What is the formula for computing the S&P 500 Index?

Obviously, the index is a function of the stock prices of the 500 companies included in the index, and I’m pretty sure it’s some sort of weighted average, but the details are what I’m after.

How is each stock weighted?

How is the divisor computed?

Are dividends included in some way? If so, how?

How are stock splits handled?

How is the computation affected when a company decides to issue more stock?

How are adjustments made when a new stock is brought into the index to replace one that is leaving?

I believe the Dow Jones Average is an unweighted index. Other than that, are there any differences between the Dow and the S&P 500 computations with respect to the questions above?

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The S&P 500 is an index of the total market capitalization of the component stocks. The choice of comanies and their weight in the index is made by the S&P Index Committee. The make-up changes from time-to-time but radical changes are quite unusual.

The gory details are explained here.