27 @@ end;
 
 IsIsomorphicRMS := function(R, S)
   local uR, uS, map, mat, next, row, entry;
-  # TODO check that R and S have the same dimensions, and same size underlying group
+  
   R := CanonicalReesMatrixSemigroup(R);
   uR := UnderlyingSemigroup(R);
   uS := UnderlyingSemigroup(S);
-  # TODO check if uR, uS is a group
+
+  if NrRows(Matrix(R)) <> NrRows(Matrix(S)) then
+    return false;
+  fi;
+  if NrCols(Matrix(R)) <> NrCols(Matrix(S)) 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
+    return false;
+  fi;
+
   map := IsomorphismGroups(uS, uR);
   if map = fail then
     return false;

From a74a7176b3d3c19db31b415739bc0cda9b76fa77 Mon Sep 17 00:00:00 2001
From: awesometillman <tillmanfroehlich@gmail.com>
Date: Fri, 5 Jul 2024 12:12:26 +0100
Subject: [PATCH 14/23] Added new isomorphism function to isomorph.gi

---
 gap/attributes/isomorph.gi | 84 ++++++++++++++++++++++++++++----------
 1 file changed, 63 insertions(+), 21 deletions(-)

diff --git a/gap/attributes/isomorph.gi b/gap/attributes/isomorph.gi
index c43fe624f..23cf6ef5f 100644
--- a/gap/attributes/isomorph.gi
+++ b/gap/attributes/isomorph.gi
@@ -105,28 +105,70 @@ end);
 
 InstallMethod(IsIsomorphicSemigroup, "for semigroups",
 [IsSemigroup, IsSemigroup],
-function(S, T)
-  #if IsSimpleSemigroup(S) and IsSimpleSemigroup(T) then
-  #  return IsIsomorphicSemigroup(Range(IsomorphismReesMatrixSemigroup(S)), 
-  #                               Range(IsomorphismReesMatrixSemigroup(T)));
-  #fi;
-  return IsomorphismSemigroups(S, T) <> fail;
-end);
+{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;
+
+  # Take an isomorphism of R to an RMS if appropriate
+  if not (IsReesMatrixSemigroup(R) and IsWholeFamily(R)
+      and IsPermGroup(UnderlyingSemigroup(R))) then
+    isoR := IsomorphismReesMatrixSemigroupOverPermGroup(R);
+    rmsR := Range(isoR);
+  else
+    rmsR := R;
+  fi;
+  # Take an isomorphism of S to an RMS if appropriate
+  if not (IsReesMatrixSemigroup(S) and IsWholeFamily(S)
+      and IsPermGroup(UnderlyingSemigroup(S))) then
+    isoS := IsomorphismReesMatrixSemigroupOverPermGroup(S);
+    rmsS := Range(isoS);
+  else
+    rmsS := S;
+  fi;
+  
+  rmsR := CanonicalReesMatrixSemigroup(rmsR);
+  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
+    return false;
+  fi;
 
-#InstallMethod(IsIsomorphicSemigroup, "for Rees matrix semigroups",
-#[IsReesMatrixSemigroup, IsReesMatrixSemigroup],
-#IsIsomorphicRMS);
-
-#InstallMethod(IsIsomorphicSemigroup, "for semigroups",
-#[IsSimpleSemigroup, IsSimpleSemigroup],
-#function(S, T)
-#  local SS;
-#  if not IsReesMatrixSemigroup(S) then
-#    SS := Range(IsomorphismReesMatrixSemigroupOverPermGroup(S));
-#  fi;
-#  # Same for T
-#  return CanonicalReesMatrixSemigroup(S) = CanonicalReesMatrixSemigroup(T);
-#end);
+  map := IsomorphismGroups(uS, uR);
+  if map = fail then
+    return false;
+  fi;
+
+  mat := [];
+  for row in Matrix(rmsS) do
+    next := [];
+    for entry in row do
+      Add(next, entry ^ map);
+    od;
+    Add(mat, next);
+  od;
+
+  # Make sure underlying groups are the same, and then compare
+  # canonical Rees matrix semigroups of both R and S
+  rmsS := ReesMatrixSemigroup(uR, mat);
+  rmsS := CanonicalReesMatrixSemigroup(rmsS);
+  return Matrix(rmsR) = Matrix(rmsS);
+end);
 
 InstallMethod(IsomorphismSemigroups, "for finite simple semigroups",
 [IsSimpleSemigroup and IsFinite, IsSimpleSemigroup and IsFinite],

From 8952697f0f31c5962a28da96d8f8111ebcc7cd46 Mon Sep 17 00:00:00 2001
From: awesometillman <tillmanfroehlich@gmail.com>
Date: Fri, 5 Jul 2024 13:38:58 +0100
Subject: [PATCH 15/23] Added tests to isomorph.tst for new function

---
 tst/standard/attributes/isomorph.tst | 20 ++++++++++++++++++++
 1 file changed, 20 insertions(+)

diff --git a/tst/standard/attributes/isomorph.tst b/tst/standard/attributes/isomorph.tst
index 92d9ae609..78d4d0165 100644
--- a/tst/standard/attributes/isomorph.tst
+++ b/tst/standard/attributes/isomorph.tst
@@ -118,6 +118,26 @@ gap> T := JonesMonoid(4);
 gap> IsIsomorphicSemigroup(S, T);
 false
 
+# isomorph: IsIsomorphicSemigroup, for finite simple semigroups
+gap> M := [[(1,2,3),()],[(),()],[(),()]];
+[ [ (1,2,3), () ], [ (), () ], [ (), () ] ]
+gap> N := [[(1,3,2),()],[(),(1,2,3)],[(1,3,2),(1,3,2)]];
+[ [ (1,3,2), () ], [ (), (1,2,3) ], [ (1,3,2), (1,3,2) ] ]
+gap> R := ReesMatrixSemigroup(AlternatingGroup([1..3]),M);
+<Rees matrix semigroup 2x3 over Alt( [ 1 .. 3 ] )>
+gap> S := ReesMatrixSemigroup(Group([(1,2,3)]),N);
+<Rees matrix semigroup 2x3 over Group([ (1,2,3) ])>
+gap> IsIsomorphicSemigroup(R,S);
+true
+gap> L := [[(),()],[(),()],[(1,2,3),()]];
+[ [ (), () ], [ (), () ], [ (1,2,3), () ] ]
+gap> T := ReesMatrixSemigroup(SymmetricGroup([1..3]),L);
+<Rees matrix semigroup 2x3 over Sym( [ 1 .. 3 ] )>
+gap> IsIsomorphicSemigroup(S,T);
+false
+gap> IsIsomorphicSemigroup(T,T);
+true
+
 # isomorph: IsomorphismSemigroups, for infinite semigroup(s)
 gap> S := FreeSemigroup(1);;
 gap> T := TrivialSemigroup();;

From 549141ca3d898dc99d3e3ba59b3b8776eaf98dd2 Mon Sep 17 00:00:00 2001
From: awesometillman <tillmanfroehlich@gmail.com>
Date: Fri, 5 Jul 2024 13:43:58 +0100
Subject: [PATCH 16/23] Added local variables used in test

---
 tst/standard/attributes/isomorph.tst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/tst/standard/attributes/isomorph.tst b/tst/standard/attributes/isomorph.tst
index 78d4d0165..19ec8feed 100644
--- a/tst/standard/attributes/isomorph.tst
+++ b/tst/standard/attributes/isomorph.tst
@@ -9,7 +9,7 @@
 ##
 
 #@local A, BruteForceInverseCheck, BruteForceIsoCheck, F, G, S, T, U, V, inv
-#@local map, x, y
+#@local map, x, y, M, N, R, L
 gap> START_TEST("Semigroups package: standard/attributes/isomorph.tst");
 gap> LoadPackage("semigroups", false);;
 

From 08f27cd888b251667b255957efa4dae7f94f832f Mon Sep 17 00:00:00 2001
From: awesometillman <tillmanfroehlich@gmail.com>
Date: Fri, 5 Jul 2024 14:19:42 +0100
Subject: [PATCH 17/23] Deleted isomtest.g

---
 gap/attributes/isomtest.g | 132 --------------------------------------
 1 file changed, 132 deletions(-)
 delete mode 100644 gap/attributes/isomtest.g

diff --git a/gap/attributes/isomtest.g b/gap/attributes/isomtest.g
deleted file mode 100644
index 60fabe39c..000000000
--- a/gap/attributes/isomtest.g
+++ /dev/null
@@ -1,132 +0,0 @@
-RandomIsomorphicRMS := function(R)
-  local table, p, S;
-  if Size(R) > 1000 then
-    ErrorNoReturn("Tillman what were you thinking???");
-  fi;
-  table := MultiplicationTable(R);
-  p := Random(SymmetricGroup(Size(R)));
-  S := SemigroupByMultiplicationTableNC(OnMultiplicationTable(table, p));
-  return Range(IsomorphismReesMatrixSemigroup(S));
-end;
-
-# TODO check that this is faster than computing CanonicalMultiplicationTable (CMT)
-
-IsIsomorphicByCMT := function(S, T)
-  # Checks if the canonical multiplication tables of S and T are the same
-  return CanonicalMultiplicationTable(S) = CanonicalMultiplicationTable(T);
-end;
-
-IsIsomorphicRMS := function(R, S)
-  local uR, uS, map, mat, next, row, entry;
-  
-  R := CanonicalReesMatrixSemigroup(R);
-  uR := UnderlyingSemigroup(R);
-  uS := UnderlyingSemigroup(S);
-
-  if NrRows(Matrix(R)) <> NrRows(Matrix(S)) then
-    return false;
-  fi;
-  if NrCols(Matrix(R)) <> NrCols(Matrix(S)) 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
-    return false;
-  fi;
-
-  map := IsomorphismGroups(uS, uR);
-  if map = fail then
-    return false;
-  fi;
-
-  mat := [];
-  for row in Matrix(S) do
-    next := [];
-    for entry in row do
-      Add(next, entry ^ map);
-    od;
-    Add(mat, next);
-  od;
-  S := ReesMatrixSemigroup(uR, mat);
-  S := CanonicalReesMatrixSemigroup(S);
-  return Matrix(R) = Matrix(S);
-end;
-
-# TODO similar thing for RZMS
-
-MakeSomeRMS := function(n)
-  # Makes n random Rees matrix semigroups which aren't too large
-  local semigroups_list, S;
-
-  semigroups_list := [];
-  while Length(semigroups_list) < n do
-    S := RandomSemigroup(IsReesMatrixSemigroup, 4, 5, AlternatingGroup(4));
-    if Size(S) < 1000 then
-      Append(semigroups_list, [S]);
-    fi;
-  od;
-
-  return semigroups_list;
-end;
-
-TestRMS := function(S, n)
-  # Runs both the new and old isomorphism algorithms on
-  # n semigroups isomorphic to S and n randomly generated
-  # Rees matrix semigroups, then compares times and answers
-  local T, i, runtime, oldres, oldtime, newres, newtime, badres, badtime, score, mismatches, testlist;
-
-  score := [0, 0, 0];
-  mismatches := 0;
-
-  testlist := MakeSomeRMS(n);
-  for i in [1 .. n] do
-    T := RandomIsomorphicRMS(S);
-    Append(testlist, [T]);
-  od;
-
-  Print("Finished making test list \n");
-
-  for i in [1 .. (2*n)] do
-
-    runtime := Runtime();
-    newres := IsIsomorphicRMS(S, testlist[i]);
-    newtime := Runtime() - runtime;
-
-    runtime := Runtime();
-    oldres := IsIsomorphicSemigroup(S, testlist[i]);
-    oldtime := Runtime() - runtime;
-
-    runtime := Runtime();
-    badres := IsIsomorphicByCMT(S, testlist[i]);
-    badtime := Runtime() - runtime;
-
-    if not ((newres = oldres) and (newres = badres)) then
-      mismatches := mismatches + 1;
-    fi;
-
-    if newtime < oldtime then
-      if newtime < badtime then
-        score[1] := score[1] + 1;
-      else;
-        score[3] := score[3] + 1;
-      fi;
-    else
-      if oldtime < badtime then
-        score[2] := score[2] + 1;
-      else
-        score[3] := score[3] + 1;
-      fi;
-    fi;
-
-    Print("Finished test ", i, "\n");
-
-  od;
-
-  Print("Score: ", score, "\n");
-  Print("Mismatches: ", mismatches);
-end;
\ No newline at end of file

From 6febcf7eab8b2b378bae242192312d82cb7fc18b Mon Sep 17 00:00:00 2001
From: awesometillman <tillmanfroehlich@gmail.com>
Date: Tue, 9 Jul 2024 11:53:38 +0100
Subject: [PATCH 18/23] Fixed code styling

---
 gap/attributes/isomorph.gi | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/gap/attributes/isomorph.gi b/gap/attributes/isomorph.gi
index 23cf6ef5f..a2a46b624 100644
--- a/gap/attributes/isomorph.gi
+++ b/gap/attributes/isomorph.gi
@@ -128,7 +128,7 @@ function(R, S)
   else
     rmsS := S;
   fi;
-  
+
   rmsR := CanonicalReesMatrixSemigroup(rmsR);
   uR := UnderlyingSemigroup(rmsR);
   uS := UnderlyingSemigroup(rmsS);
@@ -316,7 +316,7 @@ end;
 InstallMethod(IsomorphismSemigroups, "for semigroups",
 [IsSemigroup, IsSemigroup],
 function(S, T)
-  local invariants, map, DS, DT, p, inv;
+  local invariants, map, p, inv;
 
   # TODO(later) more invariants
   invariants := [IsFinite, IsSimpleSemigroup, IsZeroSimpleSemigroup, Size,

From 74396f1fa03b3c9b0100de4976ee3aa8a90b889a Mon Sep 17 00:00:00 2001
From: awesometillman <tillmanfroehlich@gmail.com>
Date: Tue, 9 Jul 2024 12:01:12 +0100
Subject: [PATCH 19/23] Fixed styling in test file

---
 tst/standard/attributes/isomorph.tst | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/tst/standard/attributes/isomorph.tst b/tst/standard/attributes/isomorph.tst
index 19ec8feed..e04fab6b9 100644
--- a/tst/standard/attributes/isomorph.tst
+++ b/tst/standard/attributes/isomorph.tst
@@ -119,23 +119,23 @@ gap> IsIsomorphicSemigroup(S, T);
 false
 
 # isomorph: IsIsomorphicSemigroup, for finite simple semigroups
-gap> M := [[(1,2,3),()],[(),()],[(),()]];
+gap> M := [[(1, 2, 3), ()], [(), ()], [(), ()]];
 [ [ (1,2,3), () ], [ (), () ], [ (), () ] ]
-gap> N := [[(1,3,2),()],[(),(1,2,3)],[(1,3,2),(1,3,2)]];
+gap> N := [[(1, 3, 2), ()], [(), (1, 2, 3)], [(1, 3, 2), (1, 3, 2)]];
 [ [ (1,3,2), () ], [ (), (1,2,3) ], [ (1,3,2), (1,3,2) ] ]
-gap> R := ReesMatrixSemigroup(AlternatingGroup([1..3]),M);
+gap> R := ReesMatrixSemigroup(AlternatingGroup([1 .. 3]), M);
 <Rees matrix semigroup 2x3 over Alt( [ 1 .. 3 ] )>
-gap> S := ReesMatrixSemigroup(Group([(1,2,3)]),N);
+gap> S := ReesMatrixSemigroup(Group([(1, 2, 3)]), N);
 <Rees matrix semigroup 2x3 over Group([ (1,2,3) ])>
-gap> IsIsomorphicSemigroup(R,S);
+gap> IsIsomorphicSemigroup(R, S);
 true
-gap> L := [[(),()],[(),()],[(1,2,3),()]];
+gap> L := [[(), ()], [(), ()], [(1, 2, 3), ()]];
 [ [ (), () ], [ (), () ], [ (1,2,3), () ] ]
-gap> T := ReesMatrixSemigroup(SymmetricGroup([1..3]),L);
+gap> T := ReesMatrixSemigroup(SymmetricGroup([1 .. 3]), L);
 <Rees matrix semigroup 2x3 over Sym( [ 1 .. 3 ] )>
-gap> IsIsomorphicSemigroup(S,T);
+gap> IsIsomorphicSemigroup(S, T);
 false
-gap> IsIsomorphicSemigroup(T,T);
+gap> IsIsomorphicSemigroup(T, T);
 true
 
 # isomorph: IsomorphismSemigroups, for infinite semigroup(s)

From 4e0431a1c409cea0d9da86c42db1c64a60759291 Mon Sep 17 00:00:00 2001
From: awesometillman <tillmanfroehlich@gmail.com>
Date: Wed, 24 Jul 2024 16:03:53 +0100
Subject: [PATCH 20/23] Changed order of processes to improve performance

---
 gap/attributes/isomorph.gi | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/gap/attributes/isomorph.gi b/gap/attributes/isomorph.gi
index a2a46b624..c8f0408f1 100644
--- a/gap/attributes/isomorph.gi
+++ b/gap/attributes/isomorph.gi
@@ -129,7 +129,6 @@ function(R, S)
     rmsS := S;
   fi;
 
-  rmsR := CanonicalReesMatrixSemigroup(rmsR);
   uR := UnderlyingSemigroup(rmsR);
   uS := UnderlyingSemigroup(rmsS);
 
@@ -165,6 +164,7 @@ function(R, S)
 
   # 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);
   return Matrix(rmsR) = Matrix(rmsS);

From c51247b359c9373f85d1d1b638a3ca24b40b2399 Mon Sep 17 00:00:00 2001
From: awesometillman <tillmanfroehlich@gmail.com>
Date: Wed, 24 Jul 2024 16:31:36 +0100
Subject: [PATCH 21/23] Added test to make sure function works on simple
 semigroups that aren't RMS already

---
 tst/standard/attributes/isomorph.tst | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/tst/standard/attributes/isomorph.tst b/tst/standard/attributes/isomorph.tst
index e04fab6b9..4577756c3 100644
--- a/tst/standard/attributes/isomorph.tst
+++ b/tst/standard/attributes/isomorph.tst
@@ -129,6 +129,10 @@ gap> S := ReesMatrixSemigroup(Group([(1, 2, 3)]), N);
 <Rees matrix semigroup 2x3 over Group([ (1,2,3) ])>
 gap> IsIsomorphicSemigroup(R, S);
 true
+gap> R := SemigroupByMultiplicationTable(MultiplicationTable(R));;
+gap> S := SemigroupByMultiplicationTable(MultiplicationTable(S));;
+gap> IsIsomorphicSemigroup(R, S);
+true
 gap> L := [[(), ()], [(), ()], [(1, 2, 3), ()]];
 [ [ (), () ], [ (), () ], [ (1,2,3), () ] ]
 gap> T := ReesMatrixSemigroup(SymmetricGroup([1 .. 3]), L);

From 418ad14a8a189855829643a7b9aa86c48da55bcb Mon Sep 17 00:00:00 2001
From: "James D. Mitchell" <jdm3@st-andrews.ac.uk>
Date: Mon, 29 Jul 2024 15:14:56 +0100
Subject: [PATCH 22/23] Remove slower code

---
 gap/attributes/isomorph.gi | 11 ++++++-----
 1 file changed, 6 insertions(+), 5 deletions(-)

diff --git a/gap/attributes/isomorph.gi b/gap/attributes/isomorph.gi
index c8f0408f1..9ec48ec89 100644
--- a/gap/attributes/isomorph.gi
+++ b/gap/attributes/isomorph.gi
@@ -316,7 +316,7 @@ end;
 InstallMethod(IsomorphismSemigroups, "for semigroups",
 [IsSemigroup, IsSemigroup],
 function(S, T)
-  local invariants, map, p, inv;
+  local invariants, map, DS, DT, p, inv;
 
   # TODO(later) more invariants
   invariants := [IsFinite, IsSimpleSemigroup, IsZeroSimpleSemigroup, Size,
@@ -342,12 +342,13 @@ function(S, T)
     return fail;
   fi;
 
-  if CanonicalMultiplicationTable(S) <> CanonicalMultiplicationTable(T) then
+  DS := SEMIGROUPS.CanonicalDigraph(S);
+  DT := SEMIGROUPS.CanonicalDigraph(T);
+  p := IsomorphismDigraphs(DS[1], DT[1], DS[2], DT[2]);
+  if p = fail then
     return fail;
   fi;
-  p := CanonicalMultiplicationTablePerm(S)
-       * CanonicalMultiplicationTablePerm(T) ^ -1;
-
+  p := RestrictedPerm(p, [1 .. Size(S)]);
   map := x -> AsSSortedList(T)[PositionSorted(S, x) ^ p];
   inv := x -> AsSSortedList(S)[PositionSorted(T, x) ^ (p ^ -1)];
   return SemigroupIsomorphismByFunctionNC(S, T, map, inv);

From b440972fed972b46019b232793fd89405546f2a2 Mon Sep 17 00:00:00 2001
From: "James D. Mitchell" <jdm3@st-andrews.ac.uk>
Date: Mon, 29 Jul 2024 15:32:35 +0100
Subject: [PATCH 23/23] Final tweaks

---
 gap/attributes/isomorph.gi           | 39 ++++++++++++----------------
 tst/standard/attributes/isomorph.tst | 14 ++++++++++
 2 files changed, 31 insertions(+), 22 deletions(-)

diff --git a/gap/attributes/isomorph.gi b/gap/attributes/isomorph.gi
index 9ec48ec89..c785ec0eb 100644
--- a/gap/attributes/isomorph.gi
+++ b/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);
diff --git a/tst/standard/attributes/isomorph.tst b/tst/standard/attributes/isomorph.tst
index 4577756c3..428e3dd2d 100644
--- a/tst/standard/attributes/isomorph.tst
+++ b/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);;