Geodesic
A Note on Multivariate Polynomial Division and Gröbner Bases
Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 43

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We first present purely combinatorial proofs of two facts: the well-known 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 Gr\"obner, and to suggest a new heuristic approach to Gr\"obner basis computations.
DOI : 10.2298/PIM141104001L
Classification : 13P10, 12Y05, 06A07 
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Aleksandar T. Lipkovski; Samira Zeada. A Note on Multivariate Polynomial Division and Gröbner Bases. Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 43 . doi: 10.2298/PIM141104001L

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