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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 (- 846a  - 14551a b - 15283a*b  + 13915b  - 2382a c - 1039a*b*c -
     ------------------------------------------------------------------------
           2           2          2        3        2                
     14451b c - 4946a*c  + 7832b*c  + 5853c  - 2846a d + 12427a*b*d -
     ------------------------------------------------------------------------
           2                                   2           2          2  
     14468b d - 13705a*c*d - 14927b*c*d + 1337c d - 6010a*d  + 5569b*d  +
     ------------------------------------------------------------------------
            2        3        2                       2                
     7993c*d  - 8869d  - 3911a e + 10591a*b*e + 13037b e + 15882a*c*e -
     ------------------------------------------------------------------------
                       2                                               2   
     14102b*c*e + 3840c e - 11145a*d*e - 9074b*d*e + 14953c*d*e - 5572d e -
     ------------------------------------------------------------------------
            2           2           2          2        3         3       2 
     6494a*e  - 12337b*e  - 13664c*e  - 4786d*e  + 4803e , - 3842a  - 757a b
     ------------------------------------------------------------------------
               2        3       2                      2            2  
     + 15821a*b  + 3067b  + 884a c - 5038a*b*c - 12489b c + 12064a*c  -
     ------------------------------------------------------------------------
            2         3        2                       2               
     1108b*c  + 11722c  - 1946a d + 15594a*b*d - 12458b d - 9178a*c*d +
     ------------------------------------------------------------------------
                        2           2           2           2         3  
     12410b*c*d - 10127c d + 8882a*d  + 14288b*d  - 15950c*d  + 12357d  +
     ------------------------------------------------------------------------
          2                     2                                 2   
     3685a e + 5981a*b*e - 7601b e - 10358a*c*e - 247b*c*e + 1615c e -
     ------------------------------------------------------------------------
                                                2            2         2  
     10910a*d*e + 2903b*d*e - 2974c*d*e + 15311d e - 12620a*e  + 906b*e  +
     ------------------------------------------------------------------------
             2          2        3       3         2           2         3  
     13253c*e  + 8023d*e  - 7099e , 5162a  - 10124a b + 6409a*b  + 13595b  +
     ------------------------------------------------------------------------
          2                      2           2           2        3        2 
     3627a c + 15706a*b*c + 9511b c + 3087a*c  + 12612b*c  - 6294c  - 6875a d
     ------------------------------------------------------------------------
                        2                                   2           2  
     + 3791a*b*d - 5456b d + 2529a*c*d + 14007b*c*d + 12527c d + 7723a*d  +
     ------------------------------------------------------------------------
            2          2        3         2                     2   
     5419b*d  + 6222c*d  - 1385d  - 11921a e - 6049a*b*e + 3160b e +
     ------------------------------------------------------------------------
                                   2                                        
     9863a*c*e - 9911b*c*e + 10541c e - 12691a*d*e + 3113b*d*e + 2072c*d*e +
     ------------------------------------------------------------------------
           2            2           2           2          2        3
     12303d e + 11591a*e  + 15758b*e  + 11977c*e  + 7879d*e  + 1282e )

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 = | ab2-849b3+866a2c+8228abc+9494b2c+2042ac2-3707bc2+15504c3-12741a2d-
     ------------------------------------------------------------------------
     3400abd+4899b2d-2011acd-11570bcd+13889c2d+10551ad2-9013bd2-7851cd2+
     ------------------------------------------------------------------------
     9342d3-1148a2e-2863abe+213b2e-278ace-75bce-2705c2e-5895ade+3698bde+
     ------------------------------------------------------------------------
     11841cde+15619d2e+12301ae2-2564be2-14364ce2+14815de2-14253e3
     ------------------------------------------------------------------------
     a2b-3924b3+2507a2c+6195abc-13257b2c+15596ac2+11752bc2+7576c3-11227a2d-
     ------------------------------------------------------------------------
     920abd-1637b2d-10812acd+11637bcd+12981c2d+13421ad2-6816bd2-3744cd2+
     ------------------------------------------------------------------------
     15228d3+5909a2e+24abe-7230b2e-13723ace-12368bce-11295c2e-11717ade-
     ------------------------------------------------------------------------
     14988bde-5739cde-9402d2e+10494ae2-12334be2-3458ce2+10735de2-4180e3
     ------------------------------------------------------------------------
     a3-2907b3+12243a2c-3630abc+12190b2c+6199ac2-12874bc2-11187c3+10637a2d-
     ------------------------------------------------------------------------
     8376abd+11320b2d-14120acd-3002bcd+9916c2d+1035ad2+7681bd2-5474cd2-
     ------------------------------------------------------------------------
     14821d3-12723a2e+1815abe-12590b2e-13740ace-1487bce-2375c2e-2272ade+
     ------------------------------------------------------------------------
     1929bde-10166cde+6325d2e-6828ae2-13626be2+7725ce2+9469de2+3590e3
     ------------------------------------------------------------------------
     b3c-14335a2c2+13458abc2-14657b2c2-117ac3+11865bc3-6579c4-14447b3d-2a2cd-
     ------------------------------------------------------------------------
     12871abcd-829b2cd-13634ac2d-12561bc2d-4208c3d-11106a2d2-15451abd2+
     ------------------------------------------------------------------------
     2916b2d2+acd2-14810bcd2-11565c2d2-4532ad3-13988bd3+472cd3+12979d4-
     ------------------------------------------------------------------------
     5634b3e+9471a2ce-5379abce+2617b2ce+11535ac2e+6255bc2e+12551c3e+9614a2de+
     ------------------------------------------------------------------------
     6892abde-7858b2de-7056acde+2153bcde-10986c2de+1654ad2e-6148bd2e+4578cd2e
     ------------------------------------------------------------------------
     +1438d3e+3101a2e2+12741abe2+1577b2e2-14675ace2+15698bce2+1610c2e2+
     ------------------------------------------------------------------------
     15916ade2-5568bde2+5551cde2-2724d2e2+421ae3-12386be3+9864ce3+4951de3-
     ------------------------------------------------------------------------
     8506e4 b4+2634a2c2+15819abc2-13575b2c2-10119ac3+4669bc3-5334c4+12240b3d-
     ------------------------------------------------------------------------
     10933a2cd-13868abcd-3495b2cd+14096ac2d+10563bc2d+6799c3d+4248a2d2-
     ------------------------------------------------------------------------
     2831abd2-3873b2d2-11255acd2+1763bcd2-15482c2d2+10658ad3-1744bd3+2121cd3+
     ------------------------------------------------------------------------
     8956d4+8540b3e-1074a2ce-12793abce+13836b2ce+8324ac2e+10801bc2e-2748c3e+
     ------------------------------------------------------------------------
     12612a2de-4902abde+14009b2de+1191acde-12874bcde-9728c2de+7195ad2e-
     ------------------------------------------------------------------------
     5389bd2e-4494cd2e-2588d3e+14922a2e2+8138abe2+73b2e2-7802ace2-8496bce2-
     ------------------------------------------------------------------------
     13114c2e2+1942ade2-3683bde2-13559cde2+238d2e2-14364ae3-15050be3-3658ce3-
     ------------------------------------------------------------------------
     5307de3-7174e4 abc3+10422b2c3-3934ac4+14009bc4-8602c5-10865a2c2d+
     ------------------------------------------------------------------------
     837abc2d-1689b2c2d-3214ac3d+8311bc3d+7935c4d-10851b3d2+2377a2cd2+
     ------------------------------------------------------------------------
     2321abcd2-1359b2cd2-390ac2d2-9818bc2d2-3144c3d2-170a2d3-14478abd3+
     ------------------------------------------------------------------------
     14250b2d3-14144acd3+12235bcd3-2317c2d3-15530ad4-10513bd4+3567cd4-2864d5-
     ------------------------------------------------------------------------
     7320a2c2e+10701abc2e-14041b2c2e+4092ac3e+12168bc3e-11384c4e-8218b3de-
     ------------------------------------------------------------------------
     491a2cde+8467abcde+13409b2cde-7986ac2de-15151bc2de+11499c3de+1479a2d2e+
     ------------------------------------------------------------------------
     2219abd2e+9480b2d2e+10177acd2e+7879bcd2e+13813c2d2e+15731ad3e-14229bd3e+
     ------------------------------------------------------------------------
     9242cd3e+10004d4e-12168b3e2-14176a2ce2-7624abce2+6900b2ce2+12681ac2e2+
     ------------------------------------------------------------------------
     8697bc2e2-5256c3e2+8481a2de2-350abde2-10956b2de2+5394acde2+6960bcde2+
     ------------------------------------------------------------------------
     12648c2de2+8491ad2e2+15280bd2e2-15917cd2e2-8088d3e2+8345a2e3+15845abe3+
     ------------------------------------------------------------------------
     10517b2e3+4226ace3+2770bce3+15790c2e3+15491ade3-12821bde3+7880cde3+
     ------------------------------------------------------------------------
     4217d2e3-13869ae4-15697be4-5638ce4+10167de4-12948e5
     ------------------------------------------------------------------------
     a2c3-10594b2c3-15928ac4-6220bc4+14122c5+14675a2c2d+5634abc2d-4699b2c2d-
     ------------------------------------------------------------------------
     3733ac3d+9693bc3d-14304c4d+11828b3d2-12933a2cd2+12164abcd2+13261b2cd2+
     ------------------------------------------------------------------------
     9129ac2d2+9831bc2d2+5535c3d2-14063a2d3+5296abd3-14780b2d3-3726acd3+
     ------------------------------------------------------------------------
     14718bcd3+2828c2d3-9965ad4-3212bd4+14147cd4-14230d5+3929a2c2e-14644abc2e
     ------------------------------------------------------------------------
     -2695b2c2e+3092ac3e-1656bc3e+1711c4e+1483b3de-7197a2cde+8354abcde+
     ------------------------------------------------------------------------
     3177b2cde-11854ac2de-3270bc2de-6828c3de-4202a2d2e+5309abd2e-4247b2d2e-
     ------------------------------------------------------------------------
     1737acd2e-12116bcd2e+4076c2d2e+11422ad3e+8879bd3e-4485cd3e+3355d4e+
     ------------------------------------------------------------------------
     6040b3e2+10672a2ce2-12458abce2+1840b2ce2-12252ac2e2-13318bc2e2-61c3e2+
     ------------------------------------------------------------------------
     6571a2de2-8601abde2-8163b2de2+13259acde2-15204bcde2-13775c2de2-1054ad2e2
     ------------------------------------------------------------------------
     -11728bd2e2-12132cd2e2+7415d3e2+10246a2e3+4356abe3-3508b2e3-13855ace3+
     ------------------------------------------------------------------------
     14980bce3-253c2e3-14215ade3-9341bde3-14337cde3+2761d2e3-2685ae4-6839be4+
     ------------------------------------------------------------------------
     3210ce4-2649de4-11951e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R