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Edit File: ___Labels.html

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    <title>Labels -- custom labels for irreducible characters</title>
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o1 = R

o1 : PolynomialRing</code></pre>
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              <pre><code class="language-macaulay2">i2 : D8 = { matrix{{x,y}},
            matrix{{-x,-y}},
            matrix{{-y,x}},
            matrix{{x,-y}},
            matrix{{y,x}} }

o2 = {| x y |, | -x -y |, | -y x |, | x -y |, | y x |}

o2 : List</code></pre>
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              <pre><code class="language-macaulay2">i3 : M = matrix {{1,1,1,1,1},
         {1,1,1,-1,-1},
         {1,1,-1,1,-1},
         {1,1,-1,-1,1},
         {2,-2,0,0,0}};

5       5
o3 : Matrix ZZ  &lt;-- ZZ</code></pre>
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              <pre><code class="language-macaulay2">i4 : T = characterTable({1,1,2,2,2},M,R,{1,2,3,4,5},
         Labels=>{&quot;triv&quot;,&quot;rho1&quot;,&quot;rho2&quot;,&quot;rho3&quot;,&quot;dim2&quot;})

o4 = Character table over R
      
           |  1   1   2   2   2
     ------+-------------------
     triv  |  1   1   1   1   1
     rho1  |  1   1   1  -1  -1
     rho2  |  1   1  -1   1  -1
     rho3  |  1   1  -1  -1   1
     dim2  |  2  -2   0   0   0

o4 : CharacterTable</code></pre>
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          <p>The same labels are automatically used when decomposing characters against a labeled character table.</p>
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              <pre><code class="language-macaulay2">i5 : A = action(R,D8)

o5 = PolynomialRing with 5 actors

o5 : ActionOnGradedModule</code></pre>
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              <pre><code class="language-macaulay2">i6 : c = character(A,0,8)

o6 = Character over R
      
     (0, {0}) => | 1 1 1 1 1 |
     (0, {1}) => | 2 -2 0 0 0 |
     (0, {2}) => | 3 3 -1 1 1 |
     (0, {3}) => | 4 -4 0 0 0 |
     (0, {4}) => | 5 5 1 1 1 |
     (0, {5}) => | 6 -6 0 0 0 |
     (0, {6}) => | 7 7 -1 1 1 |
     (0, {7}) => | 8 -8 0 0 0 |
     (0, {8}) => | 9 9 1 1 1 |

o6 : Character</code></pre>
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              <pre><code class="language-macaulay2">i7 : decomposeCharacter(c,T)

o7 = Decomposition table
      
               |  triv  rho1  rho2  rho3  dim2
     ----------+------------------------------
     (0, {0})  |     1     0     0     0     0
     (0, {1})  |     0     0     0     0     1
     (0, {2})  |     1     0     1     1     0
     (0, {3})  |     0     0     0     0     2
     (0, {4})  |     2     1     1     1     0
     (0, {5})  |     0     0     0     0     3
     (0, {6})  |     2     1     2     2     0
     (0, {7})  |     0     0     0     0     4
     (0, {8})  |     3     2     2     2     0

o7 : CharacterDecomposition</code></pre>
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          <p>The labels are stored in the character table under the key <span class="tt">Labels</span>.</p>
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        <h2>See also</h2>
        <ul>
          <li><span><a title="construct a character table" href="_character__Table.html">characterTable</a> -- construct a character table</span></li>
          <li><span><a title="decompose a character into irreducible characters" href="_decompose__Character.html">decomposeCharacter</a> -- decompose a character into irreducible characters</span></li>
        </ul>
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          <h2>Functions with optional argument named <span class="tt">Labels</span>:</h2>
          <ul>
            <li><kbd>characterTable(...,Labels=>...)</kbd></li>
          </ul>
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        <div class="waystouse">
          <h2>For the programmer</h2>
          <p>The object <a title="custom labels for irreducible characters" href="___Labels.html">Labels</a> is <span>a <a title="the class of all symbols" href="../../Macaulay2Doc/html/___Symbol.html">symbol</a></span>.</p>
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        <hr>
        <div class="waystouse">
          <p>The source of this document is in <span class="tt">BettiCharacters.m2:2846:0</span>.</p>
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