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 |