D-Algebraic Functions
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866916369055875072 |
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| author | Manssour, Rida Ait El Sattelberger, Anna-Laura Tabuguia, Bertrand Teguia |
| author_facet | Manssour, Rida Ait El Sattelberger, Anna-Laura Tabuguia, Bertrand Teguia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_02512 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | D-Algebraic Functions Manssour, Rida Ait El Sattelberger, Anna-Laura Tabuguia, Bertrand Teguia Algebraic Geometry Symbolic Computation Classical Analysis and ODEs 12H05, 68W30 (primary), 34-04 (secondary) 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. |
| title | D-Algebraic Functions |
| topic | Algebraic Geometry Symbolic Computation Classical Analysis and ODEs 12H05, 68W30 (primary), 34-04 (secondary) |
| url | https://arxiv.org/abs/2301.02512 |