DiagonalAction -- the class of all diagonal actions

Description

This class is provided by the package InvariantRing.

DiagonalAction is the class of all diagonal actions on polynomial rings by a product of a torus (possibly trivial) with a finite abelian group for the purpose of computing invariants. It is created using diagonalAction.

Functions and methods returning an object of class DiagonalAction :

diagonalAction(Matrix,List,PolynomialRing) -- see diagonalAction -- diagonal group action via weights
diagonalAction(Matrix,Matrix,List,PolynomialRing) -- see diagonalAction -- diagonal group action via weights
diagonalAction(Matrix,PolynomialRing) -- see diagonalAction -- diagonal group action via weights

Methods that use an object of class DiagonalAction :

cyclicFactors(DiagonalAction) -- see cyclicFactors -- of a diagonal action
degreesRing(DiagonalAction) -- of a diagonal action
equivariantHilbertSeries(DiagonalAction) -- see equivariantHilbertSeries -- equivariant Hilbert series for a diagonal action
invariants(DiagonalAction) -- computes the generating invariants of a group action
isInvariant(RingElement,DiagonalAction) -- see isInvariant -- check whether a polynomial is invariant under a group action
net(DiagonalAction) -- see net(RingOfInvariants) -- format for printing, as a net
numgens(DiagonalAction) -- number of generators of the finite part of a diagonal group
rank(DiagonalAction) -- of a diagonal action
reynoldsOperator(RingElement,DiagonalAction) -- see reynoldsOperator -- the image of a polynomial under the Reynolds operator
weights(DiagonalAction) -- see weights -- of a diagonal action

For the programmer

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