How to write function with variable from the outside?

Question

I hope you can help. I am looking for a way to write a function that inserts one item later. Let me show you an example:

def general_poly(L):
        """ 
        L, a list of numbers (n0, n1, n2, ... nk)
        Returns a function, which when applied to a value x, returns the value 
        n0 * x^k + n1 * x^(k-1) + ... nk * x^0 
        """
        x = 1
        res = 0
        n = len(L)-1
        for e in range(len(L)):
            res += L[e]*x**n
            n -= 1
        return res

I thought I could just give x a value here and once I do general_poly(L)(10) it will be replaced so that x = 10 but apparently it is not that easy. What do I have to change / add so that my function works? How does the function know, that the multiplication is the x? Thanks for your help, guys!

Answer 1

You are being asked to return a function but you are returning the calculated value:

def general_poly(L):
    """ 
    L, a list of numbers (n0, n1, n2, ... nk)
    Returns a function, which when applied to a value x, returns the value 
    n0 * x^k + n1 * x^(k-1) + ... nk * x^0 
    """
    def inner(x):
        res = 0
        n = len(L)-1
        for e in range(len(L)):
            res += L[e]*x**n
            n -= 1
        return res
    return inner

Now general_poly(L)(10) will do what you expect but it is probably more useful if you assign it to a value, so it can be called it multiple times, e.g.:

L = [...]
fn = general_poly(L)
print(fn(10))
print(fn(3))

You could also rewrite inner to:

def general_poly(L):
    return lambda x: sum(e*x**n for n, e in enumerate(reversed(L)))

Answer 2

def general_poly (L):
    """ L, a list of numbers (n0, n1, n2, ... nk)
    Returns a function, which when applied to a value x, returns the value 
    n0 * x^k + n1 * x^(k-1) + ... nk * x^0 """

    def inner(x):
        L.reverse()
        return sum(e*x**L.index(e) for e in L)
    return inner