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<head><title>HH_ZZ ChainComplex -- homology of a chain complex</title>
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<div><h1>HH_ZZ ChainComplex -- homology 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>HH_i C</tt></div>
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<li><span>Function: <a href="_homology.html" title="general homology functor">homology</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>i</tt>, <span>an <a href="___Z__Z.html">integer</a></span></span></li>
<li><span><tt>C</tt>, <span>a <a href="___Chain__Complex.html">chain complex</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Module.html">module</a></span>, the homology at the i-th spot 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 = ZZ/101[x,y]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : C = chainComplex(matrix{{x,y}},matrix{{x*y},{-x^2}})
1 2 1
o2 = R <-- R <-- R
0 1 2
o2 : ChainComplex</pre>
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<tr><td><pre>i3 : M = HH_1 C
o3 = subquotient ({1} | -y |, {1} | xy |)
{1} | x | {1} | -x2 |
2
o3 : R-module, subquotient of R</pre>
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<tr><td><pre>i4 : prune M
o4 = cokernel {2} | x |
1
o4 : R-module, quotient of R</pre>
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