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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} | 10576860ac+55512060bc+10760561c2+5164446ad+3907050bd+5473380cd+28
     {-2} | 7051240b2-11848920bc-1689765c2+1702588ad-9258270bd-439820cd+31151
     {-2} | 1762810ab-5627160bc-1182783c2-277092ad-602730bd+249480cd-3830820d
     {-2} | 3525620a2+13285140bc+2898308c2-486546ad+21857100bd+43680cd+152834
     {-3} | 12433751152924105472217442668839437c2d-34953797522636231913473885
     {-3} | 7105000658813774555552824382193964bcd+228638578025508380385194358
     {-3} | 174072516140937476611044197363752118c3-43350988528965208920250406
     {-3} | 124337511529241054722174426688394370bc2+4895329239639938126006974
     {-4} | 92481560000587483084840806205734426689469348146745726966013194057
     {-4} | 12330874666744997744645440827431256891929246419566096928801759207
     {-4} | 30827186666862494361613602068578142229823116048915242322004398019
     {-5} | d5                                                               
     ------------------------------------------------------------------------
     089355d2                                                                
     40d2                                                                    
     2                                                                       
     5d2                                                                     
     069760078ad2-46719732331910849188019941315770690bd2-30601016484645222396
     7249588ad2+6647416665872754335654472340240208bd2+19873061359159334846407
     8948835616ad2+50879809603613692678354543476712020bd2+1482228164643896177
     6787478303ad2-48497305221535298876091937532871760bd2-1544659868299523339
     cd3-1964992953989381714274299190334705489197510237029476465816374359657d
     6bd3+18215362076824522213642153075088341246768865176870702144245001715d4
     ad3+201231038729078683824586177910198354602168019459989303737213946425d4
                                                                             
     ------------------------------------------------------------------------
                                                                  |
                                                                  |
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     406198480228650cd2+110567191619527183443161880006002330d3    |
     69261927292cd2-8757917175097889156277699583316429d3          |
     227728153987585940cd2+637253862703583141246843188380805035d3 |
     66817676858633995cd2+7739383310234843802067854245070720d3    |
     4                                                            |
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             12       1
o2 : Matrix R   <--- R