发表机构
UiT the Arctic University of Norway（挪威北极大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对微分不变量中根式相关的矛盾，结合活动标架技术与全局Lie-Tresse定理，通过示例解释矛盾并给出算法计算全局微分不变量的方法。
AI 中文摘要
活动标架这一经典技术可有效计算群作用的微分不变量。一个常见现象是，微分不变量的表达式包含根式及更复杂的代数函数，但全局Lie-Tresse定理声称，对于代数伪群作用，微分不变量代数由射流变量的有理函数生成。本文解释这一明显矛盾，并通过几个精心构造的示例加以说明。从构造角度看，该结果提供了一种算法计算全局微分不变量的方法。
英文摘要
The classical technique of moving frames allows to effectively compute differential invariants of group actions. A standard observation is that the expressions of differential invariants contain radicals and more complicated algebraic functions, however the global Lie-Tresse theorem claims that for algebraic pseudogroup actions the algebra of differential invariants is generated by rational functions in jet variables. Here, we explain this apparent contradiction and illustrate it in a few well-elaborated examples. Constructively, our result gives a method to algorithmically compute global differential invariants.
CommentsA few minor improvements in this version
