Computing with D-algebraic sequences

Preprint

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 C²-finite sequences.

Authors: Teguia Tabuguia, B

• Publication status: Published
• Peer review status: Not peer reviewed
• Preprint server: arXiv
• Publication date: 2024-12-30
• DOI: 10.48550/arXiv.2412.20630
• Language: English
• Keywords: affine D-algebraic sequence; rationalizing difference polynomial; subsequence