Using a list to represent a polynomial

Question Q2.4.2

A list could be used as a simple representation of a polynomial, $P(x)$, with the items as the coefficients of the successive powers of $x$, and their indexes as the powers themselves. Thus, the polynomial $P(x) = 4 + 5x + 2x^3$ would be represented by the list [4, 5, 0, 2]. Why does the following attempt to differentiate a polynomial fail to produce the correct answer?

>>> P = [4, 5, 0, 2]
>>> dPdx = []
>>> for i, c in enumerate(P[1:]):
...     dPdx.append(i*c)
>>> dPdx
[0, 0, 4]            # wrong!

How can this code be fixed?


Solution