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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} | 767190ac+913986bc-1967180c2-5467455ad+363690bd-5842032cd+3109428d
     {-2} | 26851650b2-40436568bc+181986640c2+406193445ad-8999550bd+449570436
     {-2} | 40277475ab-61344bc-2142680c2-25085340ad-5061420bd-21244692cd+2824
     {-2} | 8950550a2+17720802bc-63006610c2-125221005ad+7396200bd-144735199cd
     {-3} | 10172478622762701683883812518477663426c2d+22427031480384267270555
     {-3} | 10172478622762701683883812518477663426bcd+18780182249439047966702
     {-3} | 101724786227627016838838125184776634260c3-14046522794761784121327
     {-3} | 20344957245525403367767625036955326852bc2+63293785467086243853567
     {-4} | 15559547145408330790709423166894487325917084464184009043780158871
     {-4} | 77797735727041653953547115834472436629585422320920045218900794359
     {-4} | 38898867863520826976773557917236218314792711160460022609450397179
     {-5} | d5                                                               
     ------------------------------------------------------------------------
     2                                                                       
     cd-159091254d2                                                          
     6428d2                                                                  
     +41547996d2                                                             
     409934936195400ad2-5640722711966075948267817429301856094bd2+279591502669
     12793820716135ad2-13490840062502238283891859600954498070bd2+119654433658
     0575079125431065ad2+62437865739710743911664094814272255724bd2-3771455339
     14833159638255ad2+52704643122492191188704824950200201858bd2-378351323338
     8cd3-171108239718096738774588660668366416868570682102572869854616054827d
     bd3-14621825205820434922121561016504543591200758526367575006315745168d4 
     5ad3-140591608125492468065499568091544732587266363690728324889439245014d
                                                                             
     ------------------------------------------------------------------------
                                                                             
                                                                             
                                                                             
                                                                             
     71303178842350753528823909cd2-10682927812938598677253203090718433004d3  
     31981313686562771152363118cd2-2299052093707739329804352859958982592d3   
     47996188394626835847770734933cd2-128183135586067535353991163918419213628
     48461901526251481887978446cd2-11675368831118790790881790132836013164d3  
     4                                                                       
                                                                             
     4                                                                       
                                                                             
     ------------------------------------------------------------------------
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     d3 |
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             12       1
o2 : Matrix R   <--- R