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<div class="ChapSects"><a href="chap19.html#X79D0502085B6734A">19. <span class="Heading"> Coxeter diagrams and graphs of groups</span></a>
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<h3>19. <span class="Heading"> Coxeter diagrams and graphs of groups</span></h3>
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<td class="tdleft"><code class="code"> CoxeterDiagramComponents(D) </code></p>
<p>Inputs a Coxeter diagram D and returns a list [D_1, ..., D_d] of the maximal connected subgraphs D_i.</td>
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<td class="tdleft"><code class="code"> CoxeterDiagramDegree(D,v) </code></p>
<p>Inputs a Coxeter diagram D and vertex v. It returns the degree of v (i.e. the number of edges incident with v).</td>
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<td class="tdleft"><code class="code"> CoxeterDiagramDisplay(D) </code> <br /> <code class="code"> CoxeterDiagramDisplay(D,"web browser") </code></p>
<p>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.</p>
<p>This function requires Graphviz software.</td>
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<td class="tdleft"><code class="code"> CoxeterDiagramFpArtinGroup(D) </code></p>
<p>Inputs a Coxeter diagram D and returns the corresponding finitely presented Artin group.</td>
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<td class="tdleft"><code class="code"> CoxeterDiagramFpCoxeterGroup(D) </code></p>
<p>Inputs a Coxeter diagram D and returns the corresponding finitely presented Coxeter group.</td>
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<td class="tdleft"><code class="code"> CoxeterDiagramIsSpherical(D) </code></p>
<p>Inputs a Coxeter diagram D and returns "true" if the associated Coxeter groups is finite, and returns "false" otherwise.</td>
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<td class="tdleft"><code class="code"> CoxeterDiagramMatrix(D) </code></p>
<p>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.</td>
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<td class="tdleft"><code class="code"> CoxeterSubDiagram(D,V) </code></p>
<p>Inputs a Coxeter diagram D and a subset V of its vertices. It returns the full sub-diagram of D with vertex set V.</td>
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<td class="tdleft"><code class="code"> CoxeterDiagramVertices(D) </code></p>
<p>Inputs a Coxeter diagram D and returns its set of vertices.</td>
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<td class="tdleft"><code class="code"> EvenSubgroup(G) </code></p>
<p>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.</td>
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<td class="tdleft"><code class="code"> GraphOfGroupsDisplay(D) </code> <br /> <code class="code"> GraphOfGroupsDisplay(D,"web browser") </code></p>
<p>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.</p>
<p>This function requires Graphviz software.</td>
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<td class="tdleft"><code class="code"> GraphOfGroupsTest(D) </code></p>
<p>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.</p>
<p>Note that there is no function IsHapGraphOfGroups() because no special data type has been created for these graphs.</td>
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