<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoxeterDiagramComponents</code>( <var class="Arg">D</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a Coxeter diagram <span class="SimpleMath">\(D\)</span> and returns a list <span class="SimpleMath">\([D_1, ..., D_d]\)</span> of the maximal connected subgraphs <span class="SimpleMath">\(D_i\)</span>.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoxeterDiagramDegree</code>( <var class="Arg">D</var>, <var class="Arg">v</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a Coxeter diagram <span class="SimpleMath">\(D\)</span> and vertex <span class="SimpleMath">\(v\)</span>. It returns the degree of <span class="SimpleMath">\(v\)</span> (i.e. the number of edges incident with <span class="SimpleMath">\(v\)</span>).</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoxeterDiagramDisplay</code>( <var class="Arg">D</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoxeterDiagramDisplay</code>( <var class="Arg">D</var>, <var class="Arg">str</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a Coxeter diagram <span class="SimpleMath">\(D\)</span> 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 <span class="SimpleMath">\(str\)</span>="mozilla".</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoxeterDiagramIsSpherical</code>( <var class="Arg">D</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a Coxeter diagram <span class="SimpleMath">\(D\)</span> and returns "true" if the associated Coxeter groups is finite, and returns "false" otherwise.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoxeterDiagramMatrix</code>( <var class="Arg">D</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a Coxeter diagram <span class="SimpleMath">\(D\)</span> and returns a matrix representation of it. The matrix is given as a function <span class="SimpleMath">\(DiagramMatrix(D)(i,j)\)</span> where <span class="SimpleMath">\(i,j\)</span> can range over the vertices.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoxeterSubDiagram</code>( <var class="Arg">D</var>, <var class="Arg">V</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a Coxeter diagram <span class="SimpleMath">\(D\)</span> and a subset <span class="SimpleMath">\(V\)</span> of its vertices. It returns the full sub-diagram of <span class="SimpleMath">\(D\)</span> with vertex set <span class="SimpleMath">\(V\)</span>.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoxeterDiagramVertices</code>( <var class="Arg">D</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a Coxeter diagram <span class="SimpleMath">\(D\)</span> and returns its set of vertices.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ EvenSubgroup</code>( <var class="Arg">G</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a group <span class="SimpleMath">\(G\)</span> and returns a subgroup <span class="SimpleMath">\(G^+\)</span>. The subgroup is that generated by all products <span class="SimpleMath">\(xy\)</span> where <span class="SimpleMath">\(x\)</span> and <span class="SimpleMath">\(y\)</span> range over the generating set for <span class="SimpleMath">\(G\)</span> stored by GAP. The subgroup is probably only meaningful when <span class="SimpleMath">\(G\)</span> is an Artin or Coxeter group.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ GraphOfGroupsDisplay</code>( <var class="Arg">D</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ GraphOfGroupsDisplay</code>( <var class="Arg">D</var>, <var class="Arg">str</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a graph of groups <span class="SimpleMath">\(D\)</span> 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 <span class="SimpleMath">\(str\)</span>="mozilla".</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ GraphOfResolutions</code>( <var class="Arg">D</var>, <var class="Arg">n</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a graph of groups <span class="SimpleMath">\(D\)</span> and a positive integer <span class="SimpleMath">\(n\)</span>. It returns a graph of resolutions, each resolution being of length <span class="SimpleMath">\(n\)</span>. It uses the function ResolutionGenericGroup() to produce the resolutions.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ GraphOfGroups</code>( <var class="Arg">D</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a graph of resolutions <span class="SimpleMath">\(D\)</span> and returns the corresponding graph of groups.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ GraphOfResolutionsDisplay</code>( <var class="Arg">D</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a graph of resolutions <span class="SimpleMath">\(D\)</span> and displays it as a .gif file. It uses the Mozilla web browser as a default to view the diagram.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ GraphOfGroupsTest</code>( <var class="Arg">D</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an object <span class="SimpleMath">\(D\)</span> 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 <spanclass="SimpleMath">\(D\)</span> passes the test, and false otherwise.</p>
<p>Note that there is no function <span class="SimpleMath">\(IsHapGraphOfGroups()\)</span> because no special data type has been created for these graphs.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TreeOfGroupsToContractibleGcomplex</code>( <var class="Arg">D</var>, <var class="Arg">G</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a graph of groups <span class="SimpleMath">\(D\)</span> which is a tree, and also inputs the fundamental group <span class="SimpleMath">\(G\)</span> of the tree in a form which contains each of the groups in the graph as subgroups. It returns a corresponding contractible G-complex.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TreeOfResolutionsToContractibleGcomplex</code>( <var class="Arg">D</var>, <var class="Arg">G</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a graph of resolutions <span class="SimpleMath">\(D\)</span> which is a tree, and also inputs the fundamental group <span class="SimpleMath">\(G\)</span> 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 <span class="SimpleMath">\(G\)</span>-complex.</p>
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