改进格鲁布纳基法  

The Improved Groebner Basis Method

作　　者：张纪元[1] 汪萍锋[1] 李波[1] 

机构地区：[1]上海海运学院工学院,上海200135

出　　处：《上海海运学院学报》2002年第2期1-5,共5页Journal of Shanghai Maritime University

基　　金：国家自然科学基金 ( 5 9875 0 84)

摘　　要：针对布切伯格等算法中存在的不足之处 ,采用取最高项进行约简、对多项式组彻底约简和根据秩的大小选取基组等措施对这些算法进行改进 ,从而形成本文的改进格鲁布纳基法。与现有算法相比 ,本文提出的方法以较少的计算工作量得到与原多项式组 (PS)等价的格鲁布纳基 (GS)或便于求解的三角型组 (TS)。To counter deficiencies in Buchberger algorithms, the improved Groebner basis method is suggested on the basis of Buchberger algorithms by adopting some measures, such as taking the highest term as first term in reduction of a polynomial set, thoroughly reducing a polynomial set, and selecting a base set from a polynomial set according to polynomial rank. By using the method in this paper, a Groebner basis (GS) which is equivalent to original polynomial set (PS) or a triangle form polynomial set (TS) conveniently to be solved can easily be gotten.

关 键 词：改进格鲁布纳基法 多项式议程组 格鲁布纳基 三角型组 GB算法 机械学 

分 类 号：TH11[机械工程—机械设计及理论]