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<head><title>dual(ChainComplexMap) -- dual of a chain complex</title>
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<div><h1>dual(ChainComplexMap) -- dual of a chain 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>dual C</tt></div>
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<li><span>Function: <a href="_dual.html" title="dual module or map">dual</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>C</tt>, <span>a <a href="___Chain__Complex__Map.html">chain complex map</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Chain__Complex__Map.html">chain complex map</a></span>, the dual of the chain complex <tt>C</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = QQ[a..f]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : M = coker genericMatrix(R,a,2,3)
o2 = cokernel | a c e |
| b d f |
2
o2 : R-module, quotient of R</pre>
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<tr><td><pre>i3 : res M
2 3 1
o3 = R <-- R <-- R <-- 0
0 1 2 3
o3 : ChainComplex</pre>
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<tr><td><pre>i4 : dual oo
1 3 2
o4 = R <-- R <-- R
-2 -1 0
o4 : ChainComplex</pre>
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