BigObject DisjointStackyFan<Scalar>

from application fan

This represents a stacky fan built from the orbit of a fan F under a group G that permutes the homogeneous coordinates of F's rays. It is assumed, but currently not checked, that the interior of F does not intersect the interiors of its images.

Type Parameters:

Scalar: numeric data type used for the coordinates, must be an ordered field. Default is Rational.

derived from:

PolyhedralFan

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

GENERATING_HASSE_DIAGRAM

The HASSE_DIAGRAM of the fan that was used to generate it. Must be of type Sequential because Cone::HASSE_DIAGRAM has that type

Type:

PartiallyOrderedSet<BasicDecoration,Sequential>

GENERATING_MAXIMAL_CONES

The MAXIMAL_CONES of the fan that were used to generate it.

Type:

IncidenceMatrix<NonSymmetric>

GENERATING_RAYS

The RAYS of the stacky fan that were used to generate it.

Type:

Matrix<Scalar,NonSymmetric>

N_GENERATING_RAYS

The number of RAYS of the stacky fan that were used to generate it. By the way orbit_fan works, these rays also show up at the beginning of the RAYS matrix.

Type:

Int

ORIGINAL_RAYS_ACTION_GENERATORS

for higher barycentric subdivisions, store the original RAYS_ACTION.GENERATORS They are stored outside of a GROUP object, because these generators act on the elements of the innermost sets of the VERTEX_LABELS, but not on anything directly in the object itself

Type:

Array<Array<Int>>

STACKY_FACES

From a fan F equipped with a symmetry group G acting on the coordinates, * such that the interior of F does not intersect the interiors of its images,* calculate the faces of F of all dimensions that lie in distinct orbits of G.F The data is organized as an array, one entry for each dimension starting with 1; each entry is a Set, one for each orbit of that dimension; each entry is a Set<Set<Int» of faces Set<Int> in that orbit that lie in F

Type:

Array<Set<Set<Set<Int>>>>

STACKY_F_VECTOR

Counts the number of STACKY_FACES

Type:

Vector<Int>

VERTEX_LABELS

Vertex labels as an array of Set<Set<Int». This is more efficient than the String type used in topaz::SimplicialComplex

Type:

Array<Set<Set<Int>>>