English

Ax-Schanuel and exceptional integrability

Algebraic Geometry 2022-02-09 v1

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.

Keywords

Cite

@article{arxiv.2202.04023,
  title  = {Ax-Schanuel and exceptional integrability},
  author = {Jonathan Pila and Jacob Tsimerman},
  journal= {arXiv preprint arXiv:2202.04023},
  year   = {2022}
}
R2 v1 2026-06-24T09:26:51.482Z