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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} | 8515780ac+3115395bc+1399986c2-39402ad-2345256bd+1559556cd+896961d
     {-2} | 3649620b2+518850bc+824544c2+1043694ad+752328bd+1096884cd+1633879d
     {-2} | 4257890ab+10619825bc+2169510c2-958536ad+3689272bd-1519452cd-36218
     {-2} | 2128945a2-2964350bc-963340c2+1156926ad-27836bd+618168cd+1044927d2
     {-3} | 378877447070075393439599362248c2d+460985461098137411607237570971a
     {-3} | 315731205891729494532999468540bcd+27393757846684353174091003097ad
     {-3} | 210487470594486329688666312360c3-47877298569819489264573105667ad2
     {-3} | 315731205891729494532999468540bc2+45872814086764421344064405765ad
     {-4} | 3543551410330112955899072380335247903618703788660308028925cd3+331
     {-4} | 10630654230990338867697217141005743710856111365980924086775bd3-54
     {-4} | 3543551410330112955899072380335247903618703788660308028925ad3+153
     {-5} | d5                                                               
     ------------------------------------------------------------------------
     2                                                                       
     2                                                                       
     52d2                                                                    
                                                                             
     d2+491201035305474569185705712346bd2+713419881720864302668319312720cd2+4
     2+98303471314970664590453651310bd2-164965195613316047221592118712cd2-149
     +26588051739461141589734956518bd2+11227218195917197439473778700cd2-84173
     2-17250260340171497494726131066bd2+21833877422539014197704430924cd2+1109
     9203677646261612476160862692210090705125445817912468928d4               
     65768155873363355912090586567351512645686698174269943014d4              
     9648192592990193596041367370067111565684973991438534818d4               
                                                                             
     ------------------------------------------------------------------------
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     56204537461710336708751358706d3 |
     249452272881762767733118998d3   |
     192934020543766611156170d3      |
     38764259814323315584519358d3    |
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             12       1
o2 : Matrix R   <--- R