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<head><title>groebnerBasis -- Gröbner basis, as a matrix</title>
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<div><h1>groebnerBasis -- Gröbner basis, as a matrix</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>groebnerBasis x</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>x</tt></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, the matrix whose columns are the <a href="_generators.html" title="provide matrix or list of generators">generators</a> of the Gröbner basis of <tt>x</tt>, where <tt>x</tt> is any input acceptable to <a href="_gb.html" title="compute a Gröbner basis">gb</a></span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = QQ[a..d]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : transpose groebnerBasis random(R^1,R^{4:-2})
o2 = {-2} | 5172720ac+9112770bc+2434985c2+4608270ad-6378792bd+9150610cd-29081
{-2} | 591168b2-960970bc-329973c2-140166ad+2253384bd-1875930cd+632340d2
{-2} | 1034544ab+1994842bc+840805c2+380982ad-249480bd+2533930cd+344620d2
{-2} | 5172720a2+510370bc+993545c2+253422ad-4505928bd+6794130cd+10116300
{-3} | 10524943954418595084207199653110c2d+10594884246892386972632264952
{-3} | 3007126844119598595487771329460bcd-131250952677876334424422270161
{-3} | 184186519202325413973625993929425c3+24058826845531426773423380555
{-3} | 315748318632557852526215989593300bc2-1869466825568289850563542129
{-4} | 348880282654385144069596518845086296103721442271048634261756055cd
{-4} | 23258685510292342937973101256339086406914762818069908950783737bd3
{-4} | 69776056530877028813919303769017259220744288454209726852351211ad3
{-5} | d5
------------------------------------------------------------------------
940d2
d2
285ad2+1674490211969838014940007715826bd2+293566325971319223673152010868
5ad2+1905587899933851569007785517234bd2+1736812264172792464110717484955c
47645ad2-1964648497746148022164416189016902bd2+1355866617041620646670053
094485ad2+1414143830757233433203408810220942bd2-213198472964266401040163
3+202303810217212663812800618197891353796901783937570821276770484d4
+35130638967170529737455525240563074463728109352104722709947531d4
+24877972264561068524149689074549943247658972752030156593463216d4
------------------------------------------------------------------------
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95cd2+41778487833651593767105306329270d3 |
d2+528904256568740328294092908030d3 |
599979985cd2-1834393267989993185897191497190190d3 |
3594406235cd2-510278531754624944861910833933810d3 |
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12 1
o2 : Matrix R <--- R</pre>
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