A theoretical basis for the reduction of polynomials to canonical forms

Authors:
B. Buchberger
Affiliations:
Universität Linz, Linz, Austria
Venue:
ACM SIGSAM Bulletin
Year:
1976

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Abstract

We define a certain type of bases of polynomial ideals whose usefulness stems from the fact that a number of computability problems in the theory of polynomial ideals (e.g. the problem of constructing canonical forms for polynomials) is reducible to the construction of bases of this type. We prove a characterization theorem for these bases which immediately leads to an effective method for their construction.