<h4>1.1 <span class="Heading">Getting started with RepnDecomp</span></h4>
<p>This package allows computations of various decompositions of a representation <span class="SimpleMath">\(\rho : G \to GL(V)\)</span> where <span class="SimpleMath">\(G\)</span> is finite and <span class="SimpleMath">\(V\)</span> is a finite-dimensional <span class="SimpleMath">\(\mathbb{C}\)</span>-vector space.</p>
<p>To install this package, refer to the installation instructions in the README file in the sourcecode. It is located here: <span class="URL"><a href="https://github.com/gap-packages/RepnDecomp/blob/master/README.md">https://github.com/gap-packages/RepnDecomp/blob/master/README.md</a></span>.</p>
<h5>1.1-2 <span class="Heading">Note on what is meant by a representation</span></h5>
<p>Throughout this documentation, mathematical terminology is used e.g. representation. It is clear what is meant mathematically, but it is not entirely clear what is meant in terms of GAP types - what are you supposed to pass in when I say "pass in a representation". Occasionally I will not even mention what we are passing in and assume the reader knows that <var class="Arg">rho</var> or <span class="SimpleMath">\(\rho\)</span> refers to a representation. A representation we can use is, in GAP, a homomorphism from a finite group to a matrix group where all matrices have coefficients in a cyclotomic field (<code class="code">Cyclotomics</code> is the union of all such fields in GAP). You can check whether something you want to pass is suitable with the function <code class="func">IsFiniteGroupLinearRepresentation</code> (<a href="chap4_mj.html#X8631A1417C3C1D88"><span class="RefLink">4.1-1</span></a>).</p>
<p>Here's an example of a representation rho in GAP:
<p>The algorithms implemented can be divided into two groups: methods due to Serre from his book Linear Representations of Finite Groups, and original methods due to the authors of this package.</p>
<p>The default is to use the algorithms due to Serre. If you pass the option <code class="code">method := "alternate"</code> to a function, it will use the alternate method. Passing the option <code class="code">parallel</code> will try to compute in parallel as much as possible. See the individual functions for options you can pass.</p>
<p>The main functions implemented in this package are:</p>
<p>For decomposing representations into canonical and irreducible direct summands:</p>
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