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# 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.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/InvariantRing/AbelianGroupsDoc.m2:103:0.