Groebner基判定的Buchberger准则的推广
An extension of Buchberger's criteria for Groebner basis decision
摘要：
Groebner基理论中的两个基本问题是判定（“多项式理想的基G是Groebner基吗？“）和转换（“如果不是，我们如何将它转换成Groebner基？“）本文考虑第一个问题。众所周知，G是Groebner基当且仅当某个多项式集合（S-多项式）满足某个性质。一般有m（m-1）/2的这些，其中m是在G多项式的数量，但标准由于布赫伯格和其他人往往允许考虑一个较小的数字。本文提出了两个原始结果。第一个是一个新的特征定理Groebner基地，使使用一个新的标准，扩展布赫伯格的标准。第二个是一类多项式系统G的识别，新的标准具有显着的影响，减少了最坏情况下的情况下，从m（m-1）/2 S-多项式的m-1。
英文摘要：
Two fundamental questions in the theory of Groebner bases are decision ("Is a basis G of a polynomial ideal a Groebner basis?") and transformation ("If it is not, how do we transform it into a Groebner basis?") This paper considers the first question. It is well-known that G is a Groebner basis if and only if a certain set of polynomials (the S-polynomials) satisfy a certain property. In general there are m(m-1)/2 of these, where m is the number of polynomials in G, but criteria due to Buchberger and others often allow one to consider a smaller number. This paper presents two original results. The first is a new characterization theorem for Groebner bases that makes use of a new criterion that extends Buchberger's Criteria. The second is the identification of a class of polynomial systems G for which the new criterion has dramatic impact, reducing the worst-case scenario from m(m-1)/2 S-polynomials to m-1.
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