next | previous | forward | backward | up | top | index | toc | Macaulay2 website
InvariantRing :: group

group -- list all elements of the group of a finite group action

Synopsis

Description

This function is provided by the package InvariantRing.

The following example defines the permutation action of a symmetric group on three elements.

i1 : R = QQ[x_1..x_3]

o1 = R

o1 : PolynomialRing
i2 : L = apply(2, i -> permutationMatrix(3, [i + 1, i + 2] ) )

o2 = {| 0 1 0 |, | 1 0 0 |}
      | 1 0 0 |  | 0 0 1 |
      | 0 0 1 |  | 0 1 0 |

o2 : List
i3 : S3 = finiteAction(L, R)

o3 = R <- {| 0 1 0 |, | 1 0 0 |}
           | 1 0 0 |  | 0 0 1 |
           | 0 0 1 |  | 0 1 0 |

o3 : FiniteGroupAction
i4 : group S3

o4 = {| 1 0 0 |, | 0 1 0 |, | 1 0 0 |, | 0 0 1 |, | 0 1 0 |, | 0 0 1 |}
      | 0 0 1 |  | 1 0 0 |  | 0 1 0 |  | 0 1 0 |  | 0 0 1 |  | 1 0 0 |
      | 0 1 0 |  | 0 0 1 |  | 0 0 1 |  | 1 0 0 |  | 1 0 0 |  | 0 1 0 |

o4 : List

The computation of all elements in the group is actually performed by the method schreierGraph since the process of computing the Schreier graph of the group yields other useful information about the group besides just its elements.

See also

Ways to use group :

For the programmer

The object group is a method function.