====== BigObject GeometricSimplicialComplex<Scalar> ======
//from application [[..:topaz|topaz]]//\\
\\
 A geometric simplicial complex, i.e., a simplicial complex with a geometric realization. //Scalar// is the numeric data type used for the coordinates.

  ? Type Parameters:
  :: ''Scalar'': default: ''[[..:common#Rational |Rational]]''
  ? derived from:
  : ''[[..:topaz:SimplicialComplex |SimplicialComplex]]''
===== Properties =====

==== no category ====
{{anchor:coordinates:}}
  ?  **''COORDINATES''**
  :: Coordinates for the vertices of the simplicial complex, such that the complex is embedded without crossings in some R<sup>e</sup>.  Vector (x<sub>1</sub>, .... x<sub>e</sub>) represents a point in Euclidean e-space.
    ? Type:
    :''[[..:common#Matrix |Matrix]]<Scalar,[[..:common#NonSymmetric |NonSymmetric]]>''


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{{anchor:g_dim:}}
  ?  **''G_DIM''**
  :: Dimension e of the space in which the ''[[..:topaz:GeometricSimplicialComplex#COORDINATES |COORDINATES]]'' of the complex is embedded.
    ? Type:
    :''[[..:common#Int |Int]]''


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{{anchor:n_unimodular:}}
  ?  **''N_UNIMODULAR''**
  :: Count how many simplices of a geometric simplicial complex are unimodular.
    ? Type:
    :''[[..:common#Int |Int]]''
    ? Example:
    :: Non-regular quadrangle, triangulated.
    :: <code perl> > $C = new GeometricSimplicialComplex(COORDINATES=>[[0,0],[1,0],[0,1],[2,1]],FACETS=>[[0,1,2],[1,2,3]]);
 > print $C->N_UNIMODULAR
 1
</code>


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{{anchor:signature:}}
  ?  **''SIGNATURE''**
  :: Signature of a geometric simplicial complex embedded in the integer lattice. Like ''[[..:topaz:SimplicialComplex#DUAL_GRAPH_SIGNATURE |DUAL_GRAPH_SIGNATURE]]'', but only simplices with odd normalized volume are counted.
    ? Type:
    :''[[..:common#Int |Int]]''


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{{anchor:unimodular:}}
  ?  **''UNIMODULAR''**
  :: A geometric simplicial complex is unimodular if all simplices have unit normalized volume.
    ? Type:
    :''[[..:common#Bool |Bool]]''
    ? Example:
    :: Unit square, triangulated.
    :: <code perl> > $C = new GeometricSimplicialComplex(COORDINATES=>[[0,0],[1,0],[0,1],[1,1]], FACETS=>[[0,1,2],[1,2,3]]);
 > print $C->UNIMODULAR
 true
</code>


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{{anchor:volume:}}
  ?  **''VOLUME''**
  :: Volume of a geometric simplicial complex.
    ? Type:
    :''Scalar''


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===== Methods =====

==== no category ====
{{anchor:visual:}}
  ?  **''VISUAL()''**
  :: TODO: consider all inherited user methods; then: user_method ... : COORDINATES ... 
    ? Options:
    : option list ''[[..:common#Visual_Polygon_decorations |Visual::Polygon::decorations]]''
    : option list ''[[..:graph#Visual_Graph_decorations |Visual::Graph::decorations]]''


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