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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 (- 5854a  - 7749a b + 9127a*b  + 7806b  + 11938a c + 12655a*b*c +
     ------------------------------------------------------------------------
           2           2           2        3        2               
     14937b c - 4203a*c  + 12589b*c  - 8816c  - 7554a d + 2429a*b*d +
     ------------------------------------------------------------------------
           2                                  2           2          2  
     14386b d - 9151a*c*d + 10096b*c*d + 8532c d - 5574a*d  + 9598b*d  +
     ------------------------------------------------------------------------
            2         3         2                       2               
     7268c*d  - 14798d  - 15064a e - 14934a*b*e - 15649b e - 6477a*c*e +
     ------------------------------------------------------------------------
                      2                                               2   
     3155b*c*e + 2226c e - 12967a*d*e - 3287b*d*e + 9661c*d*e + 13911d e +
     ------------------------------------------------------------------------
           2          2          2          2         3       3        2   
     165a*e  - 2801b*e  + 9141c*e  - 9188d*e  - 13413e , 9681a  + 8809a b -
     ------------------------------------------------------------------------
             2        3         2                     2            2  
     11953a*b  + 2273b  - 11682a c + 9806a*b*c + 3157b c - 11304a*c  +
     ------------------------------------------------------------------------
             2        3        2                      2               
     10584b*c  + 9824c  - 7882a d - 4841a*b*d - 11993b d + 1773a*c*d -
     ------------------------------------------------------------------------
                       2           2          2          2        3        2 
     3981b*c*d + 11231c d - 8750a*d  + 3962b*d  + 6155c*d  + 8966d  - 5120a e
     ------------------------------------------------------------------------
                          2                                  2              
     + 13171a*b*e + 13031b e - 3598a*c*e - 14833b*c*e - 2179c e + 13646a*d*e
     ------------------------------------------------------------------------
                                    2           2          2          2  
     + 6752b*d*e + 3652c*d*e + 6249d e - 8582a*e  - 1454b*e  + 9596c*e  +
     ------------------------------------------------------------------------
            2        3         3        2           2         3        2   
     9599d*e  + 8354e , - 2098a  - 6228a b + 6862a*b  + 10026b  + 8403a c -
     ------------------------------------------------------------------------
                       2           2           2         3       2   
     13075a*b*c + 4368b c + 2474a*c  + 10476b*c  - 14808c  + 441a d +
     ------------------------------------------------------------------------
                       2                                  2           2  
     14355a*b*d + 8171b d + 1474a*c*d - 15209b*c*d + 4996c d - 6295a*d  +
     ------------------------------------------------------------------------
           2          2       3        2                    2                
     211b*d  + 7354c*d  - 773d  - 7388a e + 300a*b*e + 6962b e + 11007a*c*e +
     ------------------------------------------------------------------------
                     2                                             2   
     9900b*c*e + 123c e - 8770a*d*e - 418b*d*e - 9428c*d*e + 15333d e +
     ------------------------------------------------------------------------
             2           2          2           2        3
     10696a*e  - 13211b*e  - 8166c*e  - 11242d*e  - 6058e )

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+4888b3-14221a2c+2909abc-7353b2c+11624ac2-13893bc2-10808c3-1251a2d+
     ------------------------------------------------------------------------
     14abd+372b2d+10810acd+12082bcd-8480c2d+3154ad2-4275bd2-5266cd2-11460d3+
     ------------------------------------------------------------------------
     8522a2e+10074abe+14590b2e-10975ace-7294bce-9112c2e+1288ade+3968bde-
     ------------------------------------------------------------------------
     5201cde-8537d2e+5234ae2+8086be2+3397ce2-7764de2+4451e3
     ------------------------------------------------------------------------
     a2b+14501b3-6539a2c+4920abc+7521b2c-6557ac2-10540bc2-779c3+5277a2d+
     ------------------------------------------------------------------------
     15855abd-5377b2d-15980acd-14061bcd-3708c2d-7338ad2-5256bd2-15198cd2+
     ------------------------------------------------------------------------
     2317d3+9493a2e-4361abe+7708b2e-5221ace-652bce+8379c2e-4637ade-7945bde+
     ------------------------------------------------------------------------
     10488cde-14351d2e-14795ae2+14922be2+11412ce2+13241de2+11741e3
     ------------------------------------------------------------------------
     a3-7295b3+7048a2c-2537abc+14577b2c+10195ac2-5218bc2-6519c3+12780a2d+
     ------------------------------------------------------------------------
     9550abd-8864b2d+6645acd-11617bcd+14723c2d-6689ad2-11239bd2-4877cd2+
     ------------------------------------------------------------------------
     3095d3+7781a2e+560abe-4056b2e-5164ace+528bce+467c2e-4655ade-3097bde-
     ------------------------------------------------------------------------
     487cde-12526d2e+13990ae2-12672be2-9888ce2-15455de2+1246e3
     ------------------------------------------------------------------------
     b3c-12225a2c2-7748abc2+4276b2c2-7519ac3+13509bc3-2325c4+14688b3d-
     ------------------------------------------------------------------------
     4573a2cd+9736abcd-4978b2cd-7860ac2d+8753bc2d+1726c3d-3031a2d2-2622abd2+
     ------------------------------------------------------------------------
     8896b2d2-5334acd2-9876bcd2-9223c2d2+15552ad3-86bd3+3042cd3-10155d4+
     ------------------------------------------------------------------------
     6709b3e+12422a2ce+1944abce+15969b2ce+5613ac2e-7637bc2e-5106c3e-14015a2de
     ------------------------------------------------------------------------
     -13459abde+1361b2de-2049acde+8640bcde-11113c2de+9400ad2e+4219bd2e+
     ------------------------------------------------------------------------
     951cd2e-12742d3e+2406a2e2+4012abe2-9371b2e2+3430ace2+7083bce2+462c2e2-
     ------------------------------------------------------------------------
     5733ade2+15457bde2+2613cde2+1764d2e2-15373ae3+9287be3+4859ce3-2078de3+
     ------------------------------------------------------------------------
     11730e4 b4+15262a2c2+15523abc2+8027b2c2+11997ac3+1477bc3+13171c4-
     ------------------------------------------------------------------------
     14332b3d-1568a2cd+11806abcd-6613b2cd-6812ac2d-1449bc2d+13055c3d-4603a2d2
     ------------------------------------------------------------------------
     +3222abd2+29b2d2-10674acd2-2847bcd2-5900c2d2+2137ad3-3176bd3+10354cd3-
     ------------------------------------------------------------------------
     6511d4-1811b3e-11466a2ce+6719abce+11035b2ce-2311ac2e-12486bc2e+4860c3e+
     ------------------------------------------------------------------------
     6541a2de-1175abde+8601b2de+2847acde+1749bcde+854c2de+460ad2e+10422bd2e-
     ------------------------------------------------------------------------
     4611cd2e-9066d3e+9407a2e2+408abe2+8700b2e2+659ace2+1204bce2-8312c2e2-
     ------------------------------------------------------------------------
     1823ade2+15668bde2+5558cde2+1241d2e2+1669ae3-9291be3+3518ce3+14602de3-
     ------------------------------------------------------------------------
     31e4 abc3+12156b2c3+8614ac4+11316bc4-15974c5+6304a2c2d+9446abc2d+
     ------------------------------------------------------------------------
     12271b2c2d-5228ac3d-3147bc3d+14866c4d+4158b3d2-8038a2cd2-2327abcd2-
     ------------------------------------------------------------------------
     8846b2cd2-10970ac2d2-4927bc2d2-12478c3d2-165a2d3+13102abd3+8433b2d3-
     ------------------------------------------------------------------------
     5556acd3+300bcd3-11007c2d3-4795ad4+13040bd4-907cd4+5821d5-5303a2c2e-
     ------------------------------------------------------------------------
     14057abc2e-14267b2c2e-15500ac3e-7610bc3e+4920c4e+674b3de-12870a2cde-
     ------------------------------------------------------------------------
     3756abcde-10462b2cde+1717ac2de-4507bc2de-10875c3de-3840a2d2e+935abd2e-
     ------------------------------------------------------------------------
     3881b2d2e-10350acd2e-8331bcd2e-12437c2d2e+4188ad3e-3847bd3e+4075cd3e-
     ------------------------------------------------------------------------
     9119d4e-5029b3e2+6487a2ce2-14746abce2+11659b2ce2+1201ac2e2+7488bc2e2-
     ------------------------------------------------------------------------
     11652c3e2+2927a2de2+6060abde2+4679b2de2+577acde2-4727bcde2+12726c2de2-
     ------------------------------------------------------------------------
     10784ad2e2+2850bd2e2+6861cd2e2-385d3e2-14907a2e3+10361abe3+1044b2e3+
     ------------------------------------------------------------------------
     928ace3+5440bce3+13176c2e3-70ade3+2484bde3-9131cde3-5492d2e3-64ae4-
     ------------------------------------------------------------------------
     11394be4+7746ce4+2479de4+8019e5
     ------------------------------------------------------------------------
     a2c3-2118b2c3+5674ac4-5859bc4+3586c5-4490a2c2d+4030abc2d-13452b2c2d-
     ------------------------------------------------------------------------
     12087ac3d+2937bc3d+3482c4d+14535b3d2+13027a2cd2+5180abcd2+13582b2cd2-
     ------------------------------------------------------------------------
     14492ac2d2-6886bc2d2+7607c3d2+11807a2d3+15717abd3+996b2d3+6077acd3-
     ------------------------------------------------------------------------
     12089bcd3-8905c2d3-13665ad4-2890bd4+12822cd4+4562d5+15091a2c2e-7889abc2e
     ------------------------------------------------------------------------
     +2192b2c2e+661ac3e+8389bc3e-3414c4e+2069b3de+1540a2cde-9144abcde-
     ------------------------------------------------------------------------
     4326b2cde+14406ac2de+6786bc2de-11616c3de-8879a2d2e+1056abd2e-13939b2d2e+
     ------------------------------------------------------------------------
     5751acd2e-2753bcd2e+3772c2d2e+6466ad3e-10497bd3e-3701cd3e-9848d4e-
     ------------------------------------------------------------------------
     3812b3e2-7147a2ce2+5966abce2-7282b2ce2-9358ac2e2+11968bc2e2-2333c3e2-
     ------------------------------------------------------------------------
     10697a2de2-12025abde2-9385b2de2+8558acde2-14436bcde2-6855c2de2+9685ad2e2
     ------------------------------------------------------------------------
     +2822bd2e2-9245cd2e2+2698d3e2-783a2e3+14899abe3+8565b2e3-14543ace3+
     ------------------------------------------------------------------------
     2236bce3+6085c2e3+11488ade3-2416bde3-13870cde3+7367d2e3-14431ae4-
     ------------------------------------------------------------------------
     11444be4-11841ce4+10976de4+4569e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R