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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 (- 5492a  - 190a b + 11018a*b  - 670b  - 15633a c - 4121a*b*c -
     ------------------------------------------------------------------------
          2            2           2        3         2                
     3033b c + 11353a*c  + 13073b*c  - 6398c  - 14815a d - 14571a*b*d -
     ------------------------------------------------------------------------
          2                                   2           2           2  
     6870b d - 3171a*c*d + 15440b*c*d + 15783c d + 3695a*d  - 10246b*d  -
     ------------------------------------------------------------------------
            2        3        2                     2                
     2277c*d  - 2890d  - 6268a e - 1968a*b*e - 6999b e + 12591a*c*e +
     ------------------------------------------------------------------------
                       2                                                2   
     4280b*c*e + 15546c e + 9607a*d*e - 10601b*d*e - 10070c*d*e + 14387d e +
     ------------------------------------------------------------------------
            2           2          2          2        3         3        2 
     4580a*e  + 11467b*e  - 7619c*e  + 6358d*e  - 2746e , - 7187a  + 1090a b
     ------------------------------------------------------------------------
            2        3        2                    2            2          2
     + 55a*b  - 8143b  + 3091a c - 1149a*b*c + 831b c - 14009a*c  - 4198b*c 
     ------------------------------------------------------------------------
             3         2                      2                           
     + 14160c  - 15055a d - 5203a*b*d + 10747b d - 8230a*c*d + 4246b*c*d +
     ------------------------------------------------------------------------
          2           2          2           2         3        2   
     7567c d - 8404a*d  + 3955b*d  + 12746c*d  - 11692d  + 7455a e -
     ------------------------------------------------------------------------
                       2                                  2                
     8882a*b*e - 10450b e - 6918a*c*e + 9477b*c*e - 11249c e - 14575a*d*e -
     ------------------------------------------------------------------------
                                    2           2          2           2  
     11172b*d*e + 7237c*d*e - 10025d e + 8540a*e  + 4683b*e  - 13727c*e  +
     ------------------------------------------------------------------------
             2         3          3        2           2        3        2   
     10156d*e  - 12374e , - 13086a  - 1244a b - 8484a*b  + 3814b  - 5282a c -
     ------------------------------------------------------------------------
                      2            2          2        3        2   
     5272a*b*c + 2497b c - 15083a*c  - 3694b*c  + 9965c  + 6528a d +
     ------------------------------------------------------------------------
                      2                                  2           2  
     7376a*b*d - 4392b d + 8861a*c*d - 10195b*c*d + 3479c d - 2032a*d  -
     ------------------------------------------------------------------------
             2          2        3         2                      2   
     11016b*d  + 6840c*d  + 9962d  + 14195a e - 5752a*b*e - 10297b e +
     ------------------------------------------------------------------------
                                  2                                         
     312a*c*e + 11063b*c*e - 6391c e + 13460a*d*e + 11374b*d*e + 3879c*d*e +
     ------------------------------------------------------------------------
           2           2         2         2         2        3
     10021d e - 6480a*e  + 341b*e  + 616c*e  + 717d*e  - 1870e )

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+5363b3+5881a2c-7163abc-6207b2c+11638ac2+7710bc2-7117c3-14588a2d-
     ------------------------------------------------------------------------
     10075abd+13550b2d+5395acd+9181bcd-11946c2d+3555ad2-5236bd2-11188cd2+
     ------------------------------------------------------------------------
     10562d3-12729a2e+9745abe+6310b2e-10876ace-7307bce-2527c2e+12513ade+
     ------------------------------------------------------------------------
     13724bde+4538cde-13992d2e+3390ae2-3632be2-755ce2-2504de2+390e3
     ------------------------------------------------------------------------
     a2b+49b3-5534a2c+8802abc+11025b2c+2847ac2+1663bc2+11602c3-1703a2d-
     ------------------------------------------------------------------------
     8793abd+7672b2d+9280acd-1204bcd+10494c2d-9950ad2-2678bd2-2514cd2-13216d3
     ------------------------------------------------------------------------
     -15773a2e+15756abe+6673b2e-12102ace-2528bce+12429c2e-4597ade-7027bde+
     ------------------------------------------------------------------------
     5401cde+8627d2e+2956ae2+7806be2-13912ce2-4767de2+12947e3
     ------------------------------------------------------------------------
     a3-14311b3+8071a2c+1543abc-1546b2c+3907ac2+11591bc2-5751c3-3093a2d-
     ------------------------------------------------------------------------
     4714abd+4788b2d-10003acd+9915bcd-5679c2d+9754ad2-5247bd2+2635cd2+3711d3+
     ------------------------------------------------------------------------
     13050a2e-10212abe+10827b2e+8275ace+4226bce-11015c2e+8391ade+14626bde+
     ------------------------------------------------------------------------
     13744cde+9779d2e-13371ae2+10698be2-4033ce2+13764de2+6675e3
     ------------------------------------------------------------------------
     b3c+7482a2c2+10914abc2+245b2c2+9253ac3-10444bc3-14509c4-1858b3d-
     ------------------------------------------------------------------------
     14412a2cd+3641abcd+9793b2cd-2700ac2d-12556bc2d-965c3d+1614a2d2+6295abd2-
     ------------------------------------------------------------------------
     3637b2d2+7543acd2+9107bcd2+6542c2d2+14029ad3+1937bd3+15025cd3-9494d4-
     ------------------------------------------------------------------------
     14620b3e+7613a2ce-1301abce-11090b2ce-13480ac2e-10940bc2e-11228c3e-
     ------------------------------------------------------------------------
     2931a2de-4422abde+15768b2de+12027acde+5978bcde-3134c2de+11906ad2e+
     ------------------------------------------------------------------------
     14989bd2e+1945cd2e+8248d3e-14630a2e2-15287abe2-12347b2e2-4062ace2-
     ------------------------------------------------------------------------
     11853bce2+4231c2e2-15802ade2+9745bde2-3723cde2+14d2e2-1009ae3-6464be3-
     ------------------------------------------------------------------------
     8376ce3-15000de3-14862e4
     ------------------------------------------------------------------------
     b4-7866a2c2-3100abc2-14094b2c2+9193ac3-7133bc3-579c4+5287b3d-9908a2cd+
     ------------------------------------------------------------------------
     2584abcd-7703b2cd+9043ac2d+2919bc2d+10499c3d+11377a2d2-8260abd2+6039b2d2
     ------------------------------------------------------------------------
     -8389acd2+5954bcd2-12453c2d2+971ad3+12698bd3-7730cd3-8906d4+15982b3e+
     ------------------------------------------------------------------------
     11748a2ce-11026abce-2927b2ce+5700ac2e-11199bc2e-6109c3e-7418a2de-
     ------------------------------------------------------------------------
     9180abde+10562b2de+13038acde+4386bcde-312c2de+4148ad2e+3264bd2e-
     ------------------------------------------------------------------------
     13673cd2e+8797d3e+8229a2e2-15575abe2-12224b2e2+9435ace2-15234bce2-
     ------------------------------------------------------------------------
     408c2e2+15195ade2-5853bde2+13277cde2+11478d2e2-7718ae3+10786be3+4659ce3-
     ------------------------------------------------------------------------
     7975de3-2703e4 abc3-1154b2c3-15599ac4+13403bc4-2286c5-760a2c2d+8705abc2d
     ------------------------------------------------------------------------
     -12040b2c2d-10534ac3d+3785bc3d-8117c4d-9375b3d2-7958a2cd2-14800abcd2+
     ------------------------------------------------------------------------
     1741b2cd2-2863ac2d2-8080bc2d2+4772c3d2-10900a2d3+7558abd3-7704b2d3+
     ------------------------------------------------------------------------
     6518acd3+8645bcd3-1173c2d3+8390ad4-7671bd4-8922cd4-5956d5+11140a2c2e-
     ------------------------------------------------------------------------
     13388abc2e-461b2c2e-2345ac3e+1329bc3e+2269c4e-11653b3de+7902a2cde+
     ------------------------------------------------------------------------
     875abcde+9737b2cde-131ac2de-3601bc2de+548c3de+7166a2d2e+7594abd2e+
     ------------------------------------------------------------------------
     9335b2d2e+9400acd2e+6642bcd2e+5166c2d2e-12531ad3e-537bd3e+14481cd3e-
     ------------------------------------------------------------------------
     7013d4e+11768b3e2-7451a2ce2+393abce2+9221b2ce2+4605ac2e2+8535bc2e2-
     ------------------------------------------------------------------------
     5677c3e2-10178a2de2-8448abde2-14083b2de2-11248acde2+7813bcde2+10769c2de2
     ------------------------------------------------------------------------
     -1903ad2e2-7044bd2e2+11716cd2e2-1722d3e2+7026a2e3-6878abe3+6321b2e3-
     ------------------------------------------------------------------------
     9345ace3-7592bce3-12529c2e3-12018ade3+12267bde3-12978cde3+9076d2e3-
     ------------------------------------------------------------------------
     8288ae4+1434be4+15516ce4+591de4-4457e5
     ------------------------------------------------------------------------
     a2c3+9014b2c3+9175ac4+15098bc4+2389c5-142a2c2d-5165abc2d+8838b2c2d-
     ------------------------------------------------------------------------
     3360ac3d+4166bc3d-12201c4d-4474b3d2+15266a2cd2+3753abcd2-12905b2cd2-
     ------------------------------------------------------------------------
     10757ac2d2+287bc2d2+8070c3d2-5488a2d3-4248abd3-5055b2d3-3579acd3+
     ------------------------------------------------------------------------
     3734bcd3-3509c2d3+13875ad4-3425bd4+7560cd4+1863d5-1164a2c2e-4662abc2e-
     ------------------------------------------------------------------------
     877b2c2e+7484ac3e-14872bc3e-5681c4e-1265b3de+1774a2cde-5562abcde+
     ------------------------------------------------------------------------
     12916b2cde-15701ac2de-12619bc2de+4225c3de+6490a2d2e-5574abd2e+9094b2d2e+
     ------------------------------------------------------------------------
     15040acd2e+8576bcd2e-12934c2d2e+1213ad3e-11558bd3e+15191cd3e-4523d4e-
     ------------------------------------------------------------------------
     8260b3e2-4946a2ce2+2128abce2-7950b2ce2-10716ac2e2+6599bc2e2+6404c3e2-
     ------------------------------------------------------------------------
     2816a2de2+4075abde2+2529b2de2+14688acde2-5204bcde2+1351c2de2+10132ad2e2+
     ------------------------------------------------------------------------
     14941bd2e2-8095cd2e2-5092d3e2-12318a2e3-5228abe3-6238b2e3+9186ace3-
     ------------------------------------------------------------------------
     5343bce3+13279c2e3-9898ade3-4868bde3-14236cde3+2704d2e3+7867ae4+8761be4-
     ------------------------------------------------------------------------
     10741ce4-7321de4+13949e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R