BigObject VectorConfiguration<Scalar>

from application polytope

An object of type VectorConfiguration deals with properties of row vectors, assembled into an n x d matrix called VECTORS. The entries of these row vectors are interpreted as non-homogeneous coordinates. In particular, the coordinates of a VECTOR will *NOT* be normalized to have a leading 1.

Type Parameters:

Scalar: default: Rational

These properties are for input only. They allow redundant information.

VECTORS

The Vectors of the configuration

Type:

Matrix<Scalar,NonSymmetric>

These properties capture geometric information of the object. Geometric properties depend on geometric information of the object, like, e.g., vertices or facets.

FULL_DIM

VECTOR_AMBIENT_DIM and VECTOR_DIM coincide.

Type:

Bool

GALE_TRANSFORM

Coordinates of the Gale transform.

Type:

Matrix<Scalar,NonSymmetric>

LINEAR_SPAN

Dual basis of the linear hull of the vector configuration

Type:

Matrix<Scalar,NonSymmetric>

MULTIPLE_VECTORS

Tells if there exists multiple vectors.

Type:

Bool

N_VECTORS

Number of VECTORS.

Type:

Int

POSITIVE

True if all VECTORS have non-negative coordinates, that is, if they all lie entirely in the positive orthant.

Type:

Bool

VECTOR_AMBIENT_DIM

Dimension of the space in which the vector configuration lives. Similar to CONE_AMBIENT_DIM.

Type:

Int

VECTOR_DIM

Dimension of the linear hull of the vector configuration. Similar to CONE_DIM.

Type:

Int

Properties which belong to the corresponding (oriented) matroid

CHIROTOPE

Chirotope corresponding to VECTORS

Type:

Text

depends on extension:

topcom

CIRCUITS

Oriented circuits of VECTORS, oriented matroid version of CIRCUITS.

Type:

Set<Pair<Set<Int>,Set<Int>>>

COCIRCUITS

Oriented cocircuits of VECTORS, oriented matroid version of COCIRCUITS.

Type:

Set<Pair<Set<Int>,Set<Int>>>

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

GROUP

Type:

Group

Properties of GROUP:

MATRIX_ACTION

Type:

MatrixActionOnVectors<Scalar>

These properties are for visualization.

LABELS

Unique names assigned to the VECTORS. If specified, they are shown by visualization tools instead of point indices.

Type:

Array<String>

These methods are for visualization.

VISUAL()

Visualize a vector configuration.

Options:

option list Visual::Polygons::decorations

option list geometric_options_linear

Returns:

Visual::PointConfiguration