documentation:latest:group:group

Available versions of this document: latest release, release 4.0, release 3.6, release 3.5, nightly master

Reference documentation for older polymake versions: release 3.4, release 3.3, release 3.2

# BigObject Group

from application group

Object encoding a finite group.

These properties capture information of the object that is concerned with the action of permutation groups.

CHARACTER_TABLE

The character table. NOTE: We do not support complex characters, but for the moment only real ones.

Type:
Matrix<QuadraticExtension<Rational>,NonSymmetric>

CONJUGACY_CLASS_SIZES

The sizes of the conjugacy classes

Type:
Array<Int>

FACETS_ACTION

operates on indices

Type:
PermutationAction<Int,Rational>

FACET_NORMALS_ACTION

operates on indices

Type:
PermutationAction<Int,Rational>

HOMOGENEOUS_COORDINATE_ACTION

operates on indices, including the '0'-th homogeneous coordinate

Type:
PermutationAction<Int,Rational>

IMPLICIT_SET_ACTION

an action on sets where only one representative for each orbit is stored

Type:
ImplicitActionOnSets

INEQUALITIES_ACTION

operates on indices

Type:
PermutationAction<Int,Rational>

INPUT_CONES_ACTION

operates on indices

Type:
PermutationAction<Int,Rational>

INPUT_RAYS_ACTION

operates on indices

Type:
PermutationAction<Int,Rational>

MAXIMAL_CONES_ACTION
Type:
PermutationAction<Int,Rational>

ORDER

The number of elements in the group

Type:
Integer

PERMUTATION_ACTION

a permutation action on integers

Type:
PermutationAction<Int,Rational>

RAYS_ACTION

operates on indices

Type:
PermutationAction<Int,Rational>

REGULAR_REPRESENTATION
Type:
MatrixActionOnVectors<Rational>

SET_ACTION

a permutation action on a collection of sets of integers

Type:
PermutationAction<Set<Int>,Rational>

SIMPLEXITY_LOWER_BOUND

The symmetrized version of SIMPLEXITY_LOWER_BOUND.

Type:
Int

VECTOR_ACTION

operates on indices

Type:
PermutationAction<Int,Rational>

• documentation/latest/group/group.txt