For my Memoir titled

Basic Global Relative Invariants for Homogeneous Linear Differential Equations

and published as Number 744 by the American Mathematical Society in March of 2002, a check on the theoretical deductions was provided by the computations of pages 28--30.  They were written for Version 3.0 of  MATHEMATICA and run efficiently on that version.  However, it is interesting that they run less efficiently on some later versions of MATHEMATICA.   A slight modification suffices.  By removing two expressions that look like  Together[  ]   in the original formulation, we obtain a program that runs efficiently on both Version 3.0 and Version 4.1. 

To download the original program that contains the two superfluous  Together[  ] commands (that runs efficiently on Version 3.0 and inefficiently on Version 4.1), click here. 

To download the recently modified version from which the two superfluous  Together[  ] commands have been removed so that it runs efficiently on both Versions 3.0 and 4.1 of MATHEMATICA, click here. 

As an addition of March 17, 2006, we note that the preceding observations were written several years ago.  Version 5.2 of MATHEMATICA has recently become available and we have found that the two surplus  Together[]  commands do not present a problem for it.  Version 5.2 and Version 3.0 appear to run the original program of pages 28-30 with about the same efficiency.

(Comment added in early 2009:  Version 6.0 is far less capable of doing the basic computations that earlier versions did splendidly for the more recent notebooks that may be accessed by clicking here.)