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<head><title>id -- identity map</title>
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<div><h1>id -- identity map</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>id_F</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>F</tt>, <span>a <a href="___Ring.html">ring</a></span>, <span>a <a href="___Module.html">module</a></span>, or <span>a <a href="___Chain__Complex.html">chain complex</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Ring__Map.html">ring map</a></span>, <span>a <a href="___Matrix.html">matrix</a></span>, or <span>a <a href="___Chain__Complex__Map.html">chain complex map</a></span> the identity map on <tt>F</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = QQ[a..d];</pre>
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<tr><td><pre>i2 : id_R
o2 = map(R,R,{a, b, c, d})
o2 : RingMap R <--- R</pre>
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<tr><td><pre>i3 : id_(R^3)
o3 = | 1 0 0 |
| 0 1 0 |
| 0 0 1 |
3 3
o3 : Matrix R <--- R</pre>
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<tr><td><pre>i4 : C = res coker vars R
1 4 6 4 1
o4 = R <-- R <-- R <-- R <-- R <-- 0
0 1 2 3 4 5
o4 : ChainComplex</pre>
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<tr><td><pre>i5 : id_C
1 1
o5 = 0 : R <--------- R : 0
| 1 |
4 4
1 : R <------------------- R : 1
{1} | 1 0 0 0 |
{1} | 0 1 0 0 |
{1} | 0 0 1 0 |
{1} | 0 0 0 1 |
6 6
2 : R <----------------------- R : 2
{2} | 1 0 0 0 0 0 |
{2} | 0 1 0 0 0 0 |
{2} | 0 0 1 0 0 0 |
{2} | 0 0 0 1 0 0 |
{2} | 0 0 0 0 1 0 |
{2} | 0 0 0 0 0 1 |
4 4
3 : R <------------------- R : 3
{3} | 1 0 0 0 |
{3} | 0 1 0 0 |
{3} | 0 0 1 0 |
{3} | 0 0 0 1 |
1 1
4 : R <------------- R : 4
{4} | 1 |
5 : 0 <----- 0 : 5
0
o5 : ChainComplexMap</pre>
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<div class="waystouse"><h2>Ways to use <tt>id</tt> :</h2>
<ul><li>id _ ChainComplex</li>
<li>id _ Module</li>
<li>id _ Ring</li>
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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="_id.html" title="identity map">id</a> is <span>a <a href="___Scripted__Functor.html">scripted functor</a></span>.</p>
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