Smooth and algebraic invariants of a group action: Local and global constructions
We provide an algebraic formulation of the moving frame method for constructing local smooth invariants on a manifold under an action of a Lie group. This formulation gives rise to algorithms for constructing rational and replacement invariants. The latter are algebraic over the field of rational invariants and play a role analogous to Cartan's normalized invariants in the smooth theory. The algebraic algorithms can be used for computing fundamental sets of differential invariants.
moving frame method rational and algebraic invariants smooth and differential invariants algebraic and lie group actions cross-section grobner basis