On The Relationship Between Differential Algebra and Tropical Differential Algebraic Geometry

François Boulier (1) , Sebastian Falkensteiner (2) , Marc Paul Noordman (3)

1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
2 JKU - University of Linz - Johannes Kepler Universität Linz
3 Bernoulli Institute for Mathematics for Mathematics, Computer Science and Artificial Intelligence Groningen,

This paper presents some relationship between differential algebra and tropical differential algebraic geometry, mostly focusing on the existence problem of formal power series solutions for systems of polynomial ODE and PDE. Moreover, it improves an approximation theorem involved in the proof of the Fundamental Theorem of tropical differential algebraic geometry which permits to improve this latter by dropping the base field uncountability hypothesis used in the original version.

Domaines: Calcul formel [cs.SC]; Algèbre commutative [math.AC]

François Boulier, Sebastian Falkensteiner, Marc Paul Noordman. On The Relationship Between Differential Algebra and Tropical Differential Algebraic Geometry. 2021. ⟨hal-03225922v1⟩