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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} | 86400ac-2667636bc+1407700c2+6768720ad-64849050bd-88284945cd-54372
     {-2} | 504000b2-386244bc+139300c2+1028880ad-9144450bd-12144405cd-8160831
     {-2} | 1512000ab+1658484bc-265300c2-4873680ad+44991450bd+61290705cd+3964
     {-2} | 172800a2+4722156bc-2338700c2-11283120ad+109610550bd+148915095cd+9
     {-3} | 1184856579694986225278506847118100c2d+411912560841770932868439729
     {-3} | 5077956770121369536907886487649bcd-299750397280170989658924481300
     {-3} | 67706090268284927158771819835320c3+215662400561207467775649303866
     {-3} | 135412180536569854317543639670640bc2+9642870556878855851640753751
     {-4} | 19778620714537744920387764945710771389465941616801431760870046145
     {-4} | 19778620714537744920387764945710771389465941616801431760870046145
     {-4} | 39557241429075489840775529891421542778931883233602863521740092291
     {-5} | d5                                                               
     ------------------------------------------------------------------------
     339d2                                                                   
     d2                                                                      
     9491d2                                                                  
     1902069d2                                                               
     1437360ad2-40377042137877800144398822729587498bd2-5703077461531177154159
     0ad2+27831866477093761432060793793676bd2+3287383780781342720337808427635
     17200ad2-212275075412969189432602558523792868bd2-31194512130478118541018
     663120ad2-91467290061796215142047030856688146bd2-13495188389613654619454
     906675cd3+37508986762302598328844648888940673893403775730006653278924073
     906675bd3+99703127030065149935773509987764038915359044967634751099371988
     813350ad3-14696133771800463544763413278644843938810042635822526547298080
                                                                             
     ------------------------------------------------------------------------
                                                             |
                                                             |
                                                             |
                                                             |
     4155914209369cd2-33361153225827873988902468117587907d3  |
     8cd2+24361899063062410461637526016460d3                 |
     8470145581605cd2-174084889611611251871946072861865347d3 |
     2832572988703cd2-75419607756875629133325066142301689d3  |
     13782141d4                                              |
     09936832d4                                              |
     128129267d4                                             |
                                                             |

             12       1
o2 : Matrix R   <--- R