论文标题
参与移动帧II； Lie-Arterne定理
Involutive moving frames II; The Lie-Tresse theorem
论文作者
论文摘要
本文继续该项目以\ cite {imf}开始，以协调卡坦的经典等效方法和现代的均等运动框架，以配音为\ emph {参与式移动帧}。为了证明我们框架的富有成果，我们获得了liefterse定理（基本基础定理）的新，建设性和直观的证明，以及对谎言伪群的产生差异不变性数量的最小数量的第一个一般上限。此外，我们通过研究两个独立变量中的一阶PDE的等效问题来证明该框架的计算优势，在点转换下的一个因变量。
This paper continues the project, begun in \cite{IMF}, of harmonizing Cartan's classical equivalence method and the modern equivariant moving frame in a framework dubbed \emph{involutive moving frames}. As an attestation of the fruitfulness of our framework, we obtain a new, constructive and intuitive proof of the Lie-Tresse theorem (Fundamental basis theorem) and a first general upper bound on the minimal number of generating differential invariants for Lie pseudo-groups. Further, we demonstrate the computational advantages of this framework by studying the equivalence problem for first order PDE in two independent variables and one dependent variable under point transformations.
