What is "elementary symmetric polynomial"

n. (context algebra English) a coefficient of some power of ''t'' in $(t-x\_1)(t-x\_2)cdots(t-x\_n)$, for any $ninN$

In mathematics, specifically in commutative algebra, the elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be expressed as a polynomial in elementary symmetric polynomials. That is, any symmetric polynomial P is given by an expression involving only additions and multiplication of constants and elementary symmetric polynomials. There is one elementary symmetric polynomial of degree d in n variables for each nonnegative integer d ≤ n, and it is formed by adding together all distinct products of d distinct variables.