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groebnerBasis -- Gröbner basis, as a matrix

Synopsis

Description

i1 : R = QQ[a..d]

o1 = R

o1 : PolynomialRing
i2 : transpose groebnerBasis random(R^1,R^{4:-2})

o2 = {-2} | 1818348ac-28728bc-2116310c2-2159500ad+2638545bd+156620cd+2021670d
     {-2} | 129882b2+1001550bc-1542310c2+1642340ad+1108695bd+408920cd+745290d
     {-2} | 909174ab+1438002bc+29365c2+561862ad+3149580bd+344080cd+2564100d2 
     {-2} | 1818348a2-17919192bc+37555350c2-21176540ad-24602235bd-6376440cd-1
     {-3} | 110606399487116130068658265064035c2d+5918336605098557931521038291
     {-3} | 18961097054934193726055702582406bcd+48455514896509532641251360608
     {-3} | 9290937556917754925767294265378940c3+2843314056335588182494022063
     {-3} | 265455358769078712164779836153684bc2-5313398295416378387622169698
     {-4} | 90347099834545535614544082724948221549956933565702371651765cd3+60
     {-4} | 18069419966909107122908816544989644309991386713140474330353bd3+16
     {-4} | 72277679867636428491635266179958577239965546852561897321412ad3+10
     {-5} | d5                                                               
     ------------------------------------------------------------------------
     2                                                                       
     2                                                                       
                                                                             
     6114980d2                                                               
     4382ad2+122124327058142078055672061004985bd2-699342652776332162038347957
     544ad2+67079117852432871394415167313415bd2-17804316191841488544125319494
     813744ad2+4657422021851179715210000062341735bd2-202886977886860672984125
     39200ad2-2005956794273583265738875636751905bd2+8305156104083968948728027
     265167388552288986031388762336139969846055259960403830781d4             
     401116494616264771968931351399897049147149938626786314806d4             
     443018937623508748498409384422921379961862375486492488425d4             
                                                                             
     ------------------------------------------------------------------------
                                                       |
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     71540cd2+90104935481723419751719614720450d3       |
     480cd2+47788049078663761665248312673210d3         |
     987940180cd2+4403912258933605914570681292234290d3 |
     00354180cd2-1400845793332023651757035949849470d3  |
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             12       1
o2 : Matrix R   <--- R