An important lesson we have learned from the previous chapters is that computing the product of a series of polynomials is central to the exact analysis of common discrete data models. Often, only some terms from the product are needed. For the purpose of illustrating the main ideas, the sample sizes in the worked examples of these chapters were very small. The multiplications were thereby done with ease. But such an effort grows fast with sample size. Often the data structure may remain sufficiently sparse to preclude an asymptotic alternative. Barring an efficient method of computation, exact analysis can then be infeasible even on modern computers. Data that are too sparse for the asymptotic method, but in which the numbers are sufficiently large to make computational feasibility a barrier to exact analysis are not uncommon. An efficient computational strategy is therefore imperative.