Purpose: Find out a basis of all possible brackets consisting of
=======  a few non-commutative algebra's elements.

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

Files in this directory:
===== == ==== =========

  Driver Routines: (Some of these driver routines compute bases of
  ------ --------   spaces that are equivalent, e.g., X13.X32 and X13.X22.) 

     X12.X2.X3  --- For two X[1]'s, one X[2], and one X[3]

     X12.X22    --- For two X[1]'s, and two X[2]'s

     X12.X3.X5  --- For two X[1]'s, one X[3], and one X[5]

     X12.X32    --- For two X[1]'s, and two X[2]'s

     X12.X33    --- For two X[1]'s, and three X[3]'s

     X13.X22    --- For three X[1]'s, and two X[2]'s

     X13.X3.X5  --- For three X[1]'s, one X[3], and one X[5]

     X13.X32    --- For three X[1]'s, and two X[3]'s

     X14.X32    --- For four X[1]'s, and two X[3]'s

     X15.X32    --- For five X[1]'s, and two X[3]'s

             *-*-*-*-*-*-*-*-*-*-*-*-*

     X2Y2  --- For two  X's, and two    Y's

     X2Y3  --- For two  X's, and three  Y's

     X2Y4  --- For two  X's, and four   Y's

     X2Y5  --- For two  X's, and five   Y's

     X3Y2  --- For three X's, and two   Y's

     X3Y3  --- For three X's, and three Y's

     X3Y4  --- For three X's, and four  Y's

     X4Y2  --- For four  X's, and two   Y's

     X4Y3  --- For four  X's, and three Y's

     X5Y2  --- For five  X's, and two   Y's

  Auxiliary Routines:
  --------- --------

     ReduceHi --- In the heads of every driver routine for brackets
                  by X[i]'s

     ReduceH  --- In the heads of every driver routine for brackets
                  with X, and Y.

     ReduceT  --- In the tails of every driver routine

To Run: Take any driver routine XXXX, and type <<XXXX after Mathematica
== ===  prompt.
