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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 (- 9278a  - 9869a b + 1944a*b  - 5159b  - 2654a c - 1763a*b*c -
     ------------------------------------------------------------------------
          2            2          2        3         2               
     7288b c + 10510a*c  - 7604b*c  + 6912c  - 12879a d + 7925a*b*d +
     ------------------------------------------------------------------------
           2                                  2           2           2  
     15813b d + 8341a*c*d + 7757b*c*d + 13527c d + 9112a*d  - 15218b*d  -
     ------------------------------------------------------------------------
            2        3         2                     2               
     5857c*d  - 1505d  + 10253a e + 3847a*b*e - 4371b e + 1394a*c*e -
     ------------------------------------------------------------------------
                      2                                               2   
     4102b*c*e + 7888c e - 1044a*d*e + 14229b*d*e + 8592c*d*e - 15044d e -
     ------------------------------------------------------------------------
           2           2           2          2        3         3         2 
     601a*e  + 11097b*e  + 13446c*e  + 2007d*e  + 7887e , - 6822a  - 10984a b
     ------------------------------------------------------------------------
              2        3        2                       2            2  
     - 2670a*b  - 1896b  + 5134a c + 14619a*b*c - 14377b c + 10681a*c  +
     ------------------------------------------------------------------------
           2        3         2                      2              
     952b*c  + 9258c  + 15825a d + 5445a*b*d + 14074b d + 973a*c*d -
     ------------------------------------------------------------------------
                     2          2          2           2        3        2   
     8370b*c*d + 888c d + 950a*d  + 8066b*d  - 14288c*d  - 1313d  - 5984a e +
     ------------------------------------------------------------------------
                      2                                  2                
     2596a*b*e + 7000b e - 12557a*c*e - 14209b*c*e - 143c e + 14193a*d*e -
     ------------------------------------------------------------------------
                                    2           2          2          2  
     12697b*d*e + 10647c*d*e + 6974d e - 3864a*e  + 5479b*e  + 5187c*e  +
     ------------------------------------------------------------------------
             2         3       3        2           2         3        2   
     11830d*e  + 15402e , 2925a  - 2615a b - 8553a*b  - 12583b  - 3330a c -
     ------------------------------------------------------------------------
                      2           2          2         3       2             
     265a*b*c + 11149b c + 6416a*c  + 2707b*c  + 15042c  + 532a d - 4679a*b*d
     ------------------------------------------------------------------------
            2                                   2            2           2  
     - 3982b d - 13671a*c*d + 1420b*c*d - 15726c d + 15483a*d  - 10544b*d  -
     ------------------------------------------------------------------------
            2         3       2                     2                
     9875c*d  + 14651d  - 470a e + 2851a*b*e + 2726b e - 14992a*c*e +
     ------------------------------------------------------------------------
                      2                                                2   
     4999b*c*e + 3378c e + 14085a*d*e + 11917b*d*e - 4418c*d*e - 14575d e -
     ------------------------------------------------------------------------
           2           2           2          2        3
     679a*e  + 10879b*e  + 14251c*e  + 5735d*e  + 4957e )

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+9366b3-13434a2c-8737abc+1597b2c+10454ac2+15909bc2-1764c3-507a2d+
     ------------------------------------------------------------------------
     1562abd-12064b2d-15502acd-12774bcd-3094c2d-10997ad2+8576bd2+14412cd2+
     ------------------------------------------------------------------------
     3043d3+145a2e-13368abe+615b2e+2122ace+12023bce+9684c2e+9245ade-14595bde-
     ------------------------------------------------------------------------
     3114cde-11816d2e+11208ae2+5655be2-4703ce2+7562de2-13511e3
     ------------------------------------------------------------------------
     a2b-4558b3-1147a2c-11548abc+7745b2c+4523ac2+11831bc2-7930c3+1135a2d-
     ------------------------------------------------------------------------
     13498abd+4857b2d-805acd+6699bcd-2110c2d+15766ad2-1591bd2+5439cd2-4617d3+
     ------------------------------------------------------------------------
     4613a2e+12659abe+10870b2e+3072ace+4981bce-14307c2e+9624ade+11953bde-
     ------------------------------------------------------------------------
     7485cde+12404d2e-1078ae2+1258be2+1795ce2-9048de2-1580e3
     ------------------------------------------------------------------------
     a3+6732b3+7329a2c+9884abc+10996b2c+8454ac2-7543bc2-11969c3-10446a2d-
     ------------------------------------------------------------------------
     4263abd+13628b2d+2733acd-10148bcd+12705c2d+7995ad2-8330bd2-14893cd2-
     ------------------------------------------------------------------------
     7807d3+7885a2e+8127abe-12630b2e+6014ace+8035bce-11552c2e+10368ade+
     ------------------------------------------------------------------------
     8944bde-15033cde-9287d2e-3476ae2+8769be2-6825ce2+5086de2-14200e3
     ------------------------------------------------------------------------
     b3c-13529a2c2-15292abc2-742b2c2-3341ac3+3679bc3+5171c4-14272b3d+6505a2cd
     ------------------------------------------------------------------------
     +3420abcd-9622b2cd+2471ac2d-1950bc2d+6913c3d-7452a2d2-11374abd2-7262b2d2
     ------------------------------------------------------------------------
     -12186acd2-2111bcd2+4844c2d2-7060ad3+14636bd3+8566cd3-12275d4+8544b3e-
     ------------------------------------------------------------------------
     7377a2ce-978abce+13248b2ce-5688ac2e-3352bc2e-2647c3e+568a2de+6306abde-
     ------------------------------------------------------------------------
     7038b2de+11379acde+11259bcde-13650c2de-7582ad2e-5787bd2e+1597cd2e-
     ------------------------------------------------------------------------
     9858d3e-1987a2e2+11586abe2-10424b2e2+14311ace2-4911bce2+13228c2e2-
     ------------------------------------------------------------------------
     10493ade2-11007bde2-10314cde2-11900d2e2+15787ae3-12704be3-12457ce3+
     ------------------------------------------------------------------------
     8991de3+15816e4 b4-9114a2c2+9070abc2+5968b2c2+8699ac3+11982bc3-1538c4+
     ------------------------------------------------------------------------
     12730b3d-8749a2cd+1070abcd+14368b2cd-10327ac2d-5102bc2d+4926c3d-2851a2d2
     ------------------------------------------------------------------------
     -12755abd2+2780b2d2-9481acd2+1255bcd2+8291c2d2+11940ad3-8371bd3-7208cd3+
     ------------------------------------------------------------------------
     1303d4+10894b3e-3704a2ce+14095abce+6113b2ce-13588ac2e+1463bc2e-14648c3e+
     ------------------------------------------------------------------------
     4233a2de+5428abde-2672b2de-9424acde-8562bcde+13190c2de+14823ad2e+
     ------------------------------------------------------------------------
     2959bd2e+2855cd2e-15325d3e+6312a2e2-6111abe2+7092b2e2+11851ace2+8690bce2
     ------------------------------------------------------------------------
     -13957c2e2-9599ade2-14156bde2+14311cde2-15929d2e2+384ae3+4013be3+7345ce3
     ------------------------------------------------------------------------
     -11115de3+14194e4 abc3+6318b2c3+494ac4-11841bc4+13804c5+13943a2c2d-
     ------------------------------------------------------------------------
     12330abc2d-10194b2c2d-8424ac3d-2823bc3d-10425c4d-14065b3d2-602a2cd2+
     ------------------------------------------------------------------------
     7706abcd2-4070b2cd2-9856ac2d2-15942bc2d2+2675c3d2-12479a2d3+3629abd3+
     ------------------------------------------------------------------------
     7125b2d3+3362acd3+14207bcd3+6275c2d3+15256ad4+1938bd4+7527cd4-3944d5+
     ------------------------------------------------------------------------
     8619a2c2e+11683abc2e-5570b2c2e-4820ac3e-13942bc3e+2987c4e+1048b3de-
     ------------------------------------------------------------------------
     6660a2cde-1199abcde+7206b2cde+489ac2de-8582bc2de-1529c3de-8956a2d2e+
     ------------------------------------------------------------------------
     6762abd2e+9095b2d2e+8163acd2e+9312bcd2e+5407c2d2e-3871ad3e-4241bd3e-
     ------------------------------------------------------------------------
     7018cd3e+15230d4e-10545b3e2+8406a2ce2-9688abce2-9058b2ce2+8765ac2e2-
     ------------------------------------------------------------------------
     9320bc2e2+12535c3e2+181a2de2-10865abde2+5955b2de2-146acde2+3444bcde2+
     ------------------------------------------------------------------------
     8505c2de2+15275ad2e2-11773bd2e2-4248cd2e2-7496d3e2+7574a2e3-2168abe3-
     ------------------------------------------------------------------------
     9127b2e3-3841ace3-9916bce3-7178c2e3+14303ade3+400bde3-11371cde3+8085d2e3
     ------------------------------------------------------------------------
     +1509ae4-1573be4+4032ce4-13527de4+13063e5
     ------------------------------------------------------------------------
     a2c3+8124b2c3+11080ac4+6228bc4-9601c5-11804a2c2d+12892abc2d-15113b2c2d-
     ------------------------------------------------------------------------
     14257ac3d+4405bc3d-10298c4d+12881b3d2+5734a2cd2+8051abcd2+2878b2cd2+
     ------------------------------------------------------------------------
     7351ac2d2-4938bc2d2-383c3d2-9023a2d3-11074abd3+14900b2d3-2876acd3-
     ------------------------------------------------------------------------
     5320bcd3+14881c2d3+10645ad4+4258bd4+15896cd4-4143d5+11807a2c2e+3287abc2e
     ------------------------------------------------------------------------
     +13238b2c2e-4361ac3e+268bc3e+2212c4e+2768b3de-15547a2cde-14043abcde-
     ------------------------------------------------------------------------
     14138b2cde-14793ac2de-9781bc2de-4093c3de-1021a2d2e-4452abd2e+15279b2d2e-
     ------------------------------------------------------------------------
     11008acd2e-10303bcd2e-11678c2d2e+4326ad3e-13356bd3e+9362cd3e+14483d4e-
     ------------------------------------------------------------------------
     7510b3e2-14291a2ce2+15402abce2+6124b2ce2-1400ac2e2+15466bc2e2-8450c3e2-
     ------------------------------------------------------------------------
     3412a2de2-8632abde2+12610b2de2-12929acde2-6123bcde2+8837c2de2+15277ad2e2
     ------------------------------------------------------------------------
     -14495bd2e2-4741cd2e2+4440d3e2-11881a2e3+14654abe3-5120b2e3+422ace3-
     ------------------------------------------------------------------------
     4177bce3-8512c2e3+1205ade3-1583bde3+15983cde3-5183d2e3-14949ae4+15047be4
     ------------------------------------------------------------------------
     -1057ce4-975de4-5869e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R