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<head><title>buildSymmetricGB(PolynomialRing) -- Groebner basis of elementary symmetric polynomials algebra</title>
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<div><h1>buildSymmetricGB(PolynomialRing) -- Groebner basis of elementary symmetric polynomials algebra</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>buildSymmetricGB R</tt></div>
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<li><span>Function: <a href="_build__Symmetric__G__B.html" title="Groebner basis of elementary symmetric polynomials algebra">buildSymmetricGB</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>R</tt>, <span>a <a href="../../Macaulay2Doc/html/___Polynomial__Ring.html">polynomial ring</a></span>, a<a href="../../Macaulay2Doc/html/___Polynomial__Ring.html" title="the class of all ordered monoid rings">PolynomialRing</a></span></li>
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<li><div class="single">Outputs:<ul><li><span>the Groebner basis of the elementary symmetric algebra</span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : n=5;</pre>
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<tr><td><pre>i2 : R=QQ[x_1..x_n];</pre>
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<tr><td><pre>i3 : buildSymmetricGB R
5 4 3 2 4 3 3 2 2 2
o3 = {- x + x e - x e + x e - x e + e , x + x x - x e + x x - x x e
5 5 1 5 2 5 3 5 4 5 4 4 5 4 1 4 5 4 5 1
------------------------------------------------------------------------
2 3 2 4 3 2
+ x e + x x - x x e + x x e - x e + x - x e + x e - x e + e , -
4 2 4 5 4 5 1 4 5 2 4 3 5 5 1 5 2 5 3 4
------------------------------------------------------------------------
3 2 2 2 2 2
x - x x - x x + x e - x x - x x x + x x e - x x + x x e - x e
3 3 4 3 5 3 1 3 4 3 4 5 3 4 1 3 5 3 5 1 3 2
------------------------------------------------------------------------
3 2 2 2 3 2 2
- x - x x + x e - x x + x x e - x e - x + x e - x e + e , x +
4 4 5 4 1 4 5 4 5 1 4 2 5 5 1 5 2 3 2
------------------------------------------------------------------------
2 2
x x + x x + x x - x e + x + x x + x x - x e + x + x x - x e +
2 3 2 4 2 5 2 1 3 3 4 3 5 3 1 4 4 5 4 1
------------------------------------------------------------------------
2
x - x e + e , - x - x - x - x - x + e }
5 5 1 2 1 2 3 4 5 1
o3 : List</pre>
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<p>This function should work up to a size of 15 variables in the base ring</p>
<p>This function is part of the package SymmetricPolynomials.</p>
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