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<head><title>Hom(ChainComplex,ChainComplex) -- Create the homomorphism complex of a pair of chain complexes.</title>
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<div><h1>Hom(ChainComplex,ChainComplex) -- Create the homomorphism complex of a pair of chain complexes.</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>Hom(F,F)</tt></div>
</dd></dl>
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<li><span>Function: <a href="../../Macaulay2Doc/html/___Hom.html" title="module of homomorphisms">Hom</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>F</tt>, <span>a <a href="../../Macaulay2Doc/html/___Chain__Complex.html">chain complex</a></span>, </span></li>
<li><span><tt>G</tt>, <span>a <a href="../../Macaulay2Doc/html/___Chain__Complex.html">chain complex</a></span>, </span></li>
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<li><div class="single">Outputs:<ul><li><span>Hom(F,G)</span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = ZZ/101[a,b,c]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : kRes = res coker vars R
1 3 3 1
o2 = R <-- R <-- R <-- R <-- 0
0 1 2 3 4
o2 : ChainComplex</pre>
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<tr><td><pre>i3 : Hom(kRes,kRes)
1
o3 = 0 <-- image {-3} | 1 | <-- image {-2} | 1 0 0 0 0 0 | <-- image {-1} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {1} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {2} | 1 0 0 0 0 0 | <-- R <-- 0
{-2} | 0 1 0 0 0 0 | {-1} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {1} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | {2} | 0 1 0 0 0 0 |
-4 -3 {-2} | 0 0 1 0 0 0 | {-1} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {1} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | {2} | 0 0 1 0 0 0 | 3 4
{-2} | 0 0 0 1 0 0 | {-1} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {1} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | {2} | 0 0 0 1 0 0 |
{-2} | 0 0 0 0 1 0 | {-1} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {1} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | {2} | 0 0 0 0 1 0 |
{-2} | 0 0 0 0 0 1 | {-1} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {1} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | {2} | 0 0 0 0 0 1 |
{-1} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | {1} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |
-2 {-1} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | {1} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | 2
{-1} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | {1} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |
{-1} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | {1} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |
{-1} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | {1} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |
{-1} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | {1} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |
{-1} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | {1} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |
{-1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |
{-1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |
-1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | 1
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |
0
o3 : ChainComplex</pre>
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