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<head><title>permanents -- ideal generated by square permanents of a matrix</title>
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<div><h1>permanents -- ideal generated by square permanents of a matrix</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>permanents(n,M)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>n</tt>, <span>an <a href="___Z__Z.html">integer</a></span>, the size of the permanents</span></li>
<li><span><tt>M</tt>, <span>a <a href="___Matrix.html">matrix</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>an <a href="___Ideal.html">ideal</a></span>, generated by the permanents of the <tt>n</tt> by <tt>n</tt> subpermanents of <tt>M</tt></span></li>
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<div class="single"><h2>Description</h2>
<div>The permanent of a square matrix <tt>N</tt> has the Laplace transform similar to the Laplace transform of the determinant of <tt>N</tt>: but all signs are positive. Permanents are used in combinatorics and in probability. They are computationally difficult.<table class="examples"><tr><td><pre>i1 : R = ZZ[a..f];</pre>
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<tr><td><pre>i2 : M = genericMatrix(R,a,2,3)
o2 = | a c e |
| b d f |
2 3
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : permanents(2,M)
o3 = ideal (b*c + a*d, b*e + a*f, d*e + c*f)
o3 : Ideal of R</pre>
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<div class="single"><h2>Caveat</h2>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_determinant.html" title="determinant of a matrix">determinant</a> -- determinant of a matrix</span></li>
<li><span><a href="_minors_lp__Z__Z_cm__Matrix_rp.html" title="ideal generated by minors">minors</a> -- ideal generated by minors</span></li>
<li><span><a href="_matrices.html" title="">matrices</a></span></li>
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<div class="waystouse"><h2>Ways to use <tt>permanents</tt> :</h2>
<ul><li>permanents(ZZ,Matrix)</li>
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