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<head><title>universalGroebnerBasis -- the union of all reduced Groebner bases of an ideal.</title>
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<div><h1>universalGroebnerBasis -- the union of all reduced Groebner bases 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>B = universalGroebnerBasis(I)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, of which to compute the universal Groebner basis</span></li>
<li><span><tt>Symmetries</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, of permutations of the variables leaving the ideal invariant. See <a href="_gfan.html" title="all initial ideals of an ideal">gfan</a>.</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>B</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, containing the polynomials that form the universal Groebner basis of <tt>I</tt>.</span></li>
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<li><div class="single"><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_universal__Groebner__Basis.html">Symmetries => ...</a>, -- the union of all reduced Groebner bases of an ideal.</span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = QQ[symbol x, symbol y, symbol z]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : I = ideal(x+y, y+z)
o2 = ideal (x + y, y + z)
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : universalGroebnerBasis(I)
LP algorithm being used: "cddgmp".
o3 = {x + y, x - z, y + z}
o3 : List</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_gfan.html" title="all initial ideals of an ideal">gfan</a> -- all initial ideals of an ideal</span></li>
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<div class="waystouse"><h2>Ways to use <tt>universalGroebnerBasis</tt> :</h2>
<ul><li>universalGroebnerBasis(Ideal)</li>
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