Algebraic Equations Of Lagrange's Theory

Lagrange's Theory of Solving Algebraic Equations is one of the most essential theories in the history of solving algebraic equations, which mainly focuses on his auxiliary equation theory and the idea of applying permutation to solve algebraic equations. This theory completely changed people's thinking, and made many mathematicians begin to search for a general and universal means to solve algebraic equations; also it changed the connotation of solving algebraic equations, that is, from finding the roots formula to the resolvent and then following a certain procedure; Lagrange's discussion on the idea of permutation promoted the new birth of algebra, which made it epoch-marking. To expound the content of Lagrange's theory of solving algebraic equations, to present his auxiliary equation theory and permutation thought, to figure out the key points in the history of solving algebraic equations, to understand the stern influence of Lagrange's theory and outstand Lagrange's figure of great mathematician, this dissertation precisely describes the background and reasons, content and influence of auxiliary equation theory based on the French original material Reflexions sur la Resolution Algebrique des Equations This paper restores the process of the emergence of Lagrange's permutation idea as well as its background and reasons, and influence. This paper also analyses the way in which Lagrange applied in solving algebraic equations from a general perspective; at the same time, it explains how this theory changed the connotation of solving algebraic equations. At last, it expounds the great influence of Lagrange's theory of solving algebraic equations.