求解多项式方程组的综合消元法  

Synthetic Elimination Method for Solving a Polynomial System of Equations

作　　者：张纪元[1] 汪萍锋[1] 李学领[1] 

机构地区：[1]上海海运学院物流工程学院,上海200135

出　　处：《上海海运学院学报》2003年第3期257-261,共5页Journal of Shanghai Maritime University

基　　金：上海市高等学校科学技术发展基金(03IK07)

摘　　要：给出一多项式组(PS)与一三角型组(TS)同解的一个判断准则,充分利用伪除法、结式消无法和主幂积项消无法的优点,形成求一多项式组(PS)格鲁布纳基(GS)的综合消元法,并构造了该法的计算步骤。实例计算表明,综合消元法具有计算效率高、消元效果好等优点。In this paper, a criterion for distinguishing the same solutions between a polynomial set (PS) and a triangle form set (TS) is given, a synthetic elimination method is suggested by making use of advantages of synthetic division, the method of elimination by resultant and the method of elimination by principal power product in order to find a Groebner basis (GS) of a PS, and an algorithm of the method is constructed. Calculation results of many examples illustrate that the method has some merits, such as high calculating efficiency and good elimination effect, etc.

关 键 词：多项式方程组 综合消元法 伪除法 结式消元法 主幂积项消元法 格鲁布纳基 代数方程 计算方法 

分 类 号：O241.6[理学—计算数学]