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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} | 174281999ac+3577105bc+514399275c2-49064475ad-2201180bd+128571510c
     {-2} | 1045691994b2+31828615bc-441553665c2-12165885ad+284170950bd+423815
     {-2} | 1219973993ab+3623664030bc+20039554080c2+2248865540ad+282519420bd+
     {-2} | 18299609895a2+2552868220bc-27699328650c2+5122671060ad+545203500bd
     {-3} | 2489371429860300787841102000539156430925c2d-119670469880054795067
     {-3} | 165958095324020052522740133369277095395bcd+3839405728242531094629
     {-3} | 156830400081198949633989426033966855148275c3+47891053401480407684
     {-3} | 10455360005413263308932628402264457009885bc2-81868324532235231193
     {-4} | 10229159899437550947369646863899534416597615907828418941813574879
     {-4} | 34097199664791836491232156212998448055325386359428063139378582930
     {-4} | 10229159899437550947369646863899534416597615907828418941813574879
     {-5} | d5                                                               
     ------------------------------------------------------------------------
     d+427354478d2                                                           
     910cd-509577110d2                                                       
     5422637430cd+21084278628d2                                              
     -6209120400cd-23886883888d2                                             
     0306564368447464440ad2+325829645795713609679068219986813167244bd2-986911
     86180407200386115ad2-82661952410571557060125971701089761954bd2+183879805
     10570368080744008820ad2-23614213288314218279029169335027329424732bd2+154
     04496220479203852470ad2+12666001292417189190552545597260876593670bd2-348
     134793cd3+24962802137644775987326286200348254601369520050686126046978442
     44931bd3+279475174183664072753448522750385304001348832541532308869629029
     134793ad3-47462924737925815086959325996319919798940288149532315299601080
                                                                             
     ------------------------------------------------------------------------
                                                                             
                                                                             
                                                                             
                                                                             
     3864494063579616496145639914770cd2+2078926871738247243322470246234320916
     847287531081847310003805031464cd2+15715311246650413691597345574970893335
     409097685351262354010515275161321722210cd2-32395022550287806679353816163
     0352460181904190752255252675103714084cd2-2131675998390863603753638439515
     541384262d4                                                             
     8156850d4                                                               
     33642909d4                                                              
                                                                             
     ------------------------------------------------------------------------
                    |
                    |
                    |
                    |
     990d3          |
     6d3            |
     527376350420d3 |
     840308080d3    |
                    |
                    |
                    |
                    |

             12       1
o2 : Matrix R   <--- R