cyclicFactors -- of a diagonal action

Synopsis

• 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

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