next | previous | forward | backward | up | top | index | toc | Macaulay2 web site

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 (- 11532a  - 6391a b + 14118a*b  - 15346b  + 4549a c - 3933a*b*c -
     ------------------------------------------------------------------------
           2           2         2        3         2                     2 
     10599b c + 8435a*c  - 371b*c  + 7012c  + 13794a d - 6510a*b*d + 5941b d
     ------------------------------------------------------------------------
                                      2          2           2          2  
     + 2332a*c*d - 15195b*c*d - 11666c d - 424a*d  + 12379b*d  - 1831c*d  +
     ------------------------------------------------------------------------
          3        2                      2                            
     3828d  - 3117a e - 6780a*b*e + 10454b e - 8810a*c*e - 11863b*c*e -
     ------------------------------------------------------------------------
           2                                              2          2  
     15075c e + 5400a*d*e - 6649b*d*e + 1627c*d*e + 14667d e + 299a*e  +
     ------------------------------------------------------------------------
            2           2           2       3       3         2           2  
     7606b*e  + 10504c*e  + 13424d*e  - 802e , 2542a  + 14803a b - 6079a*b  -
     ------------------------------------------------------------------------
          3        2                       2            2           2  
     5252b  + 1894a c + 11026a*b*c - 14043b c - 14811a*c  - 10744b*c  +
     ------------------------------------------------------------------------
           3        2                      2                            
     12768c  + 3357a d + 1453a*b*d - 12339b d - 12988a*c*d + 9913b*c*d +
     ------------------------------------------------------------------------
          2           2           2          2         3         2   
     3756c d - 9264a*d  + 10695b*d  - 8935c*d  + 14294d  - 11758a e +
     ------------------------------------------------------------------------
                      2                                 2                
     4101a*b*e + 8352b e + 5639a*c*e + 11760b*c*e - 382c e - 10795a*d*e -
     ------------------------------------------------------------------------
                                     2            2          2           2  
     14920b*d*e + 13476c*d*e + 11001d e - 14803a*e  + 7980b*e  + 14489c*e  -
     ------------------------------------------------------------------------
           2        3        3        2            2        3         2   
     336d*e  + 5795e , - 153a  + 1870a b + 14636a*b  + 9772b  + 13402a c -
     ------------------------------------------------------------------------
                      2            2          2        3        2   
     5383a*b*c - 9733b c + 15658a*c  - 3521b*c  - 3513c  - 5234a d -
     ------------------------------------------------------------------------
                       2                                  2            2  
     12919a*b*d + 4499b d + 1076a*c*d - 9091b*c*d - 11659c d + 13931a*d  +
     ------------------------------------------------------------------------
            2          2        3        2                       2   
     6059b*d  + 7635c*d  + 2439d  + 9787a e - 11356a*b*e + 14735b e +
     ------------------------------------------------------------------------
                                   2                                         
     4191a*c*e - 2977b*c*e - 13788c e - 14203a*d*e + 13380b*d*e + 8254c*d*e -
     ------------------------------------------------------------------------
           2            2          2           2          2         3
     15597d e + 13809a*e  - 2511b*e  - 11661c*e  - 4168d*e  - 10478e )

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+15368b3+8085a2c+3015abc+14402b2c+1431ac2+11304bc2+13926c3+864a2d-
     ------------------------------------------------------------------------
     9480abd+719b2d+3762acd-7964bcd+1418c2d+7805ad2-11672bd2+10743cd2-4647d3-
     ------------------------------------------------------------------------
     1133a2e+15048abe+2865b2e+12455ace-8633bce+605c2e-10818ade-7443bde+
     ------------------------------------------------------------------------
     9574cde-451d2e-6951ae2+3775be2-1514ce2-9928de2+6387e3
     ------------------------------------------------------------------------
     a2b+2173b3-115a2c+6487abc-10306b2c+654ac2-15450bc2-2436c3+6203a2d+
     ------------------------------------------------------------------------
     2556abd+12540b2d-14009acd-8458bcd-7407c2d-503ad2-15727bd2-5816cd2-9898d3
     ------------------------------------------------------------------------
     -9296a2e+8243abe-10035b2e+15437ace+13124bce+7474c2e-13245ade-2521bde+
     ------------------------------------------------------------------------
     9898cde+4104d2e+12280ae2+2558be2-4979ce2+9470de2+15833e3
     ------------------------------------------------------------------------
     a3-12352b3-7239a2c-7724abc-13052b2c-13561ac2-11919bc2+15390c3-12602a2d-
     ------------------------------------------------------------------------
     15636abd+15357b2d-9857acd+4366bcd+6705c2d+4947ad2-15715bd2-10241cd2-
     ------------------------------------------------------------------------
     2857d3-8293a2e-5241abe+14732b2e+5220ace-14264bce+7287c2e-4164ade+5512bde
     ------------------------------------------------------------------------
     +10584cde+14231d2e+14265ae2+7316be2-2922ce2-6675de2+14111e3
     ------------------------------------------------------------------------
     b3c-14926a2c2-8776abc2-9849b2c2+8350ac3+2062bc3+631c4+11152b3d-3987a2cd+
     ------------------------------------------------------------------------
     3830abcd-119b2cd-10169ac2d-4615bc2d+2508c3d+12127a2d2-425abd2+11319b2d2-
     ------------------------------------------------------------------------
     5374acd2+7203bcd2-4641c2d2-8480ad3+13991bd3+1779cd3+11994d4+14061b3e+
     ------------------------------------------------------------------------
     7141a2ce-15597abce+606b2ce-1964ac2e+13811bc2e-15506c3e+377a2de+14581abde
     ------------------------------------------------------------------------
     +1392b2de+9062acde-13252bcde-12889c2de+3185ad2e-7929bd2e+14955cd2e+
     ------------------------------------------------------------------------
     1717d3e-7372a2e2+9107abe2-11641b2e2-4996ace2+2064bce2+866c2e2-9550ade2+
     ------------------------------------------------------------------------
     7259bde2+1403cde2+952d2e2+5935ae3+14360be3+9907ce3-15199de3+10229e4
     ------------------------------------------------------------------------
     b4-4779a2c2-8348abc2+5141b2c2+2015ac3-8948bc3+8539c4+12438b3d+1195a2cd-
     ------------------------------------------------------------------------
     669abcd+6938b2cd-7995ac2d-11374bc2d+11668c3d-1075a2d2+7511abd2-2629b2d2-
     ------------------------------------------------------------------------
     15304acd2-11396bcd2-4086c2d2-14798ad3-6963bd3-11699cd3-453d4-8233b3e+
     ------------------------------------------------------------------------
     765a2ce+7953abce+12478b2ce+4372ac2e-10144bc2e+15034c3e-10886a2de-
     ------------------------------------------------------------------------
     11976abde-6446b2de-9017acde+3969bcde+549c2de-9062ad2e-13789bd2e+1196cd2e
     ------------------------------------------------------------------------
     +11644d3e+8816a2e2+1156abe2-9056b2e2-3919ace2-14962bce2-9473c2e2-
     ------------------------------------------------------------------------
     1123ade2+2064bde2-811cde2+14454d2e2-12356ae3+3514be3+6910ce3-12096de3+
     ------------------------------------------------------------------------
     8057e4 abc3-1370b2c3+2638ac4+9533bc4-13175c5+10206a2c2d+13677abc2d-
     ------------------------------------------------------------------------
     11409b2c2d-10995ac3d-2337bc3d-6559c4d-2653b3d2-1178a2cd2+8213abcd2-
     ------------------------------------------------------------------------
     13133b2cd2-13844ac2d2-9766bc2d2-9974c3d2-4610a2d3+658abd3+1332b2d3+
     ------------------------------------------------------------------------
     2704acd3+14049bcd3+13167c2d3-7925ad4-14843bd4-6822cd4-12138d5+4288a2c2e+
     ------------------------------------------------------------------------
     15764abc2e-658b2c2e-12975ac3e-7317bc3e+15626c4e-11728b3de+1721a2cde-
     ------------------------------------------------------------------------
     9179abcde-5528b2cde+9504ac2de+175bc2de-6118c3de-11822a2d2e+2391abd2e+
     ------------------------------------------------------------------------
     3613b2d2e-9735acd2e+11984bcd2e-8668c2d2e-7138ad3e-10173bd3e+2922cd3e-
     ------------------------------------------------------------------------
     10867d4e-12039b3e2+4360a2ce2-4586abce2-9866b2ce2-1337ac2e2-15128bc2e2-
     ------------------------------------------------------------------------
     4114c3e2+4298a2de2-14650abde2-9642b2de2-12785acde2+8101bcde2-4262c2de2-
     ------------------------------------------------------------------------
     15423ad2e2+4925bd2e2-4764cd2e2-5275d3e2-7717a2e3-12621abe3+12183b2e3+
     ------------------------------------------------------------------------
     1491ace3+14917bce3+10321c2e3+7614ade3+13207bde3-404cde3-8681d2e3-
     ------------------------------------------------------------------------
     13941ae4+8809be4+9343ce4-6144de4-491e5
     ------------------------------------------------------------------------
     a2c3+11499b2c3-12934ac4-2878bc4+10406c5-8238a2c2d-14319abc2d-5997b2c2d-
     ------------------------------------------------------------------------
     13602ac3d+13330bc3d+536c4d-15299b3d2+742a2cd2+6346abcd2+4616b2cd2+
     ------------------------------------------------------------------------
     12210ac2d2+13827bc2d2-13809c3d2-7104a2d3+688abd3-8283b2d3+2134acd3+
     ------------------------------------------------------------------------
     5486bcd3-12990c2d3-8540ad4-9955bd4-9609cd4+12342d5-14625a2c2e+6410abc2e-
     ------------------------------------------------------------------------
     12795b2c2e-213ac3e-4754bc3e+14889c4e+15021b3de-2654a2cde+136abcde-
     ------------------------------------------------------------------------
     6942b2cde-711ac2de-14160bc2de+1578c3de-1417a2d2e-4216abd2e-12575b2d2e+
     ------------------------------------------------------------------------
     14256acd2e+7233bcd2e-6568c2d2e+2748ad3e+4037bd3e+3127cd3e-6118d4e+
     ------------------------------------------------------------------------
     4981b3e2-1768a2ce2-159abce2-9901b2ce2-10151ac2e2-11564bc2e2-15075c3e2+
     ------------------------------------------------------------------------
     9752a2de2+5214abde2-10754b2de2+14082acde2+3788bcde2+13780c2de2-
     ------------------------------------------------------------------------
     15345ad2e2-6093bd2e2+12507cd2e2+7185d3e2-607a2e3-2788abe3+13275b2e3+
     ------------------------------------------------------------------------
     11773ace3-11334bce3-12816c2e3+3612ade3+5128bde3+9754cde3+11928d2e3-
     ------------------------------------------------------------------------
     7179ae4-4736be4-12931ce4+4788de4+14787e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R