I'm trying to reproduce the operation in this short segment of a presentation on Galois theory in here and here. The code is:
$$\begin{align}\text{In}:\quad &Δ^2 = (x - y)^2 * (x - z)^2 * (y -z)^2\ &\text{SymmetricReduction}[Δ, {x, y, z}, {s1, s2, s3}]\ \text{Out}: &\quad {s1^2 s2^2 -4 s2^3 -4 s1^3s3+ 18 s1s2s3-27 s3^2, 0} \end{align}$$
