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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} | 14660835ac+11426346bc-11087664c2+20495475ad+13561030bd+38179225cd
     {-2} | 29321670b2+22613040bc-1340024c2-17986640ad+8855210bd-13903085cd-4
     {-2} | 11728668ab+33195690bc+5658996c2-6453090ad+21160090bd+4752370cd-33
     {-2} | 14660835a2-49990275bc+18309480c2+18317285ad-30551290bd-5018125cd+
     {-3} | 140334841899616010370438429861318c2d-2099138230518477771178434611
     {-3} | 77963801055342227983576905478510bcd+43755340132279795124103456793
     {-3} | 4210045256988480311113152895839540c3+2177442703008810803324970344
     {-3} | 6315067885482720466669729343759310bc2-459680314155235989741487690
     {-4} | 51284852661083819590765342007171724831606779868820021938007702478
     {-4} | 20513941064433527836306136802868689932642711947528008775203080991
     {-4} | 51284852661083819590765342007171724831606779868820021938007702478
     {-5} | d5                                                               
     ------------------------------------------------------------------------
     +8557605d2                                                              
     365501d2                                                                
     80517d2                                                                 
     8435721d2                                                               
     42007ad2+172064933179151711470640338230244bd2-76287592440511844416081813
     573ad2-163808127925728210861886783215760bd2-1264112051120631193304729166
     343147ad2+12075334237621076624350663134803030bd2+14851652158343300869441
     3847208ad2+18596067835218600663777467843192480bd2+1315189934982917969027
     5cd3+756011038275964315779357288298118982311063011729197676077298064236d
     4bd3-297618953088504534746221096802530351538408028205486079705815965013d
     5ad3-786659385792751196380554777247616493337499943353243767125638748681d
                                                                             
     ------------------------------------------------------------------------
                                                          |
                                                          |
                                                          |
                                                          |
     740902cd2-86540468382267238072085849610480d3         |
     29712cd2+1789686669558484002673305156603d3           |
     563723197267cd2+1710824024898025505125472681501202d3 |
     9365021283462cd2-455975943195650534961574983988653d3 |
     4                                                    |
     4                                                    |
     4                                                    |
                                                          |

             12       1
o2 : Matrix R   <--- R