Lex Least Dyclet

gap/utilities.g

@@ -46,3 +46,65 @@
 );
 
 
+
+#############################################################################
+##
+#F LexicographicallyLeastDyclet . . . . . . .  lexicographically least dyclet
+## 
+## A dyclet represents the orbit of a list under the diherdral group of the
+## list. Find the lexicographically least representative of the dyclet.
+##
+
+# called for lists of sets
+BindGlobal( "__SIMPLICIAL_LexicographicallyLeastDyclet",
+    function(dyclet)
+
+    local n, min_dyclet, k, perm, mirror_dyclet;
+
+    if (Filtered(dyclet,i-> not IsInt(i))<>[]) or (Length(dyclet)=0) then
+        Error("Dyclet must be a list of integers");
+        return fail;
+    fi;
+    n := Size(dyclet);
+    # current candidate for minimal dyclet
+    min_dyclet := ShallowCopy(dyclet);
+    perm := Reversed(dyclet);
+    if perm < min_dyclet then min_dyclet := perm; fi;
+
+    # Generate all cyclic permutations and their mirror images
+    for k in [1..n-1] do
+        perm := Concatenation(dyclet{[1+k..n]}, dyclet{[1..k]});
+        mirror_dyclet := Reversed(perm);
+
+        if perm < min_dyclet then
+            min_dyclet := perm;
+        fi;
+
+        if mirror_dyclet < min_dyclet then
+            min_dyclet := mirror_dyclet;
+        fi;
+    od;
+
+    return min_dyclet;
+end
+);
+
+
+#############################################################################
+##
+#F LtDyclet . . . . . . . . . . . . less than comparisons of dyclets
+##
+BindGlobal( "__SIMPLICIAL_LtDyclet",
+     function( dyc1, dyc2 )
+
+    if __SIMPLICIAL_LexicographicallyLeastDyclet(dyc1)
+       < __SIMPLICIAL_LexicographicallyLeastDyclet(dyc2) then return true;
+    fi;
+
+    return false;
+
+end
+);
+
+
+