Vol. 318, No. 2, 2022

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Initial forms and a notion of basis for tropical differential equations

Alex Fink and Zeinab Toghani

Vol. 318 (2022), No. 2, 453–468
Abstract

We show that solution sets of systems of tropical differential equations can be characterised in terms of monomial-freeness of an initial ideal. We discuss a candidate definition of tropical differential basis and give a nonexistence result for such bases in an example.

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Keywords
differential algebra, tropical geometry, tropical differential equations, initial form, tropical basis
Mathematical Subject Classification
Primary: 12H05, 13P15, 14T10, 14T90, 34A99
Milestones
Received: 12 November 2020
Revised: 12 April 2022
Accepted: 4 June 2022
Published: 20 August 2022
Authors
Alex Fink
School of Mathematical Sciences
Queen Mary University of London
London
United Kingdom
Zeinab Toghani
Department of Mathematics
Universidad de los Andes
Bogotá
Colombia