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<head><title>numgens(Ideal) -- number of generators of an ideal</title>
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<div><h1>numgens(Ideal) -- number of generators of an ideal</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 I</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>I</tt>, <span>an <a href="___Ideal.html">ideal</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 I</span></li>
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<div class="single"><h2>Description</h2>
<div>In Macaulay2, each ideal comes equipped with a matrix of generators. It is the number of columns of this matrix that is returned. If the ideal is homogeneous, 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 : I = ideal(a^2-b*d, a^2-b*d, c^2, d^2);
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : numgens I
o3 = 4</pre>
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In order to find a more efficient set of of generators, use <a href="_mingens.html" title="minimal generator matrix">mingens</a> or <a href="_trim.html" title="minimize generators and relations">trim</a>.<table class="examples"><tr><td><pre>i4 : mingens I
o4 = | d2 c2 a2-bd |
1 3
o4 : Matrix R <--- R</pre>
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<tr><td><pre>i5 : numgens trim I
o5 = 3</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_mingens.html" title="minimal generator matrix">mingens</a> -- minimal generator matrix</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="_generators.html" title="provide matrix or list of generators">generators</a> -- provide matrix or list of generators</span></li>
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