FiniteGroupAction -- the class of all finite group actions

Description

This class is provided by the package InvariantRing.

FiniteGroupAction is the class of all finite matrix group actions on polynomial rings for the purpose of computing invariants. It is created using finiteAction. Note that diagonal actions of finite abelian groups can be created with the class DiagonalAction which implements more efficient methods for computing invariants.

Functions and methods returning an object of class FiniteGroupAction:

finiteAction(List,PolynomialRing) -- see finiteAction -- the group action generated by a list of matrices
finiteAction(Matrix,PolynomialRing) -- see finiteAction -- the group action generated by a list of matrices

Methods that use an object of class FiniteGroupAction:

generators(FiniteGroupAction) -- generators of a finite group
group(FiniteGroupAction) -- see group -- list all elements of the group of a finite group action
hironakaDecomposition(FiniteGroupAction) -- see hironakaDecomposition -- calculates a Hironaka decomposition for the invariant ring of a finite group
invariants(FiniteGroupAction) -- computes the generating invariants of a group action
invariants(FiniteGroupAction,List) -- see invariants(FiniteGroupAction,ZZ) -- basis for graded component of invariant ring
invariants(FiniteGroupAction,ZZ) -- basis for graded component of invariant ring
isAbelian(FiniteGroupAction) -- see isAbelian -- check whether a finite matrix group is Abelian
isInvariant(RingElement,FiniteGroupAction) -- see isInvariant -- check whether a polynomial is invariant under a group action
molienSeries(FiniteGroupAction) -- see molienSeries -- computes the Molien (Hilbert) series of the invariant ring of a finite group
net(FiniteGroupAction) -- see net(RingOfInvariants) -- format for printing, as a net
numgens(FiniteGroupAction) -- number of generators of a finite group
primaryInvariants(FiniteGroupAction) -- see primaryInvariants -- computes a list of primary invariants for the invariant ring of a finite group
relations(FiniteGroupAction) -- relations of a finite group
reynoldsOperator(RingElement,FiniteGroupAction) -- see reynoldsOperator -- the image of a polynomial under the Reynolds operator
schreierGraph(FiniteGroupAction) -- see schreierGraph -- Schreier graph of a finite group
secondaryInvariants(List,FiniteGroupAction) -- see secondaryInvariants -- computes secondary invariants for the invariant ring of a finite group
words(FiniteGroupAction) -- see words -- associate a word in the generators of a group to each element

For the programmer

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

The source of this document is in InvariantRing/FiniteGroupsDoc.m2:73:0.