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<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a>  <a href="chap1.html">1</a>  <a href="chap2.html">2</a>  <a href="chap3.html">3</a>  <a href="chap4.html">4</a>  <a href="chap5.html">5</a>  <a href="chap6.html">6</a>  <a href="chap7.html">7</a>  <a href="chap8.html">8</a>  <a href="chap9.html">9</a>  <a href="chap10.html">10</a>  <a href="chap11.html">11</a>  <a href="chap12.html">12</a>  <a href="chap13.html">13</a>  <a href="chap14.html">14</a>  <a href="chap15.html">15</a>  <a href="chap16.html">16</a>  <a href="chap17.html">17</a>  <a href="chap18.html">18</a>  <a href="chap19.html">19</a>  <a href="chap20.html">20</a>  <a href="chap21.html">21</a>  <a href="chap22.html">22</a>  <a href="chap23.html">23</a>  <a href="chap24.html">24</a>  <a href="chap25.html">25</a>  <a href="chap26.html">26</a>  <a href="chap27.html">27</a>  <a href="chap28.html">28</a>  <a href="chap29.html">29</a>  <a href="chap30.html">30</a>  <a href="chap31.html">31</a>  <a href="chap32.html">32</a>  <a href="chap33.html">33</a>  <a href="

<div class="

<p id="mathjaxlink
<> "" ""<a>p
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<<h5>.2IdentityAmongRelatorsDisplay</>
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<class"">brspanclass=nocss"  /span<a ="chap17.tmlX7F49A86A82EB2420"1711 CayleyGraphOfGroupDisplay</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap17.html#X82C8B87287602BFA">17.1-2 IdentityAmongRelatorsDisplay</a></span>
<span class="ContSS"><br /><span
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap17.html#X878938C3835871D7">17.1-4 PresentationOfResolution</a></span>
<span class="ContSS"><br /><span class="nocss"> <pThis functionusesGraphViz software.<p
</div></div>
<<><strong class="utton>Examples</strong> <span class="URL"><a href="../tutorial/chap6.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutPeriodic.html">2</a></span> , <span class="URL"

<h3>17 <span class=

<p><a id

<h4>17.pInputsafreegroup< class""F/>andaset< class""R/pan> words < class""F/>.Itperforms test onthe- CW-pace< class=SimpleMath>/>associatedthisfor group<class"SimpleMath"GF/>lt<span class""R/>gtspan="impleMath"^F/>.<p

<p< id"" name=X7F49A86A82EB2420<java.lang.StringIndexOutOfBoundsException: Range [25, 23) out of bounds for length 311

<h5>17.1-1 CayleyGraphOfGroupDisplay</h5>

<div class="
< class"unc"><class"unc"width="100%"><tr><td class="tdleft"><code class="func">&#8227; CayleyGraphOfGroupDisplay</code>( 
<p>Inputs a finite group <span class="SimpleMath">G<<p<strong class"button">Examples</strong> <span class="RL">< href"..tutorialchap3.tml>1/a</span ,<span class=URL><a href="..tutorialchap6.html">2</a</pan>  span class="URL"><a href="../www/SideLinks/About/aboutAspherical.html">3</a></span> , <span class="URL"><a href="../www/SideLinks

<p>The argument <span class="SimpleMath">G</span> can also be a finite set of elements in a (possibly infinitepInputs    terms   span=SimpleMathZG/>- spanclass=><andjava.lang.StringIndexOutOfBoundsException: Range [134, 133) out of bounds for length 196

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<pli

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<p/ul

<>wherespanclass""<span>isomorphicto span ="F/ modulothe normal closure of <span class="SimpleMath">S</span>. This presentation for <span class="SimpleMath">G</span> corresponds to the 2-skeleton

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap6.html">1</a></span> , <span 

<

<h5>  < =Gspanjava.lang.StringIndexOutOfBoundsException: Range [73, 72) out of bounds for length 190

<div class="func"><table class="func" width="100
""F/>anda<classS><span    span=SimpleMathFspan>It a   2dimensional -pace< class=""K/ to forthe< class=SimpleMath>=/spanl;spanclassS"R/span>>span =""^</>.<p

<p>The function returns "true" if <span class="SimpleMath">K</span> has trivial second homotopy java.lang.StringIndexOutOfBoundsException: Index 100 out of bounds for length 0

<p>Otherwise it returns "fail" and prints: Presentation is NOT piece-wise Euclidean non-positively curved. (In this 

<p><p>The

<> <spanclass=URL>< href./tutorial/chap3.html">1</a></span> , <span class="URL"><a href="../tutorial/chap6.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutAspherical.html">3</a></span> , <span class=""<ahref".//SideLinks//.html"4/>/span> />

<p><a id="X878938C3835871D7" name="X878938C3835871D7"></a></p>

<h5>17.1-4 PresentationOfResolution</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; PresentationOfResolution</code>( <var class="Arg">R</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs at least two terms of a reduced <span class="SimpleMath">ZG</span>-resolution <span class="SimpleMath">R</span> and returns a record <span class="SimpleMath">P</span> with components</p>


<ul>
<li><p><span class="SimpleMath">P.freeGroup</span> is a free group <span class="SimpleMath">F</span>,</p>

</li>
<li><p><span class="SimpleMath">P.relators</span> is a list <span class="SimpleMath">S</span> of words in <span class="SimpleMath">F</span>,</p>

</li>
<li><p><span class="SimpleMath">P.gens</span> is a list of positive integers such that the <span class="SimpleMath">i</span>-th generator of the presentation corresponds to the group element R!.elts[P[i]] .</p>

</li>
</ul>
<p>where <span class="SimpleMath">G</span> is isomorphic to <span class="SimpleMath">F</span> modulo the normal closure of <span class="SimpleMath">S</span>. This presentation for <span class="SimpleMath">G</span> corresponds to the 2-skeleton of the classifying CW-space from which <span class="SimpleMath">R</span> was constructed. The resolution <span class="SimpleMath">R</span> requires no contracting homotopy.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap6.html">1</a></span> , <span class="URL"><a href="../tutorial/chap13.html">2</a></span> , <span class="URL"><a href="../tutorial/chap14.html">3</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutPolytopes.html">4</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutSpaceGroup.html">5</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutTopology.html">6</a></span> </p>

<p><a id="X7F71698178AF48DD" name="X7F71698178AF48DD"></a></p>

<h5>17.1-5 TorsionGeneratorsAbelianGroup</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; TorsionGeneratorsAbelianGroup</code>( <var class="Arg">G</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an abelian group <span class="SimpleMath">G</span> and returns a generating set <span class="SimpleMath">[x_1, ... ,x_n]</span> where no pair of generators have coprime orders.</p>

<p><strong class="button">Examples:</strong></p>


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