标题： D-代数超越级数的零测试 显示英文标题

标题： A zero-test for D-algebraic transseries

摘要： 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的解，同时具有足够数量的初始条件。 给定$P\in \mathbb{Q}[F_1,\ldots,F_k]$，已经提出了几种算法来测试$P(f_1,\ldots,f_k)=0$。 在本文中，我们为$f_1,\ldots,f_k$为所谓的拟指数级数而非幂级数的情况提供这样的算法。 显示英文摘要

摘要： 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.