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Edit File: _SpechtModule__Element.html

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    <title>SpechtModuleElement -- the class of Specht Module elements</title>
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o1 = Partition{3, 2, 1}

o1 : Partition</code></pre>
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              <pre><code class="language-macaulay2">i2 : y = youngTableau(p,{2,0,3,4,5,1})

o2 = | 2 0 3 |
     | 4 5 |
     | 1 |

o2 : YoungTableau</code></pre>
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              <pre><code class="language-macaulay2">i3 : e = spechtModuleElement(y,-2)

o3 = -2 | 2 0 3 |
        | 4 5 |
        | 1 |

o3 : SpechtModuleElement</code></pre>
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          <p>More complex elements can be made by adding or subtracting previously build elements and multiplying by any element of the base field (which is assumed to be \mathbb{Q}).</p>
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              <pre><code class="language-macaulay2">i4 : y2 = youngTableau(p,{5,0,2,4,1,3})

o4 = | 5 0 2 |
     | 4 1 |
     | 3 |

o4 : YoungTableau</code></pre>
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              <pre><code class="language-macaulay2">i5 : e2 = spechtModuleElement(y2)

o5 = | 5 0 2 |
     | 4 1 |
     | 3 |

o5 : SpechtModuleElement</code></pre>
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              <pre><code class="language-macaulay2">i6 : e+e2

o6 = -2 | 2 0 3 | + | 5 0 2 |
        | 4 5 |     | 4 1 |
        | 1 |       | 3 |

o6 : SpechtModuleElement</code></pre>
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              <pre><code class="language-macaulay2">i7 : e-e2

o7 = -2 | 2 0 3 | - | 5 0 2 |
        | 4 5 |     | 4 1 |
        | 1 |       | 3 |

o7 : SpechtModuleElement</code></pre>
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              <pre><code class="language-macaulay2">i8 : 3*oo

o8 = -6 | 2 0 3 | - 3 | 5 0 2 |
        | 4 5 |       | 4 1 |
        | 1 |         | 3 |

o8 : SpechtModuleElement</code></pre>
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          <p>The element SpechtModuleElement is implemented as a MutableHashTable. The keys are the filling of the tableaux that label the polytabloids and they point to their respective coefficients</p>
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              <pre><code class="language-macaulay2">i9 : peek oo

o9 = SpechtModuleElement{partition => Partition{3, 2, 1}    }
                         values => MutableHashTable{...2...}</code></pre>
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              <pre><code class="language-macaulay2">i10 : peek ooo#values

o10 = MutableHashTable{{2, 0, 3, 4, 5, 1} => -6}
                       {5, 0, 2, 4, 1, 3} => -3</code></pre>
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          <p>The method terms is used to retrieve the polytabloid with their respective coefficient. This is given as a list of pairs of tableaux and coefficients.</p>
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              <pre><code class="language-macaulay2">i11 : terms (3*(e-e2))

o11 = {(| 2 0 3 |, -6), (| 5 0 2 |, -3)}
        | 4 5 |          | 4 1 |
        | 1 |            | 3 |

o11 : List</code></pre>
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          <p>A method was implemented to apply a permutation to a SpechtModuleElement. The action is defined by permuting the entries of the tableaux that label the polytabloids.</p>
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              <pre><code class="language-macaulay2">i12 : {0,1,2,3,4,5} (3*(e-e2))

o12 = -6 | 2 0 3 | - 3 | 5 0 2 |
         | 4 5 |       | 4 1 |
         | 1 |         | 3 |

o12 : SpechtModuleElement</code></pre>
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              <pre><code class="language-macaulay2">i13 : {1,0,2,3,4,5} (3*(e-e2))

o13 = -6 | 2 1 3 | - 3 | 5 1 2 |
         | 4 5 |       | 4 0 |
         | 0 |         | 3 |

o13 : SpechtModuleElement</code></pre>
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        <h2>See also</h2>
        <ul>
          <li><span><a title="the constructor for the class SpechtModuleElement" href="_specht__Module__Element.html">spechtModuleElement</a> -- the constructor for the class SpechtModuleElement</span></li>
        </ul>
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        <div class="waystouse">
          <h2>Functions and methods returning an object of class SpechtModuleElement:</h2>
          <ul>
            <li><span><a title="an algorithm for expressing any polytabloid as linear combinations of standard polytabloids" href="_straightening__Algorithm.html">straighteningAlgorithm</a> -- an algorithm for expressing any polytabloid as linear combinations of standard polytabloids</span></li>
          </ul>
          <h2>Methods that use an object of class SpechtModuleElement:</h2>
          <ul>
            <li><span><a title="a method for sorting the columns of the tableaux in a SpechtModuleElement" href="_sort__Columns__Tableau_lp__Specht__Module__Element_rp.html">sortColumnsTableau(SpechtModuleElement)</a> -- a method for sorting the columns of the tableaux in a SpechtModuleElement</span></li>
            <li><kbd>List SpechtModuleElement</kbd></li>
            <li><kbd>net(SpechtModuleElement)</kbd></li>
            <li><kbd>QQ * SpechtModuleElement</kbd></li>
            <li><kbd>SpechtModuleElement + SpechtModuleElement</kbd></li>
            <li><kbd>SpechtModuleElement - SpechtModuleElement</kbd></li>
            <li><kbd>terms(SpechtModuleElement)</kbd></li>
            <li><kbd>trim(SpechtModuleElement)</kbd></li>
            <li><kbd>ZZ * SpechtModuleElement</kbd></li>
            <li><span><kbd>straighteningAlgorithm(SpechtModuleElement)</kbd> -- see <span><a title="an algorithm for expressing any polytabloid as linear combinations of standard polytabloids" href="_straightening__Algorithm.html">straighteningAlgorithm</a> -- an algorithm for expressing any polytabloid as linear combinations of standard polytabloids</span></span></li>
          </ul>
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          <h2>For the programmer</h2>
          <p>The object <a title="the class of Specht Module elements" href="___Specht__Module__Element.html">SpechtModuleElement</a> is <span>a <a title="the class of all mutable types" href="../../Macaulay2Doc/html/___Type.html">type</a></span>, with ancestor classes <a title="the class of all hash tables" href="../../Macaulay2Doc/html/___Hash__Table.html">HashTable</a> &lt; <a title="the class of all things" href="../../Macaulay2Doc/html/___Thing.html">Thing</a>.</p>
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        <div class="waystouse">
          <p>The source of this document is in <span class="tt">SpechtModule.m2:3305:0</span>.</p>
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Edit File: ___Specht__Module__Element.html

Edit File: _SpechtModule__Element.html