We mentioned earlier that NCProcess uses the Gröbner Basis algorithm. This GBA is implemented via the command NCMakeGB. If NCProcess consisted of a call to the GBA and the formatted output (§18.2) alone, then NCProcess would not be a powerful enough tool to generate solutions to engineering or math problems. This is because it would generate too many equations. It is our hope that the equations which it generates contain all of the equations essential to solution of whatever problem you are treating. For the problems we have considered, this has been our experience. On the other hand, it contains equations derived from these plus equations derived from those derived from these as well as precursor equations which are no longer relevant. That is, a GB contains a few jewels and lots of garbage. In technical language a GB is almost never a small basis for an ideal and what a human seeks in discovering a theorem is a small basis for an ideal. 10 Thus we have algorithms and substantial software for finding small (or smallest) sets of equations associated to a problem. The process of running GBA followed by an algorithm for finding small sets of equations is what constitutes NCProcess.
DELETE?? IN CDC Deciding when a strategy stops (§ 19.3.2) is highly dependent upon finding small lists of equations.