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# cyclicFactors -- of a diagonal action

- Usage:
    `cyclicFactors D`
- Inputs:
  - D, an instance of the type DiagonalAction
- Outputs:
  - a list, of orders of cyclic abelian factors in the decomposition of the diagonal group

## Description

This function is provided by the package InvariantRing.

Use this function to recover the cyclic abelian factors of a diagonal action on a polynomial ring.

The following example defines an action of a product of two cyclic groups of order 3 acting on a three-dimensional vector space.

    i1 : R = QQ[x_1..x_3]

    o1 = R

    o1 : PolynomialRing

    i2 : d = {3,3}

    o2 = {3, 3}

    o2 : List

    i3 : W = matrix{{1,0,1},{0,1,1}}

    o3 = | 1 0 1 |
         | 0 1 1 |

                  2       3
    o3 : Matrix ZZ  <-- ZZ

    i4 : A = diagonalAction(W, d, R)

    o4 = R <- ZZ/3 x ZZ/3 via

         | 1 0 1 |
         | 0 1 1 |

    o4 : DiagonalAction

    i5 : cyclicFactors A

    o5 = {3, 3}

    o5 : List

## See also

- DiagonalAction -- the class of all diagonal actions
- diagonalAction -- diagonal group action via weights

## Ways to use cyclicFactors:

- `cyclicFactors(DiagonalAction)`

## For the programmer

The object cyclicFactors is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/InvariantRing/AbelianGroupsDoc.m2:315:0.