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Communication Dans Un Congrès Année : 2020

The Fundamental Theorem of Tropical Partial Differential Algebraic Geometry

Résumé

Tropical Differential Algebraic Geometry considers difficult or even intractable problems in Differential Equations and tries to extract information on their solutions from a restricted structure of the input. The Fundamental Theorem of Tropical Differential Algebraic Geometry states that the support of solutions of systems of ordinary differential equations with formal power series coefficients over an uncountable algebraically closed field of characteristic zero can be obtained by solving a so-called tropicalized differential system. Tropicalized differential equations work on a completely different algebraic structure which may help in theoretical and computational questions. We show that the Fundamental Theorem can be extended to the case of systems of partial differential equations by introducing vertex sets of Newton polytopes.

Dates et versions

hal-02472809 , version 1 (10-02-2020)

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Citer

Sebastian Falkensteiner, Cristhian Emmanuel Garay-Lopez, Mercedes Haiech, Marc Paul Noordman, Zeinab Toghani, et al.. The Fundamental Theorem of Tropical Partial Differential Algebraic Geometry. ISSAC'20 : International Symposium on Symbolic and Algebraic Computation 2020, Jul 2020, Kalamata, Greece. pp.178-185, ⟨10.1145/3373207.3404040⟩. ⟨hal-02472809⟩
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