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<head><title>splitCharacter -- Decomposes a symmetric polynomial as a sum of schur functions</title>
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<div><h1>splitCharacter -- Decomposes a symmetric polynomial as a sum of schur functions</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>splitCharacter(c)</tt></div>
</dd></dl>
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</li>
<li><div class="single">Inputs:<ul><li><span><tt>c</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, A Symmetric polynomial</span></li>
</ul>
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</li>
<li><div class="single">Outputs:<ul><li><span><tt>p</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span></span></li>
</ul>
</div>
</li>
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<div class="single"><h2>Description</h2>
<div><div>Expresses a symmetric polynomial c as a linear combination of schur functions</div>
<table class="examples"><tr><td><pre>i1 : c=character({{1,1,1},{2}},4)
3 3 4 3 2 2 3 4 3 2 2 2 2 3 2
o1 = x x + x x x + 2x x x + 2x x x + x x x + 2x x x + 2x x x + 2x x x
0 1 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
------------------------------------------------------------------------
3 3 2 3 2 3 3 3 4 4 3 2 2 3
+ x x + 2x x x + 2x x x + x x + x x x + x x x + 2x x x + 2x x x
0 2 0 1 2 0 1 2 1 2 0 1 2 0 1 3 0 1 3 0 1 3
------------------------------------------------------------------------
4 4 3 2 2 3 4 3 2
+ x x x + x x x + 4x x x x + 5x x x x + 4x x x x + x x x + 2x x x
0 1 3 0 2 3 0 1 2 3 0 1 2 3 0 1 2 3 1 2 3 0 2 3
------------------------------------------------------------------------
2 2 2 2 3 2 2 3 3 2 3
+ 5x x x x + 5x x x x + 2x x x + 2x x x + 4x x x x + 2x x x +
0 1 2 3 0 1 2 3 1 2 3 0 2 3 0 1 2 3 1 2 3
------------------------------------------------------------------------
4 4 3 2 2 2 2 3 2 3 2 2 2
x x x + x x x + 2x x x + 2x x x + 2x x x + 2x x x + 5x x x x +
0 2 3 1 2 3 0 1 3 0 1 3 0 1 3 0 2 3 0 1 2 3
------------------------------------------------------------------------
2 2 3 2 2 2 2 2 2 2 2 2 3 2 3 2
5x x x x + 2x x x + 2x x x + 5x x x x + 2x x x + 2x x x + 2x x x
0 1 2 3 1 2 3 0 2 3 0 1 2 3 1 2 3 0 2 3 1 2 3
------------------------------------------------------------------------
3 3 2 3 2 3 3 3 2 3 3 2 3
+ x x + 2x x x + 2x x x + x x + 2x x x + 4x x x x + 2x x x +
0 3 0 1 3 0 1 3 1 3 0 2 3 0 1 2 3 1 2 3
------------------------------------------------------------------------
2 3 2 3 3 3 4 4 4
2x x x + 2x x x + x x + x x x + x x x + x x x
0 2 3 1 2 3 2 3 0 1 3 0 2 3 1 2 3
o1 : R</pre>
</td></tr>
<tr><td><pre>i2 : splitCharacter(c)
o2 = s + s
4,1,1 3,3
o2 : schurRing (s, 4)</pre>
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<div class="waystouse"><h2>Ways to use <tt>splitCharacter</tt> :</h2>
<ul><li>splitCharacter(RingElement)</li>
</ul>
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