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<div class="ChapSects"><a href="chap25.html#X7C5563A37D566DA5">25. <span class="Heading"> Miscellaneous</span></a>
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<h3>25. <span class="Heading"> Miscellaneous</span></h3>
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<td class="tdleft"><code class="code"> BigStepLCS(G,n) </code></p>
<p>Inputs a group G and a positive integer n. It returns a subseries G=L_1>L_2>... L_k=1 of the lower central series of G such that L_i/L_i+1 has order greater than n.</td>
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<td class="tdleft"><code class="code"> Classify(L,Inv) </code></p>
<p>Inputs a list of objects L and a function Inv which computes an invariant of each object. It returns a list of lists which classifies the objects of L according to the invariant..</td>
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<td class="tdleft"><code class="code"> RefineClassification(C,Inv) </code></p>
<p>Inputs a list C:=Classify(L,OldInv) and returns a refined classification according to the invariant Inv.</td>
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<td class="tdleft"><code class="code"> Compose(f,g) </code></p>
<p>Inputs two FpG-module homomorphisms f:M --> N and g:L --> M with Source(f)=Target(g) . It returns the composite homomorphism fg:L --> N .</p>
<p>This also applies to group homomorphisms f,g.</td>
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<td class="tdleft"><code class="code"> HAPcopyright() </code></p>
<p>This function provides details of HAP'S GNU public copyright licence.</td>
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<td class="tdleft"><code class="code"> IsLieAlgebraHomomorphism(f) </code></p>
<p>Inputs an object f and returns true if f is a homomorphism f:A --> B of Lie algebras (preserving the Lie bracket).</td>
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<td class="tdleft"><code class="code"> IsSuperperfect(G) </code></p>
<p>Inputs a group G and returns "true" if both the first and second integral homology of G is trivial. Otherwise, it returns "false".</td>
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<td class="tdleft"><code class="code">MakeHAPManual()</code></p>
<p>This function creates the manual for HAP from an XML file.</td>
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<td class="tdleft"><code class="code"> PermToMatrixGroup(G,n) </code></p>
<p>Inputs a permutation group G and its degree n. Returns a bijective homomorphism f:G --> M where M is a group of permutation matrices.</td>
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<td class="tdleft"><code class="code"> SolutionsMatDestructive(M,B) </code></p>
<p>Inputs an m×n matrix M and a k×n matrix B over a field. It returns a k×m matrix S satisfying SM=B.</p>
<p>The function will leave matrix M unchanged but will probably change matrix B.</p>
<p>(This is a trivial rewrite of the standard GAP function SolutionMatDestructive(<mat>,<vec>) .)</td>
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<td class="tdleft"><code class="code"> TestHap() </code></p>
<p>This runs a representative sample of HAP functions and checks to see that they produce the correct output.</td>
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