Question

def evaluatePoly(poly, x):
    '''
    Computes the value of a polynomial function at given value x. Returns that
    value as a float.

    poly: list of numbers, length > 0
    x: number
    returns: float
    '''
    for n in range(len(poly)):
        poly[n] = (poly[n]) * (x**n)

    return float(sum(poly[:]))

def computeDeriv(poly):
    '''
    Computes and returns the derivative of a polynomial function as a list of
    floats. If the derivative is 0, returns [0.0].

    poly: list of numbers, length > 0
    returns: list of numbers (floats)

    >>> print computeDeriv([-13.39, 0.0, 17.5, 3.0, 1.0])
    [0.0, 35.0, 9.0, 4.0]
    >>> print computeDeriv([6, 1, 3, 0])
    [1.0, 6.0, 0.0]
    >>> print computeDeriv([20])
    [0.0]

    '''
    if len(poly) == 1:
        poly = [0.0]
        return poly
    for m in range(len(poly)):
        poly[m] = float(m) * poly[m]
    return poly[1:]

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

    poly: list 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: list [float, int]

    >>> print computeRoot([-13.39, 0.0, 17.5, 3.0, 1.0], 0.1,  .0001)
    [0.806790753796352, 7]
    >>> print computeRoot([1, 9, 8], -3, .01)
    [-1.0000079170005467, 5]
    >>> print computeRoot([1, -1, 1, -1], 2, .001)
    [1.0002210630197605, 4]
    '''
    x = x_0
    iter = 0
    list = []
    polyStart = poly[:]
    while abs(evaluatePoly(poly, x)) >= epsilon:
        poly = polyStart[:]
        l = evaluatePoly(poly,x)
        if abs(l) < epsilon:
            list.append(x)
            list.append(iter)
            return list
        else:
            poly = polyStart[:]
            d = computeDeriv(poly)
            dn = evaluatePoly(d, x)
            x = (x - (l/dn))
            iter = iter + 1

Answer 1

I assume you mean this function is returning None on some particular input:

def computeRoot(poly, x_0, epsilon):
    x = x_0
    iter = 0
    list = []
    polyStart = poly[:]
    while abs(evaluatePoly(poly, x)) >= epsilon:
        poly = polyStart[:]
        l = evaluatePoly(poly,x)
        if abs(l) < epsilon:
            list.append(x)
            list.append(iter)
            return list
        else:
            poly = polyStart[:]
            d = computeDeriv(poly)
            dn = evaluatePoly(d, x)
            x = (x - (l/dn))
            iter = iter + 1

How do I know? Because there’s only one return, and it’s not at the end of the function. If abs(evaluatePoly(poly, x)) >= epsilon is False, then the while loop will end, and there’s nothing after it, so the function ends and returns None by default (any function which doesn’t explicitly return returns None).

So, you need to figure out what the correct return value is in that situation and add a return statement and the end of the function.