<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MajoranaRepresentation</code>( <var class="Arg">input</var>, <var class="Arg">index</var>[, <var class="Arg">options</var>] )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: a record giving a Majorana representation</p>
<p>This takes two or three arguments, the first of which must be the output of the function <code class="func">ShapesOfMajoranaRepresentation</code> (<a href="chap2.html#X7AEAA41E813BB13C"><span class="RefLink">2.1-1</span></a>) and the second of which is the index of the desired shape in list <var class="Arg">input.shapes</var>.</p>
<p>If the optional argument <var class="Arg">options</var> is given then it must be a record. The following components of <var class="Arg">options</var> are recognised:</p>
<dl>
<dt><strong class="Mark"><code class="code">axioms</code></strong></dt>
<dd><p>This component must be bound to the string <var class="Arg">"AllAxioms"</var> or <var class="Arg">"NoAxioms"</var>. If bound to <var class="Arg">"AllAxioms"</var> then the algorithm assumes the axioms 2Aa, 2Ab, 3A, 4A and 5A as in Seress (2012). If bound to <var class="Arg">"NoAxioms"</var> then the algorithm only assumes the Majorana axioms M1 - M7. The default value is <var class="Arg">"AllAxioms"</var>.</p>
</dd>
<dt><strong class="Mark"><code class="code">form</code></strong></dt>
<dd><p>If this is bound to <var class="Arg">true</var> then the algorithm assume the existence of an inner product (as in the definition of a Majorana algebra). Otherwise, if bound to <var class="Arg">false</var> then no inner product is assumed (and we are in fact constructing an axial algebra that satisfies the Majorana fusion law). The default value is <var class="Arg">true</var>.</p>
</dd>
<dt><strong class="Mark"><code class="code">embedding</code></strong></dt>
<dd><p>If this is bound to <var class="Arg">true</var> then the algorithm first attempts to construct large subalgebras of the final representation before starting the main construction. The default value is <var class="Arg">false</var>.</p>
<p>A Majorana algebra <span class="Math">V</span> generated by a set of axes <span class="Math">A</span> is called <span class="Math">n</span>-closed if it is spanned as a vector space by products of elements of <span class="Math">A</span> of length at most <span class="Math">n</span>. As most known Majorana algebras are <span class="Math">2</span>-closed, the function <code class="func">MajoranaRepresentation</code> (<a href="chap3.html#X7F601CB47EBEAA6A"><span class="RefLink">3.1-1</span></a>) only attempts to construct the <span class="Math">2</span>-closed part.</p>
<p>If it is not successful then the output is a partial Majorana representation, i.e. a Majorana representation with some missing algebra products. In this case, the function <code class="func">MAJORANA_IsComplete</code> (<a href="chap4.html#X7B229A8480CD11D3"><span class="RefLink">4.2-1</span></a>) returns false.</p>
<p>If the user wishes, they may then pass this incomplete Majorana representation to the function <code class="func">NClosedMajoranaRepresentation</code> (<a href="chap3.html#X8155D0F98405BD1E"><span class="RefLink">3.2-1</span></a>) in order to attempt construction of the <span class="Math">3</span>-closed part. This process may then be repeated as many times as the user wishes.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ NClosedMajoranaRepresentation</code>( <var class="Arg">rep</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Takes as its input an incomplete Majorana representation rep that has been generated using the function <code class="func">MajoranaRepresentation</code> (<a href="chap3.html#X7F601CB47EBEAA6A"><span class="RefLink">3.1-1</span></a>). Again runs the main algorithm in order to attempt construction of the <span class="Math">3</span>-closed part of the algebra. If the function <codeclass="func">NClosedMajoranaRepresentation</code> is called <span class="Math">n</span> times on the same Majorana representation rep then this representation will be the <span class="Math">n + 2</span>-closed part of the algebra.</p>
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