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December 21, 2025Open Access

Bounds for D-Algebraic Closure Properties

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Authors

MKManuel KauersRPRaphaël Pagès

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Overview

This paper demonstrates bounds on the degree of differential equations from D-algebraic functions, suggesting a method for evaluating closure properties.

Key Points

  • The aim is to establish bounds on the size of polynomial differential equations using closure properties for D-algebraic functions.
  • Analyzed closure properties related to D-algebraic functions
  • Derived bounds on the order of polynomial differential equations
  • Focused on conditions necessary for defining differential equations
  • Provided specific bounds on the degree of these differential equations under technical conditions
  • Showed that obtaining bounds on the size is easier compared to those on the degree

Cite This Study

Kauers et al. (2025) studied this question.

synapsesocial.com/papers/69473b64db9c958d0dfca858https://doi.org/10.48550/arxiv.2505.07304
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Also Consider

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  1. 1Differential Algebraic Closure for Characteristic Polynomials of Linear Ordinary Differential Equations: Finite Representation of Solutions, Algebraic Special Values, and Applications2025
  2. 2Arithmetic of D-algebraic functions2024 · 3 citations
  3. 3Construction, Classification, and Applications in Mathematical Physics of Differential-Algebraic Closures: A Unified Theoretical Framework for Hilbert's 22th Problem2025
  4. 4Unified Analytic Solution of Polynomial Equations in Commutative Banach Algebras via Differential Algebraic Methods2025
  5. 5Unified Analytic Solution of Polynomial Equations in Differential Algebraic Closure2025