root calculator

# cbrt(x) = n such that n^3 = x
# n^3 = x
# n^3 - x = 0
# f(n) = n^3 - x
# f'(n) = 3n^2
# g(n) = n - (f(n)/f'(n))
# cbrt(x) = (approx) g^10(1) where x = x in all above functions
# we can generalize this to other 1/x exponents

def root(e, x):
    f  = lambda g: g**e - float(x)
    fp = lambda g: e * g**(e-1)
    g  = lambda g: g - f(g) / fp(g)
    guess = 1.0

    for i in range(10):
        guess = g(guess)

    return guess

# example usage: root(4, 3) calculates the 4th root of 3 (n where n*n*n*n = 3)
#                ~1.316074012952492