====== BigObject VectorConfiguration<Scalar> ======
//from application [[..:polytope|polytope]]//\\
\\
 An object of type VectorConfiguration deals with properties of row vectors, assembled into an n x d matrix called ''[[..:polytope:VectorConfiguration#VECTORS |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: ''[[..:common#Rational |Rational]]''
===== Properties =====

==== Input property ====
 These properties are for input only. They allow redundant information.
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{{anchor:vectors:}}
  ?  **''VECTORS''**
  :: The Vectors of the configuration
    ? Type:
    :''[[..:common#Matrix |Matrix]]<Scalar,[[..:common#NonSymmetric |NonSymmetric]]>''


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==== Geometry ====
 These properties capture geometric information of the object.  Geometric properties depend on geometric information of the object, like, e.g., vertices or facets.
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{{anchor:full_dim:}}
  ?  **''FULL_DIM''**
  :: ''[[..:polytope:VectorConfiguration#VECTOR_AMBIENT_DIM |VECTOR_AMBIENT_DIM]]'' and ''[[..:polytope:VectorConfiguration#VECTOR_DIM |VECTOR_DIM]]'' coincide.
    ? Type:
    :''[[..:common#Bool |Bool]]''


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{{anchor:gale_transform:}}
  ?  **''GALE_TRANSFORM''**
  :: Coordinates of the Gale transform.
    ? Type:
    :''[[..:common#Matrix |Matrix]]<Scalar,[[..:common#NonSymmetric |NonSymmetric]]>''


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{{anchor:linear_span:}}
  ?  **''LINEAR_SPAN''**
  :: Dual basis of the linear hull of the vector configuration
    ? Type:
    :''[[..:common#Matrix |Matrix]]<Scalar,[[..:common#NonSymmetric |NonSymmetric]]>''


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{{anchor:multiple_vectors:}}
  ?  **''MULTIPLE_VECTORS''**
  :: Tells if there exists multiple vectors.
    ? Type:
    :''[[..:common#Bool |Bool]]''


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{{anchor:n_vectors:}}
  ?  **''N_VECTORS''**
  :: Number of ''[[..:polytope:VectorConfiguration#VECTORS |VECTORS]]''.
    ? Type:
    :''[[..:common#Int |Int]]''


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{{anchor:positive:}}
  ?  **''POSITIVE''**
  :: True if all ''[[..:polytope:VectorConfiguration#VECTORS |VECTORS]]'' have non-negative coordinates, that is, if they all lie entirely in the positive orthant.
    ? Type:
    :''[[..:common#Bool |Bool]]''


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{{anchor:vector_ambient_dim:}}
  ?  **''VECTOR_AMBIENT_DIM''**
  :: Dimension of the space in which the vector configuration lives. Similar to ''[[..:polytope:Cone#CONE_AMBIENT_DIM |CONE_AMBIENT_DIM]]''.
    ? Type:
    :''[[..:common#Int |Int]]''


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{{anchor:vector_dim:}}
  ?  **''VECTOR_DIM''**
  :: Dimension of the linear hull of the vector configuration. Similar to ''[[..:polytope:Cone#CONE_DIM |CONE_DIM]]''.
    ? Type:
    :''[[..:common#Int |Int]]''


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==== Matroid properties ====
 Properties which belong to the corresponding (oriented) matroid
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{{anchor:chirotope:}}
  ?  **''CHIROTOPE''**
  :: Chirotope corresponding to ''[[..:polytope:VectorConfiguration#VECTORS |VECTORS]]''
    ? Type:
    :''[[..:common#Text |Text]]''
    ? depends on extension:
    : [[:external_software|topcom]]


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{{anchor:circuits:}}
  ?  **''CIRCUITS''**
  :: Oriented circuits of ''[[..:polytope:VectorConfiguration#VECTORS |VECTORS]]'', oriented matroid version of ''[[..:matroid:Matroid#CIRCUITS |CIRCUITS]]''.
    ? Type:
    :''[[..:common#Set |Set]]<[[..:common#Pair |Pair]]<[[..:common#Set |Set]]<[[..:common#Int |Int]]>,[[..:common#Set |Set]]<[[..:common#Int |Int]]%%>>%%>''


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{{anchor:cocircuits:}}
  ?  **''COCIRCUITS''**
  :: Oriented cocircuits of ''[[..:polytope:VectorConfiguration#VECTORS |VECTORS]]'', oriented matroid version of ''[[..:matroid:Matroid#COCIRCUITS |COCIRCUITS]]''.
    ? Type:
    :''[[..:common#Set |Set]]<[[..:common#Pair |Pair]]<[[..:common#Set |Set]]<[[..:common#Int |Int]]>,[[..:common#Set |Set]]<[[..:common#Int |Int]]%%>>%%>''


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==== Symmetry ====
 These properties capture information of the object that is concerned with the action of permutation groups.
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{{anchor:group:}}
  ?  **''GROUP''**
  ::
    ? Type:
    :''[[..:group:Group |Group]]''
    ? Properties of GROUP:
    :
      ?  **''MATRIX_ACTION''**
      ::
        ? Type:
        :''[[..:group:MatrixActionOnVectors |MatrixActionOnVectors]]<Scalar>''


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==== Visualization ====
 These properties are for visualization.
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{{anchor:labels:}}
  ?  **''LABELS''**
  :: Unique names assigned to the ''[[..:polytope:VectorConfiguration#VECTORS |VECTORS]]''. If specified, they are shown by visualization tools instead of point indices.
    ? Type:
    :''[[..:common#Array |Array]]<[[..:common#String |String]]>''


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===== Methods =====

==== Visualization ====
 These methods are for visualization.
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{{anchor:visual:}}
  ?  **''VISUAL()''**
  :: Visualize a vector configuration.
    ? Options:
    : option list ''[[..:common#Visual_Polygons_decorations |Visual::Polygons::decorations]]''
    : option list ''[[..:common#geometric_options_linear |geometric_options_linear]]''
    ? Returns:
    :''[[..:polytope:Visual_PointConfiguration |Visual::PointConfiguration]]''


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