poly = (0.0, 0.0, 5.0, 9.3, 7.0)
x = -13

def evaluate_poly(poly, x):
    """
    Computes the polynomial function for a given value x. Returns that value.

    Example:
    >>> poly = (0.0, 0.0, 5.0, 9.3, 7.0)    # f(x) = 7x^4 + 9.3x^3 + 5x^2
    >>> x = -13
    >>> print evaluate_poly(poly, x)  # f(-13) = 7(-13)^4 + 9.3(-13)^3 + 5(-13)^2
    180339.9

    poly: tuple of numbers, length > 0
    x: number
    returns: float
    """
    # TO DO ...
    answer = 0
    for power in range (0, len(poly)):
        answer = answer + poly[power]*(x**power)
    return answer

print evaluate_poly(poly, x)

poly1 = (-13.39, 0.0, 17.5, 3.0, 1.0)
# derivative would be (0, 35, 9, 4)

def compute_deriv(poly1):
    """
    Computes and returns the derivative of a polynomial function. If the
    derivative is 0, returns (0.0,).

    Example:
    >>> poly = (-13.39, 0.0, 17.5, 3.0, 1.0)    # x^4 + 3x^3 + 17.5x^2 - 13.39
    >>> print compute_deriv(poly)        # 4x^3 + 9x^2 + 35^x
    (0.0, 35.0, 9.0, 4.0)

    poly: tuple of numbers, length > 0
    returns: tuple of numbers
    """
    # TO DO ...
    answer = ()
    for a in range (1, len(poly1)):
        answer = answer + (a*poly1[a],)
    return answer

print compute_deriv(poly1)


x_0 = .1
poly = (-13.39, 0.0, 17.5, 3.0, 1.0)
epsilon = .0001

def compute_root(poly, x_0, epsilon):
    """
    Uses Newton's method to find and return a root of a polynomial function.
    Returns a tuple containing the root and the number of iterations required
    to get to the root.

    Example:
    >>> poly = (-13.39, 0.0, 17.5, 3.0, 1.0)    #x^4 + 3x^3 + 17.5x^2 - 13.39
    >>> x_0 = 0.1
    >>> epsilon = .0001
    >>> print compute_root(poly, x_0, epsilon)
    (0.80679075379635201, 8.0)

    poly: tuple of numbers, length > 1.
         Represents a polynomial function containing at least one real root.
         The derivative of this polynomial function at x_0 is not 0.
    x_0: float
    epsilon: float > 0
    returns: tuple (float, int)
    """
    # TO DO ...
    guesses = 1
    while abs(evaluate_poly(poly, x_0)) >= epsilon:
        x_0 = x_0 - evaluate_poly(poly, x_0)/evaluate_poly(compute_deriv(poly), x_0)
        guesses = guesses +1
    if abs(evaluate_poly(poly, x_0)) <= epsilon:
        return "The root of the polynomial is", (x_0,guesses)
    else:
        return "The polynomial has no root"

print compute_root(poly, x_0, epsilon)