一句话：为流演算中的多项式方程组建立隐函数定理，并展示其相对于经典隐函数定理的计算优势与应用。
本文在流演算（stream calculus）框架下研究多项式流方程组的求解。作者提出流演算版本的隐函数定理（IFT），刻画在什么条件下方程组可由部分流变量唯一确定其余流变量，并讨论它与经典微积分隐函数定理的联系与区别。证明与构造基于流演算的余归纳方法和行为微分方程，强调其计算视角的优势。文章还通过若干示例应用展示该定理在流方程求解与变换中的实用价值。
In the context of the stream calculus, we present an Implicit Function Theorem (IFT) for polynomial systems, and discuss its relations with the classical IFT from calculus. In particular, we demonstrate the advantages of the stream IFT from a computational point of view, and provide a few example applications where its use turns out to be valuable.
@article{paperbot2753,
title = {An implicit function theorem for the stream calculus},
author = {Michele Boreale and Luisa Collodi and Daniele Gorla},
journal = {Logical Methods in Computer Science},
volume = {Volume 20, Issue 2},
year = {2024},
doi = {10.46298/lmcs-20(2:15)2024}
}