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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} | 46656ac+357084bc-67716c2+992304ad-307800bd+954360cd-42755d2      
     {-2} | 6200145b2-10219482bc-1209492c2+220752ad+14042160bd+13965840cd+890
     {-2} | 8817984ab-5180364bc+7629876c2-62956656ad+8628120bd-62337240cd-204
     {-2} | 33067440a2-27095292bc+24762348c2-83023920ad+55439640bd-87406200cd
     {-3} | 1435074749917101300398734595611620c2d-639784068983492892387173207
     {-3} | 159452749990789033377637177290180bcd+2585865499680902375464134571
     {-3} | 1435074749917101300398734595611620c3-1381545502125532108324174673
     {-3} | 1435074749917101300398734595611620bc2+307148393383775444178941824
     {-4} | 20990533909658725120019416343901357080919581047580545334643927898
     {-4} | 83962135638634900480077665375605428323678324190322181338575711592
     {-4} | 18658252364141088995572814527912317405261849820071595853016824798
     {-5} | d5                                                               
     ------------------------------------------------------------------------
                                                                             
     3615d2                                                                  
     9985d2                                                                  
     +320915d2                                                               
     8946058ad2-389444766536723178007532324777625bd2-680804208406388762402583
     24122ad2-139409590428268476754302495420975bd2+23489753404599711277785985
     8533384ad2-4542662497667387209080774659309385bd2-19704198401816326115907
     236264ad2-922476961484588873385887179540815bd2+1387357175100050220792743
     2cd3+45862420640563468059115874063294798852755914318798055025543446417d4
     8bd3+201957220862203288631097874981962575571344555100080219184237226627d
     4ad3-27323198597789987186309713533184113501890767897466256261521230675d4
                                                                             
     ------------------------------------------------------------------------
                                                          |
                                                          |
                                                          |
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     5428000185cd2-881583793226472198275558589483305d3    |
     0420665cd2-42646995935818897993483859834980d3        |
     275441629065cd2-3345418020012310382652803562263260d3 |
     4428190cd2-378141225440497863028175391181340d3       |
                                                          |
     4                                                    |
                                                          |
                                                          |

             12       1
o2 : Matrix R   <--- R