I have 6 functions of four variables $ f_i: \mathbb{R}^4 \rightarrow \mathbb{R},\, i \in 1..6$
For each function $f_j$ I want to find the subset of $ \mathbb{R}^4 $, called $S_j$, for which it is less than all the other functions
i.e.
$f_j(w,x,y,z) \le f_i(w,x,y,z) \; \forall i \in 1..6 \; \forall (w,x,y,z) \in S_j$
In particular the functions I'm working with are as follows:
{
1/2 (-x - y + Sqrt[4 w^2 + x^2 - 2 x y + y^2]),
1/2 (-x - y - Sqrt[4 w^2 + x^2 - 2 x y + y^2]),
-z,
x + y - Sqrt[4 w^2 + x^2 - 2 x y + y^2],
x + y + Sqrt[4 w^2 + x^2 - 2 x y + y^2],
2 z
}
Your help is appreciated,
Reid