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<head><title>gaussRing -- ring of gaussian correlations on n random variables</title>
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<div><h1>gaussRing -- ring of gaussian correlations on n random variables</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>gaussRing n</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>n</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, the number of random variables</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Ring.html">ring</a></span>, a ring with indeterminates s_(i,j), 1 <= i <= j <= n</span></li>
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<li><div class="single"><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><tt>CoefficientRing => </tt><span><span>default value QQ</span>, a coefficient field or ring</span></span></li>
<li><span><tt>Variable => </tt><span><span>default value s</span>, a symbol, the variables in the ring will be s_(1,1),...</span></span></li>
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<div class="single"><h2>Description</h2>
<div>The routines <tt>gaussMinors</tt> (missing documentation<!-- tag: gaussMinors -->), <a href="_gauss__Ideal.html" title="correlation ideal of a Bayesian network of joint Gaussian variables">gaussIdeal</a>, <tt>gaussTrekIdeal</tt> (missing documentation<!-- tag: gaussTrekIdeal -->) all require that the ring be created by this function.<p/>
<table class="examples"><tr><td><pre>i1 : R = gaussRing 5;</pre>
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<tr><td><pre>i2 : gens R
o2 = {s , s , s , s , s , s , s , s , s , s , s , s ,
1,1 1,2 1,3 1,4 1,5 2,2 2,3 2,4 2,5 3,3 3,4 3,5
------------------------------------------------------------------------
s , s , s }
4,4 4,5 5,5
o2 : List</pre>
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<tr><td><pre>i3 : genericSymmetricMatrix(R,5)
o3 = | s_(1,1) s_(1,2) s_(1,3) s_(1,4) s_(1,5) |
| s_(1,2) s_(2,2) s_(2,3) s_(2,4) s_(2,5) |
| s_(1,3) s_(2,3) s_(3,3) s_(3,4) s_(3,5) |
| s_(1,4) s_(2,4) s_(3,4) s_(4,4) s_(4,5) |
| s_(1,5) s_(2,5) s_(3,5) s_(4,5) s_(5,5) |
5 5
o3 : Matrix R <--- R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><tt>gaussMinors</tt> (missing documentation<!-- tag: gaussMinors -->)</span></li>
<li><span><a href="_gauss__Ideal.html" title="correlation ideal of a Bayesian network of joint Gaussian variables">gaussIdeal</a> -- correlation ideal of a Bayesian network of joint Gaussian variables</span></li>
<li><span><tt>gaussTrekIdeal</tt> (missing documentation<!-- tag: gaussTrekIdeal -->)</span></li>
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<div class="waystouse"><h2>Ways to use <tt>gaussRing</tt> :</h2>
<ul><li>gaussRing(ZZ)</li>
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