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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 (12074a  + 10214a b + 6108a*b  + 4740b  - 13563a c + 637a*b*c -
     ------------------------------------------------------------------------
          2           2          2        3        2                     2   
     9636b c - 6785a*c  + 7171b*c  - 4513c  - 8291a d + 4323a*b*d + 6398b d +
     ------------------------------------------------------------------------
                                   2           2          2          2  
     6989a*c*d + 8820b*c*d - 11701c d - 8120a*d  + 2556b*d  + 2823c*d  -
     ------------------------------------------------------------------------
          3        2                      2                            
     1048d  - 4980a e + 13425a*b*e + 5570b e - 13454a*c*e - 8338b*c*e +
     ------------------------------------------------------------------------
          2                                               2           2  
     3464c e - 6683a*d*e - 6348b*d*e - 15081c*d*e + 10976d e - 8478a*e  +
     ------------------------------------------------------------------------
             2          2          2        3       3        2          2  
     10587b*e  + 3297c*e  - 2628d*e  + 4240e , 5280a  - 1420a b + 330a*b  +
     ------------------------------------------------------------------------
          3        2                      2           2          2         3
     6590b  - 1647a c + 7122a*b*c - 12561b c - 7810a*c  - 5668b*c  - 13990c 
     ------------------------------------------------------------------------
             2                      2                                 2   
     + 15872a d + 10757a*b*d - 4329b d + 3133a*c*d + 1209b*c*d + 2225c d +
     ------------------------------------------------------------------------
             2           2           2         3        2                
     11146a*d  - 15952b*d  - 10999c*d  + 14919d  - 9194a e - 11899a*b*e +
     ------------------------------------------------------------------------
          2                                  2                           
     4488b e + 1499a*c*e + 1841b*c*e + 14526c e + 7590a*d*e - 3713b*d*e -
     ------------------------------------------------------------------------
                      2           2          2          2           2  
     527c*d*e + 11003d e - 2712a*e  - 4669b*e  + 5324c*e  - 10042d*e  -
     ------------------------------------------------------------------------
           3       3        2           2        3        2               
     14672e , 3320a  - 5752a b + 4203a*b  - 6218b  - 8459a c - 2018a*b*c +
     ------------------------------------------------------------------------
          2           2          2         3         2                     2 
     2044b c - 1365a*c  - 6529b*c  + 11112c  - 12259a d - 2245a*b*d + 3826b d
     ------------------------------------------------------------------------
                                     2           2           2          2  
     - 11453a*c*d - 2826b*c*d - 7270c d - 1990a*d  - 11016b*d  - 8100c*d  -
     ------------------------------------------------------------------------
          3        2                     2                            
     1481d  + 7227a e + 5060a*b*e + 9824b e - 13030a*c*e - 4496b*c*e +
     ------------------------------------------------------------------------
          2                                             2          2  
     9281c e - 3792a*d*e - 6905b*d*e - 2049c*d*e + 9035d e - 383a*e  -
     ------------------------------------------------------------------------
            2          2           2        3
     8238b*e  - 8167c*e  - 15093d*e  + 1710e )

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 = | ab2-14927b3+11953a2c+15747abc+12322b2c-14437ac2-7780bc2+1920c3-3950a2d
     ------------------------------------------------------------------------
     +4941abd+9316b2d+646acd+2009bcd-296c2d+8955ad2+13764bd2-3536cd2-9328d3-
     ------------------------------------------------------------------------
     3819a2e+15193abe-8154b2e-15682ace-13716bce+2608c2e+10440ade+15679bde+
     ------------------------------------------------------------------------
     844cde-10868d2e+13107ae2+8417be2+8576ce2-11459de2+12220e3
     ------------------------------------------------------------------------
     a2b+9510b3+3614a2c+14279abc-447b2c+8981ac2-8604bc2+5650c3+12100a2d+
     ------------------------------------------------------------------------
     11937abd+6969b2d+13915acd+569bcd-12270c2d-14893ad2-13113bd2-14597cd2+
     ------------------------------------------------------------------------
     7176d3-8438a2e+2483abe-10142b2e+1261ace+6289bce-10264c2e-6872ade-2903bde
     ------------------------------------------------------------------------
     +12742cde-15411d2e+14918ae2+15052be2-10595ce2-2164de2+8267e3
     ------------------------------------------------------------------------
     a3+1431b3+15129a2c-6986abc+5817b2c+7559ac2+329bc2-967c3+11723a2d+
     ------------------------------------------------------------------------
     13153abd-509b2d+8606acd+9768bcd-3978c2d-8636ad2+13333bd2+6676cd2-2412d3-
     ------------------------------------------------------------------------
     13985a2e+7250abe-15285b2e+14939ace+4931bce-4145c2e-8621ade-14605bde-
     ------------------------------------------------------------------------
     4451cde-1651d2e-15270ae2-10462be2-2948ce2+11794de2+8512e3
     ------------------------------------------------------------------------
     b3c+4720a2c2+13835abc2-7162b2c2-8714ac3-13285bc3+9994c4+8584b3d-4319a2cd
     ------------------------------------------------------------------------
     +4232abcd+10239b2cd-13942ac2d+6205bc2d+2326c3d-35a2d2+15850abd2+
     ------------------------------------------------------------------------
     12179b2d2+14370acd2+14165bcd2+14140c2d2-6662ad3+13705bd3+3762cd3+5949d4+
     ------------------------------------------------------------------------
     5244b3e-6583a2ce-2020abce+7016b2ce-8531ac2e+5872bc2e+13299c3e-13444a2de-
     ------------------------------------------------------------------------
     5794abde-15402b2de+14211acde-462bcde-10358c2de+4669ad2e-11962bd2e-
     ------------------------------------------------------------------------
     11619cd2e+3890d3e+9674a2e2+12967abe2-14739b2e2-8114ace2+10780bce2+
     ------------------------------------------------------------------------
     8220c2e2+3662ade2+521bde2-12475cde2+12012d2e2+15466ae3+9818be3+15574ce3+
     ------------------------------------------------------------------------
     13730de3+9183e4 b4+5258a2c2+2397abc2-15790b2c2-14847ac3-14708bc3+9147c4-
     ------------------------------------------------------------------------
     4639b3d+12163a2cd-14817abcd+9724b2cd+1624ac2d+3742bc2d-10267c3d-
     ------------------------------------------------------------------------
     15844a2d2+9404abd2+2673b2d2+1072acd2-6991bcd2+929c2d2+3440ad3+6393bd3-
     ------------------------------------------------------------------------
     5598cd3-6152d4-15554b3e-11802a2ce+5291abce-4167b2ce+14273ac2e+3522bc2e+
     ------------------------------------------------------------------------
     11300c3e+14182a2de-7378abde-14777b2de-13189acde-14032bcde-14387c2de+
     ------------------------------------------------------------------------
     3819ad2e-3021bd2e+8679cd2e-3900d3e+1516a2e2+6986abe2-1141b2e2-10681ace2-
     ------------------------------------------------------------------------
     3446bce2-15139c2e2-8198ade2+6356bde2+6829cde2-15372d2e2+414ae3-13460be3+
     ------------------------------------------------------------------------
     1260ce3+10601de3+13765e4
     ------------------------------------------------------------------------
     abc3-1170b2c3+2972ac4+1930bc4-15637c5-2114a2c2d-14898abc2d+5462b2c2d+
     ------------------------------------------------------------------------
     15969ac3d-10676bc3d-11150c4d-8224b3d2-4043a2cd2-1453abcd2-6497b2cd2-
     ------------------------------------------------------------------------
     1284ac2d2-2072bc2d2-6773c3d2+8604a2d3+6819abd3+5397b2d3+4663acd3-
     ------------------------------------------------------------------------
     11700bcd3+14882c2d3+2479ad4+2037bd4-6852cd4-7224d5+7256a2c2e-809abc2e+
     ------------------------------------------------------------------------
     12979b2c2e-12898ac3e+10601bc3e-1763c4e-1835b3de+14573a2cde-10326abcde-
     ------------------------------------------------------------------------
     12812b2cde-2522ac2de-13451bc2de-6348c3de-6444a2d2e+301abd2e-11497b2d2e-
     ------------------------------------------------------------------------
     12912acd2e-9819bcd2e+9503c2d2e-6792ad3e+104bd3e-9016cd3e+7153d4e-
     ------------------------------------------------------------------------
     14576b3e2+756a2ce2-10142abce2+7248b2ce2+2714ac2e2-11712bc2e2-11557c3e2+
     ------------------------------------------------------------------------
     247a2de2+5533abde2-6801b2de2-9459acde2+2692bcde2-13351c2de2+9270ad2e2+
     ------------------------------------------------------------------------
     121bd2e2+8985cd2e2-3414d3e2+12720a2e3-13526abe3-3421b2e3-10408ace3+
     ------------------------------------------------------------------------
     13382bce3+2582c2e3+13983ade3+7723bde3+13811cde3+8640d2e3-5455ae4+3663be4
     ------------------------------------------------------------------------
     +29ce4-7655de4-4424e5 a2c3+11967b2c3-418ac4-4689bc4+15085c5+15792a2c2d-
     ------------------------------------------------------------------------
     9272abc2d-14367b2c2d+13077ac3d-13034bc3d+9059c4d-7259b3d2+13515a2cd2-
     ------------------------------------------------------------------------
     930abcd2-8326b2cd2+10261ac2d2+3384bc2d2+13169c3d2+12271a2d3-5750abd3-
     ------------------------------------------------------------------------
     7674b2d3-64acd3-14913bcd3-14192c2d3-5802ad4+8183bd4-11222cd4-12938d5+
     ------------------------------------------------------------------------
     10906a2c2e-13729abc2e-10620b2c2e-4941ac3e+10433bc3e-1123c4e-7467b3de-
     ------------------------------------------------------------------------
     14822a2cde-14311abcde+683b2cde+1079ac2de-12547bc2de+13647c3de+15687a2d2e
     ------------------------------------------------------------------------
     +15451abd2e+4816b2d2e+9892acd2e-6292bcd2e-11822c2d2e-6862ad3e-12765bd3e-
     ------------------------------------------------------------------------
     5663cd3e-10281d4e+979b3e2+4403a2ce2-1190abce2+3701b2ce2+8648ac2e2-
     ------------------------------------------------------------------------
     6483bc2e2+5971c3e2-8689a2de2+4233abde2-9934b2de2-9318acde2+10605bcde2-
     ------------------------------------------------------------------------
     6215c2de2-13251ad2e2-7934bd2e2+13324cd2e2-10646d3e2+15701a2e3+12970abe3-
     ------------------------------------------------------------------------
     8932b2e3+187ace3+12499bce3-8509c2e3-6458ade3-13214bde3+7179cde3+9564d2e3
     ------------------------------------------------------------------------
     -11027ae4-9375be4+9704ce4-7443de4+12162e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R