On deciding transcendence of power series
Number Theory
2025-04-24 v1 Symbolic Computation
Classical Analysis and ODEs
Abstract
It is well known that algebraic power series are differentially finite (D-finite): they satisfy linear differential equations with polynomial coefficients. The converse problem, whether a given D-finite power series is algebraic or transcendental, is notoriously difficult. We prove that this problem is decidable: we give two theoretical algorithms and a transcendence test that is efficient in practice.
Cite
@article{arxiv.2504.16697,
title = {On deciding transcendence of power series},
author = {Alin Bostan and Bruno Salvy and Michael F. Singer},
journal= {arXiv preprint arXiv:2504.16697},
year = {2025}
}
Comments
28 pages