The essence of objects or phenomena lies in their invariants, which remain unchanged through transformations. This concept is vital in mathematics, where group actions shape the study of various invariants. Ongoing research focuses on understanding and computing invariants, with vast applications. This paper delves into the connection between differential and algebraic invariant theories. It presents an algorithm for computing rational invariants using an algebraic adaptation of the moving frame method. Additionally, it explores the significance of the differential invariant signature in solving equivalence problems in geometry and algebra. The paper highlights both successes and challenges in developing algorithms based on this concept. It was submitted by Irina Kogan on December 17, 2024.
https://arxiv.org/abs/2412.13306