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<head><title>generators(GroebnerBasis) -- the generator matrix of a Gröbner basis</title>
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<div><h1>generators(GroebnerBasis) -- the generator matrix of a Gröbner basis</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 g</tt><br/><tt>gens g</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>g</tt>, <span>a <a href="___Groebner__Basis.html">Groebner basis</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>, whose columns are the generators of the Gröbner basis <tt>g</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>The following ideal defines a set of 18 points over the complex numbers. We compute a lexicographic Gröbner basis of the ideal.<table class="examples"><tr><td><pre>i1 : R = QQ[a..d, MonomialOrder=>Lex];</pre>
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<tr><td><pre>i2 : I = ideal(a^7-b-3, a*b-1, a*c^2-3, b*d-4);
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : gens gb I
o3 = | d8-49152d-65536 16384c2-3d7+147456 16384b-d7+49152 4a-d |
1 4
o3 : Matrix R <--- R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Gröbner_spbases.html" title="">Gröbner bases</a></span></li>
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