# Section8.2Fractions and Series

Many generating series can be expressed as rational functions, and such expressions provide useful information. We illustrate this. First we create a ring of polynomials, and the corresponding field of fractions. (We will not need the latter, as it happens.)

Now we can work with our series $L(t)$ from the previous section.

Note that t is the generator of Rt, which is $\rats[[t]]$. So we have used subs() to convert a rational function to a power series.

We can also compute partial fraction decompositions. For these to be useful the zeros of the denominator should belong to the field we are working over.