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<head><title>koszul(Matrix) -- the Koszul complex</title>
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<div><h1>koszul(Matrix) -- the Koszul complex</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>g = koszul f</tt></div>
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<li><span>Function: <a href="_koszul.html" title="Koszul complex or specific matrix in the Koszul complex">koszul</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, a <tt>1</tt> by <tt>n</tt> matrix</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>g</tt>, <span>a <a href="___Chain__Complex.html">chain complex</a></span>, the Koszul complex of the matrix <tt>f</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = QQ[x_1..x_4];</pre>
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<tr><td><pre>i2 : f = matrix{{x_1..x_4}}
o2 = | x_1 x_2 x_3 x_4 |
1 4
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : C = koszul f
1 4 6 4 1
o3 = R <-- R <-- R <-- R <-- R
0 1 2 3 4
o3 : ChainComplex</pre>
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<tr><td><pre>i4 : C.dd^2
1 6
o4 = 0 : R <----- R : 2
0
4 4
1 : R <----- R : 3
0
6 1
2 : R <----- R : 4
0
o4 : ChainComplexMap</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_eagon__Northcott_lp__Matrix_rp.html" title="Eagon-Northcott complex of a matrix of linear forms">eagonNorthcott</a> -- Eagon-Northcott complex of a matrix of linear forms</span></li>
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