Coxeter diagrams and graphs of groups

CoxeterDiagramComponents
CoxeterDiagramComponents(D)

Inputs a Coxeter diagram D and returns a list [D_1, ..., D_d] of the maximal connected subgraphs D_i.
CoxeterDiagramDegree
CoxeterDiagramDegree(D,v)

Inputs a Coxeter diagram D and vertex v. It returns the degree of v (i.e. the number of edges incident with v).
CoxeterDiagramDisplay
CoxeterDiagramDisplay(D)
CoxeterDiagramDisplay(D,"web browser")

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.

This function requires Graphviz software.
CoxeterDiagramFpArtinGroup
CoxeterDiagramFpArtinGroup(D)

Inputs a Coxeter diagram D and returns the corresponding finitely presented Artin group.
CoxeterDiagramFpCoxeterGroup
CoxeterDiagramFpCoxeterGroup(D)

Inputs a Coxeter diagram D and returns the corresponding finitely presented Coxeter group.
CoxeterDiagramIsSpherical
CoxeterDiagramIsSpherical(D)

Inputs a Coxeter diagram D and returns "true" if the associated Coxeter groups is finite, and returns "false" otherwise.
CoxeterDiagramMatrix
CoxeterDiagramMatrix(D)

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.
CoxeterSubDiagram
CoxeterSubDiagram(D,V)

Inputs a Coxeter diagram D and a subset V of its vertices. It returns the full sub-diagram of D with vertex set V.
CoxeterDiagramVertices
CoxeterDiagramVertices(D)

Inputs a Coxeter diagram D and returns its set of vertices.
EvenSubgroup
EvenSubgroup(G)

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
GraphOfGroupsDisplay(D)
GraphOfGroupsDisplay(D,"web browser")

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 a second argument.

This function requires Graphviz software.
GraphOfResolutions
GraphOfResolutions(D,n)

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.
GraphOfGroups
GraphOfGroups(D)

Inputs a graph of resolutions D and returns the corresponding graph of groups.
GraphOfResolutionsDisplay
GraphOfResolutionsDisplay(D)

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.
GraphOfGroupsTest
GraphOfGroupsTest(D)

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.
TreeOfGroupsToContractibleGcomplex
TreeOfGroupsToContractibleGcomplex(D,G)

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.
TreeOfResolutionsToContractibleGcomplex
TreeOfResolutionsToContractibleGcomplex(D,G)

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.