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<head><title>Hom(Matrix,Module) -- induced map on Hom modules</title>
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<div><h1>Hom(Matrix,Module) -- induced map on Hom modules</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>Hom(f,M)</tt><br/><tt>Hom(M,f)</tt></div>
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<li><span>Function: <a href="___Hom.html" title="module of homomorphisms">Hom</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, a map <tt>N1 --> N2</tt> of modules or <span>a <a href="___Chain__Complex.html">chain complex</a></span></span></li>
<li><span><tt>M</tt>, <span>a <a href="___Module.html">module</a></span>, over the same ring <tt>R</tt> as <tt>f</tt></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, either the map <tt>Hom_R(N2,M) --> Hom_R(N1,M)</tt> in the first case, or the map <tt>Hom_R(M,N1) --> Hom_R(M,N2)</tt> in the second case</span></li>
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<div class="single"><h2>Description</h2>
<div>If <tt>f</tt> is a map of chain complexes, then the result is a <span>a <a href="___Chain__Complex__Map.html">chain complex map</a></span>.<table class="examples"><tr><td><pre>i1 : R = QQ[a..d];</pre>
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<tr><td><pre>i2 : I = ideal(a*b,c*d);
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : J = I + ideal(a*d);
o3 : Ideal of R</pre>
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<tr><td><pre>i4 : f = inducedMap(module J,module I)
o4 = {2} | 1 0 |
{2} | 0 1 |
{2} | 0 0 |
o4 : Matrix</pre>
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<tr><td><pre>i5 : g = Hom(R^3,f)
o5 = {2} | 1 0 0 0 0 0 |
{2} | 0 1 0 0 0 0 |
{2} | 0 0 0 0 0 0 |
{2} | 0 0 1 0 0 0 |
{2} | 0 0 0 1 0 0 |
{2} | 0 0 0 0 0 0 |
{2} | 0 0 0 0 1 0 |
{2} | 0 0 0 0 0 1 |
{2} | 0 0 0 0 0 0 |
o5 : Matrix</pre>
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<tr><td><pre>i6 : ker g
o6 = image 0
3
o6 : R-module, submodule of R</pre>
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<tr><td><pre>i7 : image g
o7 = image | ab cd 0 0 0 0 |
| 0 0 ab cd 0 0 |
| 0 0 0 0 ab cd |
3
o7 : R-module, submodule of R</pre>
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<div class="single"><h2>Caveat</h2>
<div>Not all possible combinations are implemented yet</div>
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