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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} | 263006940ac-344640600bc-965900880c2+151254355ad-828358800bd+15891
     {-2} | 17533796b2+19039240bc+51712444c2+1007195ad+37406736bd+1216544cd-4
     {-2} | 13150347ab+24946920bc-1191960c2+5104645ad-1289640bd+10359468cd+44
     {-2} | 350675920a2+410000760bc+1374566760c2-94864385ad+1328183760bd-3133
     {-3} | 241614354540417215218456152974340c2d-1403078309797995516401703054
     {-3} | 1449686127242503291310736917846040bcd+155192276646217223816911870
     {-3} | 3624215318106258228276842294615100c3-2224549297032865859558902047
     {-3} | 10872645954318774684830526883845300bc2+73368829581832341341367591
     {-4} | 3128731979775847695842189454917763253467018269185920455691cd3+126
     {-4} | 2085821319850565130561459636611842168978012179457280303794bd3-794
     {-4} | 1042910659925282565280729818305921084489006089728640151897ad3-290
     {-5} | d5                                                               
     ------------------------------------------------------------------------
     8256cd+577843560d2                                                      
     295760d2                                                                
     12940d2                                                                 
     89216cd-746880120d2                                                     
     4235ad2+219638619125072950020419730576000bd2+483066254185735935892170985
     4358745ad2-1483722008646457190211238088780400bd2+20066710162980372716292
     415155ad2+2780033564884699732562011524610000bd2-426722055459651696990244
     40029155ad2-9659016305982518896384336866865200bd2+1321902127409188338093
     3987775477450763538346816730474240871917839480017979675d4               
     360155870095601884289887787720271908697564077331023415d4                
     330480814283310582262120757589432752266853339767926316d4                
                                                                             
     ------------------------------------------------------------------------
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     00128cd2-35443152485083867171315005731520d3           |
     48826998624cd2-551409849054946501253022187427160d3    |
     1202115806cd2+1362020919518723565349588608358790d3    |
     1959883595556cd2-3660962530005059880568515687987540d3 |
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             12       1
o2 : Matrix R   <--- R