Newton's Iterative Formula in SageMath

nif.py

# Function variable x
x = var('x');

# Function f(x)
f(x) = (x-3)*ln(x)-1;

# Derivative f'(x)
df = diff(f,x);

# Newton's Iterative Formula
nif(x) = x-(f/df)(x);

x1 = 5; # Initial guess
i = 10; # Number of iterations

for _ in range(i):
    x=N(nif(x1));
    print(x, "<-- iteration", _+1)
    x1=x