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arXiv · 2602.01188

A zero-test for D-algebraic transseries

Shaoshi Chen·Hanqian Fang·Joris van der Hoeven
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Abstract

Consider formal power series $f_1,\ldots, f_k\in\mathbb{Q}[[z]]$ that are defined as the solutions of a system of polynomial differential equations together with a sufficient number of initial conditions. Given $P\in \mathbb{Q}[F_1,\ldots,F_k]$, several algorithms have been proposed in order to test whether $P(f_1,\ldots,f_k)=0$. In this paper, we present such an algorithm for the case where $f_1,\ldots,f_k$ are so-called transseries instead of power series.

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Shaoshi Chen, Hanqian Fang, Joris van der Hoeven. 2026-02-01. A zero-test for D-algebraic transseries. https://arxiv.org/abs/2602.01188

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