Add specializations of the Opposite() operator.

gap/structure.gi

@@ -235,3 +235,31 @@ InstallMethod(RightPerms,
   function(fam)
     return List(TransposedMat(MultiplicationTable(fam)), x->PermList(x));
 end);
+
+## Special case the Opposite function from LOOPS package, since the opposite
+## of a left quasigroup is a right quasigroup and vice versa
+
+# Is there a way to do this just once for each direction?
+InstallMethod(Opposite, "for left quasigroup",
+  [ IsLeftQuasigroup ],
+  L -> RightQuasigroupByMultiplicationTable(
+         TransposedMat(MultiplicationTable(L))
+       )
+);
+
+InstallMethod(Opposite, "for left rack",
+  [ IsLeftRack ],
+  L -> RightRackByMultiplicationTableNC(TransposedMat(MultiplicationTable(L)))
+);
+
+InstallMethod(Opposite, "for right quasigroup",
+  [ IsRightQuasigroup ],
+  L -> LeftQuasigroupByMultiplicationTable(
+         TransposedMat(MultiplicationTable(L))
+       )
+);
+
+InstallMethod(Opposite, "for right rack",
+  [ IsRightRack ],
+  L -> LeftRackByMultiplicationTableNC(TransposedMat(MultiplicationTable(L)))
+);