# cyclicFactors -- of a diagonal action

## Synopsis

• Usage:
cyclicFactors D
• Inputs:
• 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