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Finding different sets of noncommutative polynomials which
generate the same ideal is one of the main tasks underlying
this paper. The two implementable operations we
find critical to this paper are the
Gröbner Basis Algorithm and the ``shrinking''
of a basis for a polynomial ideal to a smaller
generating set.
These operations are
encapsulated in the
NCProcess commands.
In Part I we give enough of an explanation of
the theory behind the NCProcess commands
(§,
§ and
§)
for
a practitioner, analyst or engineer
to understand the results given in Part I.
Part II of the paper
gives details and properties of the algorithms of this paper
and completes the
description of the theory behind the NCProcess commands.

*Helton *

Wed Jul 3 10:27:42 PDT 1996