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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 (10356a  - 1976a b - 15394a*b  - 11918b  + 11567a c + 1851a*b*c -
     ------------------------------------------------------------------------
          2            2           2        3        2                
     7124b c - 15224a*c  - 12085b*c  + 3998c  - 2368a d - 11142a*b*d +
     ------------------------------------------------------------------------
           2                                2           2           2  
     15957b d + 8143a*c*d + 8725b*c*d + 105c d - 2094a*d  + 10683b*d  -
     ------------------------------------------------------------------------
             2        3         2                      2               
     13853c*d  - 2663d  + 15816a e - 1184a*b*e - 10543b e - 2765a*c*e -
     ------------------------------------------------------------------------
                       2                                                2   
     4124b*c*e - 11361c e + 11958a*d*e + 11152b*d*e - 11936c*d*e - 5071d e +
     ------------------------------------------------------------------------
            2          2           2           2        3       3        2   
     1278a*e  - 1856b*e  + 15070c*e  + 10341d*e  - 1444e , 2327a  + 5072a b +
     ------------------------------------------------------------------------
            2        3        2                     2            2  
     5576a*b  - 5039b  - 2180a c + 4983a*b*c - 4213b c - 15895a*c  +
     ------------------------------------------------------------------------
             2        3        2                      2               
     15209b*c  + 7722c  + 9765a d + 5586a*b*d - 13160b d + 3379a*c*d +
     ------------------------------------------------------------------------
                      2           2          2          2         3       2 
     9587b*c*d - 5563c d + 2669a*d  + 8626b*d  + 9264c*d  - 12693d  + 438a e
     ------------------------------------------------------------------------
                        2                                  2               
     - 2697a*b*e - 7177b e - 15641a*c*e + 3626b*c*e - 2698c e - 3116a*d*e +
     ------------------------------------------------------------------------
                                  2            2           2          2  
     638b*d*e + 11843c*d*e + 5100d e + 14342a*e  - 11608b*e  + 2339c*e  -
     ------------------------------------------------------------------------
             2         3       3        2           2        3       2   
     11888d*e  + 12727e , 1087a  + 1088a b - 6008a*b  + 4808b  - 704a c -
     ------------------------------------------------------------------------
                        2            2          2        3        2   
     10960a*b*c - 14972b c - 12423a*c  - 8762b*c  + 5212c  - 8077a d -
     ------------------------------------------------------------------------
                       2                                    2           2  
     9444a*b*d + 13345b d + 16000a*c*d + 11671b*c*d - 12529c d - 1880a*d  -
     ------------------------------------------------------------------------
            2           2        3         2                      2   
     7230b*d  + 12817c*d  - 9744d  - 12950a e - 1463a*b*e - 13551b e +
     ------------------------------------------------------------------------
                                   2                                         
     4016a*c*e + 14840b*c*e + 1394c e + 14877a*d*e + 13546b*d*e - 1648c*d*e -
     ------------------------------------------------------------------------
           2        2          2          2           2         3
     12587d e - 4a*e  + 5640b*e  - 5646c*e  + 12368d*e  + 10904e )

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 = | ab2-5736b3-6934a2c-7188abc-2675b2c-15280ac2+10498bc2-6399c3-15215a2d-
     ------------------------------------------------------------------------
     15024abd+9175b2d+10644acd+15849bcd-5959c2d+15490ad2-4621bd2+4324cd2+
     ------------------------------------------------------------------------
     5807d3+12640a2e-105abe-13633b2e-6518ace+11627bce-13184c2e-3759ade+
     ------------------------------------------------------------------------
     13508bde+7391cde+5873d2e-8477ae2+11072be2-7777ce2-12876de2+12602e3
     ------------------------------------------------------------------------
     a2b+12375b3-6789a2c+9875abc-5562b2c-5625ac2-2171bc2+4380c3-995a2d+
     ------------------------------------------------------------------------
     15941abd-8539b2d+6362acd-8267bcd+8741c2d+773ad2+13542bd2-7796cd2-1235d3-
     ------------------------------------------------------------------------
     3385a2e+4992abe-15018b2e-12057ace+265bce+14511c2e-4949ade-1669bde-
     ------------------------------------------------------------------------
     6020cde+12084d2e+15063ae2-6440be2-3314ce2-324de2+2361e3
     ------------------------------------------------------------------------
     a3+12295b3+15046a2c+8465abc+7020b2c-13034ac2-15741bc2-15252c3-4704a2d+
     ------------------------------------------------------------------------
     9812abd+623b2d-2843acd+8679bcd-14375c2d-2631ad2+15571bd2+15492cd2+7503d3
     ------------------------------------------------------------------------
     -10051a2e+13176abe-5718b2e+9256ace-13625bce-11728c2e+4211ade+5831bde-
     ------------------------------------------------------------------------
     3470cde-6261d2e+4637ae2-9666be2-3489ce2-8975de2+11037e3
     ------------------------------------------------------------------------
     b3c-10437a2c2+923abc2+4737b2c2-6441ac3-15918bc3+1224c4-15637b3d-
     ------------------------------------------------------------------------
     14826a2cd-10999abcd-9503b2cd-13767ac2d-3070bc2d-8542c3d+983a2d2+7278abd2
     ------------------------------------------------------------------------
     -3939b2d2+7125acd2+8401bcd2-5872c2d2-14870ad3-6685bd3+5376cd3+2614d4-
     ------------------------------------------------------------------------
     1969b3e-5001a2ce-8442abce-2054b2ce-13973ac2e-13022bc2e-541c3e-6168a2de-
     ------------------------------------------------------------------------
     4657abde-2189b2de+837acde+8098bcde+4682c2de+2019ad2e+4062bd2e+3746cd2e+
     ------------------------------------------------------------------------
     550d3e-12980a2e2-12712abe2-8646b2e2+11915ace2-2400bce2-7712c2e2-4571ade2
     ------------------------------------------------------------------------
     -15704bde2+7367cde2+7382d2e2+107ae3+10876be3+384ce3-10601de3+15140e4
     ------------------------------------------------------------------------
     b4+11698a2c2-3153abc2+13518b2c2+15176ac3-10418bc3-15934c4-6663b3d-
     ------------------------------------------------------------------------
     9498a2cd+4066abcd-14081b2cd-505ac2d-12608bc2d-3305c3d-12867a2d2-4286abd2
     ------------------------------------------------------------------------
     -2053b2d2-7308acd2-1745bcd2-1568c2d2+12132ad3+7116bd3-5933cd3-5415d4+
     ------------------------------------------------------------------------
     6900b3e-4188a2ce+8697abce+12560b2ce+13311ac2e-13856bc2e-12896c3e-
     ------------------------------------------------------------------------
     2056a2de+12057abde+2252b2de-2089acde-10524bcde+1857c2de+5028ad2e-
     ------------------------------------------------------------------------
     10758bd2e-10360cd2e+2672d3e-8237a2e2-10abe2-12311b2e2-12200ace2-
     ------------------------------------------------------------------------
     12897bce2+4585c2e2-2231ade2-454bde2+10970cde2+12583d2e2-8883ae3-6113be3+
     ------------------------------------------------------------------------
     7447ce3-9189de3-2265e4 abc3+5916b2c3-898ac4-5017bc4-13023c5+2908a2c2d-
     ------------------------------------------------------------------------
     13533abc2d+3027b2c2d-15787ac3d-2856bc3d+5749c4d-11626b3d2-6620a2cd2-
     ------------------------------------------------------------------------
     6595abcd2+590b2cd2-15131ac2d2+11073bc2d2-12541c3d2-12501a2d3-11378abd3-
     ------------------------------------------------------------------------
     9013b2d3-4267acd3-7117bcd3+8396c2d3-4197ad4-4745bd4-13800cd4+9134d5+
     ------------------------------------------------------------------------
     12892a2c2e+11017abc2e+2612b2c2e+11993ac3e+14069bc3e+11645c4e-9969b3de-
     ------------------------------------------------------------------------
     303a2cde+2654abcde+8601b2cde+7173ac2de+6893bc2de+10295c3de-10202a2d2e-
     ------------------------------------------------------------------------
     6299abd2e+13422b2d2e+812acd2e+2253bcd2e+5037c2d2e+5025ad3e-1496bd3e+
     ------------------------------------------------------------------------
     4402cd3e+15397d4e-4972b3e2+2363a2ce2+4304abce2+13489b2ce2+9863ac2e2+
     ------------------------------------------------------------------------
     13428bc2e2+9961c3e2+12440a2de2-6362abde2+1259b2de2+1194acde2-14721bcde2-
     ------------------------------------------------------------------------
     189c2de2-6008ad2e2-15432bd2e2-4352cd2e2-565d3e2-10469a2e3-9120abe3-
     ------------------------------------------------------------------------
     9743b2e3-4987ace3-8506bce3+13905c2e3-6052ade3+9780bde3-14533cde3-
     ------------------------------------------------------------------------
     4713d2e3-3573ae4+14616be4+3856ce4+10798de4-10055e5
     ------------------------------------------------------------------------
     a2c3-10505b2c3+4274ac4+3051bc4+10122c5+1848a2c2d+15707abc2d+5882b2c2d-
     ------------------------------------------------------------------------
     3830ac3d-13165bc3d-7046c4d+4464b3d2+11693a2cd2-7026abcd2+5090b2cd2-
     ------------------------------------------------------------------------
     8889ac2d2-3922bc2d2-15573c3d2-2619a2d3+571abd3-4185b2d3-13123acd3+
     ------------------------------------------------------------------------
     12988bcd3+4926c2d3-10378ad4-10156bd4-817cd4-13191d5-5201a2c2e-8284abc2e+
     ------------------------------------------------------------------------
     2633b2c2e+14529ac3e-705bc3e-13453c4e+6833b3de-3205a2cde+10455abcde-
     ------------------------------------------------------------------------
     5310b2cde+7224ac2de+1629bc2de-10622c3de-15036a2d2e-10314abd2e-3444b2d2e-
     ------------------------------------------------------------------------
     8270acd2e+10124bcd2e-3870c2d2e+7162ad3e+2346bd3e-3030cd3e+3366d4e+
     ------------------------------------------------------------------------
     1493b3e2+7533a2ce2+583abce2-8428b2ce2+4132ac2e2+836bc2e2-302c3e2-
     ------------------------------------------------------------------------
     8653a2de2-2552abde2+1361b2de2+3016acde2+3901bcde2+2249c2de2+12330ad2e2+
     ------------------------------------------------------------------------
     4946bd2e2-15834cd2e2-13042d3e2-11123a2e3+7806abe3-15899b2e3-9490ace3-
     ------------------------------------------------------------------------
     954bce3-4166c2e3+9144ade3-5996bde3-4243cde3+14232d2e3-2301ae4-14066be4+
     ------------------------------------------------------------------------
     14100ce4+1125de4-6606e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R