LinearlyReductiveAction is the class of all linearly reductive group actions on (quotients of) polynomial rings for the purpose of computing invariants. It is created using linearlyReductiveAction. This class should not be used for actions of tori or finite groups, as its methods for computing invariants are in general less efficient than specialized methods for the classes FiniteGroupAction, and DiagonalAction.

- linearlyReductiveAction(Ideal,Matrix,PolynomialRing) -- see linearlyReductiveAction -- Linearly reductive group action
- linearlyReductiveAction(Ideal,Matrix,QuotientRing) -- see linearlyReductiveAction -- Linearly reductive group action

- actionMatrix(LinearlyReductiveAction) -- see actionMatrix -- matrix of a linearly reductive action
- groupIdeal(LinearlyReductiveAction) -- see groupIdeal -- ideal defining a linearly reductive group
- hilbertIdeal(LinearlyReductiveAction) -- see hilbertIdeal -- compute generators for the Hilbert ideal
- QuotientRing ^ LinearlyReductiveAction -- see invariantRing -- the ring of invariants of a group action
- invariants(LinearlyReductiveAction) -- invariant generators of Hilbert ideal
- invariants(LinearlyReductiveAction,List) -- see invariants(LinearlyReductiveAction,ZZ) -- basis for graded component of invariant ring
- invariants(LinearlyReductiveAction,ZZ) -- basis for graded component of invariant ring
- isInvariant(RingElement,LinearlyReductiveAction) -- see isInvariant -- check whether a polynomial is invariant under a group action
- net(LinearlyReductiveAction) -- see net(RingOfInvariants) -- format for printing, as a net

The object LinearlyReductiveAction is a type, with ancestor classes GroupAction < HashTable < Thing.