Coefficients of Power Series

You can extract any coefficient from a power series -- even on that hasn't been computed yet. This is possible because in Axiom, infinite series are represented by a list of the coefficients that have already been determined, together with a function for computing additional coefficients. (This is known as lazy evaluation.) When you ask for a coefficient that hasn't yet been computed, Axiom computes whatever additional coefficients it needs and then stores them in the representation of the power series. Here's an example of how to extract the coefficients of a power series.

This coefficient is readily available

But let's get the fifteenth coefficient of y

If you look at y then you see that the coefficients up to order 15 have all been computed.