Available versions of this document: latest release, release 3.5, nightly master
Reference documentation for older polymake versions: release 3.4, release 3.3, release 3.2
BigObject Action
from application group
parametrized object used for encoding group actions (representations).
 GeneratorType is
Array<Int>
for permutation groups, orMatrix<Scalar>
for matrix groups.
 DomainType is
Int
for permutation groups,Vector<Scalar>
for matrix groups acting on facets or vertices,Set<Int>
orBitset
for groups acting on simplices,IncidenceMatrix
for groups acting on (maximal) cones of a fan
 OrbitGeneratorScalarType is the type of the entries of vectors that generate a geometric orbit; default
Rational
Properties
Symmetry
These properties capture information of the object that is concerned with the action of permutation groups.

ALL_GROUP_ELEMENTS
All elements of the group, as expressed in the present action Notice that this is a temporary property; it will not be stored in any file.
 Type:
Array<GeneratorType>

CHARACTER
The character of the action. The ordering corresponds to the columns of the CHARACTER_TABLE
 Type:

CONJUGACY_CLASSES
The conjugacy classes themselves
 Type:

CONJUGACY_CLASS_REPRESENTATIVES
A set of representatives for each conjugacy class. The order of these representatives must agree with the implicit order of the columns of the CHARACTER_TABLE.
 Type:
Array<GeneratorType>

DEGREE
The degree of the representation. For permutation groups, this is the number of permuted indices, for matrix groups it is the dimension of the vector space the group acts on
 Type:

DOMAIN_NAME
the name of the property that we act on, for example MAX_INTERIOR_SIMPLICES or INTERIOR_RIDGES
 Type:

EQUATIONS_GENERATORS
A set of generators for equations, stored as the rows of a matrix. The list of generators may be redundant and noncanonical.
 Type:
Matrix<OrbitGeneratorScalarType,NonSymmetric>

EXPLICIT_ORBIT_REPRESENTATIVES
the representatives of orbits explicitly, not via their indices
 Type:
Array<DomainType>

EXPLICIT_ORBIT_REPRESENTATIVE_MATRIX
the representatives of orbits explicitly, not via their indices
 Type:
Matrix<OrbitGeneratorScalarType,NonSymmetric>

FACETS_GENERATORS
A set of generators for facets, stored as the rows of a matrix. The list of generators may be redundant and noncanonical.
 Type:
Matrix<OrbitGeneratorScalarType,NonSymmetric>

GENERATORS
The generators of the group action
 Type:
Array<GeneratorType>

IMAGES
The images of all domain elements under each group element: [ [ g(x) for x in D ] for g in G ]
 Type:

INDEX_OF
The map giving the index of each group element This is a temporary property; it will not be stored in any file.
 Type:

INDUCED_FROM
the name of a different action that this action is induced from
 Type:

INEQUALITIES_GENERATORS
A set of generators for inequalities, stored as the rows of a matrix. The list of generators may be redundant and noncanonical.
 Type:
Matrix<OrbitGeneratorScalarType,NonSymmetric>

INPUT_LINEALITY_GENERATORS
A set of generators for input lineality, stored as the rows of a matrix. The list of generators may be redundant and noncanonical.
 Type:
Matrix<OrbitGeneratorScalarType,NonSymmetric>

INPUT_RAYS_GENERATORS
A set of generators for input rays, stored as the rows of a matrix. The list of generators may be redundant and noncanonical.
 Type:
Matrix<OrbitGeneratorScalarType,NonSymmetric>

IRREDUCIBLE_DECOMPOSITION
The multiplicities of each irreducible representation in this action. The ordering corresponds to the rows of the CHARACTER_TABLE
 Type:

LINEALITY_SPACE_GENERATORS
A set of generators for input lineality, stored as the rows of a matrix. The list of generators may be redundant and noncanonical.
 Type:
Matrix<OrbitGeneratorScalarType,NonSymmetric>

MAXIMAL_CONES_GENERATORS
A set of generators for the maximal cones of a fan, stored in terms of indices of vertex generators. The list of generators may be redundant and noncanonical.
 Type:

N_EQUATIONS_GENERATORS
The number of generators for orbits.
 Type:

N_FACETS_GENERATORS
The number of generators for orbits.
 Type:

N_INEQUALITIES_GENERATORS
The number of generators for orbits.
 Type:

N_INPUT_LINEALITY_GENERATORS
The number of generators for orbits.
 Type:

N_INPUT_RAYS_GENERATORS
The number of generators for orbits.
 Type:

N_LINEALITY_SPACE_GENERATORS
The number of generators for orbits.
 Type:

N_MAXIMAL_CONES_GENERATORS
The number of generators for orbits.
 Type:

N_ORBITS
The number of orbits in the domain under the group action
 Type:

N_ORBIT_REPRESENTATIVES
the number of representatives of orbits
 Type:

N_RAYS_GENERATORS
The number of generators for orbits.
 Type:

ORBITS
The orbits of the domain, represented via their indices
 Type:

ORBIT_REPRESENTATIVES
A collection of representatives for each orbit, represented via their indices
 Type:

ORBIT_REPRESENTATIVE_LABELS
Labels for the orbit representatives
 Type:

ORBIT_SIZES
The cardinality of each orbit
 Type:

PERMUTATION_TO_ORBIT_ORDER
A permutation that orders the domain elements by orbits
 Type:

RAYS_GENERATORS
A set of generators for rays, stored as the rows of a matrix. The list of generators may be redundant and noncanonical.
 Type:
Matrix<OrbitGeneratorScalarType,NonSymmetric>