unfortunately no, it does not depend on how much of full plane you use, as long as there's infinite amount of numbers. take a look at the graph, and especially contour plot of your function below - every curve on contour plot represents a set of (x,y) points that evaluate in the same value.
yes... I know they're circular... but is there ever more than one pair of whole integers described? I mean, could any two integers produce the same result as any other two integers, so that
[ f(x1,y1) , f(y1,x1) ] == [ f(x2,y2) , f(y2,x2) ] ?
If not... then this would satisfy to give a unique identifier of two ID's combined...
aah, integers - I kinda thought of any real numbers. it might work with integers, indeed, maybe run 100000x100000 check loop? if you have a couple of hours to waste
It works, at least to 1000 x 1000...and I don't see why it wouldn't work infinitely =)
It also works to produce unique identifiers for reversible combinations of more than two integers, like this:
[unique floating id from a set of three integers]
(a^2+b^2+c^2)+( sin(atan(a/b))*cos(atan(a/b))*sin(atan(a/c))*cos(atan(a/c))*sin(atan(b/c))*cos(atan(b/c)) )
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