m≥n的结式消元法  

The Method of Elimination by Eliminant for m≥n

作　　者：张纪元[1] 李波[1] 汪萍锋[1] 

机构地区：[1]上海海运学院机械系,上海200135

出　　处：《南京理工大学学报》2002年第2期213-216,共4页Journal of Nanjing University of Science and Technology

基　　金：国家自然科学基金资助项目 (5 9875 0 84 );交通部重点资助项目 (95 - 0 4 - 0 3- 37)

摘　　要：设一个多项式方程组中的方程个数为m >0 ,变元个数为n>0 ,该文在m=n的基组结式消元法的基础上 ,针对m ≥n的情况 ,建立了相应的理论 ,构造了新的消元步骤。用该文方法 ,可将m≥n的一个多项式组 (PS)化成一个三角形组(TS) ={b1(x1) ,b2 (x1,x2 ) ,… ,bn(x1,… ,xn) },使得Zero(PS) Zero(TS) ,且诸bi 在同类多项式中具有最低的度。该文方法在解决空间机构和机器人机构分析与综合等工程问题中具有较大的理论意义和重大的实用价值。In a polynomial system of equations (PS)=0,let m>0 be the number of equations,and n>0 be the number of variables.In this paper,corresponding theory has been built up and new elimination step has been constructed for m≥n on the basis of the elimination by eliminant with aid of basic sets about m=n.A polynomial set (PS) of m≥n can be changed into a triangular form polynomial set (TS)={b 1(x 1),b 2(x 1,x 2),...,b n(x 1,...,x n)} by making use of the method in this paper.For such (TS),b i(i=1,...,n) has lowest degree in polynomials belong to same type,and Zero(PS)Zero(TS).The method has important theoretical significance and practical value in solving problems of analysis and synthesis about spatial mechanisms,manipulate mechanisms and other engineering.

关 键 词：多项式 机构学 结式消元 多项式方程组 

分 类 号：TH12[机械工程—机械设计及理论] O174.14[理学—数学]