‣ CoxeterDiagramComponents( D ) | ( function ) |
Inputs a Coxeter diagram D and returns a list [D_1, ..., D_d] of the maximal connected subgraphs D_i.
Examples:
‣ CoxeterDiagramDegree( D, v ) | ( function ) |
Inputs a Coxeter diagram D and vertex v. It returns the degree of v (i.e. the number of edges incident with v).
Examples:
‣ CoxeterDiagramDisplay( D ) | ( function ) |
‣ CoxeterDiagramDisplay( D, str ) | ( function ) |
Inputs a Coxeter diagram D and displays it as a .gif file. It uses the Mozilla web browser as a default to view the diagram. An alternative browser can be set using a second argument str="mozilla".
This function requires Graphviz software.
Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7
‣ CoxeterDiagramFpArtinGroup( D ) | ( function ) |
Inputs a Coxeter diagram D and returns the corresponding finitely presented Artin group.
Examples: 1
‣ CoxeterDiagramFpCoxeterGroup( D ) | ( function ) |
Inputs a Coxeter diagram D and returns the corresponding finitely presented Coxeter group.
Examples: 1
‣ CoxeterDiagramIsSpherical( D ) | ( function ) |
Inputs a Coxeter diagram D and returns "true" if the associated Coxeter groups is finite, and returns "false" otherwise.
Examples: 1
‣ CoxeterDiagramMatrix( D ) | ( function ) |
Inputs a Coxeter diagram D and returns a matrix representation of it. The matrix is given as a function DiagramMatrix(D)(i,j) where i,j can range over the vertices.
Examples:
‣ CoxeterSubDiagram( D, V ) | ( function ) |
Inputs a Coxeter diagram D and a subset V of its vertices. It returns the full sub-diagram of D with vertex set V.
Examples:
‣ CoxeterDiagramVertices( D ) | ( function ) |
Inputs a Coxeter diagram D and returns its set of vertices.
Examples:
‣ EvenSubgroup( G ) | ( function ) |
Inputs a group G and returns a subgroup G^+. The subgroup is that generated by all products xy where x and y range over the generating set for G stored by GAP. The subgroup is probably only meaningful when G is an Artin or Coxeter group.
‣ GraphOfGroupsDisplay( D ) | ( function ) |
‣ GraphOfGroupsDisplay( D, str ) | ( function ) |
Inputs a graph of groups D and displays it as a .gif file. It uses the Mozilla web browser as a default to view the diagram. An alternative browser can be set using the second argument str="mozilla".
This function requires Graphviz software.
‣ GraphOfResolutions( D, n ) | ( function ) |
Inputs a graph of groups D and a positive integer n. It returns a graph of resolutions, each resolution being of length n. It uses the function ResolutionGenericGroup() to produce the resolutions.
Examples:
‣ GraphOfGroups( D ) | ( function ) |
Inputs a graph of resolutions D and returns the corresponding graph of groups.
‣ GraphOfResolutionsDisplay( D ) | ( function ) |
Inputs a graph of resolutions D and displays it as a .gif file. It uses the Mozilla web browser as a default to view the diagram.
This function requires Graphviz software.
Examples:
‣ GraphOfGroupsTest( D ) | ( function ) |
Inputs an object D and itries to test whether it is a Graph of Groups. However, it DOES NOT test the injectivity of any homomorphisms. It returns true if D passes the test, and false otherwise.
Note that there is no function IsHapGraphOfGroups() because no special data type has been created for these graphs.
Examples:
‣ TreeOfGroupsToContractibleGcomplex( D, G ) | ( function ) |
Inputs a graph of groups D which is a tree, and also inputs the fundamental group G of the tree in a form which contains each of the groups in the graph as subgroups. It returns a corresponding contractible G-complex.
Examples:
‣ TreeOfResolutionsToContractibleGcomplex( D, G ) | ( function ) |
Inputs a graph of resolutions D which is a tree, and also inputs the fundamental group G of the tree in a form which contains each of the groups in the graph as subgroups. It returns a corresponding contractible G-complex. The resolutions are stored as a component of the contractible G-complex.
Examples:
generated by GAPDoc2HTML