Other areas

It is clear that we have not covered all the areas that formal computation can address in this article, but we have described the main ones. The following areas are also worth mentioning.

In arithmetic and combinatorics, formal calculus excels in its manipulation of real integers; in these fields, it is possible to solve integer equations and counting problems. The study of real sequences allows us to solve recurrence problems (calculating the values of a sequence) and to compute the limits of a sequence. In particular, formal calculus allows for the computation of sums (Σ) and products (Π) over large classes of expressions.

Series are a powerful tool for problems that do not have exact solutions: one can calculate series or asymptotic expansions of sequences, integrals, or solutions to equations (ordinary or differential), whose coefficients...