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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} | 7243362ac+1449273bc+3720465c2+10081480ad+8973552bd+2367190cd+1354
     {-2} | 10347660b2+2556579bc+9066645c2+83469640ad-15912564bd-519230cd+680
     {-2} | 2012045ab-301119bc-1786365c2-6397220ad+8992452bd+649390cd-4257015
     {-2} | 72433620a2+6884724bc-7067970c2-88627160ad+11005176bd+11676280cd+9
     {-3} | 87012605442857619369513715109700c2d+52605190693777522531562261187
     {-3} | 191236495478807954658271901340bcd-558584243942961330074232217070a
     {-3} | 913632357150005003379894008651850c3-20328313748901208245352856444
     {-3} | 2007983202527483523911854964070bc2+506587756332497033261705317699
     {-4} | 792124592304322021784625925565019280364703450317253534127894364cd
     {-4} | 792124592304322021784625925565019280364703450317253534127894364bd
     {-4} | 1584249184608644043569251851130038560729406900634507068255788728a
     {-5} | d5                                                               
     ------------------------------------------------------------------------
     3005d2                                                                  
     0745d2                                                                  
     d2                                                                      
     509745d2                                                                
     9770ad2-517086577921821909378120397432947bd2-615335020961143417069338338
     d2+221747481213724762950361982727bd2+103620703448903889773910019480cd2+6
     531980ad2-27695378104839593707155836325926322bd2+30568518257907460272510
     0ad2+53622756244207696618857363373011bd2+8060683084999424201908791820615
     3+1819666828502765072805466320817285791920424307096778781024399893d4    
     3-378456355888878502612355920272171658593125366131511827323961025d4     
     d3-359452147815851511348910313194859324117001367312444537285137985d4    
                                                                             
     ------------------------------------------------------------------------
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     09230cd2+143205861705414277641860340652440d3       |
     4001728649822540009569945860d3                     |
     4739968745cd2+3520332073116936081148654706516040d3 |
     cd2-1733988083887646386213045382520d3              |
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             12       1
o2 : Matrix R   <--- R