Question

What are some examples of a symmetric function?

Answer 1

`f(x, y) = x^2 + xy + y^2`
`g(x, y, z) = xy + yz + zx + 1/(x^2+y^2+z^2)`

Explanation:

A symmetric function is a function in several variable which remains unchanged for any permutation of the variables.

For example, if `f(x, y) = x^2 + xy + y^2`, then `f(y, x) = f(x, y)` for all `x` and `y`.