LL5 := X[1]*X[2]*X[4]*X[3]-X[1]*(-X[1]+X[2])*(-X[1]+X[4])*(-X[1]+X[3])-X[2]*(-
X[2]+X[1])*(-X[2]+X[4])*(-X[2]+X[3])-X[4]*(-X[4]+X[1])*(-X[4]+X[2])*(-X[4]+X[3
])-X[3]*(-X[3]+X[1])*(-X[3]+X[2])*(-X[3]+X[4]);
denom_f := X[1]^2+X[2]^2+X[3]^2+X[4]^2;
t_newton := .32e-1;
r_min := 0;
vec_d := Vector(20, [1,4/7,7/6,0,8/11,11/9,1,0,0,0,4,0,0,0,0,0,0,0,0,0]);
q_list := Vector(20, [X[4]^3-1/2*X[3]*X[4]^2-1/2*X[3]^2*X[4]-1/2*X[2]*X[4]^2+X
[2]*X[3]*X[4]-1/2*X[2]^2*X[4]-1/2*X[1]*X[4]^2+X[1]*X[3]*X[4]+X[1]*X[2]*X[4]-1/
2*X[1]^2*X[4],7/4*X[3]*X[4]^2-5/4*X[3]^2*X[4]-1/2*X[3]^3-3/4*X[2]*X[4]^2-1/2*X
[2]*X[3]*X[4]+X[2]*X[3]^2+3/4*X[2]^2*X[4]-1/2*X[2]^2*X[3]-3/4*X[1]*X[4]^2-1/2*
X[1]*X[3]*X[4]+X[1]*X[3]^2-1/2*X[1]*X[2]*X[3]+3/4*X[1]^2*X[4]-1/2*X[1]^2*X[3],
6/7*X[3]^2*X[4]-6/7*X[3]^3+3/14*X[2]*X[4]^2-6/7*X[2]*X[3]*X[4]+3/14*X[2]*X[3]^
2-3/14*X[2]^2*X[4]+9/14*X[2]^2*X[3]+3/14*X[1]*X[4]^2-6/7*X[1]*X[3]*X[4]+3/14*X
[1]*X[3]^2-6/7*X[1]*X[2]*X[3]-3/14*X[1]^2*X[4]+9/14*X[1]^2*X[3],0,11/8*X[2]*X[
4]^2-1/2*X[2]*X[3]*X[4]-1/8*X[2]*X[3]^2-7/8*X[2]^2*X[4]+5/8*X[2]^2*X[3]-1/2*X[
2]^3-9/8*X[1]*X[4]^2+3/8*X[1]*X[3]^2-1/2*X[1]*X[2]*X[4]-1/2*X[1]*X[2]*X[3]+X[1
]*X[2]^2+9/8*X[1]^2*X[4]-3/8*X[1]^2*X[3]-1/2*X[1]^2*X[2],9/11*X[2]*X[3]*X[4]-6
/11*X[2]*X[3]^2-9/11*X[2]^2*X[4]-3/11*X[2]^2*X[3]+9/11*X[2]^3-9/22*X[1]*X[4]^2
+3/22*X[1]*X[3]^2+9/11*X[1]*X[2]*X[4]+9/11*X[1]*X[2]*X[3]-3/22*X[1]*X[2]^2+9/
22*X[1]^2*X[4]-3/22*X[1]^2*X[3]-15/22*X[1]^2*X[2],X[2]*X[3]^2-X[2]^2*X[3]-X[1]
*X[3]^2+X[1]*X[2]^2+X[1]^2*X[3]-X[1]^2*X[2],0,0,0,1/4*X[1]*X[4]^2-1/2*X[1]*X[3
]*X[4]+1/4*X[1]*X[3]^2-1/2*X[1]*X[2]*X[4]-1/2*X[1]*X[2]*X[3]+1/4*X[1]*X[2]^2+1
/4*X[1]^2*X[4]+1/4*X[1]^2*X[3]+1/4*X[1]^2*X[2]-1/2*X[1]^3,0,0,0,0,0,0,0,0,0]);