This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong. ====== 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]]>'' ---- {{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]]'' ---- {{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> ---- {{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]]'' ---- {{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> ---- {{anchor:volume:}} ? **''VOLUME''** :: Volume of a geometric simplicial complex. ? Type: :''Scalar'' ---- ===== 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]]'' ---- documentation/master/topaz/geometricsimplicialcomplex.txt Last modified: 2020/04/26 04:52by 127.0.0.1