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<head><title>inducedMap(Module,Module) -- compute the map induced by the identity</title>
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<div><h1>inducedMap(Module,Module) -- compute the map induced by the identity</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>inducedMap(M,N)</tt></div>
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<li><span>Function: <a href="_induced__Map.html" title="compute an induced map">inducedMap</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="___Module.html">module</a></span></span></li>
<li><span><tt>N</tt>, <span>a <a href="___Module.html">module</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, the homomorphism <tt>M <-- N</tt> induced by the identity.</span></li>
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<li><div class="single"><a href="_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_induced__Map_lp..._cm_sp__Degree_sp_eq_gt_sp..._rp.html">Degree => ...</a>, -- specify the degree of a map</span></li>
<li><span><a href="_induced__Map_lp..._cm_sp__Verify_sp_eq_gt_sp..._rp.html">Verify => ...</a>, </span></li>
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<div class="single"><h2>Description</h2>
<div>The modules <tt>M</tt> and <tt>N</tt> must both be <a href="_subquotient_spmodules.html" title="the way Macaulay2 represents modules">subquotient modules</a> of the same ambient free module <tt>F</tt>. If <tt>M = M1/M2</tt> and <tt>N = N1/N2</tt>, where <tt>M1</tt>, <tt>M2</tt>, <tt>N1</tt>, <tt>N2</tt> are all submodules of <tt>F</tt>, then return the map induced by <tt>F --> F</tt>. If the optional argument <tt>Verify</tt> is given, check that the result defines a well defined homomorphism.<p/>
In this example, we make the inclusion map between two submodules of <tt>R^3</tt>. M is defined by two elements and N is generated by one element in M<table class="examples"><tr><td><pre>i1 : R = ZZ/32003[x,y,z];</pre>
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<tr><td><pre>i2 : P = R^3;</pre>
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<tr><td><pre>i3 : M = image(x*P_{1}+y*P_{2} | z*P_{0})
o3 = image | 0 z |
| x 0 |
| y 0 |
3
o3 : R-module, submodule of R</pre>
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<tr><td><pre>i4 : N = image(x^4*P_{1} + x^3*y*P_{2} + x*y*z*P_{0})
o4 = image | xyz |
| x4 |
| x3y |
3
o4 : R-module, submodule of R</pre>
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<tr><td><pre>i5 : h = inducedMap(M,N)
o5 = {1} | x3 |
{1} | xy |
o5 : Matrix</pre>
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<tr><td><pre>i6 : source h == N
o6 = true</pre>
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<tr><td><pre>i7 : target h == M
o7 = true</pre>
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<tr><td><pre>i8 : ambient M == ambient N
o8 = true</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_induces__Well__Defined__Map.html" title="whether a map is well defined">inducesWellDefinedMap</a> -- whether a map is well defined</span></li>
<li><span><a href="_subquotient.html" title="make a subquotient module">subquotient</a> -- make a subquotient module</span></li>
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