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A problem from <<Thinking in Problems>> by Roytvarf, Birkhauser

I got a problem, which turned to be from the book "Thinking in Problems How Mathematicians Find Creative Solutions" by Roytvarf, Chapter One, Jacobi Identities and Related Combinatorial Formulas : ...
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3answers
462 views

How do I find out the symmetry of a function?

For example, how do I know that with: $$f(x_1,x_2,x_3,x_4)=\frac{x_1 x_2+x_3 x_4-x_2 x_3-x_1 x_4}{x_1 x_2+x_3 x_4-x_1 x_3-x_2 x_4}$$ $f$ has the property: ...