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      <h1>qdim -- Compute principal specialization of character or quantum dimension</h1>
      <ul>
        <li>
          <dl class="element">
            <dt>Usage: </dt>
            <dd><code class="language-macaulay2">qdim M</code></dd>
            <dd><code class="language-macaulay2">qdim(M,l)</code></dd>
          </dl>
        </li>
        <li>Inputs:          <ul>
            <li><span><span class="tt">M</span>, <span>an instance of the type <a title="class for Lie algebra modules" href="___Lie__Algebra__Module.html">LieAlgebraModule</a></span>, </span></li>
            <li><span><span class="tt">l</span>, <span>an <a title="the class of all integers" href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, </span></li>
          </ul>
        </li>
        <li>Outputs:          <ul>
            <li><span><span class="tt">P</span>, <span>a <a title="the class of all ring elements handled by the engine" href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, </span></li>
          </ul>
        </li>
      </ul>
      <div>
        <h2>Description</h2>
        <div>
          <p><span class="tt">qdim M</span> computes the principal specialization of the character of <span class="tt">M</span>. <span class="tt">qdim (M,l)</span> evaluates it modulo the appropriate cyclotomic polynomial, so that upon specialization of the variable $q$ to be the corresponding root of unity of smallest positive argument, it provides the quantum dimension of <span class="tt">M</span>.</p>
        </div>
        <table class="examples">
          <tr>
            <td>
              <pre><code class="language-macaulay2">i1 : g=simpleLieAlgebra(&quot;A&quot;,2)

o1 = g

o1 : simple LieAlgebra</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i2 : W=weylAlcove(g,3)

o2 = {{0, 0}, {0, 1}, {0, 2}, {0, 3}, {1, 0}, {1, 1}, {1, 2}, {2, 0}, {2, 1},
     ------------------------------------------------------------------------
     {3, 0}}

o2 : List</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i3 : L=LL_(1,1) (g)

o3 = L

o3 : irreducible LieAlgebraModule over g</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i4 : M=matrix table(W,W,(v,w)->fusionCoefficient(L,LL_v g,LL_w g,3))

o4 = | 0 0 0 0 0 1 0 0 0 0 |
     | 0 1 0 0 0 0 1 1 0 0 |
     | 0 0 1 0 1 0 0 0 1 0 |
     | 0 0 0 0 0 1 0 0 0 0 |
     | 0 0 1 0 1 0 0 0 1 0 |
     | 1 0 0 1 0 2 0 0 0 1 |
     | 0 1 0 0 0 0 1 1 0 0 |
     | 0 1 0 0 0 0 1 1 0 0 |
     | 0 0 1 0 1 0 0 0 1 0 |
     | 0 0 0 0 0 1 0 0 0 0 |

10       10
o4 : Matrix ZZ   &lt;-- ZZ</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i5 : first eigenvalues M

o5 = 2.999999999999997

o5 : CC (of precision 53)</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i6 : qdim L

4     2         -2    -4
o6 = q  + 2q  + 2 + 2q   + q

o6 : ZZ[q]</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i7 : qdim (L,3)

o7 = 3

ZZ[q]
o7 : -----------
      4    2
     q  - q  + 1</code></pre>
            </td>
          </tr>
        </table>
      </div>
      <div>
        <div class="waystouse">
          <h2>Ways to use <span class="tt">qdim</span>:</h2>
          <ul>
            <li><kbd>qdim(LieAlgebraModule)</kbd></li>
            <li><kbd>qdim(LieAlgebraModule,ZZ)</kbd></li>
          </ul>
        </div>
        <div class="waystouse">
          <h2>For the programmer</h2>
          <p>The object <a title="Compute principal specialization of character or quantum dimension" href="_qdim.html">qdim</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function.html">method function</a></span>.</p>
        </div>
        <hr>
        <div class="waystouse">
          <p>The source of this document is in <span class="tt">LieTypes.m2:2456:0</span>.</p>
        </div>
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