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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 (13347a  - 15088a b - 4621a*b  + 11203b  - 8750a c + 13583a*b*c -
     ------------------------------------------------------------------------
           2            2          2       3       2                     2   
     10088b c + 12253a*c  - 7866b*c  - 602c  + 876a d - 13977a*b*d - 666b d -
     ------------------------------------------------------------------------
                                  2           2           2          2  
     244a*c*d - 13652b*c*d + 6961c d - 5119a*d  - 14094b*d  - 8631c*d  -
     ------------------------------------------------------------------------
          3         2                      2                            
     7519d  - 14539a e + 15237a*b*e - 1348b e - 14841a*c*e - 4300b*c*e -
     ------------------------------------------------------------------------
          2                                              2           2  
     5688c e - 11915a*d*e - 7204b*d*e - 393c*d*e + 13305d e + 6325a*e  +
     ------------------------------------------------------------------------
             2           2          2         3          3        2   
     11004b*e  - 12165c*e  - 5615d*e  + 14441e , - 10465a  + 3336a b -
     ------------------------------------------------------------------------
             2         3         2                    2            2  
     12820a*b  + 13971b  + 15642a c - 1076a*b*c + 551b c + 10040a*c  +
     ------------------------------------------------------------------------
            2        3        2                   2                
     3386b*c  + 6646c  + 7706a d - 6956a*b*d + 56b d + 13435a*c*d -
     ------------------------------------------------------------------------
                       2           2          2           2        3      2 
     14566b*c*d - 5337c d + 4169a*d  + 8997b*d  + 13260c*d  + 7175d  - 83a e
     ------------------------------------------------------------------------
                        2                                  2                
     - 2224a*b*e - 1135b e - 9850a*c*e - 10729b*c*e + 9165c e + 15753a*d*e +
     ------------------------------------------------------------------------
                                    2            2           2           2  
     13429b*d*e - 8388c*d*e - 15506d e + 15889a*e  + 13894b*e  - 15568c*e  -
     ------------------------------------------------------------------------
             2         3          3         2           2         3  
     13214d*e  + 10890e , - 15120a  + 15759a b - 9048a*b  - 12926b  -
     ------------------------------------------------------------------------
           2                     2            2          2        3        2 
     13419a c + 7218a*b*c - 3194b c - 11464a*c  - 6976b*c  - 8166c  - 9221a d
     ------------------------------------------------------------------------
                         2                                  2           2  
     - 7659a*b*d - 12893b d - 8850a*c*d - 6381b*c*d + 13355c d + 6816a*d  +
     ------------------------------------------------------------------------
            2         2       3        2                     2               
     2469b*d  - 931c*d  - 390d  + 7751a e - 472a*b*e + 11740b e + 8716a*c*e +
     ------------------------------------------------------------------------
                       2                                               2   
     10708b*c*e + 2936c e + 7595a*d*e + 1741b*d*e + 10126c*d*e + 12574d e -
     ------------------------------------------------------------------------
            2          2           2          2        3
     7488a*e  + 6598b*e  - 15863c*e  + 8884d*e  + 3931e )

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 = | ab2-1932b3-11602a2c-3153abc-2639b2c-11632ac2+3102bc2-15112c3+1516a2d+
     ------------------------------------------------------------------------
     14615abd+8706b2d+2966acd-14316bcd-12147c2d+9648ad2-3785bd2-9134cd2+
     ------------------------------------------------------------------------
     4730d3-11869a2e+134abe-7950b2e+44ace+7566bce+7008c2e+6010ade-6515bde+
     ------------------------------------------------------------------------
     4759cde+15653d2e+12711ae2+12425be2+1598ce2-9253de2-4986e3
     ------------------------------------------------------------------------
     a2b+12515b3+4177a2c+12192abc+6662b2c+3893ac2+7216bc2+5104c3-12374a2d-
     ------------------------------------------------------------------------
     4055abd+1182b2d+8260acd-10226bcd+1395c2d+3627ad2+11940bd2-9641cd2+3922d3
     ------------------------------------------------------------------------
     +3070a2e-13980abe+8484b2e-15093ace-4543bce+7224c2e+14530ade-3489bde-
     ------------------------------------------------------------------------
     4286cde+1638d2e-14598ae2+8199be2-14425ce2+15480de2-9667e3
     ------------------------------------------------------------------------
     a3-12064b3-4717a2c-2208abc-934b2c-599ac2+12506bc2+6604c3+10222a2d-
     ------------------------------------------------------------------------
     5517abd-6900b2d-9916acd-5996bcd+971c2d+10725ad2+7858bd2+14069cd2+3975d3+
     ------------------------------------------------------------------------
     4170a2e+7404abe-15593b2e+10414ace-9621bce-6384c2e-3830ade+7467bde+
     ------------------------------------------------------------------------
     8144cde-2132d2e-8991ae2-9306be2+12525ce2-8004de2+12533e3
     ------------------------------------------------------------------------
     b3c-7789a2c2+10145abc2+8603b2c2+4641ac3+1139bc3-12616c4-5612b3d+
     ------------------------------------------------------------------------
     11664a2cd-4346abcd-6432b2cd+1405ac2d+6072bc2d-9275c3d+3862a2d2-7905abd2+
     ------------------------------------------------------------------------
     11824b2d2+7471acd2-5430bcd2-5855c2d2-8750ad3+14266bd3-10400cd3-14379d4-
     ------------------------------------------------------------------------
     4895b3e-5698a2ce+13403abce+8934b2ce-11127ac2e+11982bc2e-6261c3e+8812a2de
     ------------------------------------------------------------------------
     -323abde+12862b2de-284acde+10599bcde-11220c2de-5330ad2e+14214bd2e+
     ------------------------------------------------------------------------
     12950cd2e-14306d3e+1061a2e2-6771abe2-14988b2e2-13303ace2+2835bce2-
     ------------------------------------------------------------------------
     12127c2e2-9476ade2-2770bde2-15743cde2+4765d2e2-7113ae3-14705be3+13225ce3
     ------------------------------------------------------------------------
     -9226de3+15354e4 b4-3002a2c2-5171abc2-8477b2c2+4075ac3-9961bc3-14608c4-
     ------------------------------------------------------------------------
     10585b3d-13200a2cd-264abcd-14083b2cd+13058ac2d+6722bc2d+5836c3d-
     ------------------------------------------------------------------------
     13991a2d2+11161abd2-14000b2d2-11152acd2-2918bcd2-10135c2d2-12610ad3+
     ------------------------------------------------------------------------
     9983bd3+8015cd3+4464d4-8823b3e+15443a2ce-15359abce+11589b2ce+4964ac2e-
     ------------------------------------------------------------------------
     10615bc2e+2973c3e-11876a2de+271abde-7822b2de-12715acde+2501bcde+188c2de+
     ------------------------------------------------------------------------
     8328ad2e+15103bd2e-13570cd2e+10258d3e-12329a2e2-424abe2-6983b2e2-
     ------------------------------------------------------------------------
     7327ace2-14172bce2+3697c2e2+12997ade2+3216bde2-10451cde2+3255d2e2-
     ------------------------------------------------------------------------
     1539ae3+2485be3+12979ce3-9043de3+7013e4
     ------------------------------------------------------------------------
     abc3-5506b2c3+1886ac4-10253bc4-11558c5-12674a2c2d+1432abc2d+13044b2c2d-
     ------------------------------------------------------------------------
     1238ac3d+13617bc3d-4572c4d-7915b3d2+4960a2cd2+7257abcd2-5735b2cd2+
     ------------------------------------------------------------------------
     9226ac2d2-6387bc2d2-9159c3d2-6026a2d3+6081abd3+12852b2d3+6082acd3-
     ------------------------------------------------------------------------
     15009bcd3-11080c2d3+4181ad4+2967bd4+5826cd4-11095d5+9157a2c2e-5585abc2e-
     ------------------------------------------------------------------------
     2986b2c2e-9605ac3e+10071bc3e-1649c4e+781b3de-11517a2cde-5406abcde-
     ------------------------------------------------------------------------
     10242b2cde-13196ac2de+12652bc2de+15517c3de+6462a2d2e-11034abd2e+
     ------------------------------------------------------------------------
     13363b2d2e-12586acd2e+13969bcd2e-770c2d2e-3874ad3e+7654bd3e-14513cd3e+
     ------------------------------------------------------------------------
     8772d4e-4088b3e2+9264a2ce2-11163abce2-13842b2ce2+15008ac2e2-15812bc2e2-
     ------------------------------------------------------------------------
     14955c3e2+11797a2de2+14546abde2-15790b2de2+14203acde2+4566bcde2+
     ------------------------------------------------------------------------
     6989c2de2+3790ad2e2-14725bd2e2-2116cd2e2-7115d3e2+14261a2e3-3456abe3-
     ------------------------------------------------------------------------
     3984b2e3-6417ace3+10807bce3+9987c2e3-9044ade3-6333bde3+4811cde3+6056d2e3
     ------------------------------------------------------------------------
     +10814ae4+8924be4-15185ce4+2348de4+15470e5
     ------------------------------------------------------------------------
     a2c3-11161b2c3+8441ac4-11868bc4-881c5-15037a2c2d-1142abc2d-10834b2c2d-
     ------------------------------------------------------------------------
     11662ac3d-9666bc3d-11276c4d-6638b3d2+11112a2cd2+6298abcd2-6794b2cd2-
     ------------------------------------------------------------------------
     1102ac2d2+11965bc2d2+2611c3d2-13892a2d3-10704abd3+14827b2d3-15325acd3+
     ------------------------------------------------------------------------
     6327bcd3-8344c2d3+6315ad4+3661bd4+7018cd4-6502d5-545a2c2e-8257abc2e-
     ------------------------------------------------------------------------
     6167b2c2e+14606ac3e+4637bc3e-15435c4e+12218b3de-9604a2cde-12881abcde-
     ------------------------------------------------------------------------
     1265b2cde+5650ac2de-8298bc2de+12048c3de-4540a2d2e+11061abd2e+3627b2d2e-
     ------------------------------------------------------------------------
     3086acd2e+9284bcd2e-8761c2d2e+3122ad3e+12542bd3e-13670cd3e+3654d4e+
     ------------------------------------------------------------------------
     5524b3e2-13221a2ce2-2872abce2+11082b2ce2+12885ac2e2-2510bc2e2+10680c3e2+
     ------------------------------------------------------------------------
     13815a2de2-4559abde2+12591b2de2+2140acde2+14806bcde2-11122c2de2-
     ------------------------------------------------------------------------
     8835ad2e2-13014bd2e2+15503cd2e2+10409d3e2+8050a2e3+10009abe3+4913b2e3+
     ------------------------------------------------------------------------
     10092ace3+15710bce3-27c2e3-2837ade3+1965bde3+13408cde3-7550d2e3+11332ae4
     ------------------------------------------------------------------------
     +14404be4+14240ce4+5955de4+1722e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R