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<head><title>straighten -- computes straightening of a tableau</title>
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<div><h1>straighten -- computes straightening of a tableau</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>straighten(t)straighten(t, h)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>t</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, a tableau to straighten; a tableau looks like {{3,4}, {1,2}} for example, where we list the entries from left to right, top to bottom</span></li>
<li><span><tt>h</tt>, <span>a <a href="../../Macaulay2Doc/html/___Mutable__Hash__Table.html">mutable hash table</a></span>, where the answers should be stored</span></li>
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<li><div class="single">Consequences:<ul><li>If provided, the hashtable h is updated with any calculations which are performed as a result of calling this function. </li>
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<div class="single"><h2>Description</h2>
<div>If a hashtable h is provided, then this outputs nothing, it simply just modifies h. When looking up values, remember that the keys are stored with rows weakly increasing. If no hashtable is provided, then the user is simply given the straightening of the tableau in terms of semistandard tableaux. The answer is in the form a hashtable: each key is a semistandard tableaux, and the value of the key is the coefficient of that semistandard tableaux used to write the input t as a linear combination. <table class="examples"><tr><td><pre>i1 : h = new MutableHashTable from {}
o1 = MutableHashTable{}
o1 : MutableHashTable</pre>
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<tr><td><pre>i2 : straighten({{3,4}, {1,2}}, h)</pre>
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<tr><td><pre>i3 : h#{{3,4}, {1,2}} -- get the coefficients
o3 = HashTable{{{1, 2}, {3, 4}} => 1}
o3 : HashTable</pre>
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<tr><td><pre>i4 : straighten({{3,4}, {1,2}}) -- just get the answer instead
o4 = HashTable{{{1, 2}, {3, 4}} => 1}
o4 : HashTable</pre>
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<div class="waystouse"><h2>Ways to use <tt>straighten</tt> :</h2>
<ul><li>straighten(List)</li>
<li>straighten(List,MutableHashTable)</li>
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