Symmetric Function

A MATLAB program related to Symmetric Function.

Background

A multivaraible function $f(x_1,x_2,...,x_n)$ is said to be symmetric if
$$f(x_1,x_2,...,x_n) = f(x_{\sigma(1)}, x_{\sigma(2)}, ..., x_{\sigma(n)})$$ where $\sigma$ is any permutation of $X_n =$ $\{1,2,...,n\}$

Example 1:
$f(x,y,z) = x^2 + y^2 + z^2$ is symmetric as $$f(x,y,z) = f(x,z,y) = f(y,x,z) = f(y,z,x) = f(z,x,y) = f(z,y,x)$$

Example 2:
$f(x,y,z) = x^2 + y^2 + z$ is not symmetric as $$f(x,y,z) = x^2 + y^2 + z \neq x^2 + z^2 + y = f(x,z,y)$$

Specification

Definition of rational function:

A function $f$ is said to be a rational function if and only if it can be written in the form of $$f = \frac{P}{Q}$$ where $P$ and $Q$ are polynomials and $Q$ is not zero.

Objective:

Let $f$ be a rational function. Write a function issym(f). The function returns TRUE if $f$ is symmetric, returns FALSE if $f$ is not symmetric.