Examples
- Consider the real function
- By definition, a symmetric function with n variables has the property that
- etc.
- In general, the function remains the same for every permutation of its variables. This means that, in this case,
- and so on, for all permutations of
- Consider the function
- If x and y are interchanged the function becomes
- which yields gives exactly the same results as the original f(x,y).
- Consider now the function
- If x and y are interchanged, the function becomes
- This function is obviously not the same as the original if a ≠ b, which makes it non-symmetric.
Read more about this topic: Symmetric Functions
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