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<head><title>transpose(ChainComplexMap) -- transpose a map of chain complexes</title>
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<div><h1>transpose(ChainComplexMap) -- transpose a map 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>transpose f</tt></div>
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<li><span>Function: <a href="_transpose.html" title="transpose a table or a matrix">transpose</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>
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<div class="single"><h2>Description</h2>
<div>The output of <tt>transpose</tt> is a map from the duals of the original source and target free modules. See the degree of the target module in the following example<table class="examples"><tr><td><pre>i1 : S = ZZ/10007[x,y,z];</pre>
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<tr><td><pre>i2 : F = res ideal vars S;</pre>
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<tr><td><pre>i3 : F.dd
1 3
o3 = 0 : S <------------- S : 1
| x y z |
3 3
1 : S <-------------------- S : 2
{1} | -y -z 0 |
{1} | x 0 -z |
{1} | 0 x y |
3 1
2 : S <-------------- S : 3
{2} | z |
{2} | -y |
{2} | x |
1
3 : S <----- 0 : 4
0
o3 : ChainComplexMap</pre>
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<tr><td><pre>i4 : transpose F.dd
1 3
o4 = -3 : S <------------------- S : -2
{-3} | z -y x |
3 3
-2 : S <-------------------- S : -1
{-2} | y -x 0 |
{-2} | z 0 -x |
{-2} | 0 z -y |
3 1
-1 : S <-------------- S : 0
{-1} | x |
{-1} | y |
{-1} | z |
o4 : ChainComplexMap</pre>
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Note that <tt>M2</tt> treats the differentials of a chain complex map as map of degree -1.</div>
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