Absolutely Symmetric Function/Examples/Arbitrary Example 1

Examples of Absolutely Symmetric Functions

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.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): symmetric function
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): symmetric function