D-Algebraic Functions
Algebraic Geometry
2024-08-27 v3 Symbolic Computation
Classical Analysis and ODEs
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.
Cite
@article{arxiv.2301.02512,
title = {D-Algebraic Functions},
author = {Rida Ait El Manssour and Anna-Laura Sattelberger and Bertrand Teguia Tabuguia},
journal= {arXiv preprint arXiv:2301.02512},
year = {2024}
}
Comments
32 pages, comments welcome