 Elementary symmetric polynomial

The elementary symmetric polynomials in $x_1,\dots ,x_n$ are the sums of all products of $k$ distinct variables, for $k=1,\dots ,n$.

Elementary symmetric polynomials are a fundamental class of symmetric polynomials in algebra. Given a set of \( n \) variables, \( x_1, x_2, ..., x_n \), the elementary symmetric polynomials are defined as follows: 1. The first elementary symmetric polynomial \( e_1(x_1, x_2, ...