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<head><title>map(Module,Module,RingElement) -- construct the map induced by multiplication by a ring element on the generators</title>
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<div><a href="_map.html" title="make a map">map</a> > <a href="_map_lp__Module_cm__Module_cm__Ring__Element_rp.html" title="construct the map induced by multiplication by a ring element on the generators">map(Module,Module,RingElement)</a></div>
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<div><h1>map(Module,Module,RingElement) -- construct the map induced by multiplication by a ring element on the generators</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>map(M,N,r)</tt></div>
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<li><span>Function: <a href="_map.html" title="make a map">map</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>, over the same ring <tt>R</tt> as <tt>M</tt>. An integer here stands for the free module of that rank.</span></li>
<li><span><tt>r</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span>, in the ring <tt>R</tt></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, The map induced by multiplication by <tt>r</tt> on the generators</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="_map_lp..._cm_sp__Degree_sp_eq_gt_sp..._rp.html">Degree => ...</a>, -- set the degree of a map</span></li>
<li><span><a href="_map_lp__Ring_cm__Ring_cm__Matrix_rp.html">DegreeLift => ...</a>, -- make a ring map</span></li>
<li><span><a href="_map_lp__Ring_cm__Ring_cm__Matrix_rp.html">DegreeMap => ...</a>, -- make a ring map</span></li>
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<div class="single"><h2>Description</h2>
<div>If <tt>r</tt> is not zero, then either <tt>M</tt> and <tt>N</tt> should be equal, or they should have the same number of generators. This gives the same map as r * map(M,N,1). map(M,N,1) is the map induced by the identity on the generators of M and N.<table class="examples"><tr><td><pre>i1 : R = QQ[x];</pre>
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<tr><td><pre>i2 : map(R^2,R^3,0)
o2 = 0
2 3
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : f = map(R^2,R^2,x)
o3 = | x 0 |
| 0 x |
2 2
o3 : Matrix R <--- R</pre>
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<tr><td><pre>i4 : f == x *map(R^2,R^2,1)
o4 = true</pre>
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<div class="single"><h2>Caveat</h2>
<div>If <tt>M</tt> or <tt>N</tt> is not free, then we don't check that the the result is a well defined homomorphism.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_induced__Map.html" title="compute an induced map">inducedMap</a> -- compute an induced map</span></li>
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