Goal: Establish recursion formulas which will be used to derive
====  determining equaitons for palindromic schemes of orders
      up to 7.

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

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

  Mathematica Codes:
  ----------------

     XDriver       ---   the driver routine to generate coefficient 
                         formulas for newW, where 

                         exp(newW) = exp(t d X) exp( W )

     YDriver       ---   the driver routine to generate coefficient 
                         formulas for newW, where 

                         exp(newW) = exp(t g Y) exp( W )

     CompHead      ---   Preparations before calling CompCoeff

     CompCoeff     ---   Most computations for coefficient formulas
                         are done here.

     DefFun        ---   Define basis brackets

     DumpCoeff     ---   Dump coefficient formulas

     expXexpY      ---   BCH Formula

     TestXCoeff    ---   Testing the correctness of the computed 
                         coefficient formulas in XCoeff (or XCoeffp).

     TestYCoeff    ---   Testing the correctness of the computed 
                         coefficient formulas in YCoeff (or YCoeffp).

     TestHead      ---   Preparations before calling TestXCoeff or TestYCoeff

     TestWork      ---   Most heavy computations for testing are done here

  Output:
  ------

     XCoeff  (by XDriver) ---   coefficient formulas
     XCoeffp (by XDriver) ---   coefficient formulas arranged differently.
     YCoeff  (by YDriver) ---   coefficient formulas
     YCoeffp (by YDriver) ---   coefficient formulas arranged differently.

To Run:    In Mathematica, type <<XDriver
======                          <<YDriver

To Check:  In Mathematica, type <<TestXCoeff
========                        <<TestYCoeff

Warning:   Be prepared to wait for hours (or days), 
=======    especially when running TestXCoeff or TestYCoeff.
