t_newton := .47e-1;
delzell := X[2]^2*X[4]^2*X[1]^4-3*X[1]^2*X[2]^2*X[3]^2*X[4]^2+X[1]^2*X[3]^4*X[
4]^2+X[3]^8+X[2]^4*X[3]^2*X[4]^2;
denom_f := 2*X[3]^2+2*X[2]^2+2*X[1]^2;
vec_d := Vector(12, [1/2,1/2,1/2,1/2,1/2,1/2,1/2,0,2/3,0,0,0]);
q_list := Vector(12, [2*X[3]^5,2*X[2]*X[3]^4,2*X[2]^2*X[3]^2*X[4]-X[1]^2*X[3]^
2*X[4]-X[1]^2*X[2]^2*X[4],2*X[2]^3*X[3]*X[4]-2*X[1]^2*X[2]*X[3]*X[4],2*X[1]*X[
3]^3*X[4]-2*X[1]*X[2]^2*X[3]*X[4],2*X[1]*X[3]^4,2*X[1]*X[2]*X[3]^2*X[4]-2*X[1]
^3*X[2]*X[4],0,3/2*X[1]^2*X[3]^2*X[4]-3/2*X[1]^2*X[2]^2*X[4],0,0,0]);