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<head><title>Module _ List -- map from free module to some generators</title>
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<div><h1>Module _ List -- map from free module to some 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>M_p</tt></div>
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<li><span>Operator: <a href="__us.html" title="a binary operator, used for subscripting and access to elements">_</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="___Module.html">module</a></span>, or <span>an <a href="___Ideal.html">ideal</a></span></span></li>
<li><span><tt>p</tt>, <span>a <a href="___List.html">list</a></span>, of integers</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, a map from a free module to the module <tt>M</tt> which sends the basis vectors to the generators of <tt>M</tt> whose index numbers are listed.</span></li>
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<div class="single"><h2>Description</h2>
<div>If <tt>M</tt> is an ideal, then the map maps to <tt>module M</tt>.<table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : I = ideal vars R
o2 = ideal (x, y, z)
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : f = I_{0,2}
o3 = {1} | 1 0 |
{1} | 0 0 |
{1} | 0 1 |
o3 : Matrix</pre>
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<tr><td><pre>i4 : image f
o4 = image | x z |
1
o4 : R-module, submodule of R</pre>
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<tr><td><pre>i5 : M = image syz vars R
o5 = image {1} | -y 0 -z |
{1} | x -z 0 |
{1} | 0 y x |
3
o5 : R-module, submodule of R</pre>
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<tr><td><pre>i6 : g = M_{1}
o6 = {2} | 0 |
{2} | 1 |
{2} | 0 |
o6 : Matrix</pre>
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<tr><td><pre>i7 : source g
1
o7 = R
o7 : R-module, free, degrees {2}</pre>
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<tr><td><pre>i8 : target g
o8 = image {1} | -y 0 -z |
{1} | x -z 0 |
{1} | 0 y x |
3
o8 : R-module, submodule of R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_module_lp__Ideal_rp.html" title="turn an ideal into a module">module(Ideal)</a> -- turn an ideal into a module</span></li>
<li><span><a href="_generators_spof_spideals_spand_spmodules.html" title="">Module _ ZZ</a></span></li>
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