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.

翻译：考虑形式幂级数$f_1,\ldots, f_k\in\mathbb{Q}[[z]]$，它们被定义为多项式微分方程组在给定足够数量初始条件下的解。对于给定的$P\in \mathbb{Q}[F_1,\ldots,F_k]$，已有多种算法被提出用于检验是否满足$P(f_1,\ldots,f_k)=0$。本文针对$f_1,\ldots,f_k$为超级数而非幂级数的情形，提出了一种相应的检验算法。