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>

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G_DIM

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

Type:

Int

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N_UNIMODULAR

Count how many simplices of a geometric simplicial complex are unimodular. If the simplicial complex is lower dimensional, each simplex is considered in its affine hull.

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

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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

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UNIMODULAR

A geometric simplicial complex is unimodular if all simplices have unit normalized volume. If the simplicial complex is lower dimensional, each simplex is considered in its affine hull.

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

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VOLUME

Volume of a geometric simplicial complex.

Type:

Scalar

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VISUAL()

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

Options:

option list Visual::Polygon::decorations

option list Visual::Graph::decorations

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