On Formal Power Series Solutions of Regular Differential Chains

François Boulier (1) , François Lemaire (1)

1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189

In their celebrated 1984 article, Denef and Lipshitz provide an algorithm for deciding whether a finite system of ordinary differential polynomials has formal power series solutions. This algorithm has never been implemented. In this paper, we describe some key algorithmic tools for transforming this decision result into practical software.

Mots clés: Differential algebra; Computer algebra; Formal power series; Regular chains

Domaines: Logiciel mathématique [cs.MS]; Algèbre commutative [math.AC]

François Boulier, François Lemaire. On Formal Power Series Solutions of Regular Differential Chains. 2024. ⟨hal-04547418v1⟩