D-algebraic functions

IF 0.6 4区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Journal of Symbolic Computation Pub Date : 2024-08-28 DOI:10.1016/j.jsc.2024.102377

Rida Ait El Manssour , Anna-Laura Sattelberger , Bertrand Teguia Tabuguia

引用次数: 0

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.

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D 代函数

微分代数（D-代数）函数是函数、其导数和自变量中多项式方程的解。我们通过提供构造性证明来重新审视这些函数的闭包性质。我们提出了为单变量 D- 代数函数的合成和算术运算计算代数微分方程的算法，并推导出了所得微分方程的阶数边界。我们将我们的方法应用于科学领域的实例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Symbolic Computation 工程技术-计算机：理论方法

CiteScore

2.10

自引率

14.30%

发文量

审稿时长

142 days

期刊介绍： An international journal, the Journal of Symbolic Computation, founded by Bruno Buchberger in 1985, is directed to mathematicians and computer scientists who have a particular interest in symbolic computation. The journal provides a forum for research in the algorithmic treatment of all types of symbolic objects: objects in formal languages (terms, formulas, programs); algebraic objects (elements in basic number domains, polynomials, residue classes, etc.); and geometrical objects. It is the explicit goal of the journal to promote the integration of symbolic computation by establishing one common avenue of communication for researchers working in the different subareas. It is also important that the algorithmic achievements of these areas should be made available to the human problem-solver in integrated software systems for symbolic computation. To help this integration, the journal publishes invited tutorial surveys as well as Applications Letters and System Descriptions.