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arXiv · 2412.20630

Computing with D-Algebraic Sequences

Bertrand Teguia Tabuguia
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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 $C^2$-finite sequences.

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Bertrand Teguia Tabuguia. 2024-12-30. Computing with D-Algebraic Sequences. https://arxiv.org/abs/2412.20630

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