The InvariantRing package for Macaulay2 (Q6569459)

The study of group actions is very important for several areas of mathematics, such as projective geometry, and a computational perspective in invariant theory can offer valuable contributions. Thus, the significant improvement of the existing InvariantRing package for the Macaulay2 software system, which is presented in this paper, is naturally of great interest.\N\NThe authors essentially focus on the implementation of several algorithms to compute generators of subrings of invariant polynomials for finite group actions, diagonal actions, and linearly reductive actions. Each of these types of actions is discussed in a dedicated section. Usage examples and technical aspects, such as the introduction of specialized types and subtypes, are clearly described. The paper concludes with performance considerations and suggestions for future directions.