Tropical differential Gröbner bases

DOI10.1007/s11786-020-00481-1zbMath1482.14066arXiv1904.02275OpenAlexW3033633724MaRDI QIDQ2035624

Youren Hu, Xiao-Shan Gao

Publication date: 25 June 2021

Published in: Mathematics in Computer Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.02275

zbMATH Keywords

Buchberger criteriontropical differential algebratropical differential Gröbner basis

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Differential algebra (12H05) Computational aspects in algebraic geometry (14Q99) Differential algebra (13N99) Foundations of tropical geometry and relations with algebra (14T10)

Related Items (4)

Initial forms and a notion of basis for tropical differential equations ⋮ On initials and the fundamental theorem of tropical partial differential algebraic geometry ⋮ Exploring tropical differential equations ⋮ A general framework for tropical differential equations

Cites Work

• Tropical differential equations
• Differential valuations
• Matrix-F5 algorithms and tropical Gröbner bases computation
• Ritt-Wu characteristic set method for Laurent partial differential polynomial systems
• Computing tropical varieties over fields with valuation
• Sparse differential resultant for Laurent differential polynomials
• Computing tropical varieties
• The fundamental theorem of tropical differential algebraic geometry
• Solving Ordinary Differential Equations in Terms of Series with Real Exponents
• ON THE SERIES DEFINED BY DIFFERENTIAL EQUATIONS, WITH AN EXTENSION OF THE PUISEUX POLYGON CONSTRUCTION TO THESE EQUATIONS
• Gröbner bases over fields with valuations
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