The set of differentially algebraic power series in several variables over an effective field of characteristic zero forms an effective ”tribe”: it is closed under the effective ring operations, restricted division, composition, the implicit function theorem, as well as restricted monomial transformations with rational exponents.

Given an effective tribe with an effective zero test, we shall prove an effective version of the Weierstrass division theorem and show how to use this for the development of an effective elimination theory for power series equations, given through elements in the tribe.

Occasion: Differential Algebra and Related Topics (DART), Beijing, May 26, 2025

Documents: slideshow, TeXmacs source