Publications de l'Institut Mathématique, Nouvelle Série Vol. 97(111), pp. 43–48 (2015) 

A NOTE ON MULTIVARIATE POLYNOMIAL DIVISION AND GRÖBNER BASESAleksandar T. Lipkovski, Samira ZeadaMatematicki fakultet, Univerzitet u Beogradu, Beograd, SerbiaAbstract: We first present purely combinatorial proofs of two facts: the wellknown fact that a monomial ordering must be a well ordering, and the fact (obtained earlier by Buchberger, but not widely known) that the division procedure in the ring of multivariate polynomials over a field terminates even if the division term is not the leading term, but is freely chosen. The latter is then used to introduce a previously unnoted, seemingly weaker, criterion for an ideal basis to be Gröbner, and to suggest a new heuristic approach to Gröbner basis computations. Classification (MSC2000): 13P10;12Y05;06A07 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 16 Apr 2015. This page was last modified: 21 Apr 2015.
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