A note on multivariate polynomial division and Gröbner bases
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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 Grobner, and to suggest a new heuristic approach to Grobner basis computations.
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2011 ◽
Vol 48
(4)
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pp. 458-474
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2010 ◽
Vol 13
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pp. 111-129
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2015 ◽
Vol 4
(2)
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pp. 1-14
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2018 ◽
Vol 28
(04)
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pp. 553-571
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