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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} | 105175440ac-26337150bc-11431245c2-186115230ad+9852360bd-58489830c
     {-2} | 16360624b2+16848030bc-5837475c2+103837230ad+16600360bd+126422310c
     {-2} | 294491232ab+151167330bc+23287635c2+953756370ad+111748728bd+403234
     {-2} | 368114040a2-113748570bc+224120505c2-941027850ad-125384280bd-10346
     {-3} | 41074049027393995037448129519105c2d+60465001305483886863506656273
     {-3} | 41074049027393995037448129519105bcd+71894977782411148519527265759
     {-3} | 41074049027393995037448129519105c3+393726481442119100446692174927
     {-3} | 1173544257925542715355660843403bc2-485639256912177878781194890029
     {-4} | 405738669019391977160131887920390753316227958312944076383101125cd
     {-4} | 10819697840517119390936850344543753421766078888345175370216030bd3
     {-4} | 81147733803878395432026377584078150663245591662588815276620225ad3
     {-5} | d5                                                               
     ------------------------------------------------------------------------
     d-4086796d2                                                             
     d+1591996d2                                                             
     650cd+28020580d2                                                        
     48370cd+113735692d2                                                     
     0824ad2+78793415911930940849600365713446bd2+3439809910483730506660080120
     2765ad2+69453176389328320221367146097187bd2+4822862694512175660074300831
     8250ad2+528044688546503237281290396648638bd2+248713775228183068650915330
     24ad2-7287912086692207966546027382050bd2-3074589700372177308706780904667
     3-66424616333912802802018022616561690016283685491414772315839254d4      
     -34319088754430751256507954610702972472478707337185303151303111d4       
     +43308791581355917143777850948520180163393082818170590987503013d4       
                                                                             
     ------------------------------------------------------------------------
                                                  |
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     93300cd2+6218198610108409874123971737186d3   |
     43375cd2-13270035708646139821591957111105d3  |
     7066500cd2-2016021264722349641090518289810d3 |
     0cd2+287352503115754228397410547762d3        |
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             12       1
o2 : Matrix R   <--- R