Computing with D-Algebraic Sequences
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915542896476160 |
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| author | Tabuguia, Bertrand Teguia |
| author_facet | Tabuguia, Bertrand Teguia |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_20630 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computing with D-Algebraic Sequences Tabuguia, Bertrand Teguia Algebraic Geometry Numerical Analysis Symbolic Computation 12H10, 68W30 (primary), 39-04, 13Pxx (secondary) I.1.2; G.4 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. |
| title | Computing with D-Algebraic Sequences |
| topic | Algebraic Geometry Numerical Analysis Symbolic Computation 12H10, 68W30 (primary), 39-04, 13Pxx (secondary) I.1.2; G.4 |
| url | https://arxiv.org/abs/2412.20630 |