next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
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} | 6132060ac+960476bc+2691150c2+5213547ad+7138640bd+1880220cd-229482
     {-2} | 55746b2-52546bc-119820c2-379458ad-392260bd+296445cd+615486d2     
     {-2} | 2044020ab+84568bc-4898850c2-4386213ad+12606940bd-9866100cd-961818
     {-2} | 27873a2+29470bc+103782c2+179613ad-23240bd+7665cd-35910d2         
     {-3} | 298482864474344336108548950090c2d+332481760960016898502253815373a
     {-3} | 218887433947852513146269230066bcd+85428293814499179033814543369ad
     {-3} | 361164266013956646691344229608900c3+10989993718950248446192344509
     {-3} | 12038808867131888223044807653630bc2-24376293369275553876325021693
     {-4} | 1237386495363824196795455778020665015688831041360245816267cd3+876
     {-4} | 412462165121274732265151926006888338562943680453415272089bd3-8914
     {-4} | 1237386495363824196795455778020665015688831041360245816267ad3+130
     {-5} | d5                                                               
     ------------------------------------------------------------------------
     0d2                                                                     
                                                                             
     0d2                                                                     
                                                                             
     d2-112281261400457356014034959340bd2+243896672917087076107391977160cd2+1
     2-34568024345689101455331720670bd2-24167352179504123540941957250cd2+2889
     7191ad2+573387570792541031756673661104220bd2-102148777885589212193637340
     81ad2-77043838841073847695555320877370bd2+298173749865611371632762898209
     8474632982970470241526517235544639486507904366993526010d4               
     1308706944979396847483727853862316092427015202169704d4                  
     29887866944019178646342461481134424507228319319740189100d4              
                                                                             
     ------------------------------------------------------------------------
                                                     |
                                                     |
                                                     |
                                                     |
     29119140329913468851466518940d3                 |
     52592933430962969052127640d3                    |
     3141080cd2-1157595698248770786112490362692020d3 |
     85cd2+78902655405307334887770845392570d3        |
                                                     |
                                                     |
                                                     |
                                                     |

             12       1
o2 : Matrix R   <--- R