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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} | 33619853610ac-10425426750bc+5091493092c2-3654018900ad-3729132540b
     {-2} | 2401418115b2-1141783110bc+109684344c2+1221776640ad+1877290830bd+2
     {-2} | 2241323574ab+3024196650bc+1061233502c2+1363664190ad+580349070bd-5
     {-2} | 747107858a2+315128895bc+14265888c2+173223540ad+110889828bd+580219
     {-3} | 85493143399825297576114811111460673653486c2d-16194938202699836633
     {-3} | 2035551033329173751812257407415730325083bcd+701376848929718393304
     {-3} | 1795356011396331249098411033340674146723206c3-5130110254628794064
     {-3} | 128239715099737946364172216667191010480229bc2+6684658877909592962
     {-4} | 62503615501076438920310740156102625851204487279725060708777462422
     {-4} | 31251807750538219460155370078051312925602243639862530354388731211
     {-4} | 31251807750538219460155370078051312925602243639862530354388731211
     {-5} | d5                                                               
     ------------------------------------------------------------------------
     d-1772502220cd+2247794955d2                                             
     802150560cd+9396220365d2                                                
     79499310cd-2917975095d2                                                 
     40cd+33275025d2                                                         
     229502003016699760330ad2+75179812168501228911065816910343895516115bd2+53
     4634085286910234427ad2+865412651307582158901295895476780971969bd2-132638
     368996846029635467436520ad2+859200737202660016820687006142834855061860bd
     4584586570180887518785ad2+24290152103390721952913188725003693508305bd2+1
     36681694cd3+797206854657839688238346995174335716479745767401032329412436
     18340847bd3-160244288920711471753687693399936056684356187545937245676296
     18340847ad3+115398489855205577076528308973910166882012013795100060121897
                                                                             
     ------------------------------------------------------------------------
                                                                             
                                                                             
                                                                             
                                                                             
     6834300019250305181606267341492895880090cd2+1897839523411138165760063173
     6783461854031986259610294474016370cd2-1681526574779508141943650716828641
     2+952077742720630926303524346917171808628915cd2+205727356045745545284720
     82807654460735358850166782545599021750875cd2+858189892649310260136825629
     7412553960609d4                                                         
     50863805081985d4                                                        
     7975608843568d4                                                         
                                                                             
     ------------------------------------------------------------------------
                           |
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     70532388805535d3      |
     321170d3              |
     4940909566938713700d3 |
     38497980032500d3      |
                           |
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             12       1
o2 : Matrix R   <--- R