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<head><title>ChainComplex _ ZZ -- component</title>
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<div><h1>ChainComplex _ ZZ -- component</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_i</tt></div>
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<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>C</tt>, <span>a <a href="___Chain__Complex.html">chain complex</a></span>, or <span>a <a href="___Graded__Module.html">graded module</a></span></span></li>
<li><span><tt>i</tt>, <span>an <a href="___Z__Z.html">integer</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 <tt>i</tt>-th component of <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[x,y,z]/(x^3,y^3,z^3,x*y*z);</pre>
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<tr><td><pre>i2 : C = res(coker vars R, LengthLimit=>8)
1 3 7 16 37 86 200 465 1081
o2 = R <-- R <-- R <-- R <-- R <-- R <-- R <-- R <-- R
0 1 2 3 4 5 6 7 8
o2 : ChainComplex</pre>
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<tr><td><pre>i3 : rank C_7
o3 = 465</pre>
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<tr><td><pre>i4 : C.dd_3
o4 = {2} | x 0 -z2 0 0 -xy 0 y2 0 0 0 0 0 xz2 xy2 0 |
{2} | -y 0 0 -z2 yz y2 0 0 0 0 x2 0 0 0 0 x2y |
{2} | z 0 0 0 0 0 0 0 0 -y2 0 x2 0 0 0 0 |
{3} | 0 z y x 0 0 0 0 0 0 0 0 0 0 0 0 |
{3} | 0 0 0 0 z y x 0 0 0 0 0 0 0 0 0 |
{3} | 0 0 0 0 0 0 0 z y x 0 0 0 0 0 0 |
{3} | 0 0 0 0 0 0 0 0 0 0 z y x 0 0 0 |
7 16
o4 : Matrix R <--- R</pre>
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<h2>Programming hint</h2>
The chain complex <tt>C</tt> is implemented as a hash table, but since the computation of a projective resolution can be stopped prematurely, Macaulay2 doesn't bother populating the hash table with the relevant free modules until explicitly requested by the user, for example, in response to the command <tt>C_i</tt> described above. The hash table <tt>C</tt> can be examined directly with code like <tt>C#i</tt>, but in order to populate the hash table completely, use <a href="_complete_lp__Chain__Complex_rp.html" title="complete the internal parts">complete(ChainComplex)</a>.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_resolution.html" title="projective resolution">resolution</a> -- projective resolution</span></li>
<li><span><a href="___Chain__Complex_sp^_sp__Z__Z.html" title="access member, cohomological degree">ChainComplex ^ ZZ</a> -- access member, cohomological degree</span></li>
<li><span><a href="___Chain__Complex__Map_sp_us_sp__Z__Z.html" title="component map">ChainComplexMap _ ZZ</a> -- component map</span></li>
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