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<head><title>ChainComplexMap _ ZZ = Thing -- install component of chain complex map</title>
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<div><h1>ChainComplexMap _ ZZ = Thing -- install component of chain complex map</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>f_i = g</tt></div>
</dd></dl>
</div>
</li>
<li><span>Operator: <a href="__us.html" title="a binary operator, used for subscripting and access to elements">_</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Chain__Complex__Map.html">chain complex map</a></span></span></li>
<li><span><tt>i</tt>, <span>an <a href="___Z__Z.html">integer</a></span></span></li>
<li><span><tt>g</tt>, <span>a <a href="___Thing.html">thing</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span>install <tt>g</tt> as the <tt>i</tt>-th module of the chain complex map <tt>f</tt></span></li>
</ul>
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</li>
</ul>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = ZZ[x..z]
o1 = R
o1 : PolynomialRing</pre>
</td></tr>
<tr><td><pre>i2 : C = chainComplex R
o2 = 0
o2 : ChainComplex</pre>
</td></tr>
<tr><td><pre>i3 : C.dd
o3 = 0
o3 : ChainComplexMap</pre>
</td></tr>
<tr><td><pre>i4 : C.dd_1 = vars R
o4 = | x y z |
1 3
o4 : Matrix R <--- R</pre>
</td></tr>
<tr><td><pre>i5 : C.dd_3 = transpose vars R
o5 = {-1} | x |
{-1} | y |
{-1} | z |
3 1
o5 : Matrix R <--- R</pre>
</td></tr>
<tr><td><pre>i6 : C.dd
1 3
o6 = 0 : R <------------- R : 1
| x y z |
3 3
1 : R <----- R : 2
0
3 1
2 : R <-------------- R : 3
{-1} | x |
{-1} | y |
{-1} | z |
o6 : ChainComplexMap</pre>
</td></tr>
<tr><td><pre>i7 : C
1 3 3 1
o7 = R <-- R <-- R <-- R
0 1 2 3
o7 : ChainComplex</pre>
</td></tr>
<tr><td><pre>i8 : HH C
o8 = 0 : cokernel | x y z |
1 : image {1} | -y 0 -z |
{1} | x -z 0 |
{1} | 0 y x |
2 : cokernel {-1} | x |
{-1} | y |
{-1} | z |
3 : image 0
o8 : GradedModule</pre>
</td></tr>
<tr><td><pre>i9 : prune HH C
o9 = 0 : cokernel | z y x |
1 : cokernel | z |
| x |
| -y |
2 : cokernel | x |
| y |
| z |
3 : 0
o9 : GradedModule</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Chain__Complex_sp_us_sp__Z__Z_sp_eq_sp__Thing.html" title="install component of chain complex">ChainComplex _ ZZ = Thing</a> -- install component of chain complex</span></li>
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