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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} | 36075000ac-9758320bc-12634900c2+13808910ad+12643580bd+4860236cd-1
     {-2} | 30062500b2+19090760bc+15298200c2-22055880ad-54800940bd-16438548cd
     {-2} | 15031250ab+1696370bc+335900c2-5055435ad-4080280bd-6079876cd-17154
     {-2} | 60125000a2-4793880bc+86393400c2+210358440ad+280178220bd+234258324
     {-3} | 12988955857076280429969199642c2d+10695310696845141880101082683ad2
     {-3} | 64944779285381402149845998210bcd-170023296307168328113333454280ad
     {-3} | 519558234283051217198767985680c3+3375273507372788999426885386524a
     {-3} | 259779117141525608599383992840bc2+1193835307898463970960372159938
     {-4} | 217807134106675988918714619299726714195168560063425908cd3+3647547
     {-4} | 544517835266689972296786548249316785487921400158564770bd3-5424993
     {-4} | 272258917633344986148393274124658392743960700079282385ad3+6299977
     {-5} | d5                                                               
     ------------------------------------------------------------------------
     0877491d2                                                               
     +8165013d2                                                              
     19d2                                                                    
     cd+137921631d2                                                          
     -82754536984726473808381853bd2+9542392028564539324918656658cd2+152512253
     2-227376349644443358722956278315bd2-141433650082631169531614353233cd2-59
     d2+6687619159152078042159227827626bd2+3757465722471712611945758748468cd2
     ad2+1957079178798185486374231833022bd2+973683664768761018238031236278cd2
     810038730597577125362094864899265614787148160491d4                      
     481141867020569630676501043889441700269204540199d4                      
     73156393317042061326615933924808834000567098653d4                       
                                                                             
     ------------------------------------------------------------------------
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     88696072312695341180d3            |
     185191052526370794606084052d3     |
     +74762909062269898422657023855d3  |
     +403458001282528621123641841227d3 |
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             12       1
o2 : Matrix R   <--- R