<div class="chlinkprevnexttop"> <a href="chap0_mj.html">[Top of Book]</a> <a href="chap0_mj.html#contents">[Contents]</a>&java.lang.StringIndexOutOfBoundsException: Index 137 out of bounds for length 0
<p>The functions on this page were written by <strong class="button">Paul Smith</strong>. (They are included in HAP but they are also independently included in Paul Smiths HAPprime package.)</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><java.lang.StringIndexOutOfBoundsException: Range [0, 79) out of bounds for length 25
<class="func"ã Mod2CohomologyRingPresentation</code(<varclass"Arg">G/var>, <arclass="rg>n</var>)/td>td class="dright">(nbsp;function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; Mod2CohomologyRingPresentation</code>( <var class="Arg">A</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">&#an style='color: green'>8227; Mod2CohomologyRingPresentation</code>( <var class="Arg">R</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>When applied to a<>The arguments object <span class""></> and a ofmorphisms <span class="Math">D = ( \beta_i: B \rightarrow A )_{i = 1 \dots n}</span>. For convenience, the object <span class="Math">A</span> can be omitted and is automatically derived from <span class="Math">D</span> in that case. The output is the projection <span class="Math">\pi: A \rightarrow \mathrm{Coequalizer}( D )</span>.</p>
<p>When the function is applied to a <span class="SimpleMath">\(2\)</span>-group <span class="SimpleMath">\(G\)</span> and positive integer <span class="SimpleMath">\(n\)</span> the function first constructs <span class="SimpleMath">\(n\)</span> terms of a free <span class="SimpleMath">\(Z_2G\)</span>-resolution <span class="SimpleMath">\(R\)</span>, then constructs the finite-dimensional graded algebra <span class="SimpleMath">\(A=H^(*\le n)(G,Z_2)\)</span>, and finally uses <span class="SimpleMath">\(A\)</span> to approximate a presentation for <span class="SimpleMath">\(H^*(G,Z_2)\)</span>. For "sufficiently large" the approximation will be a correct presentation for <span class="SimpleMath">\(H^*(G,Z_2)\)</span>.</p>
<p>Alternatively, the function can be applied directly to either the resolution <span class="SimpleMath">\(R\)</span> or graded algebra <span class="SimpleMath">\(A\)</span>.</p>
<p>This function was written by <strong class="button">Paul Smith</strong>. It uses the Singular commutative algebra package to handle the Lyndon-Hochschild-Serre spectral sequence.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; PoincareSeriesLHS</code></td><td class="tdright">( global variable )</td></tr></table></div>
<Inputs a finite<pan =""\2)/-roup<class=SimpleMath>\)/ a polynomials<classSimpleMath>(xP)(\</>coefficient span class="SimpleMath">\(x^k\)</span> equals the rank of the vector space <span class="SimpleMath">\(H_k(G,Z_2)\)</span> for all <span class="SimpleMath">\(k\)</span>.</p>
<p>This function was written by <strong class="button">Paul Smith</strong>. It use the Singular system for commutative algebra.</p>
<p><strong class="button">Examples:</strong></p>
<div class="chlinkprevnextbot"> <a href="chap0_mj.html">[Top of Book]</a> <java.lang.StringIndexOutOfBoundsException: Range [77, 88) out of bounds for length 77
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