On The Relationship Between Differential Algebra and Tropical Differential Algebraic Geometry

Francois Boulier; Sebastian Falkensteiner; Marc Paul Noordman; Omar Leon Sanchez

On The Relationship Between Differential Algebra and Tropical Differential Algebraic Geometry

Francois Boulier, Sebastian Falkensteiner, Marc Paul Noordman, Omar Leon Sanchez

Pure Mathematics

Research output: Chapter in Book/Conference proceeding › Conference contribution › peer-review

Abstract

This paper presents the 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.

Original language	English
Title of host publication	Computer Algebra in Scientific Computing 2021
Publication status	Accepted/In press - 12 Jul 2021
Event	Computer Algebra in Scientific Computing 2021 - Sochi, Russian Federation Duration: 13 Sept 2021 → 17 Sept 2021

Conference

Conference	Computer Algebra in Scientific Computing 2021
Abbreviated title	CASC-2021
Country/Territory	Russian Federation
City	Sochi
Period	13/09/21 → 17/09/21

Embargoed Document

Countable_TDAG
Accepted author manuscript, 298 KB
Embargo ends: 1/01/31

Cite this

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title = "On The Relationship Between Differential Algebra and Tropical Differential Algebraic Geometry",

abstract = "This paper presents the 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.",

author = "Francois Boulier and Sebastian Falkensteiner and Noordman, {Marc Paul} and {Leon Sanchez}, Omar",

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AU - Boulier, Francois

AU - Falkensteiner, Sebastian

AU - Noordman, Marc Paul

AU - Leon Sanchez, Omar

PY - 2021/7/12

Y1 - 2021/7/12

N2 - This paper presents the 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.

AB - This paper presents the 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.

M3 - Conference contribution

BT - Computer Algebra in Scientific Computing 2021

T2 - Computer Algebra in Scientific Computing 2021

Y2 - 13 September 2021 through 17 September 2021

ER -

On The Relationship Between Differential Algebra and Tropical Differential Algebraic Geometry

Abstract

Conference

Embargoed Document

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Cite this