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 SubdivisionOfVectors<Scalar>
from application fan
A subdivision of vectors, in contrast to PolyhedralFan
this allows cells with interior points. Similar to the distinction between Cone
and VectorConfiguration
.
 Type Parameters:
Scalar
: default:Rational
 Permutations:
 CellPerm:
permuting
MAXIMAL_CELLS
 VectorPerm:
permuting
VECTORS
Properties
Combinatorics
These properties capture combinatorial information of the object. Combinatorial properties only depend on combinatorial data of the object like, e.g., the face lattice.

MAXIMAL_CELLS
Maximal cells of the polyhedral complex. Indices refer to
VECTORS
. Points do not have to be vertices of the cells. Type:

N_MAXIMAL_CELLS
The number of
MAXIMAL_CELLS
 Type:
Geometry
These properties capture geometric information of the object. Geometric properties depend on geometric information of the object, like, e.g., vertices or facets.

CONVEX
True if
VECTORS
for each maximal cell are in convex position. Type:

FULL_DIM
AMBIENT_DIM
andDIM
coincide. Type:

LINEAR_SPAN
Dual basis of the linear hull of the vector configuration
 Type:
Matrix<Scalar,NonSymmetric>

MIN_WEIGHTS
Minimal lattice vector in secondary cone of triangulation
MAXIMAL_CELLS
. Type:

N_VECTORS
Number of
VECTORS
. Type:

VECTORS
The vectors of the subdivision,
 Type:
Matrix<Scalar,NonSymmetric>

VECTOR_AMBIENT_DIM
Dimension of the space in which the vector configuration lives.
 Type:

VECTOR_DIM
Dimension of the linear hull of the vector configuration.
 Type:
Visualization
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:
no category

ALTSHULER_DET
If M is incidence matrix between the vertices and the
MAXIMAL_CELLS
, then the Altshuler determinant is defined as max{det(M ∗ M^{T}), det(M^{T} ∗ M)}. Type:
Methods
Geometry
These methods capture geometric information of the object. Geometric properties depend on geometric information of the object, like, e.g., vertices or facets.

cell(Int i)
Returns the ith cell of the complex as a
VectorConfiguration
 Parameters:
Int
i
 Returns:

secondary_cone()
The secondary cone is the polyhedral cone of all lifting functions on the
VECTORS
which induce the subdivision given by theMAXIMAL_CELLS
. If the subdivision is not regular, the cone will be the secondary cone of the finest regular coarsening. Options:
 option list
secondary_cone_options
 Returns:
Cone<Scalar>