# buildSymmetricGB -- Groebner basis of elementary symmetric polynomials algebra

## Synopsis

• Usage:
buildSymmetricGB R
• Inputs:
• Outputs:
• the Groebner basis of the elementary symmetric algebra

## Description

 i1 : n=5; i2 : R=QQ[x_1..x_n]; i3 : buildSymmetricGB R 5 4 3 2 4 3 3 2 2 2 o3 = {- x + x e - x e + x e - x e + e , x + x x - x e + x x - x x e 5 5 1 5 2 5 3 5 4 5 4 4 5 4 1 4 5 4 5 1 ------------------------------------------------------------------------ 2 3 2 4 3 2 + x e + x x - x x e + x x e - x e + x - x e + x e - x e + e , - 4 2 4 5 4 5 1 4 5 2 4 3 5 5 1 5 2 5 3 4 ------------------------------------------------------------------------ 3 2 2 2 2 2 x - x x - x x + x e - x x - x x x + x x e - x x + x x e - x e 3 3 4 3 5 3 1 3 4 3 4 5 3 4 1 3 5 3 5 1 3 2 ------------------------------------------------------------------------ 3 2 2 2 3 2 2 - x - x x + x e - x x + x x e - x e - x + x e - x e + e , x + 4 4 5 4 1 4 5 4 5 1 4 2 5 5 1 5 2 3 2 ------------------------------------------------------------------------ 2 2 x x + x x + x x - x e + x + x x + x x - x e + x + x x - x e + 2 3 2 4 2 5 2 1 3 3 4 3 5 3 1 4 4 5 4 1 ------------------------------------------------------------------------ 2 x - x e + e , - x - x - x - x - x + e } 5 5 1 2 1 2 3 4 5 1 o3 : List

This function should work up to a size of 15 variables in the base ring

This function is part of the package SymmetricPolynomials.

## For the programmer

The object buildSymmetricGB is .