用SOS定理
4*s[x^3 (x^2 - y^2 - z^2)^2 (x^2 - y^2) (x^2 - z^2)]*s[x]^2=
s[ (2 x^4-x^3 y-x^2 y^2+x y^3-y^4-x^3 z-2 x^2 y z+x y^2 z-x^2 z^2+x y z^2+2 y^2 z^2+x z^3-z^4)^2 (-3 x^5+8 x^4 y+6 x^3 y^2-16 x^2 y^3-3 x y^4+8 y^5+8 x^4 z+9 x^3 y z+9 x^2 y^2 z-9 x y^3 z-17 y^4 z+6 x^3 z^2+9 x^2 y z^2+28 x y^2 z^2+9 y^3 z^2-16 x^2 z^3-9 x y z^3+9 y^2 z^3-3 x z^4-17 y z^4+8 z^5)]
f(x,y,z):=(-3 x^5+8 x^4 y+6 x^3 y^2-16 x^2 y^3-3 x y^4+8 y^5+8 x^4 z+9 x^3 y z+9 x^2 y^2 z-9 x y^3 z-17 y^4 z+6 x^3 z^2+9 x^2 y z^2+28 x y^2 z^2+9 y^3 z^2-16 x^2 z^3-9 x y z^3+9 y^2 z^3-3 x z^4-17 y z^4+8 z^5)
s[f(x,y,z)]=s[(4 x^2 y z^2+7/2 y (x+y-z)^2 (-x+y+z)^2+(x+y-z)^2 ((7 x z^2)/2+(7 y z^2)/2+(19 z^3)/2))]>=0
s[f(x,y,z)f(y,z,x)]=s[2 x (x-y)^2 y (x+y-z)^2 z^2+(x+y-z)^2 (x-y+z)^2 (-x+y+z)^2 (7 x y+4 z^2)+(x+y-z)^2 (2 x^2 y z^3+2 x y^2 z^3+x y z^4)]