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<head><title>chainComplex(List) -- make a chain complex</title>
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<div><h1>chainComplex(List) -- make 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>C = chainComplex{f1,f2,f3,...}</tt><br/><tt>C = chainComplex(f1,f2,f3,...)</tt></div>
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<li><span>Function: <a href="_chain__Complex.html" title="make a chain complex">chainComplex</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>f1,f2,f3,...</tt>, homomorphisms over the same ring, forming a complex</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>C</tt>, <span>a <a href="___Chain__Complex.html">chain complex</a></span>, the given complex, where <tt>f1 == C.dd_1</tt>, <tt>f2 == CC.dd_2</tt>, etc.</span></li>
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<div class="single"><h2>Description</h2>
<div>The maps f1, f2, ... must be defined over the same base ring, and they must form a complex: the target of f(i+1) is the source of fi.<p/>
The following example illustrates how chainComplex adjusts the degrees of the modules involved to ensure that sources and targets of the differentials correspond exactly.<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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We check that that this is a complex:<table class="examples"><tr><td><pre>i3 : C.dd^2 == 0
o3 = true</pre>
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The homology of this complex:<table class="examples"><tr><td><pre>i4 : HH C
o4 = 0 : cokernel | x y |
1 : subquotient ({1} | -y |, {1} | xy |)
{1} | x | {1} | -x2 |
2 : image 0
o4 : GradedModule</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_chain_spcomplexes.html" title="">chain complexes</a></span></li>
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