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Macaulay2Doc :: fine control of a Groebner basis computation

fine control of a Groebner basis computation

Sometimes a Groebner basis computation doesn't finish quickly enough. If so then this section might be of use. THIS PAGE IS UNDER CONSTRUCTION.

Partially computed Groebner bases

Suppose that you have computed part of a Groebner basis. For example, you may have interrupted the computation using CTRL-C (typing 'c' while holding the CTRL key down, in emacs, you have to type CTRL-C twice), or you may have given options requesting only partial computation.
i1 : R = ZZ/32003[a..e];
i2 : I = ideal(random(3,R),random(3,R),random(3,R))

                    3        2           2         3       2               
o2 = ideal (- 12572a  - 4287a b + 4063a*b  + 12080b  - 654a c + 9648a*b*c -
     ------------------------------------------------------------------------
           2            2          2         3        2                
     15492b c + 15982a*c  - 6496b*c  - 15526c  - 4311a d - 12087a*b*d -
     ------------------------------------------------------------------------
          2                                   2           2         2  
     4683b d - 15549a*c*d + 12433b*c*d + 5460c d - 8828a*d  + 319b*d  -
     ------------------------------------------------------------------------
            2         3         2                     2               
     2815c*d  + 12803d  + 10364a e - 4746a*b*e + 9592b e + 1216a*c*e -
     ------------------------------------------------------------------------
                      2                                              2   
     13662b*c*e + 307c e - 10025a*d*e + 6642b*d*e - 6661c*d*e - 6823d e +
     ------------------------------------------------------------------------
            2          2          2          2        3        3        2   
     7146a*e  + 6088b*e  - 9083c*e  - 7612d*e  + 2016e , 15718a  + 9336a b -
     ------------------------------------------------------------------------
            2        3        2                      2           2          2
     7760a*b  - 3662b  - 1136a c - 11261a*b*c + 7388b c - 4944a*c  - 5019b*c 
     ------------------------------------------------------------------------
            3        2                       2                             
     + 3505c  + 8290a d - 15414a*b*d + 12383b d - 11642a*c*d + 14636b*c*d -
     ------------------------------------------------------------------------
          2           2          2          2        3         2             
     9908c d + 5929a*d  - 8305b*d  + 8890c*d  + 6365d  - 14989a e + 2077a*b*e
     ------------------------------------------------------------------------
             2                                 2                            
     + 11583b e - 4167a*c*e - 7136b*c*e - 8158c e - 14271a*d*e - 3677b*d*e +
     ------------------------------------------------------------------------
                       2           2           2          2           2  
     6630c*d*e - 11616d e - 7731a*e  + 13304b*e  - 8916c*e  + 13991d*e  -
     ------------------------------------------------------------------------
          3          3        2           2        3      2                
     1028e , - 15941a  + 2206a b + 7335a*b  + 7185b  + 68a c + 10187a*b*c -
     ------------------------------------------------------------------------
          2           2          2        3        2                     2   
     4855b c + 6245a*c  - 6581b*c  - 9713c  + 8919a d - 4862a*b*d - 5712b d +
     ------------------------------------------------------------------------
                                2           2          2          2        3
     51a*c*d - 1283b*c*d - 2929c d + 2155a*d  - 9241b*d  - 2764c*d  - 4064d 
     ------------------------------------------------------------------------
            2                      2                                  2   
     + 7001a e - 6234a*b*e + 12361b e - 6084a*c*e - 12650b*c*e + 5494c e +
     ------------------------------------------------------------------------
                                                2           2         2  
     7752a*d*e + 15293b*d*e + 12564c*d*e - 2707d e - 3646a*e  - 905b*e  +
     ------------------------------------------------------------------------
            2           2        3
     8001c*e  - 14273d*e  + 8351e )

o2 : Ideal of R
i3 : gens gb(I,PairLimit=>7);

             1       7
o3 : Matrix R  <--- R
Get the Groebner basis object:
i4 : g = gb(I,StopBeforeComputation => true);
i5 : leadTerm gens g

o5 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o5 : Matrix R  <--- R
We can make a Groebner basis snapshot by using StopBeforeComputation, or gbSnapshot:
i6 : gens gb(I,StopBeforeComputation => true)

o6 = | ab2+4800b3+6176a2c-9248abc+5107b2c-7225ac2-5012bc2-1236c3-7798a2d-
     ------------------------------------------------------------------------
     15523abd-4206b2d+5652acd-9185bcd+674c2d+5632ad2-6392bd2-3879cd2-5246d3+
     ------------------------------------------------------------------------
     9359a2e-837abe+12822b2e+15457ace-10148bce+13546c2e+9383ade-7018bde-
     ------------------------------------------------------------------------
     9513cde-270d2e-12329ae2-11943be2+548ce2-86de2-14603e3
     ------------------------------------------------------------------------
     a2b+1564b3-8678a2c-3258abc-14258b2c+5796ac2-13346bc2-3297c3+7174a2d-
     ------------------------------------------------------------------------
     3644abd-11943b2d+6673acd+4808bcd+1389c2d+12142ad2+148bd2+11256cd2-1261d3
     ------------------------------------------------------------------------
     -7183a2e-9028abe+2061b2e-3764ace+1624bce+13863c2e+8249ade-15866bde-
     ------------------------------------------------------------------------
     685cde-5798d2e+831ae2-13317be2+47ce2+12133de2+2109e3
     ------------------------------------------------------------------------
     a3+1465b3+9079a2c-14805abc-13935b2c-9722ac2-12968bc2-5951c3+4786a2d-
     ------------------------------------------------------------------------
     11975abd-15304b2d-2591acd-1208bcd+10677c2d-8322ad2-4476bd2-12652cd2+
     ------------------------------------------------------------------------
     14898d3+13115a2e-10869abe+11665b2e-495ace-3145bce-7472c2e+14585ade+
     ------------------------------------------------------------------------
     4837bde+8709cde-15361d2e-7206ae2+5940be2+10003ce2-7181de2+5212e3
     ------------------------------------------------------------------------
     b3c+7606a2c2-1147abc2-7787b2c2+2234ac3-6426bc3+10650c4+7383b3d-5824a2cd-
     ------------------------------------------------------------------------
     10554abcd-12701b2cd+15840ac2d-13160bc2d+11156c3d+8138a2d2+15441abd2+
     ------------------------------------------------------------------------
     7870b2d2+14504acd2+2090bcd2+11223c2d2+14803ad3-758bd3-2177cd3-14783d4+
     ------------------------------------------------------------------------
     14484b3e+13124a2ce-12673abce+5400b2ce-13605ac2e+1489bc2e+9780c3e-
     ------------------------------------------------------------------------
     1703a2de+14783abde-6740b2de+1913acde+8074bcde-11472c2de+10929ad2e+
     ------------------------------------------------------------------------
     7156bd2e+8959cd2e-2962d3e+7376a2e2-14911abe2+356b2e2-13257ace2+8670bce2-
     ------------------------------------------------------------------------
     222c2e2+5064ade2-8213bde2+9807cde2-1480d2e2-14858ae3-8863be3-2314ce3-
     ------------------------------------------------------------------------
     12823de3+12196e4 b4+15713a2c2-13048abc2-6191b2c2-14007ac3-14242bc3-
     ------------------------------------------------------------------------
     3333c4-6245b3d+3382a2cd+9090abcd-12295b2cd-109ac2d+9053bc2d-3676c3d+
     ------------------------------------------------------------------------
     3493a2d2+8880abd2+12506b2d2-294acd2+13081bcd2-14984c2d2-1836ad3+8339bd3+
     ------------------------------------------------------------------------
     1166cd3+3350d4-14520b3e+13622a2ce-1011abce-4617b2ce-1401ac2e-15761bc2e-
     ------------------------------------------------------------------------
     12260c3e+2856a2de+3990abde-10101b2de+7873acde-12138bcde-11388c2de+
     ------------------------------------------------------------------------
     743ad2e+14571bd2e-539cd2e-1713d3e+7642a2e2-9243abe2+3094b2e2-1210ace2-
     ------------------------------------------------------------------------
     3468bce2+12446c2e2+2269ade2+13594bde2-14251cde2-8615d2e2+2265ae3-
     ------------------------------------------------------------------------
     12200be3+2512ce3+2405de3+15076e4
     ------------------------------------------------------------------------
     abc3-8730b2c3-5492ac4-7742bc4+9190c5-4037a2c2d+8622abc2d-14662b2c2d-
     ------------------------------------------------------------------------
     7527ac3d-15869bc3d+12190c4d-839b3d2+7a2cd2-13057abcd2-11103b2cd2+
     ------------------------------------------------------------------------
     14289ac2d2-13360bc2d2-4034c3d2+1729a2d3-9005abd3-6340b2d3-8032acd3-
     ------------------------------------------------------------------------
     5471bcd3+2089c2d3+8897ad4-7159bd4+2303cd4-11426d5-13724a2c2e+1879abc2e-
     ------------------------------------------------------------------------
     15644b2c2e-3569ac3e+690bc3e+13717c4e+1682b3de+3751a2cde-14967abcde+
     ------------------------------------------------------------------------
     14775b2cde+760ac2de-1335bc2de+541c3de+9039a2d2e+365abd2e+1279b2d2e+
     ------------------------------------------------------------------------
     264acd2e-13403bcd2e-15355c2d2e+12450ad3e+11119bd3e-13061cd3e-1895d4e-
     ------------------------------------------------------------------------
     918b3e2+10756a2ce2-1078abce2-1330b2ce2+11252ac2e2-6645bc2e2-6346c3e2+
     ------------------------------------------------------------------------
     8740a2de2-7714abde2-10906b2de2-11776acde2-2775bcde2+9106c2de2-9017ad2e2+
     ------------------------------------------------------------------------
     2222bd2e2-14175cd2e2-8007d3e2-2991a2e3-9127abe3+9749b2e3+12361ace3-
     ------------------------------------------------------------------------
     12976bce3+2226c2e3+12968ade3-9158bde3+3594cde3+8631d2e3+663ae4-10007be4-
     ------------------------------------------------------------------------
     11725ce4-6380de4+5701e5
     ------------------------------------------------------------------------
     a2c3+2323b2c3+683ac4-436bc4-14277c5-3350a2c2d+12929abc2d-4152b2c2d-
     ------------------------------------------------------------------------
     239ac3d+7117bc3d-13816c4d-13616b3d2-13415a2cd2-14223abcd2-718b2cd2-
     ------------------------------------------------------------------------
     3405ac2d2+4227bc2d2-2985c3d2+5744a2d3+9000abd3+13180b2d3-15291acd3-
     ------------------------------------------------------------------------
     15860bcd3-2157c2d3-15320ad4-14586bd4+1696cd4+7173d5+2103a2c2e-7135abc2e-
     ------------------------------------------------------------------------
     5463b2c2e-3230ac3e+5021bc3e-14380c4e+10031b3de-3708a2cde+11851abcde-
     ------------------------------------------------------------------------
     3184b2cde+1826ac2de+5182bc2de-6036c3de+2708a2d2e+9887abd2e+6091b2d2e+
     ------------------------------------------------------------------------
     773acd2e+3652bcd2e+456c2d2e-4784ad3e+10486bd3e-8503cd3e-10210d4e+
     ------------------------------------------------------------------------
     6757b3e2-2524a2ce2-8647abce2-9230b2ce2+14740ac2e2-9557bc2e2+9529c3e2+
     ------------------------------------------------------------------------
     1157a2de2-10091abde2-3262b2de2+9094acde2-10894bcde2+15289c2de2+
     ------------------------------------------------------------------------
     11513ad2e2+8453bd2e2+6461cd2e2-8338d3e2-6063a2e3-12510abe3-1557b2e3+
     ------------------------------------------------------------------------
     3287ace3-2762bce3-5767c2e3-11114ade3+995bde3-8153cde3-14107d2e3-13720ae4
     ------------------------------------------------------------------------
     +4503be4-5692ce4-13298de4+8086e5 |

             1       7
o6 : Matrix R  <--- R
i7 : leadTerm gbSnapshot(I)

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R