D-Algebraic Functions

2023/01/06 by Manssour, Rida Ait El, Sattelberger, Anna-Laura, Tabuguia, Bertrand Teguia · 3 citations
#12H05 #34-04 (secondary) #68W30 (primary) #Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #FOS: Computer and information sciences #FOS: Mathematics #Symbolic Computation (cs.SC)

paper · doi:10.48550/arxiv.2301.02512

Abstract

Differentially-algebraic (D-algebraic) functions are solutions of polynomial equations in the function, its derivatives, and the independent variables. We revisit closure properties of these functions by providing constructive proofs. We present algorithms to compute algebraic differential equations for compositions and arithmetic manipulations of univariate D-algebraic functions and derive bounds for the order of the resulting differential equations. We apply our methods to examples in the sciences.

Cited by

• D-algebraic Guessing
• Support bound for differential elimination in polynomial dynamical systems
• Bounds for D-Algebraic Closure Properties

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