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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 (13500a  - 12845a b + 2851a*b  - 4345b  + 14884a c - 13160a*b*c -
     ------------------------------------------------------------------------
          2            2           2        3        2               
     4662b c - 12811a*c  + 11261b*c  - 7038c  - 6801a d - 2960a*b*d +
     ------------------------------------------------------------------------
           2                               2           2          2  
     13395b d + 539a*c*d + 619b*c*d - 7061c d - 3784a*d  + 6943b*d  +
     ------------------------------------------------------------------------
             2         3        2                      2               
     12625c*d  - 11874d  - 6184a e + 15201a*b*e - 8029b e - 8401a*c*e +
     ------------------------------------------------------------------------
                       2                                              2   
     1900b*c*e - 13963c e + 10575a*d*e + 8043b*d*e + 1689c*d*e - 9554d e -
     ------------------------------------------------------------------------
            2         2           2          2        3          3        2 
     7819a*e  + 488b*e  + 13015c*e  + 8201d*e  + 3256e , - 10133a  - 8014a b
     ------------------------------------------------------------------------
             2         3        2                      2           2  
     + 357a*b  - 12922b  - 9834a c + 2853a*b*c - 14274b c + 8961a*c  +
     ------------------------------------------------------------------------
            2         3         2                      2                
     5999b*c  - 14559c  + 10433a d + 7640a*b*d + 11488b d - 14794a*c*d +
     ------------------------------------------------------------------------
                       2            2           2         2        3  
     9604b*c*d - 12651c d + 14325a*d  + 12055b*d  + 215c*d  - 6571d  -
     ------------------------------------------------------------------------
          2                      2                                  2   
     3946a e + 12033a*b*e + 2005b e - 11782a*c*e - 8145b*c*e - 3119c e -
     ------------------------------------------------------------------------
                                                 2            2          2  
     14794a*d*e + 10040b*d*e + 14971c*d*e - 2909d e - 15446a*e  + 3509b*e  -
     ------------------------------------------------------------------------
            2          2        3       3        2           2         3  
     4317c*e  - 2101d*e  - 6620e , 9602a  + 1655a b - 7545a*b  + 12999b  -
     ------------------------------------------------------------------------
          2                      2           2           2        3        2 
     4862a c - 1918a*b*c + 12161b c - 6825a*c  + 14733b*c  - 6228c  + 2688a d
     ------------------------------------------------------------------------
                         2                                  2          2  
     - 11393a*b*d + 9006b d + 12228a*c*d - 7037b*c*d + 4198c d + 576a*d  +
     ------------------------------------------------------------------------
             2           2         3        2                     2   
     14694b*d  + 13685c*d  + 11393d  + 8716a e - 8579a*b*e + 4420b e +
     ------------------------------------------------------------------------
                                 2                                         
     450a*c*e - 8217b*c*e - 3805c e + 12437a*d*e - 14234b*d*e + 7297c*d*e -
     ------------------------------------------------------------------------
           2           2           2          2          2        3
     10890d e + 1731a*e  + 14284b*e  - 8711c*e  + 2405d*e  - 3315e )

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+249b3+4680a2c-15426abc+11445b2c+11947ac2-7111bc2+4808c3-9673a2d+
     ------------------------------------------------------------------------
     14529abd+2985b2d+12185acd+442bcd-11092c2d-11782ad2-9631bd2-1172cd2-
     ------------------------------------------------------------------------
     14150d3+5623a2e+1760abe-1273b2e+9534ace+11945bce-1220c2e+6914ade+7477bde
     ------------------------------------------------------------------------
     +609cde+6445d2e+12402ae2-15463be2-9946ce2+11984de2+1593e3
     ------------------------------------------------------------------------
     a2b-2102b3-4586a2c-4677abc+13908b2c-13251ac2+14354bc2-12241c3-2861a2d+
     ------------------------------------------------------------------------
     10892abd-7990b2d+10854acd+3013bcd-10955c2d+11018ad2-11638bd2+12291cd2+
     ------------------------------------------------------------------------
     10783d3-8565a2e-10229abe-63b2e-7287ace+6182bce-662c2e-15404ade+15202bde+
     ------------------------------------------------------------------------
     13824cde-12543d2e-4889ae2-10786be2+4035ce2+13582de2-6996e3
     ------------------------------------------------------------------------
     a3+6192b3-6958a2c+11212abc+8917b2c+7628ac2+10931bc2+7717c3-1768a2d+
     ------------------------------------------------------------------------
     6425abd+6300b2d+14681acd-15371bcd+15027c2d-11057ad2+14814bd2-5751cd2-
     ------------------------------------------------------------------------
     4857d3+5109a2e-7287abe-6555b2e+11084ace-14811bce+8424c2e+3733ade+7903bde
     ------------------------------------------------------------------------
     -2550cde+2179d2e-15469ae2+11311be2-2859ce2-10632de2-10148e3
     ------------------------------------------------------------------------
     b3c+15999a2c2-14877abc2-15846b2c2-13247ac3+5143bc3+2402c4+13236b3d-
     ------------------------------------------------------------------------
     9538a2cd-11982abcd-9057b2cd-264ac2d-13370bc2d-12127c3d-5897a2d2+8921abd2
     ------------------------------------------------------------------------
     +5790b2d2+10435acd2-1641bcd2-6677c2d2+14582ad3-4897bd3-11848cd3+2258d4-
     ------------------------------------------------------------------------
     9332b3e-3346a2ce+5032abce-10420b2ce+10324ac2e-7694bc2e+10380c3e+1396a2de
     ------------------------------------------------------------------------
     -1597abde-4162b2de+5925acde-1496bcde+11869c2de-9558ad2e+14633bd2e+
     ------------------------------------------------------------------------
     8329cd2e+6874d3e+1558a2e2-812abe2+1705b2e2+14884ace2+13989bce2-1134c2e2+
     ------------------------------------------------------------------------
     4260ade2-11664bde2-3110cde2-7649d2e2-15558ae3+2462be3+4153ce3+5170de3+
     ------------------------------------------------------------------------
     8711e4 b4+12494a2c2+9834abc2-5779b2c2+4810ac3+109bc3-7585c4+15234b3d-
     ------------------------------------------------------------------------
     1362a2cd+2709abcd+9824b2cd+14251ac2d+4661bc2d-2587c3d-3495a2d2+13051abd2
     ------------------------------------------------------------------------
     -12139b2d2+10698acd2+9731bcd2+12093c2d2+10468ad3-13879bd3+1260cd3-6114d4
     ------------------------------------------------------------------------
     +10104b3e-13076a2ce-13817abce-15504b2ce+5099ac2e-8061bc2e-908c3e+19a2de+
     ------------------------------------------------------------------------
     13409abde+14747b2de+4602acde-12560bcde+2988c2de-3830ad2e+14501bd2e+
     ------------------------------------------------------------------------
     10925cd2e+12703d3e+12310a2e2-2710abe2+1444b2e2-4581ace2-1963bce2+
     ------------------------------------------------------------------------
     1028c2e2-12574ade2+3746bde2+7205cde2+10300d2e2+10663ae3-5056be3-8159ce3+
     ------------------------------------------------------------------------
     14757de3-8539e4 abc3+7342b2c3+10226ac4-3693bc4-6168c5-12033a2c2d+
     ------------------------------------------------------------------------
     11826abc2d-15251b2c2d-14438ac3d+3608bc3d+2838c4d+117b3d2+801a2cd2-
     ------------------------------------------------------------------------
     892abcd2-5919b2cd2-6451ac2d2+15124bc2d2+11293c3d2+1929a2d3-13363abd3+
     ------------------------------------------------------------------------
     7471b2d3+4601acd3+13574bcd3-8910c2d3-7454ad4+1903bd4+15902cd4+9317d5-
     ------------------------------------------------------------------------
     5614a2c2e-2351abc2e-7295b2c2e-15388ac3e-5843bc3e+1299c4e-7693b3de+
     ------------------------------------------------------------------------
     13288a2cde+7889abcde+12721b2cde-8387ac2de-3634bc2de-9306c3de-7306a2d2e-
     ------------------------------------------------------------------------
     4479abd2e+13847b2d2e+3986acd2e+1981bcd2e+4985c2d2e+3307ad3e-4933bd3e+
     ------------------------------------------------------------------------
     10806cd3e-1841d4e+9177b3e2-10659a2ce2+10995abce2-1711b2ce2-8381ac2e2+
     ------------------------------------------------------------------------
     4663bc2e2+14953c3e2-15492a2de2-823abde2+4554b2de2+14862acde2+8363bcde2-
     ------------------------------------------------------------------------
     5851c2de2+12844ad2e2-5073bd2e2-15388cd2e2+15103d3e2+1020a2e3+7640abe3+
     ------------------------------------------------------------------------
     6961b2e3-6361ace3+7992bce3+11979c2e3-6578ade3+8482bde3-13713cde3+
     ------------------------------------------------------------------------
     15409d2e3+8463ae4+3755be4-11911ce4+7229de4+7653e5
     ------------------------------------------------------------------------
     a2c3+3542b2c3-7257ac4+2983bc4-2288c5-12523a2c2d-1221abc2d-10083b2c2d+
     ------------------------------------------------------------------------
     2665ac3d-8391bc3d-4027c4d+6891b3d2+8658a2cd2+4771abcd2+6119b2cd2+
     ------------------------------------------------------------------------
     14505ac2d2+14718bc2d2+8226c3d2-10082a2d3-11771abd3-9772b2d3-14859acd3-
     ------------------------------------------------------------------------
     3159bcd3-5129c2d3+3202ad4-10643bd4+15393cd4-1988d5+385a2c2e-8930abc2e-
     ------------------------------------------------------------------------
     8469b2c2e+3501ac3e+11421bc3e-11387c4e+10002b3de+15379a2cde+12149abcde+
     ------------------------------------------------------------------------
     9186b2cde+9649ac2de-12172bc2de+1858c3de-3020a2d2e-13250abd2e-14161b2d2e+
     ------------------------------------------------------------------------
     2415acd2e+7096bcd2e-12043c2d2e+2012ad3e+8727bd3e+13694cd3e-12539d4e-
     ------------------------------------------------------------------------
     5138b3e2+14614a2ce2-12871abce2+9656b2ce2+6321ac2e2+14026bc2e2+8587c3e2+
     ------------------------------------------------------------------------
     10460a2de2+7162abde2-11465b2de2+11704acde2+4579bcde2+6121c2de2+1984ad2e2
     ------------------------------------------------------------------------
     +9433bd2e2+14935cd2e2-9369d3e2-91a2e3-5284abe3+97b2e3-14837ace3-6584bce3
     ------------------------------------------------------------------------
     +3611c2e3+5034ade3+306bde3+14328cde3-15307d2e3+3850ae4-3851be4-14554ce4-
     ------------------------------------------------------------------------
     4504de4-11703e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R