Symbolic Integration of Differential Forms: From Abel to Zeilberger
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866911350741008384 |
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| author | Chen, Shaoshi Cox, David A. Wang, Yisen |
| author_facet | Chen, Shaoshi Cox, David A. Wang, Yisen |
| contents | This paper focuses on symbolic integration of differential forms, with a particular emphasis on historical and modern developments, from Abel's addition theorems for Abelian integrals to Zeilberger's creative telescoping for parameterized integrals. It explores closed rational $p$-forms and provides algorithmic approaches for their integration, extending classical results like Hermite reduction and Liouville's theorem. The integration of closed differential forms with parameters is further examined through telescopers, offering a unified framework for handling both algebraic and transcendental cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00721 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symbolic Integration of Differential Forms: From Abel to Zeilberger Chen, Shaoshi Cox, David A. Wang, Yisen Classical Analysis and ODEs Algebraic Geometry Combinatorics 16S32, 35G35, 68W30 This paper focuses on symbolic integration of differential forms, with a particular emphasis on historical and modern developments, from Abel's addition theorems for Abelian integrals to Zeilberger's creative telescoping for parameterized integrals. It explores closed rational $p$-forms and provides algorithmic approaches for their integration, extending classical results like Hermite reduction and Liouville's theorem. The integration of closed differential forms with parameters is further examined through telescopers, offering a unified framework for handling both algebraic and transcendental cases. |
| title | Symbolic Integration of Differential Forms: From Abel to Zeilberger |
| topic | Classical Analysis and ODEs Algebraic Geometry Combinatorics 16S32, 35G35, 68W30 |
| url | https://arxiv.org/abs/2601.00721 |