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.
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Gülden Gün Polat, Peter J. Olver, Joint differential invariants of binary and ternary forms. Port. Math. 76 (2019), no. 2, pp. 169–204DOI 10.4171/PM/2032