# What are some examples of a symmetric function?

Jul 15, 2015

$f \left(x , y\right) = {x}^{2} + x y + {y}^{2}$
$g \left(x , y , z\right) = x y + y z + z x + \frac{1}{{x}^{2} + {y}^{2} + {z}^{2}}$
For example, if $f \left(x , y\right) = {x}^{2} + x y + {y}^{2}$, then $f \left(y , x\right) = f \left(x , y\right)$ for all $x$ and $y$.