Differences

This shows you the differences between two versions of the page.

--- playground:playground [2019/03/04 15:35] – oroehrig
+++ playground:playground [2020/05/21 12:24] (current) – removed benmuell
@@ Line 1: / Line 1: @@
-----
-==== Visualization ====
- These properties are for visualization.
-== MIXED_GRAPH ==
-''Type:'' /topaz/objects/SimplicialComplex/properties/Visualization/MIXED_GRAPH\\  The nodes of the mixed graph are the nodes of the primal [[/topaz/objects/SimplicialComplex/properties/Combinatorics/GRAPH]] and
- the [[/topaz/objects/SimplicialComplex/properties/Combinatorics/DUAL_GRAPH]]. Additional to the primal and dual edges, there is
- an edge between a primal and a dual node iff the primal node represents
- a vertex of the corresponding facet of the dual node.
-\\ __Properties of MIXED_GRAPH:__\\
-  * **EDGE_WEIGHTS**\\ ''Type:'' /common/property_types/Graph Types/EdgeMap\\  Associated edge weights.
-== VERTEX_LABELS ==
-''Type:'' /common/property_types/Basic Types/Array\\  Labels of the vertices.
-===== Methods =====
-----
-==== Combinatorics ====
- These methods capture combinatorial information of the object.
- Combinatorial properties only depend on combinatorial data of the object like, e.g., the face lattice.
- == BIPARTITE() ==
-  * ''Returns:'' /common/property_types/Basic Types/Bool\\ True if [[/topaz/objects/SimplicialComplex/properties/Combinatorics/GRAPH]] is a __bipartite__.
- == CONNECTED_COMPONENTS() ==
-  * ''Returns:'' /common/property_types/Set Types/PowerSet</common/property_types/Basic Types/Int>\\ The connected components of the [[/topaz/objects/SimplicialComplex/properties/Combinatorics/GRAPH]], encoded as node sets.
- == CONNECTIVITY() ==
-  * ''Returns:'' /common/property_types/Basic Types/Int\\ Node connectivity of the [[/topaz/objects/SimplicialComplex/properties/Combinatorics/GRAPH]], that is, the minimal number of nodes to be removed from the graph such that the result is disconnected.
- == DUAL_BIPARTITE() ==
-  * ''Returns:'' /common/property_types/Basic Types/Bool\\ True if [[/topaz/objects/SimplicialComplex/properties/Combinatorics/DUAL_GRAPH]] is a __bipartite__.
- == DUAL_CONNECTED_COMPONENTS() ==
-  * ''Returns:'' /common/property_types/Set Types/PowerSet</common/property_types/Basic Types/Int>\\ The connected components of the [[/topaz/objects/SimplicialComplex/properties/Combinatorics/DUAL_GRAPH]], encoded as node sets.
- == DUAL_CONNECTIVITY() ==
-  * ''Returns:'' /common/property_types/Set Types/PowerSet</common/property_types/Basic Types/Int>\\ Node connectivity of the [[/topaz/objects/SimplicialComplex/properties/Combinatorics/DUAL_GRAPH]]. Dual to [[/topaz/objects/SimplicialComplex/methods/Combinatorics/CONNECTIVITY]].
- == DUAL_GRAPH_SIGNATURE() ==
-  * ''Returns:'' /common/property_types/Basic Types/Int\\ Difference of the black and white nodes if the [[/topaz/objects/SimplicialComplex/properties/Combinatorics/DUAL_GRAPH]] is [[/topaz/objects/SimplicialComplex/methods/Combinatorics/BIPARTITE]]. Otherwise -1.
- == DUAL_MAX_CLIQUES() ==
-  * ''Returns:'' /common/property_types/Set Types/PowerSet</common/property_types/Basic Types/Int>\\ The maximal cliques of the [[/topaz/objects/SimplicialComplex/properties/Combinatorics/DUAL_GRAPH]], encoded as node sets.
- == GRAPH_SIGNATURE() ==
-  * ''Returns:'' /common/property_types/Basic Types/Int\\ Difference of the black and white nodes if the [[/topaz/objects/SimplicialComplex/properties/Combinatorics/GRAPH]] is [[/topaz/objects/SimplicialComplex/methods/Combinatorics/BIPARTITE]]. Otherwise -1.
- == MAX_CLIQUES() ==
-  * ''Returns:'' /common/property_types/Set Types/PowerSet</common/property_types/Basic Types/Int>\\ The maximal cliques of the [[/topaz/objects/SimplicialComplex/properties/Combinatorics/GRAPH]], encoded as node sets.
- == VERTEX_DEGREES() ==
-  * ''Returns:'' /common/property_types/Basic Types/Array</common/property_types/Basic Types/Int>\\ Degrees of the vertices in the [[/topaz/objects/SimplicialComplex/properties/Combinatorics/GRAPH]].
- == boundary_matrix(Int d) ==
-  * ''Parameters:'' /common/property_types/Basic Types/Int ''d'' : Dimension of the boundary matrix.
-  * ''Returns:'' /common/property_types/Algebraic Types/SparseMatrix</common/property_types/Basic Types/Integer>\\ Output the boundary matrix of dimension __d__. Indexing is according to
- the face indices in the HASSE_DIAGRAM of the complex.
- The matrix is a map via multiplying it to a vector from the __left__.
- Beware, this computes the whole face lattice of your complex, which is expensive.
- == labeled_vertices(String label ...) ==
-  * ''Parameters:'' /common/property_types/Basic Types/String ''label ...'' : vertex labels
-  * ''Returns:'' /common/property_types/Set Types/Set</common/property_types/Basic Types/Int>\\ Find the vertices by given labels.
-----
-==== Topology ====
- The following methods compute topological invariants.
- == CONNECTED() ==
-  * ''Returns:'' /common/property_types/Basic Types/Bool\\ True if the [[/topaz/objects/SimplicialComplex/properties/Combinatorics/GRAPH]] is a connected graph.
- == DUAL_CONNECTED() ==
-  * ''Returns:'' /common/property_types/Basic Types/Bool\\ True if the [[/topaz/objects/SimplicialComplex/properties/Combinatorics/DUAL_GRAPH]] is a connected graph.
- == N_CONNECTED_COMPONENTS() ==
-  * ''Returns:'' /common/property_types/Basic Types/Int\\ Number of connected components of the [[/topaz/objects/SimplicialComplex/properties/Combinatorics/GRAPH]].
- == fundamental2gap(String filename) ==
-  * ''Parameters:'' /common/property_types/Basic Types/String ''filename'' :
-  * ''Returns:'' /common/property_types/Basic Types/String\\ Writes the [[/topaz/objects/SimplicialComplex/properties/Topology/FUNDAMENTAL_GROUP]] using [[/topaz/objects/SimplicialComplex/properties/Topology/FUNDAMENTAL_GROUP_GEN_LABELS]] to
- the given file in [[wiki:external_software#GAP|GAP]] input format.
-----
-==== Visualization ====
- These methods are for visualization.
- == VISUAL() ==
-  * ''Returns:'' /topaz/objects/Visual::SimplicialComplex\\ Visualizes the complex.
- If [[/topaz/objects/GeometricSimplicialComplex/properties/G_DIM]] < 4, the [[/topaz/objects/SimplicialComplex/properties/Combinatorics/GRAPH]] and the facets
- are visualized using the [[/topaz/objects/GeometricSimplicialComplex/properties/COORDINATES]].
- Otherwise, the spring embedder and the [[/topaz/objects/SimplicialComplex/properties/Combinatorics/GRAPH]] are used to
- produce coordinates for the visualization.
- If [[wiki:external_software#javaview|JavaView]] is used to visualize the complex, all faces of
- one facet build a geometry in the jvx-file, so you may use
- __Method -> Effect -> Explode Group of Geometries__ in the JavaView menu.
- == VISUAL_DUAL_GRAPH() ==
-  * ''Returns:'' /topaz/objects/Visual::SimplicialComplex\\ Uses the spring embedder to visualize the [[/topaz/objects/SimplicialComplex/properties/Combinatorics/DUAL_GRAPH]].
- == VISUAL_FACE_LATTICE() ==
-  * ''Returns:'' /topaz/objects/Visual::SimplicialComplexLattice\\ Visualize the [[/topaz/objects/SimplicialComplex/properties/Combinatorics/HASSE_DIAGRAM]] of a simplicial complex as a multi-layer graph.
- == VISUAL_GRAPH() ==
-  * ''Returns:'' /topaz/objects/Visual::SimplicialComplex\\ Uses the spring embedder to visualize the [[/topaz/objects/SimplicialComplex/properties/Combinatorics/GRAPH]].
- == VISUAL_MIXED_GRAPH() ==
-  * ''Returns:'' /common/objects/Visualization/Visual::Container\\ Uses the spring embedder to visualize the [[/topaz/objects/SimplicialComplex/properties/Visualization/MIXED_GRAPH]].