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<head><title>numgens(Module) -- number of generators of a module</title>
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<div><h1>numgens(Module) -- number of generators of a module</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>numgens M</tt></div>
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<li><span>Function: <a href="_numgens.html" title="the number of generators">numgens</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>
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<li><div class="single">Outputs:<ul><li><span><span>an <a href="___Z__Z.html">integer</a></span>, number of generators of M</span></li>
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<div class="single"><h2>Description</h2>
<div>In Macaulay2, each module comes equipped with a matrix of generators. It is the number of columns of this matrix which is returned. If the module is graded, this may or may not be the number of minimal generators.<table class="examples"><tr><td><pre>i1 : R = QQ[a..d];</pre>
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<tr><td><pre>i2 : M = ker vars R
o2 = image {1} | -b 0 -c 0 0 -d |
{1} | a -c 0 0 -d 0 |
{1} | 0 b a -d 0 0 |
{1} | 0 0 0 c b a |
4
o2 : R-module, submodule of R</pre>
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<tr><td><pre>i3 : generators M
o3 = {1} | -b 0 -c 0 0 -d |
{1} | a -c 0 0 -d 0 |
{1} | 0 b a -d 0 0 |
{1} | 0 0 0 c b a |
4 6
o3 : Matrix R <--- R</pre>
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<tr><td><pre>i4 : numgens M
o4 = 6</pre>
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The number of generators of a free module is its rank.<table class="examples"><tr><td><pre>i5 : numgens R^10
o5 = 10</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_generators.html" title="provide matrix or list of generators">generators</a> -- provide matrix or list of generators</span></li>
<li><span><a href="_trim.html" title="minimize generators and relations">trim</a> -- minimize generators and relations</span></li>
<li><span><a href="_prune.html" title="prune, e.g., compute a minimal presentation">prune</a> -- prune, e.g., compute a minimal presentation</span></li>
<li><span><a href="_mingens.html" title="minimal generator matrix">mingens</a> -- minimal generator matrix</span></li>
<li><span><a href="_kernel.html" title="kernel of a ringmap, matrix, or chain complex">kernel</a> -- kernel of a ringmap, matrix, or chain complex</span></li>
<li><span><a href="_vars.html" title="variables">vars</a> -- variables</span></li>
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