Invariants: Advances in Computation and Applications

A tutorial paper published in the proceedings of ISSAC 2023 explores the computation and applications of invariants in mathematics. The paper focuses on the interplay between differential and algebraic invariant theories, presenting an algebraic adaptation of the moving frame method from differential geometry to compute a generating set of rational invariants. It also discusses the role of differential invariant signatures in solving equivalence problems in geometry and algebra, and the challenges in designing algorithms based on this concept.