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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 (2722a  + 2498a b - 11146a*b  + 4842b  - 4027a c - 2008a*b*c +
     ------------------------------------------------------------------------
           2           2          2         3         2               
     11826b c + 9564a*c  + 6020b*c  - 15536c  - 12020a d - 5507a*b*d +
     ------------------------------------------------------------------------
          2                                  2           2           2  
     3727b d + 14849a*c*d - 7579b*c*d + 1180c d - 4846a*d  + 15138b*d  +
     ------------------------------------------------------------------------
            2        3        2                     2              
     1220c*d  + 1960d  + 1076a e - 9171a*b*e - 3510b e + 940a*c*e -
     ------------------------------------------------------------------------
                       2                                              2   
     12602b*c*e - 1238c e - 7836a*d*e + 7705b*d*e - 5362c*d*e + 15962d e -
     ------------------------------------------------------------------------
             2           2           2          2       3        3         2 
     15406a*e  + 15157b*e  + 15662c*e  - 1093d*e  + 705e , 15766a  - 10141a b
     ------------------------------------------------------------------------
               2       3        2                     2           2  
     + 13505a*b  + 124b  + 6810a c + 4556a*b*c + 5273b c - 2990a*c  -
     ------------------------------------------------------------------------
            2         3        2                      2                
     7667b*c  - 13542c  - 4425a d + 11278a*b*d + 2627b d + 10643a*c*d +
     ------------------------------------------------------------------------
                      2           2           2         2         3        2 
     1778b*c*d + 3131c d + 8275a*d  + 12637b*d  + 369c*d  - 13354d  - 3262a e
     ------------------------------------------------------------------------
                         2                                   2              
     - 13881a*b*e + 6250b e - 11798a*c*e + 3046b*c*e + 14751c e - 13719a*d*e
     ------------------------------------------------------------------------
                                       2            2          2          2  
     + 15370b*d*e + 13552c*d*e - 13212d e + 10823a*e  - 9785b*e  - 6262c*e  +
     ------------------------------------------------------------------------
            2        3         3        2           2         3         2   
     6054d*e  + 5923e , - 8683a  - 5876a b + 8420a*b  - 11776b  - 13327a c +
     ------------------------------------------------------------------------
                        2            2           2         3       2   
     14765a*b*c + 13749b c + 11529a*c  + 13237b*c  - 15830c  - 612a d -
     ------------------------------------------------------------------------
                        2                                  2            2  
     15117a*b*d - 11650b d + 14363a*c*d - 296b*c*d - 14998c d + 14580a*d  +
     ------------------------------------------------------------------------
           2          2        3        2                      2             
     878b*d  + 3400c*d  - 7766d  + 1052a e - 13088a*b*e - 6971b e - 8454a*c*e
     ------------------------------------------------------------------------
                         2                                              2   
     + 9581b*c*e - 10219c e - 6563a*d*e - 11092b*d*e + 1093c*d*e - 1429d e -
     ------------------------------------------------------------------------
             2          2           2          2        3
     13665a*e  - 8253b*e  - 12009c*e  - 2124d*e  + 2456e )

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 = | ab2-10704b3+15408a2c+14591abc+8558b2c-2863ac2+2600bc2+3800c3-12725a2d+
     ------------------------------------------------------------------------
     14665abd-15407b2d-2532acd+525bcd-489c2d-12271ad2-5685bd2+2333cd2+2448d3-
     ------------------------------------------------------------------------
     3754a2e-2965abe-3575b2e+3039ace-67bce+5166c2e+9553ade+3315bde-3706cde+
     ------------------------------------------------------------------------
     5488d2e-7020ae2+15927be2+8553ce2-4de2-2779e3
     ------------------------------------------------------------------------
     a2b+15790b3-14192a2c+8964abc+11915b2c-5903ac2-12615bc2-5824c3+12344a2d-
     ------------------------------------------------------------------------
     898abd-7467b2d+813acd+8963bcd+5850c2d-5275ad2-13754bd2+14358cd2-13089d3-
     ------------------------------------------------------------------------
     13764a2e-11653abe-12709b2e-9567ace+3935bce-2845c2e-15418ade+1090bde-
     ------------------------------------------------------------------------
     5197cde-12525d2e+184ae2+12266be2+11028ce2-8220de2+14433e3
     ------------------------------------------------------------------------
     a3-3531b3+9981a2c-12345abc+293b2c-9383ac2+13972bc2-9787c3+920a2d+
     ------------------------------------------------------------------------
     11104abd-13262b2d+14957acd-9876bcd+3305c2d+11144ad2+15003bd2-13687cd2+
     ------------------------------------------------------------------------
     8704d3-14074a2e+13493abe-6269b2e-2737ace+5398bce+14617c2e-11236ade+
     ------------------------------------------------------------------------
     8497bde+3395cde+13750d2e-6934ae2+9113be2-14408ce2+13229de2-7118e3
     ------------------------------------------------------------------------
     b3c-11474a2c2+11748abc2+4379b2c2-3732ac3-6789bc3+9040c4-4081b3d+2970a2cd
     ------------------------------------------------------------------------
     -4992abcd-1470b2cd-2900ac2d+4040bc2d+7666c3d-15918a2d2+10490abd2-
     ------------------------------------------------------------------------
     7080b2d2-552acd2+4755bcd2+2823c2d2-961ad3-13540bd3+9094cd3+777d4-
     ------------------------------------------------------------------------
     12778b3e-5424a2ce+12879abce+4654b2ce+12171ac2e-5154bc2e-8155c3e-7614a2de
     ------------------------------------------------------------------------
     +14580abde+409b2de-1619acde+118bcde-10645c2de-13999ad2e+2271bd2e-225cd2e
     ------------------------------------------------------------------------
     +13462d3e-12790a2e2+4045abe2-4311b2e2+2598ace2-7487bce2+3124c2e2-
     ------------------------------------------------------------------------
     10526ade2-15721bde2-13923cde2-7103d2e2-8698ae3-7917be3+13016ce3+15178de3
     ------------------------------------------------------------------------
     -2079e4 b4-6142a2c2+3158abc2-8662b2c2+12771ac3+13473bc3+11152c4-13271b3d
     ------------------------------------------------------------------------
     +1202a2cd+8509abcd-8894b2cd+3623ac2d-11591bc2d-5515c3d-4930a2d2-9737abd2
     ------------------------------------------------------------------------
     +14912b2d2+4676acd2-5078bcd2-8257c2d2+10522ad3+6869bd3+11333cd3+10819d4-
     ------------------------------------------------------------------------
     2731b3e+3366a2ce-6669abce-14572b2ce-4090ac2e-14335bc2e+1482c3e+15874a2de
     ------------------------------------------------------------------------
     +12672abde-2282b2de-10559acde-11925bcde+8194c2de-10078ad2e-304bd2e+
     ------------------------------------------------------------------------
     819cd2e+12145d3e-2901a2e2-13248abe2+1232b2e2+11377ace2-14802bce2-
     ------------------------------------------------------------------------
     9072c2e2-1856ade2-173bde2+615cde2+13238d2e2+12396ae3-1633be3-8763ce3+
     ------------------------------------------------------------------------
     7668de3+6960e4 abc3+15990b2c3+13897ac4+2531bc4+14970c5+3239a2c2d-
     ------------------------------------------------------------------------
     3678abc2d+7562b2c2d+7941ac3d+11923bc3d+8260c4d+6738b3d2+8213a2cd2+
     ------------------------------------------------------------------------
     13851abcd2-11119b2cd2-4188ac2d2+10624bc2d2+4211c3d2+6290a2d3-7039abd3-
     ------------------------------------------------------------------------
     10898b2d3-1153acd3-15753bcd3-8276c2d3-11430ad4-6515bd4+12326cd4-14749d5+
     ------------------------------------------------------------------------
     6521a2c2e+9933abc2e+9805b2c2e+10933ac3e+9615bc3e-4397c4e-1745b3de+
     ------------------------------------------------------------------------
     824a2cde+12683abcde-15634b2cde+7760ac2de+14828bc2de-3336c3de+6356a2d2e-
     ------------------------------------------------------------------------
     15297abd2e+6970b2d2e+643acd2e+10474bcd2e+10360c2d2e+13438ad3e-953bd3e-
     ------------------------------------------------------------------------
     6109cd3e+12591d4e-7764b3e2-13632a2ce2-12932abce2+10987b2ce2+2913ac2e2-
     ------------------------------------------------------------------------
     2523bc2e2+13809c3e2+4543a2de2-5113abde2-4539b2de2+11599acde2+13124bcde2+
     ------------------------------------------------------------------------
     2915c2de2+10153ad2e2-12199bd2e2-8342cd2e2-6628d3e2+8655a2e3+5307abe3+
     ------------------------------------------------------------------------
     7974b2e3-6035ace3+11918bce3+2248c2e3+14297ade3+8367bde3+4082cde3-
     ------------------------------------------------------------------------
     5105d2e3-15890ae4+2939be4+15431ce4-3829de4+14549e5
     ------------------------------------------------------------------------
     a2c3+1779b2c3+14998ac4-4482bc4+15956c5-1675a2c2d-7821abc2d+7633b2c2d-
     ------------------------------------------------------------------------
     3444ac3d+97bc3d+10300c4d-2531b3d2-9757a2cd2+874abcd2+7773b2cd2+3309ac2d2
     ------------------------------------------------------------------------
     -14064bc2d2+10026c3d2+11537a2d3+6934abd3-15498b2d3-12104acd3+6990bcd3+
     ------------------------------------------------------------------------
     2725c2d3+4876ad4+7471bd4-4495cd4-8260d5-11406a2c2e+2133abc2e-3129b2c2e-
     ------------------------------------------------------------------------
     1256ac3e+9534bc3e+9336c4e+13693b3de-10549a2cde-7344abcde-1632b2cde+
     ------------------------------------------------------------------------
     14335ac2de-4922bc2de-323c3de-4182a2d2e-8500abd2e-7554b2d2e-4401acd2e-
     ------------------------------------------------------------------------
     15737bcd2e+197c2d2e-8634ad3e+12752bd3e-70cd3e+8550d4e+4766b3e2+789a2ce2-
     ------------------------------------------------------------------------
     4574abce2-8841b2ce2+12111ac2e2+4708bc2e2-7480c3e2-11171a2de2+8837abde2-
     ------------------------------------------------------------------------
     14280b2de2-10619acde2-7989bcde2+5641c2de2-1398ad2e2-12124bd2e2-
     ------------------------------------------------------------------------
     13946cd2e2+8429d3e2+6812a2e3-15781abe3-3158b2e3+6766ace3+8821bce3+
     ------------------------------------------------------------------------
     320c2e3-10582ade3-1761bde3-9143cde3+2613d2e3-5819ae4-400be4+2729ce4-
     ------------------------------------------------------------------------
     5788de4-10117e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R