From 25672bad38c240114f468b18d847004694055fae Mon Sep 17 00:00:00 2001
From: Glen Whitney <gwhitney@post.harvard.edu>
Date: Thu, 19 Oct 2017 02:26:18 +0200
Subject: [PATCH] Add NC versions of quasigroup constructors to support uniform
 Print() syntax

---
 gap/structure.gd |  2 ++
 gap/structure.gi | 29 ++++++++++++++++-------------
 2 files changed, 18 insertions(+), 13 deletions(-)

diff --git a/gap/structure.gd b/gap/structure.gd
index 5f06f56..aaa49f3 100644
--- a/gap/structure.gd
+++ b/gap/structure.gd
@@ -82,8 +82,10 @@ DeclareAttribute("RightDivisionTable", HasMultiplicationTable);
 
 # And the builders
 DeclareGlobalFunction("LeftQuasigroupByMultiplicationTable");
+DeclareGlobalFunction("LeftQuasigroupByMultiplicationTableNC");
 DeclareGlobalFunction("LeftRackByMultiplicationTable");
 DeclareGlobalFunction("LeftRackByMultiplicationTableNC");
 DeclareGlobalFunction("RightQuasigroupByMultiplicationTable");
+DeclareGlobalFunction("RightQuasigroupByMultiplicationTableNC");
 DeclareGlobalFunction("RightRackByMultiplicationTable");
 DeclareGlobalFunction("RightRackByMultiplicationTableNC");
diff --git a/gap/structure.gi b/gap/structure.gi
index ec12551..e75ee53 100644
--- a/gap/structure.gi
+++ b/gap/structure.gi
@@ -30,7 +30,7 @@ InstallGlobalFunction(LeftQuasigroup, function(arg)
   fi;
   return CloneOfTypeByGenerators(IsLeftQuasigroup, fam, arg,
                                  GeneratorsOfLeftQuasigroup, 
-                                 LeftQuasigroupByMultiplicationTable);
+                                 LeftQuasigroupByMultiplicationTableNC);
 end);
 
 InstallGlobalFunction(LeftRack, function(arg)
@@ -68,7 +68,7 @@ InstallGlobalFunction(RightQuasigroup, function(arg)
   fi;
   return CloneOfTypeByGenerators(IsRightQuasigroup, fam, arg,
                                  GeneratorsOfRightQuasigroup,
-                                 RightQuasigroupByMultiplicationTable);
+                                 RightQuasigroupByMultiplicationTableNC);
 end);
 
 InstallGlobalFunction(RightRack, function(arg)
@@ -116,26 +116,29 @@ InstallGlobalFunction(LeftQuasigroupByMultiplicationTable,
       Error("Multiplication table <T> must have each row a permutation of ",
             "the same entries.");
     fi;
-    return MagmaByMultiplicationTableCreatorNC(
-             CanonicalCayleyTableOfLeftQuasigroupTable(T), 
-             LeftQuasigroup,
-             IsLeftQuotientElement and IsMagmaByMultiplicationTableObj
-           );
+    return LeftQuasigroupByMultiplicationTableNC(
+             CanonicalCayleyTableOfLeftQuasigroupTable(T));
 end);
 
+InstallGlobalFunction(LeftQuasigroupByMultiplicationTableNC,
+  T -> MagmaByMultiplicationTableCreatorNC(T, LeftQuasigroup,
+         IsLeftQuotientElement and IsMagmaByMultiplicationTableObj)
+);
+
 InstallGlobalFunction(RightQuasigroupByMultiplicationTable,
   function(T)
     if not IsRightQuasigroupTable(T) then
-      Error("Multiplication table <T> must have each column a permutation of ",
+      Error("Multiplication table <T> must have each row a permutation of ",
             "the same entries.");
     fi;
-    return MagmaByMultiplicationTableCreatorNC(
-             CanonicalCayleyTable(T), 
-             RightQuasigroup,
-             IsRightQuotientElement and IsMagmaByMultiplicationTableObj
-           );
+    return RightQuasigroupByMultiplicationTableNC(CanonicalCayleyTable(T));
 end);
 
+InstallGlobalFunction(RightQuasigroupByMultiplicationTableNC,
+  T -> MagmaByMultiplicationTableCreatorNC(T, RightQuasigroup,
+         IsRightQuotientElement and IsMagmaByMultiplicationTableObj)
+);
+
 InstallGlobalFunction(LeftRackByMultiplicationTable,
   function(T)
     if not IsLeftQuasigroupTable(T) then