elementarySymmetric -- Expresses a symmetric polynomial as a polynomial in the elementary symmetric functions

i1 : R=QQ[x_0,x_1,x_2,x_3]

o1 = R

o1 : PolynomialRing

i2 : q=x_0^2*x_1^2*x_2^2+x_0^2*x_1^2*x_2*x_3+x_0^2*x_1*x_2^2*x_3+x_0*x_1^2*x_2^2*x_3+x_0^2*x_1^2*x_3^2+x_0^2*x_1*x_2*x_3^2+x_0*x_1^2*x_2*x_3^2+x_0^2*x_2^2*x_3^2+x_0*x_1*x_2^2*x_3^2+x_1^2*x_2^2*x_3^2

      2 2 2    2 2        2   2        2 2      2 2 2    2     2      2   2  
o2 = x x x  + x x x x  + x x x x  + x x x x  + x x x  + x x x x  + x x x x  +
      0 1 2    0 1 2 3    0 1 2 3    0 1 2 3    0 1 3    0 1 2 3    0 1 2 3  
     ------------------------------------------------------------------------
      2 2 2        2 2    2 2 2
     x x x  + x x x x  + x x x
      0 2 3    0 1 2 3    1 2 3

o2 : R

i3 : elementarySymmetric(q)

      2
o3 = e  - e e
      3    2 4

o3 : QQ[e , e , e , e ]
         1   2   3   4