(*                          Ren-Cang Li, June 1, 1996
                            na.rcli@na-net.ornl.gov   *)

<<ReduceH

(* Possible Brackets *)
cmt[1] =Expand[Cmt[X,Cmt[X,Cmt[Y,Cmt[Y,Cmt[Y,Cmt[X,Y]]]]]]];
cmt[2] =Expand[Cmt[X,Cmt[Y,Cmt[X,Cmt[Y,Cmt[Y,Cmt[X,Y]]]]]]];
cmt[6] =Expand[Cmt[X,Cmt[Y,Cmt[Y,Cmt[X,Cmt[Y,Cmt[X,Y]]]]]]];
cmt[7] =Expand[Cmt[X,Cmt[Y,Cmt[Y,Cmt[Y,Cmt[X,Cmt[X,Y]]]]]]];

cmt[3] =Expand[Cmt[Y,Cmt[X,Cmt[X,Cmt[Y,Cmt[Y,Cmt[X,Y]]]]]]];
cmt[4] =Expand[Cmt[Y,Cmt[X,Cmt[Y,Cmt[X,Cmt[Y,Cmt[X,Y]]]]]]];
cmt[8] =Expand[Cmt[Y,Cmt[X,Cmt[Y,Cmt[Y,Cmt[X,Cmt[X,Y]]]]]]];

cmt[9] =Expand[Cmt[Y,Cmt[Y,Cmt[Y,Cmt[X,Cmt[X,Cmt[X,Y]]]]]]];
cmt[5] =Expand[Cmt[Y,Cmt[Y,Cmt[X,Cmt[Y,Cmt[X,Cmt[X,Y]]]]]]];
cmt[10]=Expand[Cmt[Y,Cmt[Y,Cmt[X,Cmt[X,Cmt[Y,Cmt[X,Y]]]]]]];

NumBrackets=10;
(* Do[{Print[cmt[i]];Pause[5]},{i,NumBrackets}]; *)
(* Results: The number of independent brackets:  4.
            The independent brackets are:
                cmt[1], cmt[2], cmt[3], cmt[4].
   Relations:

            1/3 cmt[3]-cmt[4]+cmt[5]= 0
            cmt[1]-2 cmt[2]+ cmt[6] = 0
            cmt[1]-2 cmt[2]+ cmt[7] = 0
            -cmt[4]+         cmt[8] = 0
             cmt[9]                 = 0
            1/3 cmt[3]-cmt[4]+cmt[10]= 0 *)

(* The maximum possible length of these vectors *)
MaxL=7!/(4! 3!);

<<ReduceT
