# elementarySymmetricPolynomials(PolynomialRing) -- the elementary symmetric polynomials

## Synopsis

• Function: elementarySymmetricPolynomials
• Usage:
elementarySymmetricPolynomials(R)
• Inputs:
• R, , a polynomial ring
• Outputs:
• a list, the list of power elementary symmetric polynomials

## Description

As an example the elementary symmetric polynomials of a ring with three variables are calculated. These polynomials form a basis for the ring of symmetric polynomials.

 i1 : R = QQ[x_1..x_3] o1 = R o1 : PolynomialRing i2 : elementarySymmetricPolynomials R o2 = {x + x + x , x x + x x + x x , x x x } 1 2 3 1 2 1 3 2 3 1 2 3 o2 : List