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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 (107a  + 4376a b - 5307a*b  - 6203b  - 5570a c + 8570a*b*c +
     ------------------------------------------------------------------------
           2            2           2        3        2                
     12365b c - 10480a*c  - 11950b*c  + 9534c  + 3187a d - 15344a*b*d -
     ------------------------------------------------------------------------
           2                                  2           2          2  
     13508b d + 10359a*c*d + 8231b*c*d - 7216c d - 8251a*d  + 5026b*d  +
     ------------------------------------------------------------------------
            2        3        2                     2               
     7256c*d  + 9033d  + 3783a e + 8444a*b*e - 9480b e - 7464a*c*e +
     ------------------------------------------------------------------------
                       2                                              2   
     5864b*c*e - 10125c e + 2653a*d*e + 10259b*d*e - 5321c*d*e + 5107d e +
     ------------------------------------------------------------------------
            2          2          2          2        3        3         2   
     5071a*e  - 7501b*e  + 6230c*e  - 3996d*e  + 9398e , 13177a  + 13990a b +
     ------------------------------------------------------------------------
             2        3         2                     2           2  
     10866a*b  + 1031b  - 11521a c + 5398a*b*c - 2036b c + 2627a*c  -
     ------------------------------------------------------------------------
            2        3        2                     2               
     6922b*c  - 3589c  - 1309a d + 5549a*b*d - 6325b d - 5326a*c*d -
     ------------------------------------------------------------------------
                      2           2          2           2        3        2 
     5080b*c*d - 5599c d + 5679a*d  + 8922b*d  + 13707c*d  + 8971d  - 1779a e
     ------------------------------------------------------------------------
                         2                                 2               
     - 7061a*b*e - 11740b e + 2998a*c*e + 1236b*c*e + 4259c e - 7152a*d*e -
     ------------------------------------------------------------------------
                                    2            2          2         2  
     5006b*d*e - 13892c*d*e - 14165d e + 15317a*e  + 8880b*e  - 994c*e  -
     ------------------------------------------------------------------------
            2        3          3        2            2         3        2   
     3002d*e  + 2177e , - 10521a  - 1946a b - 11045a*b  - 15333b  - 7021a c +
     ------------------------------------------------------------------------
                       2           2          2        3        2   
     10370a*b*c - 7600b c - 7028a*c  - 3560b*c  + 5969c  + 1206a d -
     ------------------------------------------------------------------------
                      2                               2           2  
     9702a*b*d - 6040b d - 15a*c*d - 7194b*c*d - 5483c d + 6377a*d  -
     ------------------------------------------------------------------------
            2          2         3        2                     2   
     6627b*d  + 9074c*d  - 11726d  - 6453a e + 8886a*b*e - 3164b e -
     ------------------------------------------------------------------------
                                  2                                         
     6723a*c*e - 7092b*c*e + 5874c e - 11435a*d*e + 4700b*d*e - 15250c*d*e +
     ------------------------------------------------------------------------
          2           2          2           2         2        3
     8022d e - 1192a*e  + 9797b*e  + 10567c*e  + 295d*e  + 2292e )

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 = | ab2-11391b3-5320a2c-13396abc-13493b2c-1240ac2+7608bc2-3232c3-1589a2d-
   ------------------------------------------------------------------------
   10031abd+4261b2d-8339acd+11672bcd-8273c2d+9919ad2+2784bd2-9469cd2-467d3+
   ------------------------------------------------------------------------
   10443a2e-8047abe-804b2e-8732ace-4103bce-11320c2e+15116ade+8081bde+
   ------------------------------------------------------------------------
   13170cde+8155d2e+14681ae2+6840be2-4060ce2+4697de2-10579e3
   ------------------------------------------------------------------------
   a2b-1245b3-6307a2c-11752abc+4739b2c-7117ac2+4604bc2-2102c3-1103a2d+
   ------------------------------------------------------------------------
   14036abd+12312b2d+4931acd+10339bcd-8058c2d+11980ad2+8057bd2+13937cd2-
   ------------------------------------------------------------------------
   85d3+14455a2e+8260abe+2037b2e+9647ace-15410bce+921c2e+9551ade-3204bde-
   ------------------------------------------------------------------------
   8696cde+6879d2e+12651ae2-7056be2+10714ce2-1787de2+14941e3
   ------------------------------------------------------------------------
   a3+8403b3-1190a2c-15323abc+13420b2c+6342ac2+15466bc2-3361c3-7950a2d-
   ------------------------------------------------------------------------
   1838abd+14555b2d+12332acd+5108bcd+2903c2d-5539ad2-10429bd2-2305cd2-
   ------------------------------------------------------------------------
   7937d3-1697a2e+9091abe+14609b2e-8778ace+9245bce+4957c2e-5753ade+10314bde
   ------------------------------------------------------------------------
   +1752cde+12225d2e+15200ae2-1840be2+2970ce2+7214de2-6578e3
   ------------------------------------------------------------------------
   b3c+5081a2c2-8259abc2-14376b2c2+3188ac3-769bc3+9944c4-7494b3d+7852a2cd+
   ------------------------------------------------------------------------
   10219abcd+4847b2cd+1132ac2d-7248bc2d-1825c3d-5344a2d2-6809abd2+11727b2d2
   ------------------------------------------------------------------------
   -3821acd2-12167bcd2-7415c2d2-5912ad3+8110bd3+4202cd3+1057d4-2905b3e+
   ------------------------------------------------------------------------
   5014a2ce+6780abce+15730b2ce-14498ac2e+8288bc2e+8027c3e+4400a2de-2006abde
   ------------------------------------------------------------------------
   -11279b2de-12106acde+85bcde+4702c2de-6507ad2e+375bd2e+1276cd2e-75d3e+
   ------------------------------------------------------------------------
   8509a2e2+11161abe2-1461b2e2-13786ace2+13233bce2-13146c2e2-4294ade2+
   ------------------------------------------------------------------------
   2115bde2-8341cde2+6748d2e2-3680ae3-9994be3+13199ce3+9404de3-7442e4
   ------------------------------------------------------------------------
   b4+8597a2c2+2008abc2+10927b2c2+11183ac3-2334bc3+2651c4-11800b3d-2247a2cd
   ------------------------------------------------------------------------
   -3514abcd-10663b2cd-4703ac2d+3223bc2d-31c3d-8220a2d2-14532abd2+9140b2d2-
   ------------------------------------------------------------------------
   15426acd2-8204bcd2+4041c2d2+1695ad3-12050bd3-9450cd3-1043d4-13002b3e+
   ------------------------------------------------------------------------
   7568a2ce-8466abce+2203b2ce-520ac2e-10283bc2e+15655c3e-4914a2de+14891abde
   ------------------------------------------------------------------------
   +7008b2de+4316acde+5553bcde+13770c2de+14595ad2e-3748bd2e-3132cd2e-
   ------------------------------------------------------------------------
   4247d3e+5929a2e2-223abe2-13618b2e2-4800ace2-14221bce2-10331c2e2+
   ------------------------------------------------------------------------
   15289ade2+11676bde2+13221cde2+10864d2e2-3953ae3-12193be3-3354ce3-9362de3
   ------------------------------------------------------------------------
   +5003e4 abc3+14563b2c3+7076ac4-3805bc4-998c5-11331a2c2d+14001abc2d-
   ------------------------------------------------------------------------
   9559b2c2d+13974ac3d+1972bc3d+7522c4d-15602b3d2-5593a2cd2-14073abcd2-
   ------------------------------------------------------------------------
   9437b2cd2-3338ac2d2+3652bc2d2-7670c3d2+2680a2d3+8342abd3-14061b2d3+
   ------------------------------------------------------------------------
   1909acd3+10705bcd3+6541c2d3+1512ad4-6422bd4+6813cd4+12171d5+849a2c2e-
   ------------------------------------------------------------------------
   4307abc2e-11850b2c2e-11391ac3e-13420bc3e-15487c4e-959b3de-64a2cde+
   ------------------------------------------------------------------------
   3520abcde+11428b2cde+6361ac2de-9883bc2de-8624c3de+2129a2d2e+15459abd2e-
   ------------------------------------------------------------------------
   9432b2d2e-11415acd2e-14940bcd2e+1863c2d2e-14855ad3e-14014bd3e-2661cd3e-
   ------------------------------------------------------------------------
   4619d4e-950b3e2+10361a2ce2-5000abce2+15729b2ce2+2961ac2e2-1806bc2e2-
   ------------------------------------------------------------------------
   15236c3e2-4319a2de2-1113abde2+3734b2de2+7689acde2-1337bcde2-12800c2de2+
   ------------------------------------------------------------------------
   13550ad2e2-312bd2e2+3671cd2e2-7034d3e2-14914a2e3-9352abe3-7633b2e3-
   ------------------------------------------------------------------------
   8892ace3-5755bce3+7215c2e3-13530ade3-4610bde3-338cde3+8929d2e3-6303ae4-
   ------------------------------------------------------------------------
   9672be4-8826ce4-5872de4-14853e5
   ------------------------------------------------------------------------
   a2c3+12817b2c3+4227ac4-1643bc4+11820c5+13424a2c2d+421abc2d-9343b2c2d-
   ------------------------------------------------------------------------
   8104ac3d-208bc3d-2264c4d-4618b3d2-9256a2cd2-13197abcd2+12517b2cd2+
   ------------------------------------------------------------------------
   8613ac2d2-10602bc2d2+8080c3d2-12173a2d3+7845abd3+11470b2d3-15645acd3+
   ------------------------------------------------------------------------
   14068bcd3+1614c2d3-2477ad4+14757bd4-10489cd4+8593d5-8625a2c2e+547abc2e+
   ------------------------------------------------------------------------
   9666b2c2e-7182ac3e+4055bc3e-2460c4e+11055b3de+15233a2cde-2278abcde+
   ------------------------------------------------------------------------
   14497b2cde-8061ac2de+9802bc2de+14712c3de-8847a2d2e-2836abd2e+7338b2d2e+
   ------------------------------------------------------------------------
   9402acd2e+10024bcd2e+15998c2d2e-3436ad3e+12062bd3e+7886cd3e+7886d4e+
   ------------------------------------------------------------------------
   9628b3e2-6744a2ce2-1535abce2-1802b2ce2+10769ac2e2+269bc2e2-8136c3e2+
   ------------------------------------------------------------------------
   1243a2de2-763abde2-6341b2de2-2584acde2+11620bcde2+10174c2de2+10935ad2e2+
   ------------------------------------------------------------------------
   6495bd2e2+4855cd2e2-12580d3e2+8827a2e3+15208abe3+11344b2e3+3458ace3-
   ------------------------------------------------------------------------
   69bce3-4243c2e3+3442ade3-7654bde3-15312cde3+11297d2e3+14040ae4+10946be4+
   ------------------------------------------------------------------------
   15202ce4+14150de4+3493e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R