Symbolic Integration in Weierstrass-like Extensions
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915780523720704 |
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| author | Chen, Shaoshi Kauers, Manuel Li, Wenqiao Li, Xiuyun Masser, David |
| author_facet | Chen, Shaoshi Kauers, Manuel Li, Wenqiao Li, Xiuyun Masser, David |
| contents | This paper studies the integration problem in differential fields that may involve quantities reminiscent of the Weierstrass $\wp$ function, which are defined by a first-order nonlinear differential equation. We extend the classical notion of special polynomials to elements of Weierstrass-like extensions and present algorithms for reduction in such extensions. As an application of these results, we derive some new formulae for integrals of powers of $\wp$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_06873 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symbolic Integration in Weierstrass-like Extensions Chen, Shaoshi Kauers, Manuel Li, Wenqiao Li, Xiuyun Masser, David Symbolic Computation Algebraic Geometry Classical Analysis and ODEs 68U01 I.1.2 This paper studies the integration problem in differential fields that may involve quantities reminiscent of the Weierstrass $\wp$ function, which are defined by a first-order nonlinear differential equation. We extend the classical notion of special polynomials to elements of Weierstrass-like extensions and present algorithms for reduction in such extensions. As an application of these results, we derive some new formulae for integrals of powers of $\wp$. |
| title | Symbolic Integration in Weierstrass-like Extensions |
| topic | Symbolic Computation Algebraic Geometry Classical Analysis and ODEs 68U01 I.1.2 |
| url | https://arxiv.org/abs/2602.06873 |