实正则方形代数系统  

Realregular zeros for the square algebraic systems

作　　者：徐嘉 XU Jia(School of Mathematics,Southwest Minzu University,Chengdu 610041,China)

机构地区：[1]西南民族大学数学学院,四川成都610041

出　　处：《西南民族大学学报（自然科学版）》2021年第5期528-531,共4页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：中央高校一般项目(2020NYB40)。

摘　　要：变元个数与方程个数相同的代数系统称为方形代数系统.这是一类在实际应用中最常遇到的代数系统,我们将建立一个算法去隔离方形代数系统的实正则零点.方法分两步,首先使用Dixon结式计算单个变元所需要满足的方程,并进行单变元的实根隔离,以获得一系列Box.第二步用伴随多项式方法检查这些Box是否包含原代数系统的实正则零点.利用Maple平台,我们实现了这个算法.大量的计算实例显示了这个方法的有效性.A system is called a square algebraic system if the number of equations is the same as the number of variables.This is one of the most commonly encountered algebraic systems in practical applications.This paper gives an algorithm to isolate the real regular zeros of a square algebraic system.This method can be divided into two steps.The first step is to obtain a series of boxes by firstly calculating the single variable equation with Dixon resultant method and then isolating real roots of these single variable polynomials.The second step is to check if each box contains a zero of the original algebra system by using the adjoint polynomials method.This algorithm is implemented with Maple.A large number of computational examples show that this method is effective.

关 键 词：方形代数系统 实正则零点 Dixon结式 伴随多项式 

分 类 号：O153[理学—数学]