DART XII

Kassel (Germany) April 9^{th} - 12^{th} 2024

XII. Conference on Differential Algebra and Related Topics

April 9^{th} - 12^{th} 2024

Kassel University, Germany

In this talk, we present our partial differential Lüroth's theorem in both theoretical and algorithmic aspects. We first give a necessary and sufficient condition for a subfield of a partial differential rational function field to be a simple extension. This result generalizes Ritt and Kolchin’s classical differential Lüroth's theorem. We then give an algorithm to decide whether a given finitely generated differential subfield admits a Lüroth generator, and in the affirmative case, to compute a Lüroth generator. As an application, we solve the problem of deciding whether a unirational partial differential curve is rational.