622.sagews

def newton_find_root(func, fprime, x0, num_iterations=10, full_output=True):
    """
    Use Newton's method to find a root of ``func`` with initial guess x0
    where ``func`` is a differentiable function in one variable with derivative ``fprime``.
    """  

    x0 = float(x0)   
    for i in range (num_iterations):
        x0 = x0 - func(x0)/fprime(x0)
        
        if full_output == True:
            print float(x0)
    
    return x0

f(x) = x^2 - 2
fp = diff(f)
newton_find_root(f, fp, 10)

5.1 2.74607843137 1.73719487438 1.44423809487 1.41452565515 1.4142135968 1.41421356237 1.41421356237 1.41421356237 1.41421356237 1.41421356237310

import scipy.optimize