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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} | 260931965ac+911943045bc-3324771156c2-638642340ad-519981000bd+8158
     {-2} | 44731194b2-44118045bc+351457218c2+31773315ad+66134159bd-80215275c
     {-2} | 260931965ab-170507250bc+4094496504c2+994385910ad+542165330bd+4298
     {-2} | 2348387685a2+793213380bc-9073528380c2-570102330ad-1121455370bd+32
     {-3} | 4313056767137408772810376723172600877276c2d+735973584818575133737
     {-3} | 10782641917843521932025941807931502193190bcd+11512674801516702106
     {-3} | 77635021808473357910586781017106815790968c3+617174712660586123448
     {-3} | 1437685589045802924270125574390866959092bc2-201643458617156820592
     {-4} | 19039197297955828987709546226401008806132650668422634849099118806
     {-4} | 19039197297955828987709546226401008806132650668422634849099118806
     {-4} | 19039197297955828987709546226401008806132650668422634849099118806
     {-5} | d5                                                               
     ------------------------------------------------------------------------
     7520cd-617498343d2                                                      
     d+74084808d2                                                            
     13510cd+820898274d2                                                     
     00456700cd-1509087216d2                                                 
     718530822575899592ad2+212879860077144274619717499106259847823bd2+6672557
     40083601366451791262ad2-3973562158579283238080502046796601712915bd2+9707
     2821106350482875437ad2+3800416678227004953807008114238561424616bd2+20578
     913453487425286417ad2-88995226989437300677608287674692523135bd2+34840983
     91558905cd3+268097170439891929196640531943806018305982087964570376725523
     91558905bd3+298290371149518208849321218807773358556767389606452305093379
     91558905ad3+549897078986199406834841869933918969388599620920839565253751
                                                                             
     ------------------------------------------------------------------------
                                                                             
                                                                             
                                                                             
                                                                             
     92768339511398826439777514988001cd2+735846197502674095385059241218698869
     050955848940238639003163636548615603cd2+58308234583718334720487251210461
     807480292443734778024399617048323718cd2+31450046315025785756105176038402
     1036057584164300015169976412625cd2-1501566791125482138993042004710950014
     57923302342d4                                                           
     725678870033d4                                                          
     840718466492d4                                                          
                                                                             
     ------------------------------------------------------------------------
                |
                |
                |
                |
     517d3      |
     3154621d3  |
     07471302d3 |
     71d3       |
                |
                |
                |
                |

             12       1
o2 : Matrix R   <--- R