代数方程的Lagrange解法  

Lagrange's Method of Solving Algebraic Functions

作　　者：杨天标[1] 

机构地区：[1]长江师范学院数学与计算机学院,重庆涪陵408100

出　　处：《德州学院学报》2013年第2期33-37,共5页Journal of Dezhou University

摘　　要：用初等方法,介绍代数方程的Lagrange解法.历史上代数方程的根式求解,思想方法的发展历程可以表示为Lagrange Abel Cauchy Galois.Lagrange分析研究了先前的数学家的工作,把各种解法归纳于同一原理之下,统一利用预解式求解代数方程,并证明5次代数方程不能用预解式求解.理解Lagrange的方法,是理解代数方程近代理论的出发点.同时,与其他解法比较来看,3、4次方程的Lagrange解法本身,也因为思想方法统一而具有突出的优点.This article introduces Lagrange＇s method of solving algebraic equations, through a primarily approach. Historically, the development of the idea and method of the study of algebraic equations can by il- lustrated by Lagrange Abel Cauchy Galois. Lagrange analyzed the methods of former mathematicians, in- duced a uniform principle, and developed a universal method by resolvent. He also proved that the fifth order equation cannot be solved by this method. The method of Lagrange is the threshold of the modern theory on algebraic equations. Meanwhile, compared to the other methods, because of the unity of the method, Lagrange＇s method has the outstanding privilege.

关 键 词：3次方程 四次方程 初等对称多项式 基本对称函数 预解式 置换群 交错群 不变群 

分 类 号：O141.3[理学—数学]