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Macaulay2Doc :: groebnerBasis

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} | 9420075ac+2337615bc-1992294c2+1687094ad+694116bd-1482663cd-551974
     {-2} | 565204500b2+451347120bc-552079872c2+488273672ad+435799008bd+85708
     {-2} | 141301125ab+24602760bc+105192144c2+7430456ad-6423516bd-82993512cd
     {-2} | 18840150a2-1671180bc+8743968c2-3204668ad-1377252bd+6625836cd+1322
     {-3} | 87910687370143024434917513905140c2d+78893882890985900843843471929
     {-3} | 3076874057955005855222112986679900bcd+448475511682289747901979276
     {-3} | 4102498743940007806962817315573200c3-1074498720062746768769756271
     {-3} | 55383733043190105393998033760238200bc2-24571858971856972094719146
     {-4} | 89919888394408864021923600657568217670476149526735483826407385961
     {-4} | 89919888394408864021923600657568217670476149526735483826407385961
     {-4} | 44959944197204432010961800328784108835238074763367741913203692980
     {-5} | d5                                                               
     ------------------------------------------------------------------------
     5d2                                                                     
     2156cd+5646154815d2                                                     
     -455663880d2                                                            
     4015d2                                                                  
     9307ad2+104979361656981965720882821939071bd2+219020238486555050152545197
     47652687ad2+19284179987663880104754118248900426bd2+158017107358935429925
     7882661ad2-471702005536830684266428460613378bd2-400445476730477593739702
     2211939004ad2-120083414690226518583147434596396167bd2-156967809786366181
     2032cd3+2102670437599780173361341383459702645961973101268089431706226250
     2032bd3-2156900403414467811703471288220390610869007426096093475112534010
     6016ad3-1628840472161603451182401775594893719198674325247869887519489459
                                                                             
     ------------------------------------------------------------------------
                                                                 |
                                                                 |
                                                                 |
                                                                 |
     746815cd2+120264288110512598511482514524775d3               |
     28890499926110cd2+12278117305850332543683004997815950d3     |
     9149518630cd2-2161795465435299146603742667033350d3          |
     981401773809630620cd2-56733226385392257846099656102536275d3 |
     513853d4                                                    |
     08645d4                                                     |
     05965d4                                                     |
                                                                 |

             12       1
o2 : Matrix R   <--- R