# invariants -- computes the generating invariants of a group action

## Synopsis

• Usage:
invariants G
• Inputs:
• G, an instance of the type GroupAction, a specific type of group action on a polynomial ring
• Optional inputs:
• Strategy (missing documentation) => ..., default value UseNormaliz, the strategy used to compute diagonal invariants, options are UsePolyhedra or UseNormaliz.
• DegreeBound => ..., default value infinity, degree bound for invariants of finite groups
• DegreeLimit => ..., default value {}, GB option for invariants
• SubringLimit => ..., default value infinity, GB option for invariants
• UseCoefficientRing => ..., default value false, option to compute invariants over the given coefficient ring
• UseLinearAlgebra => ..., default value false, strategy for computing invariants of finite groups
• Outputs:
• L, a list, a minimal set of generating invariants for the group action

## Description

This function is provided by the package InvariantRing. This function can be used to compute the generating invariants of a diagonal group action, finite group action or linearly reductive group action. It can also be used to compute a basis of a graded component of the invariant ring. Below is a list of the many ways to use this function:

## Caveat

Some optional inputs are only relevant to certain use cases of this method. Please consult the documentation pages for the different cases to learn which optional inputs are used.