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<head><title>ChainComplexMap ^ ZZ -- iterated composition</title>
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<div><h1>ChainComplexMap ^ ZZ -- iterated composition</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^n</tt></div>
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<li><span>Operator: <a href="_^.html" title="a binary operator, usually used for powers">^</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>, or a <span>a <a href="___Graded__Module__Map.html">graded module map</a></span></span></li>
<li><span><tt>n</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="___Chain__Complex__Map.html">chain complex map</a></span>, the composite <tt>f o f o ... o f</tt> (<tt>n</tt> times)</span></li>
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<div class="single"><h2>Description</h2>
<div>If <tt>f</tt> is a <a href="___Graded__Module__Map.html" title="the class of all maps between graded modules">GradedModuleMap</a>, then so is the result.<p/>
One use of this function is to determine if a chain complex is well-defined. The chain complex will be well-defined if the square of the differential is zero.<table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z];</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 : C.dd^2 == 0
o3 = true</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Chain__Complex.html" title="the class of all chain complexes">ChainComplex</a> -- the class of all chain complexes</span></li>
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