“对称”,原来是几何中的概念。意思是說两个几何图形相对而相称。从一定的角度看去,这两个图形所处的地位是相同的。建筑图案以及某些艺术品往往由于具有一定的对称性而更觉美观。在解决几何問題时,对称性也往往起重要作用。代数中也有对称。一元n次方程的每一个根所处的地位也都彼此相同,把这个根或那个根叫做x_1是无关重要的。我們从这里得到了启发,要研究一元n次方程,就不能不考虑到它的根的对称性。这样,就很自然地产生了对称多項式的理論。以下我們将要初步地接触到这些理論,和它的簡单应用。一、对称多項式两个变量x_1,x_2的多項式F(x_1,x_2),如果把x_1換做x_2,把x_2換作x_1以后,得出多項式和原来的完全一样,也就是說,如果F(x_1,x_2)=F(x_2,x_1),就把F(x_1,x_2) “Symmetry” was originally a concept in geometry. This means that the two geometric figures are relative and symmetric. From a certain point of view, the two figures are in the same position. Architectural patterns and certain works of art are often more aesthetically pleasing due to their symmetry. In solving geometric problems, symmetry often plays an important role. There is also symmetry in algebra. Each root of the unary n-order equation is also in the same position. It is irrelevant to call this root or that root x_1. We have been inspired by this. To study the unitary nth order equation, we must not consider its root symmetry. In this way, the theory of symmetric polynomials is naturally produced. In the following we will have preliminary contact with these theories and their simple applications. First, the symmetric polynomial Two variables x_1, x_2 polynomial F (x_1, x_2), if the x_1 for x_2, x_2 replaced by x_1, the resulting polynomial is exactly the same as the original, that is, if F (x_1 ,x_2)=F(x_2,x_1) and put F(x_1,x_2)