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} | 11461170ac+36572760bc+2018205c2+7340865ad+9412256bd-1571220cd-561
     {-2} | 10315053b2-22276590bc+7857180c2+5009970ad-156746bd-216090cd+33965
     {-2} | 206301060ab-262179960bc+439357140c2+369134535ad+150646624bd-12341
     {-2} | 103150530a2+342788460bc-209896695c2-213372075ad-73971232bd+202111
     {-3} | 12932774635266687444183669036120c2d-13413396668511758900768924698
     {-3} | 36211768978746724843714273301136bcd-38444023288304533287644471009
     {-3} | 543176534681200872655714099517040c3-11415116077197836903296871047
     {-3} | 1086353069362401745311428199034080bc2+378030647726238676995430870
     {-4} | 2827283993611795425852153448307961749172516177560798750066276653c
     {-4} | 19790987955282567980965074138155732244207613242925591250463936571
     {-4} | 19790987955282567980965074138155732244207613242925591250463936571
     {-5} | d5                                                               
     ------------------------------------------------------------------------
     66120d2                                                                 
     820d2                                                                   
     9520cd-708504480d2                                                      
     560cd+894293640d2                                                       
     6395ad2+454564958070192267017490565710112bd2+487778396096439607546122916
     7195ad2+1096094763141411893837866710424352bd2+13188336373262315291836705
     409025ad2+33179428860106809311323003403700576bd2+40002195211690228635488
     2930525ad2-9670253835978110383310132420900576bd2-12505730833882152356630
     d3+9950646500712672075604817437358997061531723772267198405291130040d4   
     bd3+9216550986179510389091899170190721895378709046705837729871239055d4  
     ad3+150822954909565313410640282724328950571588504636257891962004283200d4
                                                                             
     ------------------------------------------------------------------------
                                                           |
                                                           |
                                                           |
                                                           |
     884040cd2+843873139946237202533464364337760d3         |
     73889240cd2+2149435942271179073312064227556960d3      |
     950395902840cd2+68152576548937569480656274291210080d3 |
     364362799000cd2-17468253530780155421891920977178080d3 |
                                                           |
                                                           |
                                                           |
                                                           |

             12       1
o2 : Matrix R   <--- R