-1
$\begingroup$

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:

$$f(x_1,x_2,x_3,x_4)=f(x_2,x_1,x_4,x_3)=f(x_4,x_3,x_2,x_1)=f(x_3,x_4,x_1,x_2)$$

I mean it's not that easy to discover all of them, right? I myself used to know only the first part of that symmetry until I find the completed one today. Is there any general method to examine the symmetry of a given function?

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    Wonderful. Now you disguised the cross ratio by multiplying it out... The symmetries are much better hidden this way, yes. By the way: *you* found it? In your deleted question somebody gave you a link...2011-07-02
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    @Theo Buehler: Okay, okay, I admit I shouldn't ask such unthoughtful questions, but at least I've learned to change my question to make it more acceptable, that's wonderful progress right?2011-07-02
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    @Theo Buehler: btw, thought I've now get the direct answer, I still can't figure out how the answer is deduced. Try to discover that f(x1,x4,x3,x2)=λ/λ-1 seems impossible for me.2011-07-02

3 Answers 3