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Gröbner Basis Background

As discussed in §9, the principal computation which the Gröbner Basis Algorithm performs is the computation of an S-polynomial s from two polynomials (say tex2html_wrap_inline6336 and tex2html_wrap_inline6338 ) and then the computation of this S-polynomial's normal form (say r) using other polynomials (say, tex2html_wrap_inline4416 ). One of the side effects of this type of computation is the fact that s lies in the ideal generated by tex2html_wrap_inline7218 . If this ideal membership relationship is stored during the process of running the GBA and one wants to find a smaller generating set for the output of the GBA, then it is helpful to use these ideal membership relationships.

Wed Jul 3 10:27:42 PDT 1996