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
.
Scalar
: default: Rational
permuting MAXIMAL_CELLS
permuting VECTORS
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.
N_MAXIMAL_CELLS
The number of MAXIMAL_CELLS
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.
FULL_DIM
AMBIENT_DIM
and DIM
coincide.
LINEAR_SPAN
Dual basis of the linear hull of the vector configuration
Matrix<Scalar,NonSymmetric>
MIN_WEIGHTS
Minimal nonnegative lattice vector in secondary cone of the subdivision given by MAXIMAL_CELLS
.
N_VECTORS
Number of VECTORS
.
VECTORS
The vectors of the subdivision,
Matrix<Scalar,NonSymmetric>
VECTOR_AMBIENT_DIM
Dimension of the space in which the vector configuration lives.
VECTOR_DIM
Dimension of the linear hull of the vector configuration.
These properties are for visualization.
LABELS
Unique names assigned to the VECTORS
. If specified, they are shown by visualization tools instead of point indices.
ALTSHULER_DET
If M is incidence matrix between the vertices and the MAXIMAL_CELLS
, then the Altshuler determinant is defined as max{det(M ∗ MT), det(MT ∗ M)}.
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 i-th cell of the complex as a VectorConfiguration
Int
i
secondary_cone()
The secondary cone is the polyhedral cone of all lifting functions on the VECTORS
which induce the subdivision given by the MAXIMAL_CELLS
. If the subdivision is not regular, the cone will be the secondary cone of the finest regular coarsening.
secondary_cone_options
Cone<Scalar>