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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 (9172a  - 1921a b - 8399a*b  - 7699b  + 2267a c - 13972a*b*c +
     ------------------------------------------------------------------------
           2           2          2        3        2                      2 
     11008b c + 2432a*c  + 1148b*c  + 3826c  - 5276a d + 12146a*b*d + 1043b d
     ------------------------------------------------------------------------
                                      2           2          2          2  
     + 5951a*c*d + 14789b*c*d + 11706c d - 5604a*d  + 2141b*d  - 1016c*d  +
     ------------------------------------------------------------------------
          3         2                    2                                2 
     7289d  - 13711a e + 324a*b*e + 4112b e - 318a*c*e - 3772b*c*e - 5644c e
     ------------------------------------------------------------------------
                                                  2           2          2  
     + 6080a*d*e + 11690b*d*e + 9649c*d*e - 10509d e + 4259a*e  + 4527b*e  -
     ------------------------------------------------------------------------
            2          2        3       3         2           2        3  
     9773c*e  + 3156d*e  + 3691e , 9209a  - 11016a b - 6213a*b  - 4136b  +
     ------------------------------------------------------------------------
          2                     2          2           2        3         2 
     7066a c + 5925a*b*c + 8794b c + 468a*c  + 15029b*c  + 8818c  + 15598a d
     ------------------------------------------------------------------------
                         2                                   2           2  
     - 12408a*b*d - 8328b d - 10364a*c*d - 14893b*c*d - 3302c d + 2189a*d  +
     ------------------------------------------------------------------------
          2          2         3        2                      2             
     41b*d  - 8247c*d  - 11888d  + 8850a e - 12846a*b*e + 7514b e - 3956a*c*e
     ------------------------------------------------------------------------
                         2                                              2   
     + 4486b*c*e + 11052c e + 4229a*d*e + 10119b*d*e + 4015c*d*e - 9700d e -
     ------------------------------------------------------------------------
            2          2           2           2        3        3        2 
     9787a*e  + 8895b*e  + 11231c*e  + 10629d*e  + 2712e , 15205a  + 6261a b
     ------------------------------------------------------------------------
               2         3        2                     2           2  
     + 11564a*b  + 12014b  - 1637a c - 6443a*b*c - 4594b c - 3919a*c  +
     ------------------------------------------------------------------------
             2         3        2                    2              
     14449b*c  - 10398c  + 2438a d - 625a*b*d - 2112b d - 711a*c*d +
     ------------------------------------------------------------------------
                       2            2          2           2         3  
     9941b*c*d - 12539c d - 13078a*d  - 1635b*d  - 10280c*d  - 11417d  -
     ------------------------------------------------------------------------
          2                      2                               2   
     2646a e - 1515a*b*e + 11092b e - 766a*c*e + 4268b*c*e - 794c e -
     ------------------------------------------------------------------------
                                                 2          2          2  
     12544a*d*e + 14257b*d*e - 14749c*d*e - 6413d e + 173a*e  - 4710b*e  -
     ------------------------------------------------------------------------
            2          2        3
     1660c*e  + 7977d*e  + 7395e )

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 = | ab2-277b3+5012a2c+1237abc+12671b2c-11426ac2+12430bc2-14136c3-690a2d+
     ------------------------------------------------------------------------
     9907abd-3284b2d-8645acd+14532bcd+12849c2d+10677ad2+14191bd2-15805cd2+
     ------------------------------------------------------------------------
     12235d3-8388a2e-7087abe+7285b2e+2409ace-2941bce+1156c2e-12957ade+5007bde
     ------------------------------------------------------------------------
     -7682cde+629d2e+15516ae2+5768be2-1006ce2-3660de2-6890e3
     ------------------------------------------------------------------------
     a2b+2094b3-6977a2c-316abc+3491b2c-6919ac2-6620bc2-13447c3+7546a2d+
     ------------------------------------------------------------------------
     6839abd+14045b2d+14042acd-6891bcd-3347c2d+348ad2-135bd2-1111cd2-11458d3-
     ------------------------------------------------------------------------
     8938a2e+11586abe-10049b2e-14775ace+9368bce+12414c2e+5941ade+14859bde+
     ------------------------------------------------------------------------
     4725cde-1258d2e+319ae2-14277be2-3396ce2+11309de2+9016e3
     ------------------------------------------------------------------------
     a3-3347b3-6062a2c-2316abc-13373b2c-12041ac2-12942bc2-4152c3+15826a2d-
     ------------------------------------------------------------------------
     5091abd-4755b2d-15896acd+10449bcd+14423c2d-15709ad2-4985bd2+8316cd2+
     ------------------------------------------------------------------------
     2943d3-7311a2e-2315abe-13277b2e-3980ace-14308bce-9929c2e+10699ade-
     ------------------------------------------------------------------------
     13188bde+9825cde-12501d2e+8979ae2-2823be2-11023ce2+7060de2-9623e3
     ------------------------------------------------------------------------
     b3c-286a2c2-2640abc2-861b2c2-14180ac3-15573bc3-4004c4-6470b3d+6738a2cd+
     ------------------------------------------------------------------------
     3153abcd+13501b2cd+794ac2d+6786bc2d+12970c3d+4963a2d2+3638abd2+1704b2d2-
     ------------------------------------------------------------------------
     383acd2+14077bcd2-12715c2d2+15359ad3+7322bd3+3693cd3-15133d4-7004b3e+
     ------------------------------------------------------------------------
     5984a2ce-12128abce+2566b2ce+1577ac2e-14724bc2e+10727c3e+14879a2de+
     ------------------------------------------------------------------------
     12341abde+2580b2de+11558acde+1923bcde-190c2de+1977ad2e-7682bd2e-9514cd2e
     ------------------------------------------------------------------------
     +6739d3e+5131a2e2+4379abe2-13853b2e2+5913ace2-4848bce2-12968c2e2+
     ------------------------------------------------------------------------
     11153ade2-12912bde2-10183cde2-5502d2e2-6144ae3-15306be3+12698ce3+
     ------------------------------------------------------------------------
     12091de3-1833e4 b4+5587a2c2+3051abc2-11310b2c2-1820ac3-3654bc3-3057c4-
     ------------------------------------------------------------------------
     7994b3d-1048a2cd-8898abcd-2799b2cd-13099ac2d+3534bc2d-12870c3d-6496a2d2-
     ------------------------------------------------------------------------
     12693abd2-9003b2d2+14990acd2-14663bcd2+12380c2d2+6918ad3+4164bd3+
     ------------------------------------------------------------------------
     13198cd3-11917d4+4829b3e+4871a2ce-15415abce-12723b2ce-3977ac2e+8153bc2e+
     ------------------------------------------------------------------------
     9378c3e-2398a2de-1689abde+14032b2de-8424acde-11213bcde+15839c2de-
     ------------------------------------------------------------------------
     2392ad2e+12373bd2e+15917cd2e-14564d3e+14011a2e2+13522abe2-4772b2e2+
     ------------------------------------------------------------------------
     13968ace2+9997bce2+8890c2e2+12183ade2-11117bde2-10359cde2-14551d2e2-
     ------------------------------------------------------------------------
     5848ae3+10454be3+11099ce3+5485de3-15270e4
     ------------------------------------------------------------------------
     abc3-1580b2c3-8152ac4-5044bc4+5526c5-890a2c2d+684abc2d-8654b2c2d-
     ------------------------------------------------------------------------
     13585ac3d-3074bc3d-2509c4d-3306b3d2+8682a2cd2-4827abcd2-10539b2cd2-
     ------------------------------------------------------------------------
     12555ac2d2-515bc2d2-1367c3d2+7086a2d3-4016abd3+13297b2d3-5277acd3+
     ------------------------------------------------------------------------
     13001bcd3+8642c2d3-10963ad4-936bd4+5657cd4+5376d5-15766a2c2e-14756abc2e+
     ------------------------------------------------------------------------
     1824b2c2e+5587ac3e-11724bc3e-2110c4e-5888b3de+2779a2cde-8701abcde-
     ------------------------------------------------------------------------
     15186b2cde-14224ac2de-593bc2de-6526c3de-3630a2d2e-768abd2e+11234b2d2e-
     ------------------------------------------------------------------------
     4820acd2e+2063bcd2e-11423c2d2e-13996ad3e-11247bd3e+11693cd3e-9907d4e+
     ------------------------------------------------------------------------
     4454b3e2+7101a2ce2-5286abce2+6942b2ce2+826ac2e2-11438bc2e2-1766c3e2+
     ------------------------------------------------------------------------
     7669a2de2+1675abde2-13061b2de2+1574acde2+10669bcde2+12094c2de2-
     ------------------------------------------------------------------------
     14871ad2e2-4693bd2e2-13835cd2e2-6192d3e2-5393a2e3+15953abe3+2792b2e3+
     ------------------------------------------------------------------------
     7023ace3+2493bce3-15263c2e3-9123ade3+706bde3-8756cde3+8818d2e3-8476ae4+
     ------------------------------------------------------------------------
     12381be4+10300ce4-1822de4+8733e5
     ------------------------------------------------------------------------
     a2c3-12718b2c3+11326ac4+4098bc4+8396c5-10332a2c2d+7046abc2d+12578b2c2d+
     ------------------------------------------------------------------------
     15325ac3d-11093bc3d-3049c4d-101b3d2+7243a2cd2+7327abcd2-58b2cd2+
     ------------------------------------------------------------------------
     3418ac2d2-9365bc2d2-14033c3d2-14174a2d3-1251abd3-11305b2d3-3499acd3-
     ------------------------------------------------------------------------
     7380bcd3+12730c2d3-732ad4+5764bd4+13728cd4+2909d5+14088a2c2e-3390abc2e+
     ------------------------------------------------------------------------
     8928b2c2e-9458ac3e-14129bc3e+528c4e+13010b3de+6021a2cde-4085abcde+
     ------------------------------------------------------------------------
     8262b2cde+12110ac2de-6027bc2de+12056c3de+6384a2d2e-10945abd2e+13472b2d2e
     ------------------------------------------------------------------------
     -13031acd2e-27bcd2e+752c2d2e+2204ad3e+15115bd3e-10293cd3e-4927d4e+
     ------------------------------------------------------------------------
     4679b3e2-15296a2ce2-15852abce2+10848b2ce2+5408ac2e2+2098bc2e2-4459c3e2-
     ------------------------------------------------------------------------
     12505a2de2-15187abde2+2156b2de2-6096acde2-11398bcde2-9296c2de2+6293ad2e2
     ------------------------------------------------------------------------
     +5309bd2e2+984cd2e2-3823d3e2-2642a2e3-3682abe3-1636b2e3-7115ace3+
     ------------------------------------------------------------------------
     8598bce3+14594c2e3+1799ade3-9383bde3-1017cde3+4221d2e3-3192ae4+5162be4+
     ------------------------------------------------------------------------
     5037ce4+14737de4+7164e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R