This talk investigates algorithmic issues related to the formal resolution of algebraic differential systems, with a stress on the problem of testing components inclusion. Index reduction and applications to control theory are also considered. News are also given of the diffalg2 maple package which improves upon Boulier's work and will be part of a future Maple distribution. The two first chapters provide a clear exposition of basic definitions and results. Some details on the low power theorem may be found in chapter 3.
Differential algebra is a generalization of classical commutative algebra.
We may then define differential fields, modules and algebras in a straightforward way. I , for all d D . I has a natural structure of differential ring. Let A be a Ritt ring, i.e. a differential ring containing Q . P is a differential domain, and we can consider its fraction field K .