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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 (7976a  - 11198a b - 1641a*b  + 14464b  - 7094a c + 5382a*b*c +
     ------------------------------------------------------------------------
          2           2           2        3        2                      2 
     7145b c + 5310a*c  + 15397b*c  + 1751c  + 4310a d + 7707a*b*d - 10871b d
     ------------------------------------------------------------------------
                                     2           2           2           2  
     - 3735a*c*d - 1089b*c*d + 14673c d + 1451a*d  - 15133b*d  - 11418c*d  +
     ------------------------------------------------------------------------
           3        2                      2                           
     11646d  + 6491a e + 15304a*b*e + 8008b e + 1601a*c*e + 1705b*c*e +
     ------------------------------------------------------------------------
          2                                               2            2  
     5644c e - 11788a*d*e + 3531b*d*e + 4668c*d*e - 10753d e + 14369a*e  -
     ------------------------------------------------------------------------
            2          2           2        3          3        2   
     3587b*e  - 5726c*e  + 13617d*e  + 6823e , - 13417a  - 2933a b -
     ------------------------------------------------------------------------
             2         3        2                       2           2  
     11260a*b  - 15091b  + 1052a c + 14184a*b*c - 11487b c + 1217a*c  +
     ------------------------------------------------------------------------
            2        3         2                      2               
     5184b*c  + 6408c  - 11369a d - 4402a*b*d - 13306b d + 6471a*c*d +
     ------------------------------------------------------------------------
                       2           2           2           2         3  
     10457b*c*d + 5002c d - 8699a*d  + 14430b*d  - 11787c*d  - 15156d  -
     ------------------------------------------------------------------------
          2                       2                                  2   
     2461a e - 15419a*b*e + 10097b e + 3662a*c*e - 3329b*c*e + 12803c e -
     ------------------------------------------------------------------------
                                             2           2          2  
     953a*d*e + 3301b*d*e - 8041c*d*e + 2177d e - 7467a*e  + 2721b*e  +
     ------------------------------------------------------------------------
            2           2         3       3         2           2        3  
     4288c*e  - 15440d*e  + 11900e , 7772a  - 10265a b + 9749a*b  - 8484b  +
     ------------------------------------------------------------------------
           2                    2           2         2        3        2   
     15922a c - 10284a*b*c + 76b c - 6332a*c  - 968b*c  + 8088c  + 2412a d +
     ------------------------------------------------------------------------
                       2                                   2            2  
     4912a*b*d + 10533b d - 2168a*c*d - 11586b*c*d - 11287c d - 10420a*d  -
     ------------------------------------------------------------------------
            2          2         3        2                     2   
     9289b*d  + 7741c*d  - 14852d  - 7876a e - 7775a*b*e + 4290b e -
     ------------------------------------------------------------------------
                                   2                                        
     14409a*c*e + 1710b*c*e + 8581c e + 14983a*d*e + 9021b*d*e - 1415c*d*e +
     ------------------------------------------------------------------------
           2           2           2           2           2         3
     15980d e - 4261a*e  - 13739b*e  - 10059c*e  - 15330d*e  + 13415e )

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 = | ab2-9220b3+4165a2c+5865abc+12878b2c+14971ac2-1182bc2-13287c3-14846a2d-
     ------------------------------------------------------------------------
     12008abd+522b2d-7995acd+4542bcd+8063c2d+1989ad2-15209bd2-5098cd2-10895d3
     ------------------------------------------------------------------------
     +11965a2e-8051abe-4312b2e+4894ace+3152bce+12375c2e-2844ade+5031bde-
     ------------------------------------------------------------------------
     15161cde+6514d2e+13497ae2-15967be2+4101ce2-418de2-7340e3
     ------------------------------------------------------------------------
     a2b-13222b3-1853a2c+15736abc-8836b2c-2479ac2-15548bc2+5352c3+14663a2d-
     ------------------------------------------------------------------------
     4117abd-2268b2d+11173acd-5823bcd-1912c2d+10408ad2+11427bd2-8008cd2+
     ------------------------------------------------------------------------
     6672d3+2144a2e-11439abe+3938b2e+15881ace+8412bce+8375c2e+3650ade-
     ------------------------------------------------------------------------
     15520bde-14838cde+10159d2e+14098ae2-13246be2-5603ce2-5592de2-2598e3
     ------------------------------------------------------------------------
     a3-11952b3-8691a2c-7118abc+7366b2c-7321ac2-70bc2-3148c3-4897a2d+10725abd
     ------------------------------------------------------------------------
     -1413b2d-2474acd+170bcd-11809c2d+7639ad2-14902bd2+11380cd2+10317d3-
     ------------------------------------------------------------------------
     12182a2e+3114abe+4434b2e+15732ace+3459bce-1195c2e+60ade-8484bde-2079cde-
     ------------------------------------------------------------------------
     7578d2e+5840ae2+10578be2-4965ce2+14450de2+10937e3
     ------------------------------------------------------------------------
     b3c-14564a2c2+15354abc2-11768b2c2-1519ac3-15072bc3+3714c4-13280b3d-
     ------------------------------------------------------------------------
     9576a2cd-4623abcd+12492b2cd+5250ac2d+6927bc2d+1351c3d+13571a2d2-297abd2-
     ------------------------------------------------------------------------
     11457b2d2+1108acd2-8370bcd2-10559c2d2+13054ad3-5622bd3+2783cd3+14260d4+
     ------------------------------------------------------------------------
     14232b3e+9918a2ce+872abce+10112b2ce+6425ac2e+1781bc2e-8334c3e+12387a2de+
     ------------------------------------------------------------------------
     5886abde+362b2de+13121acde-12614bcde-15361c2de-2035ad2e+7155bd2e-
     ------------------------------------------------------------------------
     10963cd2e-14775d3e-8168a2e2-7396abe2-15483b2e2-4740ace2-7875bce2+725c2e2
     ------------------------------------------------------------------------
     -362ade2+11802bde2+5369cde2-11761d2e2-9528ae3+4156be3+3285ce3+4472de3-
     ------------------------------------------------------------------------
     10744e4 b4+9582a2c2+13133abc2+5817b2c2+1397ac3+10150bc3+4484c4-11540b3d-
     ------------------------------------------------------------------------
     9453a2cd+2509abcd+656b2cd-14371ac2d-2590bc2d+6054c3d-13085a2d2-11859abd2
     ------------------------------------------------------------------------
     -10728b2d2+9602acd2+11038bcd2+13971c2d2+2538ad3+1158bd3+4850cd3+14435d4+
     ------------------------------------------------------------------------
     14264b3e+4138a2ce+4673abce-5459b2ce+3460ac2e-14587bc2e+3310c3e+11493a2de
     ------------------------------------------------------------------------
     +15820abde-5248b2de-13304acde+1468bcde-11786c2de-464ad2e-6377bd2e-
     ------------------------------------------------------------------------
     1528cd2e-9201d3e-12653a2e2-12486abe2+10493b2e2-2773ace2+13628bce2-
     ------------------------------------------------------------------------
     6653c2e2-3470ade2-6786bde2+12674cde2-8896d2e2-1408ae3+9224be3+3260ce3+
     ------------------------------------------------------------------------
     5760de3-12662e4 abc3-15671b2c3-6249ac4-1533bc4+1349c5-10289a2c2d-
     ------------------------------------------------------------------------
     2637abc2d-4038b2c2d-5870ac3d+2064bc3d-13614c4d-14001b3d2-12737a2cd2-
     ------------------------------------------------------------------------
     14138abcd2-385b2cd2-7404ac2d2+8354bc2d2-1045c3d2-15779a2d3+9337abd3-
     ------------------------------------------------------------------------
     15587b2d3+9807acd3-14605bcd3-4809c2d3+10855ad4+10789bd4-4629cd4+12330d5+
     ------------------------------------------------------------------------
     10432a2c2e-15725abc2e+6272b2c2e-7210ac3e-14899bc3e+3632c4e+14078b3de-
     ------------------------------------------------------------------------
     7247a2cde+5542abcde+12160b2cde-8454ac2de-5070bc2de+9370c3de-12541a2d2e-
     ------------------------------------------------------------------------
     4960abd2e-10309b2d2e+513acd2e-7124bcd2e-4028c2d2e+7103ad3e-1816bd3e-
     ------------------------------------------------------------------------
     11746cd3e+12523d4e-6694b3e2-1649a2ce2+5435abce2+15243b2ce2-6784ac2e2-
     ------------------------------------------------------------------------
     11626bc2e2+7645c3e2-15630a2de2+9283abde2+13234b2de2-3649acde2-8306bcde2-
     ------------------------------------------------------------------------
     9440c2de2+6753ad2e2+13423bd2e2+1554cd2e2-11688d3e2+8554a2e3+5850abe3-
     ------------------------------------------------------------------------
     11774b2e3-10053ace3-12637bce3+12981c2e3-15416ade3+4389bde3-1827cde3+
     ------------------------------------------------------------------------
     6870d2e3+12953ae4-11871be4+117ce4-9584de4-15563e5
     ------------------------------------------------------------------------
     a2c3-546b2c3-751ac4-11386bc4-1084c5+5474a2c2d+12688abc2d+1555b2c2d-
     ------------------------------------------------------------------------
     5293ac3d+14060bc3d-13686c4d-7482b3d2+15292a2cd2-9524abcd2-11474b2cd2-
     ------------------------------------------------------------------------
     14177ac2d2+4749bc2d2+9578c3d2+15080a2d3-11569abd3-4192b2d3-7969acd3+
     ------------------------------------------------------------------------
     13251bcd3-14277c2d3+8202ad4+9596bd4+15028cd4-15726d5-2535a2c2e+
     ------------------------------------------------------------------------
     14497abc2e-207b2c2e-14294ac3e+8322bc3e-11555c4e+14167b3de-9045a2cde-
     ------------------------------------------------------------------------
     13809abcde+12496b2cde-13598ac2de+5825bc2de+7675c3de-3574a2d2e+6985abd2e-
     ------------------------------------------------------------------------
     5930b2d2e+14067acd2e-15891bcd2e-7177c2d2e-15944ad3e-14436bd3e-8020cd3e+
     ------------------------------------------------------------------------
     10620d4e-12493b3e2-11291a2ce2-13213abce2-11477b2ce2+8900ac2e2+110bc2e2+
     ------------------------------------------------------------------------
     8892c3e2+9798a2de2-6790abde2-13276b2de2-14144acde2+11354bcde2+5200c2de2+
     ------------------------------------------------------------------------
     8390ad2e2+13592bd2e2+15603cd2e2+13342d3e2+2246a2e3-11949abe3-1760b2e3+
     ------------------------------------------------------------------------
     5398ace3-14602bce3-14307c2e3+3196ade3-3677bde3+6760cde3-15062d2e3+
     ------------------------------------------------------------------------
     6650ae4-4181be4+14470ce4+4950de4+9072e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R