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<head><title>generators(Ideal) -- the generator matrix of an ideal</title>
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<div><h1>generators(Ideal) -- the generator matrix 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>generators I</tt><br/><tt>gens I</tt></div>
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<li><span>Function: <a href="_generators.html" title="provide matrix or list of generators">generators</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>a <a href="___Matrix.html">matrix</a></span>, the one-row matrix whose entries are the generators of <tt>I</tt></span></li>
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<li><div class="single"><a href="_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><tt>CoefficientRing => </tt><span><span>default value null</span>, unused option</span></span></li>
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<div class="single"><h2>Description</h2>
<div>Each ideal in <em>Macaulay2</em> comes equipped with a one-row matrix with the generators of the ideal. It is this matrix that is returned.<table class="examples"><tr><td><pre>i1 : R = ZZ/101[a,b,c];</pre>
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<tr><td><pre>i2 : I = ideal(a^2,a*b-2,c^4,a*c-1,a*c-1)
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o2 = ideal (a , a*b - 2, c , a*c - 1, a*c - 1)
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : generators I
o3 = | a2 ab-2 c4 ac-1 ac-1 |
1 5
o3 : Matrix R <--- R</pre>
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To obtain a list of generators, rather than a matrix, use<table class="examples"><tr><td><pre>i4 : first entries generators I
2 4
o4 = {a , a*b - 2, c , a*c - 1, a*c - 1}
o4 : List</pre>
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If you want to remove unnecessary generators, use <a href="_trim.html" title="minimize generators and relations">trim</a>.<table class="examples"><tr><td><pre>i5 : I = trim I
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o5 = ideal (a*c - 1, a*b - 2, a , c )
o5 : Ideal of R</pre>
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<tr><td><pre>i6 : gens I
o6 = | ac-1 ab-2 a2 c4 |
1 4
o6 : Matrix R <--- R</pre>
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