Ax-Schanuel and exceptional integrability

2022/02/08 by Jonathan Pila, Jacob Tsimerman, Pila, Jonathan +1 · 2 citations
Computer Science · Mathematics · #11J89 #14H40 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Numerical methods for differential equations #Polynomial and algebraic computation #math.AG #msc:11J89 #msc:14H40

paper · pdf · doi:10.48550/arxiv.2202.04023

arxiv created 2022/02/08 · openalex publication_date 2022/02/08 · arxiv updated 2022/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

When can a primitive of a given algebraic function be con-structed by iteratively solving algebraic equations and composing withthe primitives of some other given algebraic functions or their inverses? We establish some results in this direction. Specifically, we establishdecision procedures for determining whether a given primitive can beexpressed in terms of finitely many others, or in terms of elliptic integrals.

Cited by

• Integration in finite terms and exponentially algebraic functions
• Symbolic Integration in Weierstrass-like Extensions

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