Concrete Resolution of Diierential Problems Using Tannakian Categories

Given a linear ODE with polynomial coeecients, one easily nds local information about its solutions. To obtain global information of algebraic nature (operator factorization, explicit nite form, algebraic relations between solutions), one classically reduces the problem to determining rational or exponential solutions of auxiliary linear ODE's. The latter are often uneasy to compute in practice, and we show by a few examples how to advantageously substitute diierential systems that are simpler to construct, solve or study.