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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 (2525a  + 8734a b - 8043a*b  + 6183b  - 6620a c + 15547a*b*c +
     ------------------------------------------------------------------------
          2           2          2         3        2                      2 
     5382b c - 1278a*c  - 6987b*c  - 15912c  - 7574a d - 6775a*b*d - 11479b d
     ------------------------------------------------------------------------
                                     2            2          2          2  
     + 14460a*c*d - 1397b*c*d + 1333c d + 10182a*d  - 8300b*d  - 5001c*d  -
     ------------------------------------------------------------------------
          3        2                     2                               2   
     5879d  - 1204a e - 11216a*b*e - 951b e + 74a*c*e + 7984b*c*e - 1196c e -
     ------------------------------------------------------------------------
                                                  2           2           2  
     10663a*d*e + 13392b*d*e - 10225c*d*e + 12148d e + 8309a*e  - 13918b*e  -
     ------------------------------------------------------------------------
             2           2        3         3        2            2         3
     11515c*e  - 12381d*e  - 4484e , - 4503a  - 8685a b + 12259a*b  + 15982b 
     ------------------------------------------------------------------------
           2                     2           2          2        3        2 
     + 832a c - 3495a*b*c + 5443b c + 9153a*c  - 2857b*c  + 9194c  + 8845a d
     ------------------------------------------------------------------------
                         2                                 2           2  
     - 15691a*b*d + 3979b d - 187a*c*d - 13287b*c*d + 5785c d - 4165a*d  +
     ------------------------------------------------------------------------
            2           2        3        2                     2   
     8403b*d  - 15179c*d  + 8836d  - 2711a e - 5000a*b*e + 7528b e -
     ------------------------------------------------------------------------
                                    2                                       
     11808a*c*e + 13967b*c*e - 8090c e + 13120a*d*e - 7366b*d*e - 13834c*d*e
     ------------------------------------------------------------------------
            2           2           2          2          2       3         3
     + 8761d e - 7410a*e  + 13120b*e  - 4568c*e  + 6924d*e  - 766e , - 4105a 
     ------------------------------------------------------------------------
             2           2        3        2                       2   
     - 12104a b + 2256a*b  - 7823b  - 6301a c - 14173a*b*c + 15313b c -
     ------------------------------------------------------------------------
            2           2        3         2                     2   
     1324a*c  - 13774b*c  + 4532c  + 12355a d + 1180a*b*d - 7378b d +
     ------------------------------------------------------------------------
                                  2           2          2          2  
     2571a*c*d - 4086b*c*d + 4451c d - 7415a*d  + 4901b*d  + 6171c*d  -
     ------------------------------------------------------------------------
           3        2                       2                           
     12637d  - 9978a e + 11710a*b*e + 13852b e + 7634a*c*e + 5565b*c*e -
     ------------------------------------------------------------------------
          2                                              2           2  
     6362c e - 1593a*d*e - 7351b*d*e + 7868c*d*e + 14098d e - 9212a*e  -
     ------------------------------------------------------------------------
            2          2          2        3
     9824b*e  - 2873c*e  - 9333d*e  + 2682e )

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 = | ab2-3401b3+6402a2c+4152abc-7b2c+6457ac2-12837bc2-15333c3-6489a2d+
     ------------------------------------------------------------------------
     385abd-1468b2d-8229acd+13113bcd-11702c2d+10547ad2-3989bd2-279cd2-13289d3
     ------------------------------------------------------------------------
     +10356a2e+831abe-10573b2e+10056ace+10715bce+4489c2e-9983ade+11991bde-
     ------------------------------------------------------------------------
     3806cde-14059d2e-13764ae2+12006be2-4685ce2+12404de2-3108e3
     ------------------------------------------------------------------------
     a2b+905b3+1562a2c-10993abc+13115b2c-5304ac2+8308bc2-4412c3-3367a2d-
     ------------------------------------------------------------------------
     3807abd-6793b2d-12038acd-10989bcd-1639c2d-4777ad2+2208bd2-5613cd2-9975d3
     ------------------------------------------------------------------------
     -7903a2e+5592abe+2263b2e+748ace-11276bce-4170c2e-3438ade-14237bde+
     ------------------------------------------------------------------------
     8687cde-8698d2e-8643ae2-9322be2+13830ce2-15296de2+3526e3
     ------------------------------------------------------------------------
     a3+7712b3-6699a2c-7236abc+14413b2c-2633ac2+11486bc2-2014c3+13040a2d-
     ------------------------------------------------------------------------
     12934abd+10540b2d-9092acd-969bcd+11919c2d-2881ad2-8205bd2-8700cd2+2653d3
     ------------------------------------------------------------------------
     +14987a2e+12920abe-11481b2e-10480ace+3796bce+53c2e-13194ade-7561bde-
     ------------------------------------------------------------------------
     5458cde+15968d2e+15233ae2-8682be2+6690ce2+8637de2+1717e3
     ------------------------------------------------------------------------
     b3c-10128a2c2-1772abc2-1474b2c2+8729ac3+2058bc3+15785c4+6349b3d+3550a2cd
     ------------------------------------------------------------------------
     -5378abcd-14472b2cd+2360ac2d+1115bc2d-2215c3d+12695a2d2-7101abd2+
     ------------------------------------------------------------------------
     11429b2d2-5029acd2-4928bcd2-9475c2d2-13726ad3-8944bd3-5037cd3+9119d4+
     ------------------------------------------------------------------------
     12466b3e+9758a2ce+1107abce+15747b2ce+4179ac2e+2172bc2e-14523c3e-773a2de-
     ------------------------------------------------------------------------
     3677abde+9989b2de-12493acde-13355bcde-9594c2de+8389ad2e+3616bd2e+
     ------------------------------------------------------------------------
     1480cd2e-6488d3e+15392a2e2-3569abe2+4175b2e2+7814ace2+2975bce2-850c2e2+
     ------------------------------------------------------------------------
     12272ade2+1072bde2-12851cde2-8811d2e2+15025ae3-14152be3-7137ce3+5983de3+
     ------------------------------------------------------------------------
     10086e4 b4+10698a2c2-14841abc2-274b2c2+10422ac3+8142bc3+14089c4+14216b3d
     ------------------------------------------------------------------------
     -8836a2cd-12277abcd-7109b2cd+11879ac2d+10349bc2d-6803c3d+9178a2d2-
     ------------------------------------------------------------------------
     15304abd2+10040b2d2+12232acd2+11794bcd2+6628c2d2+11971ad3-11941bd3-
     ------------------------------------------------------------------------
     11098cd3+5990d4-10189b3e+4856a2ce+12048abce+11924b2ce-6863ac2e-10131bc2e
     ------------------------------------------------------------------------
     +498c3e-15459a2de+1421abde-2332b2de-13341acde-7807bcde+15145c2de+
     ------------------------------------------------------------------------
     11606ad2e+8203bd2e-1005cd2e-4240d3e-9208a2e2+3363abe2+10375b2e2+
     ------------------------------------------------------------------------
     14939ace2-15775bce2+1175c2e2-2801ade2-2318bde2+12191cde2+4184d2e2-225ae3
     ------------------------------------------------------------------------
     +14967be3-11380ce3+12451de3-8653e4
     ------------------------------------------------------------------------
     abc3-3075b2c3+331ac4+3876bc4+13389c5-11633a2c2d+7728abc2d-2232b2c2d+
     ------------------------------------------------------------------------
     3467ac3d-15754bc3d+15764c4d-9465b3d2+8639a2cd2+1343abcd2+6092b2cd2-
     ------------------------------------------------------------------------
     7117ac2d2+10159bc2d2-7041c3d2-6582a2d3-765abd3-185b2d3+2901acd3-351bcd3+
     ------------------------------------------------------------------------
     14629c2d3-15501ad4+2160bd4-5491cd4+13476d5+2846a2c2e-1930abc2e-
     ------------------------------------------------------------------------
     14054b2c2e+1983ac3e-10881bc3e-13140c4e+11634b3de+12250a2cde-12837abcde+
     ------------------------------------------------------------------------
     2435b2cde-13069ac2de-12410bc2de-8110c3de+12484a2d2e+11735abd2e-4086b2d2e
     ------------------------------------------------------------------------
     -7084acd2e+1206bcd2e+10127c2d2e-14227ad3e+8862bd3e+10391cd3e+269d4e-
     ------------------------------------------------------------------------
     6803b3e2-9184a2ce2-12932abce2-137b2ce2-4955ac2e2+3063bc2e2+14482c3e2+
     ------------------------------------------------------------------------
     10605a2de2-8657abde2-4493b2de2-4433acde2-10861bcde2+4139c2de2-7994ad2e2+
     ------------------------------------------------------------------------
     5859bd2e2+12688cd2e2-1893d3e2+15971a2e3-8433abe3+6165b2e3-14264ace3-
     ------------------------------------------------------------------------
     15133bce3-15726c2e3-4528ade3-14544bde3-14449cde3+1351d2e3+13409ae4+
     ------------------------------------------------------------------------
     11465be4-7632ce4-3043de4+10234e5
     ------------------------------------------------------------------------
     a2c3+1088b2c3-8567ac4-3231bc4+15857c5+560a2c2d-3158abc2d-4049b2c2d-
     ------------------------------------------------------------------------
     3684ac3d+6386bc3d+3163c4d+15256b3d2-9544a2cd2-15450abcd2+7159b2cd2-
     ------------------------------------------------------------------------
     1408ac2d2+137bc2d2-9336c3d2+110a2d3-15187abd3-539b2d3+10378acd3-7021bcd3
     ------------------------------------------------------------------------
     +5757c2d3-14550ad4+4345bd4+457cd4-2017d5+7432a2c2e-6281abc2e+3416b2c2e+
     ------------------------------------------------------------------------
     10742ac3e-14963bc3e-4547c4e+360b3de+13702a2cde+3023abcde+6601b2cde-
     ------------------------------------------------------------------------
     9609ac2de+13321bc2de+8432c3de-12270a2d2e-1518abd2e-10725b2d2e-5696acd2e+
     ------------------------------------------------------------------------
     4869bcd2e+8435c2d2e-11119ad3e+4005bd3e-15473cd3e-8790d4e+11943b3e2+
     ------------------------------------------------------------------------
     12035a2ce2-6070abce2+8559b2ce2-11547ac2e2-13143bc2e2+5927c3e2+1108a2de2+
     ------------------------------------------------------------------------
     14001abde2+11008b2de2+3071acde2+3434bcde2+6028c2de2+3201ad2e2-3105bd2e2+
     ------------------------------------------------------------------------
     11247cd2e2+14680d3e2+9517a2e3+12144abe3+12385b2e3-183ace3+9636bce3+
     ------------------------------------------------------------------------
     5831c2e3+2214ade3-4039bde3-3350cde3+15518d2e3-8403ae4+11141be4+9834ce4+
     ------------------------------------------------------------------------
     12027de4-5527e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R