Initial forms and a notion of basis for tropical differential equations

Autor: Fink, Alex, Toghani, Zeinab

Publikováno v: Pacific J. Math. 318 (2022) 453-468

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

Externí odkaz: http://arxiv.org/abs/2004.08258

The Fundamental Theorem of Tropical Differential Algebraic Geometry

Autor: Aroca, Fuensanta, Garay, Cristhian, Toghani, Zeinab

Publikováno v: Pacific J. Math. 283 (2016) 257-270

Let $I$ be an ideal of the ring of Laurent polynomials $K[x_1^{\pm1},\ldots,x_n^{\pm1}]$ with coefficients in a real-valued field $(K,v)$. The fundamental theorem of tropical algebraic geometry states the equality $\text{trop}(V(I))=V(\text{trop}(I))

Externí odkaz: http://arxiv.org/abs/1510.01000

Sur les Initiaux et le Théorème Fondamental de la Géométrie Différentielle Tropicale Partielle

Autor: Falkensteiner, Sebastian, Garay-Lopez, Cristhian Emmanuel, Haiech, Mercedes, Noordman, Marc Paul, Boulier, François, Toghani, Zeinab

Publikováno v: Journal of Symbolic Computation
Journal of Symbolic Computation, 2023, 115C, pp.53-73. ⟨10.1016/j.jsc.2022.08.005⟩
Journal of Symbolic Computation, Elsevier, In press

International audience

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::275d8e91124287d6dca664d47ff01d16
https://hal.science/hal-03122437

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Geometría diferencial tropical

Autor: Toghani, Zeinab

Publikováno v: Universidad Nacional Autónoma de México
UNAM
Repositorio de Tesis DGBSDI, Dirección General de Bibliotecas y Servicios Digitales de Información, UNAM

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=od______3056::e4b535281f34b5c23b85eaed37f43158
https://ru.dgb.unam.mx/handle/DGB_UNAM/TES01000757248