====== BigObject DisjointStackyFan<Scalar> ======
//from application [[..:fan|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 ''[[..:common#Rational |Rational]]''.
  ? derived from:
  : ''[[..:fan:PolyhedralFan |PolyhedralFan]]''
===== Properties =====

==== Symmetry ====
 These properties capture information of the object that is concerned with the action of permutation groups.
----
{{anchor:generating_hasse_diagram:}}
  ?  **''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:
    :''[[..:graph:Lattice |Lattice]]<[[..:graph#BasicDecoration |BasicDecoration]],[[..:graph#Sequential |Sequential]]>''


----
{{anchor:generating_maximal_cones:}}
  ?  **''GENERATING_MAXIMAL_CONES''**
  :: The MAXIMAL_CONES of the fan that were used to generate it.
    ? Type:
    :''[[..:common#IncidenceMatrix |IncidenceMatrix]]<[[..:common#NonSymmetric |NonSymmetric]]>''


----
{{anchor:generating_rays:}}
  ?  **''GENERATING_RAYS''**
  :: The RAYS of the stacky fan that were used to generate it.
    ? Type:
    :''[[..:common#Matrix |Matrix]]<Scalar,[[..:common#NonSymmetric |NonSymmetric]]>''


----
{{anchor:n_generating_rays:}}
  ?  **''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:
    :''[[..:common#Int |Int]]''


----
{{anchor:original_rays_action_generators:}}
  ?  **''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:
    :''[[..:common#Array |Array]]<[[..:common#Array |Array]]<[[..:common#Int |Int]]%%>>%%''


----
{{anchor:stacky_faces:}}
  ?  **''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:
    :''[[..:common#Array |Array]]<[[..:common#Set |Set]]<[[..:common#Set |Set]]<[[..:common#Set |Set]]<[[..:common#Int |Int]]%%>>%%%%>>%%''


----
{{anchor:stacky_f_vector:}}
  ?  **''STACKY_F_VECTOR''**
  :: Counts the number of STACKY_FACES
    ? Type:
    :''[[..:common#Vector |Vector]]<[[..:common#Int |Int]]>''


----
{{anchor:vertex_labels:}}
  ?  **''VERTEX_LABELS''**
  :: Vertex labels as an array of Set<Set<Int>>. This is more efficient than the String type used in topaz::SimplicialComplex
    ? Type:
    :''[[..:common#Array |Array]]<[[..:common#Set |Set]]<[[..:common#Set |Set]]<[[..:common#Int |Int]]%%>>%%>''


----