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<head><title>sum(ChainComplexMap) -- direct sum of the components of a chain map</title>
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<div><h1>sum(ChainComplexMap) -- direct sum of the components of a chain map</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><span>Function: <a href="_sum.html" title="compute the sum">sum</a></span></li>
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<div class="single"><h2>Description</h2>
<div><tt>sum C</tt> -- yields the sum of the modules in a chain complex map.<p/>
The degrees of the components are preserved.<table class="examples"><tr><td><pre>i1 : R = ZZ/101[a..c];</pre>
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<tr><td><pre>i2 : C = 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 : sum C.dd
o3 = {0} | 0 a b c 0 0 0 0 |
{1} | 0 0 0 0 -b -c 0 0 |
{1} | 0 0 0 0 a 0 -c 0 |
{1} | 0 0 0 0 0 a b 0 |
{2} | 0 0 0 0 0 0 0 c |
{2} | 0 0 0 0 0 0 0 -b |
{2} | 0 0 0 0 0 0 0 a |
{3} | 0 0 0 0 0 0 0 0 |
8 8
o3 : Matrix R <--- R</pre>
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<tr><td><pre>i4 : betti oo
0 1
o4 = total: 8 8
-1: . 1
0: 1 3
1: 3 3
2: 3 1
3: 1 .
o4 : BettiTally</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_sum.html" title="compute the sum">sum</a> -- compute the sum</span></li>
<li><span><a href="_sum_lp__Chain__Complex_rp.html" title="direct sum of the components of a chain complex">sum(ChainComplex)</a> -- direct sum of the components of a chain complex</span></li>
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