Differential invariants of the motion group actions
Differential invariants of a (pseudo)group action can vary when restricted to invariant submanifolds (differential equations). The algebra is still governed by the Lie-Tresse theorem, but may change a lot. We describe in details the case of the motion group O(n) ⋉ Rn acting on the full (unconstraint) jet-space as well as on some invariant equations.
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