Absolutely Symmetric Function/Examples

Examples of Absolutely Symmetric Functions

Arbitrary Example $1$

Let $f: \R^3 \to \R$ be the real-valued function defined as:

$\forall \tuple {x, y, z} \in \R^3: \map f {x, y, z} = x^2 + y^2 + 2 x y z$

Then $f$ is an absolutely symmetric function.

Arbitrary Example $2$

Let $f: \R^2 \to \R$ be the real-valued function defined as:

$\forall \tuple {x, y} \in \R^2: \map f {x, y} = x^2 + 2 x y + y^2$

Then $f$ is an absolutely symmetric function.