Symmetric function: Difference between revisions

Revision as of 08:41, 6 November 2012

Revision as of 09:58, 18 November 2012

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* Consider the real function

::<math>f(x_1,x_2,x_3)=(x-x_1)(x-x_2)(x-x_3)</math>

:By definition, a symmetric function with n variables has the property that

::<math>f(x_1,x_2,...,x_n)=f(x_2,x_1,...,x_n)=f(x_3,x_1,...,x_n,x_{n-1})</math> etc.

:By definition, a symmetric function with n variables has the property that

::<math>f(x_1,x_2,...,x_n)=f(x_2,x_1,...,x_n)=f(x_3,x_1,...,x_n,x_{n-1})</math> etc.

:In general, the function remains the same for every [[permutation]] of its variables. This means that, in this case,