We use moving frames to construct and classify the joint invariants and joint differential invariants of binary and ternary forms. In particular, we prove that the differential invariant algebra of ternary forms is generated by a single third order differential invariant. To connect our results with earlier analysis of Kogan, we develop a general method for relating differential invariants associated with different choices of cross-section.

中文翻译：

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二元和三元形式的联合微分不变量

我们使用移动框架来构造和分类二元和三元形式的联合不变量和联合微分不变量。特别是，我们证明了三元形式的微分不变代数是由单个三阶微分不变量生成的。为了将我们的结果与 Kogan 的早期分析联系起来，我们开发了一种通用方法，用于关联与不同截面选择相关的微分不变量。