x, y, z, t, u, 
x^2+y^2+z^2
x*y*z
x^2*y^2+x^2*z^2+y^2*z^2
t^2+3*u^2
-t^2*u+u^3
t*y^2-t*z^2+2*u*x^2-u*y^2-u*z^2
-x^2*(t*y^2-t*z^2-u*y^2+u*z^2)
-2*t^2*x^2+t^2*y^2+t^2*z^2-6*t*u*y^2+6*t*u*z^2+6*u*x^2-3*u*y^2-3*u*z^2
t^2*x^2*y^2+t^2*x^2*z^2-2*t^2*y^2*z^2+6*t*u*x^2*y^2-6*t*u*x^2*z^2-3*u^2*x^2*y^2-3*u^2*x^2*z^2+6*u^2*y^2*z^2
t*(t^2*x^4*y^2-t^2*x^4*z^2-t^2*x^2*y^4+t^2*x^2*z^4+t^2*y^4*z^2-t^2*y^2*z^4-9*u^2*x^4*y^2+9*u^2*x^4*z^2+9*u^2*x^2*y^4-9*u^2*x^2*z^4-9*u^2*y^4*z^2+9*u^2*y^2*z^4)
