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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 (13818a  + 6534a b + 10478a*b  - 11244b  - 535a c - 14767a*b*c -
     ------------------------------------------------------------------------
           2            2          2         3        2                    2 
     12323b c - 13112a*c  - 7743b*c  - 12723c  - 6333a d - 2939a*b*d - 359b d
     ------------------------------------------------------------------------
                                      2            2          2          2  
     - 12042a*c*d + 3036b*c*d - 14055c d + 13306a*d  - 6518b*d  + 7753c*d  +
     ------------------------------------------------------------------------
           3        2                       2                            
     13809d  + 9621a e - 11806a*b*e + 11457b e + 3274a*c*e - 15881b*c*e +
     ------------------------------------------------------------------------
           2                                              2            2  
     15690c e - 1072a*d*e - 8484b*d*e - 10708c*d*e + 9069d e + 11094a*e  -
     ------------------------------------------------------------------------
             2         2           2         3          3         2   
     13556b*e  - 592c*e  - 11428d*e  + 12086e , - 13863a  - 14433a b +
     ------------------------------------------------------------------------
             2        3        2                      2           2  
     10885a*b  - 8833b  + 7820a c - 11306a*b*c + 7380b c + 3504a*c  -
     ------------------------------------------------------------------------
            2        3        2                     2               
     7095b*c  + 8036c  + 5998a d + 1532a*b*d - 2817b d + 7593a*c*d +
     ------------------------------------------------------------------------
                      2           2           2          2         3  
     7037b*c*d + 9838c d - 9723a*d  + 10986b*d  - 9958c*d  - 11509d  -
     ------------------------------------------------------------------------
          2                    2                                  2   
     5773a e - 615a*b*e + 1814b e - 13986a*c*e - 8913b*c*e + 6417c e +
     ------------------------------------------------------------------------
                                               2            2          2  
     7325a*d*e - 9272b*d*e + 8501c*d*e - 10841d e + 15618a*e  + 4244b*e  +
     ------------------------------------------------------------------------
             2          2         3        3         2           2         3
     13427c*e  + 8935d*e  + 15741e , - 537a  + 12999a b - 7133a*b  + 10981b 
     ------------------------------------------------------------------------
             2                       2           2           2        3  
     + 11246a c + 15688a*b*c + 12048b c + 3336a*c  + 12820b*c  + 7532c  +
     ------------------------------------------------------------------------
           2                      2                                 2   
     11628a d + 14982a*b*d + 4837b d - 637a*c*d - 13871b*c*d + 6083c d -
     ------------------------------------------------------------------------
            2           2           2        3        2               
     3884a*d  - 10343b*d  + 10452c*d  - 2739d  - 5164a e + 2952a*b*e +
     ------------------------------------------------------------------------
          2                                   2                             
     8463b e + 13394a*c*e + 1843b*c*e - 11323c e - 10248a*d*e - 11814b*d*e -
     ------------------------------------------------------------------------
                      2           2           2           2          2  
     2018c*d*e - 2099d e - 6462a*e  - 14853b*e  + 11231c*e  + 9418d*e  +
     ------------------------------------------------------------------------
          3
     9954e )

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 = | ab2-7707b3-3833a2c-13053abc+9462b2c-5350ac2+9993bc2-8317c3-6035a2d+
     ------------------------------------------------------------------------
     8252abd+5324b2d+12127acd-3748bcd-6690c2d+765ad2-9816bd2-10047cd2+1879d3-
     ------------------------------------------------------------------------
     9266a2e+10000abe-2757b2e+5494ace-12144bce-4812c2e+5431ade+12488bde-
     ------------------------------------------------------------------------
     406cde-12575d2e-6514ae2+5775be2+405ce2-229de2-13063e3
     ------------------------------------------------------------------------
     a2b+9350b3-9887a2c-8763abc+3628b2c+7279ac2-14120bc2-5357c3+4770a2d-
     ------------------------------------------------------------------------
     10635abd+1364b2d-9662acd+4946bcd+1362c2d-4126ad2+7078bd2-8737cd2-5552d3+
     ------------------------------------------------------------------------
     11099a2e-7195abe-8393b2e-469ace-7023bce+6771c2e-7433ade+13837bde+1202cde
     ------------------------------------------------------------------------
     +12133d2e+6148ae2-4747be2-6783ce2+3622de2+7266e3
     ------------------------------------------------------------------------
     a3-9820b3+2447a2c-4680abc+11997b2c-1137ac2+15795bc2-15996c3+2934a2d+
     ------------------------------------------------------------------------
     8853abd+2398b2d-7773acd+13515bcd+127c2d+15597ad2+4536bd2+608cd2+6804d3+
     ------------------------------------------------------------------------
     13565a2e+3253abe-10122b2e+6052ace-7327bce-52c2e-13666ade+8838bde+7377cde
     ------------------------------------------------------------------------
     -9831d2e-13929ae2+12048be2-7017ce2+8697de2+7661e3
     ------------------------------------------------------------------------
     b3c-1314a2c2-9341abc2-1889b2c2-3386ac3-15297bc3-15282c4-5459b3d+
     ------------------------------------------------------------------------
     10902a2cd-4517abcd-6531b2cd+11244ac2d+10724bc2d+2722c3d+2531a2d2+
     ------------------------------------------------------------------------
     14874abd2-1907b2d2+3846acd2-12940bcd2-7107c2d2+15946ad3-15822bd3-6390cd3
     ------------------------------------------------------------------------
     +421d4+10917b3e+11153a2ce+8543abce+10324b2ce-14014ac2e+3112bc2e-9760c3e-
     ------------------------------------------------------------------------
     4613a2de+385abde-15710b2de+2478acde-4293bcde+15695c2de+15473ad2e-
     ------------------------------------------------------------------------
     5290bd2e-3433cd2e+11873d3e+15726a2e2+2588abe2-14153b2e2+3579ace2+
     ------------------------------------------------------------------------
     3473bce2-11699c2e2+5813ade2+9559bde2+259cde2+3212d2e2-12458ae3+587be3-
     ------------------------------------------------------------------------
     15288ce3-2332de3+7598e4
     ------------------------------------------------------------------------
     b4+4915a2c2+8106abc2-2160b2c2-15375ac3+13808bc3+2764c4+15667b3d-3600a2cd
     ------------------------------------------------------------------------
     -14175abcd-14277b2cd-10292ac2d-11099bc2d-118c3d+10183a2d2+7292abd2-
     ------------------------------------------------------------------------
     4390b2d2-12801acd2-11778bcd2+7652c2d2+6253ad3+14961bd3-15415cd3+13748d4-
     ------------------------------------------------------------------------
     7853b3e-11018a2ce-13212abce+12839b2ce+13523ac2e+9623bc2e-11277c3e-
     ------------------------------------------------------------------------
     3968a2de-10353abde-4409b2de+9386acde+3863bcde-6756c2de+12342ad2e+
     ------------------------------------------------------------------------
     6580bd2e-5574cd2e-1409d3e+5122a2e2-4352abe2+10186b2e2+12608ace2+7640bce2
     ------------------------------------------------------------------------
     +8334c2e2-6610ade2+9250bde2+14467cde2-2244d2e2-4922ae3-1302be3-883ce3+
     ------------------------------------------------------------------------
     3358de3+712e4 abc3+10704b2c3+811ac4-500bc4-11731c5-5812a2c2d+15480abc2d+
     ------------------------------------------------------------------------
     6580b2c2d-6692ac3d-9135bc3d+384c4d-6458b3d2+10432a2cd2-9109abcd2+
     ------------------------------------------------------------------------
     3337b2cd2-15713ac2d2-14167bc2d2+4777c3d2-12718a2d3+6372abd3-6096b2d3+
     ------------------------------------------------------------------------
     8484acd3+14593bcd3-14972c2d3-2887ad4-15280bd4-1704cd4+10848d5+11621a2c2e
     ------------------------------------------------------------------------
     +13581abc2e-9905b2c2e+7724ac3e+13469bc3e+1129c4e+11119b3de+9529a2cde-
     ------------------------------------------------------------------------
     10003abcde+10918b2cde-6122ac2de-15262bc2de+3027c3de+8665a2d2e+7739abd2e-
     ------------------------------------------------------------------------
     11200b2d2e-5289acd2e+2568bcd2e+10900c2d2e+13773ad3e-1350bd3e+6821cd3e-
     ------------------------------------------------------------------------
     9215d4e+10853b3e2+14642a2ce2+8014abce2-10350b2ce2+13708ac2e2+12204bc2e2-
     ------------------------------------------------------------------------
     2495c3e2-8057a2de2-1066abde2+7595b2de2-3696acde2-13177bcde2-8657c2de2+
     ------------------------------------------------------------------------
     13645ad2e2+2110bd2e2+2365cd2e2+13178d3e2+9749a2e3+10920abe3-5930b2e3+
     ------------------------------------------------------------------------
     11033ace3+9266bce3+6213c2e3-10086ade3+11bde3+14089cde3+10698d2e3+3624ae4
     ------------------------------------------------------------------------
     -7865be4+2780ce4-11432de4-11319e5
     ------------------------------------------------------------------------
     a2c3-10163b2c3+11867ac4-6020bc4+2432c5+3926a2c2d+2004abc2d+6200b2c2d-
     ------------------------------------------------------------------------
     5512ac3d-7580bc3d+825c4d+809b3d2+7803a2cd2-9666abcd2-14531b2cd2+
     ------------------------------------------------------------------------
     3877ac2d2+5112bc2d2-11535c3d2-13385a2d3+15724abd3-7086b2d3-13214acd3-
     ------------------------------------------------------------------------
     5439bcd3-4893c2d3-6711ad4-13144bd4+878cd4-3830d5+10073a2c2e+14412abc2e+
     ------------------------------------------------------------------------
     12496b2c2e-1635ac3e-2582bc3e-5856c4e-6938b3de-10113a2cde+7013abcde+
     ------------------------------------------------------------------------
     2735b2cde-11136ac2de-7785bc2de+3926c3de-2016a2d2e+5229abd2e+14429b2d2e+
     ------------------------------------------------------------------------
     15994acd2e-12917bcd2e+8446c2d2e-11593ad3e-7159bd3e-232cd3e-12399d4e-
     ------------------------------------------------------------------------
     11428b3e2-3808a2ce2+8687abce2-12907b2ce2+5189ac2e2-4980bc2e2+15586c3e2+
     ------------------------------------------------------------------------
     12193a2de2+13273abde2-268b2de2+497acde2+4292bcde2-4515c2de2+2820ad2e2+
     ------------------------------------------------------------------------
     309bd2e2+10717cd2e2-10538d3e2-12245a2e3-8292abe3+8255b2e3-7198ace3-
     ------------------------------------------------------------------------
     14220bce3+15589c2e3+2563ade3+13638bde3-15698cde3-13743d2e3-9680ae4-
     ------------------------------------------------------------------------
     11041be4+13618ce4-4223de4+8394e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R