Transcendence Certificates for D-finite Functions
Manuel Kauers, Christoph Koutschan, Thibaut Verron

TL;DR
This paper introduces a new sufficient condition for certifying the transcendence of D-finite functions, addressing practical challenges where existing methods are inconclusive.
Contribution
It proposes an additional transcendence criterion that improves the ability to certify transcendence in cases where previous tests fail.
Findings
New condition detects transcendence in previously unresolved cases
Enhances practical transcendence certification methods
Addresses limitations of existing tests
Abstract
Although in theory we can decide whether a given D-finite function is transcendental, transcendence proofs remain a challenge in practice. Typically, transcendence is certified by checking certain incomplete sufficient conditions. In this paper we propose an additional such condition which catches some cases on which other tests fail.
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Taxonomy
TopicsCryptography and Data Security · Complexity and Algorithms in Graphs · Computability, Logic, AI Algorithms
