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<head><title>inversePermutation -- inverse permutation</title>
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<div><h1>inversePermutation -- inverse permutation</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>y = inversePermutation x</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>x</tt>, <span>a <a href="___List.html">list</a></span>, a list of length <tt>n</tt> whose elements are the numbers 0, 1, 2, ..., <tt>n-1</tt>, in some order, representing the permutation defined by sending <tt>i</tt> to <tt>x#i</tt></span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>y</tt>, <span>a <a href="___List.html">list</a></span>, the list representing the inverse permutation of <tt>x</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : x = {1,2,3,4,5,0}
o1 = {1, 2, 3, 4, 5, 0}
o1 : List</pre>
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<tr><td><pre>i2 : y = inversePermutation x
o2 = {5, 0, 1, 2, 3, 4}
o2 : List</pre>
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<tr><td><pre>i3 : all(#x, i -> x#(y#i) == i)
o3 = true</pre>
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<tr><td><pre>i4 : all(#x, i -> y#(x#i) == i)
o4 = true</pre>
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<p>We compose permutations with <tt>_</tt>; see <tt>(symbol _, VisibleList, List)</tt> (missing documentation<!-- tag: (symbol _, VisibleList, List) -->).</p>
<table class="examples"><tr><td><pre>i5 : x_x_x
o5 = {3, 4, 5, 0, 1, 2}
o5 : List</pre>
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<tr><td><pre>i6 : x_x_x_x_x_x
o6 = {0, 1, 2, 3, 4, 5}
o6 : List</pre>
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<tr><td><pre>i7 : x_y
o7 = {0, 1, 2, 3, 4, 5}
o7 : List</pre>
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<tr><td><pre>i8 : y_x
o8 = {0, 1, 2, 3, 4, 5}
o8 : List</pre>
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