Computing with D-Algebraic Sequences
Algebraic Geometry
2025-10-13 v2 Numerical Analysis
Symbolic Computation
Numerical Analysis
Abstract
A sequence is difference algebraic (or D-algebraic) if finitely many shifts of its general term satisfy a polynomial relationship; that is, they are the coordinates of a generic point on an affine hypersurface. The corresponding equations are denoted algebraic difference equations (ADEs). We propose a formal definition of D-algebraicity for sequences and investigate algorithms for their closure properties. We show that subsequences of D-algebraic sequences, indexed by arithmetic progressions, satisfy ADEs of the same orders as the original sequences. Additionally, we discuss the special difference-algebraic nature of holonomic and -finite sequences.
Cite
@article{arxiv.2412.20630,
title = {Computing with D-Algebraic Sequences},
author = {Bertrand Teguia Tabuguia},
journal= {arXiv preprint arXiv:2412.20630},
year = {2025}
}
Comments
29 pages, 1 figure. More comprehensive version. Specific results for $C^2$-finite sequences