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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} | 8061560ac+120220212bc+78505800c2+29326920ad-9970338bd-7625415cd+1
     {-2} | 1410773b2+62421576bc+34500000c2-5528880ad+1036588bd-4764270cd+991
     {-2} | 14107730ab-670179972bc-422713320c2-45899910ad+36280279bd+24072405
     {-2} | 2418468a2-16428804bc-6730840c2+2634590ad+3457230bd+9477895cd-7869
     {-3} | 685036337995124437084157218189100712c2d+4744458883573763599606270
     {-3} | 57086361499593703090346434849091726bcd-23524034827427421514858825
     {-3} | 27401453519804977483366288727564028480c3-174854973789452831027834
     {-3} | 456690891996749624722771478792733808bc2+1787653541477575877668521
     {-4} | 19263375700551176319959100035567279308214441747158784064247326619
     {-4} | 57790127101653528959877300106701837924643325241476352192741979857
     {-4} | 57790127101653528959877300106701837924643325241476352192741979857
     {-5} | d5                                                               
     ------------------------------------------------------------------------
     3093500d2                                                               
     4240d2                                                                  
     cd-4757620d2                                                            
     330d2                                                                   
     78102692052ad2+190177854498490203938172290732851298bd2+15698446594810185
     685196630ad2-12897004246580106668359475125011087bd2-85611177846987686064
     855363696781680ad2+19010080398195862569948904031858981822bd2-11183341177
     480030043150ad2-194476345496914108911957030871150203bd2+1164569936632208
     1cd3-197508062951139571268026750816633105916114266233051355058078090856d
     3bd3+753433132345175079375874227019194519224750201905979853646994049310d
     3ad3+612548450429138363136302043289991883278314404416819931122790461533d
                                                                             
     ------------------------------------------------------------------------
                                                                             
                                                                             
                                                                             
                                                                             
     79437881270419875981cd2-1490737178406561824114346696241903296d3         
     795609133200695cd2+78690581399603351584362738946698240d3                
     7849896419065978170273889085cd2-31868881583230500098420781900180492540d3
     548429253754880416605cd2+305866345875520146670713174023044940d3         
     4                                                                       
     4                                                                       
     4                                                                       
                                                                             
     ------------------------------------------------------------------------
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             12       1
o2 : Matrix R   <--- R