CoxeterDiagramComponents(D)
Inputs a Coxeter diagram D and returns a list [D_1, ..., D_d] of the maximal connected subgraphs D_i. |
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(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(D)
Inputs a Coxeter diagram D and returns the corresponding finitely presented Artin group. |
CoxeterDiagramFpCoxeterGroup(D)
Inputs a Coxeter diagram D and returns the corresponding finitely presented Coxeter group. |
CoxeterDiagramIsSpherical(D)
Inputs a Coxeter diagram D and returns "true" if the associated Coxeter groups is finite, and returns "false" otherwise. |
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(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(D)
Inputs a Coxeter diagram D and returns its set of vertices. |
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(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. |
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. |
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