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<!DOCTYPE html> <html lang="en"> <head> <title>spechtModuleElement -- the constructor for the class SpechtModuleElement</title> <meta content="text/html; charset=utf-8" http-equiv="Content-Type"> <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css"> <link rel="stylesheet" href="../../../../Macaulay2/Style/katex/katex.min.css"> <script defer="defer" src="../../../../Macaulay2/Style/katex/katex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script> <script> var macros = { "\\break": "\\\\", "\\ZZ": "\\mathbb{Z}", "\\NN": "\\mathbb{N}", "\\QQ": "\\mathbb{Q}", "\\RR": "\\mathbb{R}", "\\CC": "\\mathbb{C}", "\\PP": "\\mathbb{P}" }, delimiters = [ { left: "$$", right: "$$", display: true}, { left: "\\[", right: "\\]", display: true}, { left: "$", right: "$", display: false}, { left: "\\(", right: "\\)", display: false} ], ignoredTags = [ "kbd", "var", "samp", "script", "noscript", "style", "textarea", "pre", "code", "option" ]; document.addEventListener("DOMContentLoaded", function() { renderMathInElement(document.body, { delimiters: delimiters, macros: macros, ignoredTags: ignoredTags, trust: true }); }); </script> <style>.katex { font-size: 1em; }</style> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/copy-tex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/render-a11y-string.min.js"></script> <script src="../../../../Macaulay2/Style/prism.js"></script> <script>var current_version = '1.25.06';</script> <script src="../../../../Macaulay2/Style/version-select.js"></script> <link type="image/x-icon" rel="icon" href="../../../../Macaulay2/Style/icon.gif"> </head> <body> <div id="buttons"> <div> <a href="https://macaulay2.com/">Macaulay2</a> <span id="version-select-container"></span> » <a title="Macaulay2 documentation" href="../../Macaulay2Doc/html/index.html">Documentation </a> <br><a href="../../Macaulay2Doc/html/_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="a package for constructing Specht Modules" href="index.html">SpechtModule</a> :: <a title="the constructor for the class SpechtModuleElement" href="_specht__Module__Element.html">spechtModuleElement</a></span> </div> <div class="right"> <form method="get" action="https://www.google.com/search"> <input placeholder="Search" type="text" name="q" value=""> <input type="hidden" name="q" value="site:macaulay2.com/doc"> </form> <a href="_specht__Polynomial_lp__Young__Tableau_cm__Polynomial__Ring_rp.html">next</a> | <a href="___Specht__Module__Element.html">previous</a> | <a href="_specht__Polynomial_lp__Young__Tableau_cm__Polynomial__Ring_rp.html">forward</a> | <a href="___Specht__Module__Element.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>spechtModuleElement -- the constructor for the class SpechtModuleElement</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">spechtModuleElement(p,v)</code></dd> <dd><code class="language-macaulay2">spechtModuleElement(y,n)</code></dd> <dd><code class="language-macaulay2">spechtModuleElement(y,m)</code></dd> <dd><code class="language-macaulay2">spechtModueElement(y)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">y</span>, <span>an instance of the type <a title="the class of Young Tableaux" href="___Young__Tableau.html">YoungTableau</a></span>, the label of the polytabloid</span></li> <li><span><span class="tt">n</span>, <span>an <a title="the class of all integers" href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, a number. If not specified then it is assumed to be a 1.</span></li> <li><span><span class="tt">m</span>, <span>a <a title="the class of all rational numbers" href="../../Macaulay2Doc/html/___Q__Q.html">rational number</a></span>, a number. If not specified then it is assumed to be a 1.</span></li> <li><span><span class="tt">p</span>, <span>an instance of the type <a title="a type of list representing a partition of a natural number" href="../../Macaulay2Doc/html/___Partition.html">Partition</a></span>, A partition that index a module</span></li> <li><span><span class="tt">v</span>, <span>a <a title="the class of all mutable hash tables" href="../../Macaulay2Doc/html/___Mutable__Hash__Table.html">mutable hash table</a></span>, A mutable hash table from a SpechtModuleElement </span></li> </ul> </li> <li>Outputs: <ul> <li><span><span>an instance of the type <a title="the class of Specht Module elements" href="___Specht__Module__Element.html">SpechtModuleElement</a></span>, an element of the form n*poly_y, where poly_y is the polytabloid labeled by the tableau y.</span></li> </ul> </li> </ul> <div> <h2>Description</h2> <div> <p>The basic constructor builds a SpechtModuleElement from just one polytabloid and its respective coefficient.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : p = new Partition from {3,2,1} o1 = Partition{3, 2, 1} o1 : Partition</code></pre> </td> </tr> <tr> <td> <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> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : spechtModuleElement(y,-2) o3 = -2 | 2 0 3 | | 4 5 | | 1 | o3 : SpechtModuleElement</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : spechtModuleElement(y) o4 = | 2 0 3 | | 4 5 | | 1 | o4 : SpechtModuleElement</code></pre> </td> </tr> </table> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">spechtModuleElement</span>:</h2> <ul> <li><kbd>spechtModuleElement(Partition,MutableHashTable)</kbd></li> <li><kbd>spechtModuleElement(YoungTableau)</kbd></li> <li><kbd>spechtModuleElement(YoungTableau,QQ)</kbd></li> <li><kbd>spechtModuleElement(YoungTableau,ZZ)</kbd></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="the constructor for the class SpechtModuleElement" href="_specht__Module__Element.html">spechtModuleElement</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">SpechtModule.m2:3305:0</span>.</p> </div> </div> </div> </body> </html>