% Written by Rex Ford
% Tell's if Newton's Method converges to root 1, 2 or 3.
% root 1: -1
%      2: .5+i*3^0.5
%      3: -.5+i*3^0.5

function sol = newton(guess)
tol=10^-12;         %assignment's recommended tolerance
f=@(x)x^3+1;        %our function
f_prime=@(x)3*x^2;  %hand-computed derivative
max_its=15;         %in case there isn't convergence
i=0;
while i<max_its && %abs
   guess=guess-(f(guess)/f_prime(guess));
   i=i+1;
end
sol=guess;

% file 2:

function which=which_root(x)
    tol=10^-12;
    is_near=@(y)abs(real(y-x))<tol && abs(imag(y-x))<tol;
    if is_near(-1)==true, which=1;
    else if is_near((1/2)+i*sqrt(3)/2)==true, which=2;
        else which=3;
        end
    end
end