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Algorithms and their properties

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 commandsgif.

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.

Wed Jul 3 10:27:42 PDT 1996