# 6.00 Problem Set 2
#
# Successive Approximation
#

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
    """
    value = 0

    if len(poly) == 0:
        print "Enter a polynomial with length > 0"
        return

    for i, var in enumerate(poly):
        value =  value + var*x**i

    return value

def compute_deriv(poly):
    """
    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
    """

    deriv = ()

    for i, var in enumerate(poly):
        if i > 0:
            deriv = deriv + ((var * i),)

    return deriv


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)
    """
    global count
    global root
    count = count + 1
    root = evaluate_poly(poly, x_0)
    deriv = evaluate_poly(compute_deriv(poly), x_0)

    if abs(root) < epsilon:
        return (root, count)
    else:
        #count = count + 1
        x_0 = x_0 - (root / deriv)
        compute_root(poly, x_0, epsilon)

    return (root, count)


#Problem 1
#poly = (0.0, 0.0, 5.0, 9.3, 7.0)
#x = -13
#print evaluate_poly(poly, x)

#Problem 2
#poly = (-13.39, 0.0, 17.5, 3.0, 1.0)
#print compute_deriv(poly)

#Problem 3
count = 0
root = 0
poly = (-13.39, 0.0, 17.5, 3.0, 1.0)
x_0 = 0.1
epsilon = .0001
print compute_root(poly, x_0, epsilon)

