Using the lambda function for a function that depends on the input

Question

As an input, I have a list of nonnegative whole numbers which are supposed to be the coefficients of a polynomial. But I also want to evaluate the polynomial for a certain number x.

For example:

If we have L=[2,3,1] as an input and x=42 we get 2x^2+3x+1=3655 What I want is for example:

>>>p=polynomial([2,3,1])
>>>p(O)
1 
>>>p(42)
>>>3655

I guess I have to make use of the lambda function somehow, and I do know how it works for two variables on a given function, but in this case the function depends on my input.

def polynomial(coef):
coef=coef[::-1]
for i in range(len(coef)):
    p=lambda x: coef[i]*x**i
    p+=p
return lambda x: p

This is of course absolute nonsense, as I cannot add up one lambda function to another, but this is what my approaching "intuition" is.

Some hints are much appreciated.

Answer 1

The most obvious pythonic solution (using a closure - with a lambda or (preferably) a named inner function) has already been posted, but for the sake of completeness I'll add the other pythonic solution - the OO version using a custom callable class:

class Polynomial(object):
    def __init__(self, coef):
        self.coef = coef

    def __call__(self, x):
        n = len(self.coef) - 1
        return sum(c * x ** (n - i) for (i, c) in enumerate(self.coef))

p = Polynomial([2,3,1])
print p(0)
print p(42)