LinearlyReductiveAction -- the class of all (non finite, non toric) linearly reductive group actions

Description

This class is provided by the package InvariantRing.

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.

Functions and methods returning an object of class LinearlyReductiveAction :

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

Methods that use an object of class LinearlyReductiveAction :

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

For the programmer

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