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We describe a significant update to the existing InvariantRing package for Macaulay2.In addition to expanding and improving the methods of the existing package for actions of finite groups, the updated package adds functionality for computing invariants of diagonal actions of tori and finite abelian groups, as well as invariants of arbitrary linearly reductive group actions.The implementation of the package has been completely overhauled with the aim of serving as a unified resource for invariant theory computations in Macaulay2.
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Ferraro et al. (2024) studied this question.
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