Reduction systems and degree bounds for integration

• DOI: 10.48550/arxiv.2404.13042
• Publication Date: 2024-04-19
• Authors: Hao Du; Clemens G. Raab
• Keywords: Degree (music)

In symbolic integration, the Risch--Norman algorithm aims to find closed forms of elementary integrals over differential fields by an ansatz for integral, which usually is based on heuristic degree bounds. Norman presented approach that avoids bounds and only relies completion reduction systems. We give a formalization his we develop refined process, terminates in more instances. some situations when does not terminate, one can detect patterns allowing still describe infinite systems are complete. present such generated Airy functions complete elliptic integrals, respectively. Moreover, show how be used rigorous particular, general formula weighted apply it tight above examples.