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Symbolic Integration in Weierstrass-like Extensions

Year: 2026

Type: preprint

Abstract: 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 $\wp$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2602.06873

Authors: Chen, Shaoshi, Kauers, Manuel, Li, Wenqiao, Li, Xiuyun, Masser, David

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7128385108

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