BigObject GeometricSimplicialComplex<Scalar>

from application 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: Rational

derived from:

SimplicialComplex

COORDINATES

Coordinates for the vertices of the simplicial complex, such that the complex is embedded without crossings in some R^e. Vector (x₁, …. x_e) represents a point in Euclidean e-space.

Type:

Matrix<Scalar,NonSymmetric>

G_DIM

Dimension e of the space in which the COORDINATES of the complex is embedded.

Type:

Int

N_UNIMODULAR

Count how many simplices of a geometric simplicial complex are unimodular.

Type:

Int

Example:

Non-regular quadrangle, triangulated.

 > $C = new GeometricSimplicialComplex(COORDINATES=>[[0,0],[1,0],[0,1],[2,1]],FACETS=>[[0,1,2],[1,2,3]]);
 > print $C->N_UNIMODULAR
 1

SIGNATURE

Signature of a geometric simplicial complex embedded in the integer lattice. Like DUAL_GRAPH_SIGNATURE, but only simplices with odd normalized volume are counted.

Type:

Int

UNIMODULAR

A geometric simplicial complex is unimodular if all simplices have unit normalized volume.

Type:

Bool

Example:

Unit square, triangulated.

 > $C = new GeometricSimplicialComplex(COORDINATES=>[[0,0],[1,0],[0,1],[1,1]], FACETS=>[[0,1,2],[1,2,3]]);
 > print $C->UNIMODULAR
 true

VOLUME

Volume of a geometric simplicial complex.

Type:

Scalar

VISUAL()

TODO: consider all inherited user methods; then: user_method … : COORDINATES …

Options:

option list Visual::Polygon::decorations

option list Visual::Graph::decorations