next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
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 (1498a  - 957a b + 3899a*b  + 10849b  - 5058a c - 2618a*b*c +
     ------------------------------------------------------------------------
          2           2          2         3         2                     2 
     5702b c + 9344a*c  + 1628b*c  - 13488c  - 11225a d + 6491a*b*d - 6501b d
     ------------------------------------------------------------------------
                                    2           2           2          2  
     + 3202a*c*d - 7789b*c*d + 9431c d + 8748a*d  - 14106b*d  + 1623c*d  +
     ------------------------------------------------------------------------
           3        2                      2                           
     13633d  - 5268a e + 11427a*b*e + 1863b e + 8514a*c*e + 6790b*c*e -
     ------------------------------------------------------------------------
          2                                              2            2  
     2455c e + 7706a*d*e - 1804b*d*e - 4425c*d*e - 11088d e - 15875a*e  +
     ------------------------------------------------------------------------
             2          2          2         3        3        2            2
     10183b*e  - 4846c*e  + 2994d*e  + 15179e , 11219a  - 3007a b + 11187a*b 
     ------------------------------------------------------------------------
            3       2                      2            2           2  
     + 6685b  + 778a c + 3880a*b*c - 10031b c + 10883a*c  - 15180b*c  +
     ------------------------------------------------------------------------
          3        2                     2                           
     8896c  + 9985a d - 1243a*b*d - 6353b d + 2152a*c*d - 2968b*c*d +
     ------------------------------------------------------------------------
           2          2           2          2        3        2   
     13314c d - 180a*d  + 14115b*d  - 8419c*d  + 7201d  + 6940a e +
     ------------------------------------------------------------------------
                       2                                 2                
     13237a*b*e - 3232b e + 13200a*c*e + 846b*c*e + 7976c e - 10524a*d*e -
     ------------------------------------------------------------------------
                                   2           2          2           2  
     5095b*d*e + 4748c*d*e + 14502d e + 4563a*e  - 3707b*e  + 11210c*e  +
     ------------------------------------------------------------------------
             2        3         3        2           2         3         2   
     15199d*e  + 3940e , - 9882a  - 8482a b - 4586a*b  + 11086b  + 15827a c -
     ------------------------------------------------------------------------
                      2           2           2     3        2               
     2289a*b*c - 7864b c + 8498a*c  + 11006b*c  - 4c  + 4748a d - 8986a*b*d +
     ------------------------------------------------------------------------
          2                                 2            2          2  
     5070b d + 3912a*c*d + 15065b*c*d - 135c d - 12682a*d  - 1567b*d  +
     ------------------------------------------------------------------------
             2        3        2                     2                
     10734c*d  + 5371d  + 5340a e - 8227a*b*e + 3421b e + 10969a*c*e -
     ------------------------------------------------------------------------
                      2                                              2   
     9009b*c*e - 5427c e - 12537a*d*e - 4388b*d*e - 7139c*d*e - 1516d e +
     ------------------------------------------------------------------------
             2          2         2          2        3
     13220a*e  + 9472b*e  - 597c*e  + 3007d*e  + 9064e )

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 = | ab2-4006b3-10347a2c+361abc-5532b2c+9282ac2+15464bc2-10694c3-10586a2d-
     ------------------------------------------------------------------------
     9736abd+9020b2d+10591acd-4198bcd+10124c2d+521ad2-9587bd2+265cd2+2708d3+
     ------------------------------------------------------------------------
     10202a2e+4369abe+8761b2e+8946ace+4303bce-4219c2e-3008ade+1311bde-9568cde
     ------------------------------------------------------------------------
     -3643d2e-2922ae2-5164be2-11083ce2+11034de2-2404e3
     ------------------------------------------------------------------------
     a2b+10914b3-13455a2c-730abc-6000b2c+8832ac2+11450bc2+11687c3+11085a2d+
     ------------------------------------------------------------------------
     15107abd+11155b2d-3524acd-535bcd+8530c2d+6816ad2+6807bd2-7735cd2+1268d3-
     ------------------------------------------------------------------------
     10121a2e+10200abe-14829b2e+13771ace+843bce-12820c2e-4731ade-10425bde-
     ------------------------------------------------------------------------
     1565cde-8020d2e+12543ae2+2424be2+12535ce2-13741de2+307e3
     ------------------------------------------------------------------------
     a3-9576b3-2049a2c-2070abc+5613b2c+4135ac2-1059bc2+2840c3+2069a2d-7774abd
     ------------------------------------------------------------------------
     +864b2d-6593acd+5965bcd+10232c2d+1701ad2+12244bd2+15285cd2+9815d3+
     ------------------------------------------------------------------------
     4684a2e-14846abe-422b2e-3009ace-4504bce-14387c2e+8337ade+7103bde-
     ------------------------------------------------------------------------
     14084cde-8745d2e+4456ae2+6643be2+3695ce2+13756de2-8534e3
     ------------------------------------------------------------------------
     b3c+7045a2c2-15076abc2+14013b2c2-5877ac3-14265bc3-14399c4-4237b3d-
     ------------------------------------------------------------------------
     7662a2cd-4522abcd+5369b2cd-13956ac2d-990bc2d+6799c3d-13020a2d2-7075abd2-
     ------------------------------------------------------------------------
     2968b2d2+15891acd2-7101bcd2-11145c2d2-2256ad3-10874bd3-12379cd3+10231d4+
     ------------------------------------------------------------------------
     1075b3e+9228a2ce-3612abce+892b2ce+15190ac2e-3363bc2e+1079c3e-6504a2de-
     ------------------------------------------------------------------------
     14516abde+3162b2de-1401acde-60bcde+5423c2de+2875ad2e-5238bd2e-7144cd2e+
     ------------------------------------------------------------------------
     8958d3e-8999a2e2-7426abe2+13361b2e2-15374ace2-15537bce2-13154c2e2+
     ------------------------------------------------------------------------
     9004ade2+5371bde2-2083cde2-3456d2e2+12788ae3-15548be3-6725ce3+7058de3-
     ------------------------------------------------------------------------
     8438e4 b4-13609a2c2-1500abc2-12851b2c2+10817ac3+11572bc3-6788c4-1998b3d-
     ------------------------------------------------------------------------
     5292a2cd-1246abcd-5507b2cd+15346ac2d-13145bc2d+11751c3d+4310a2d2-
     ------------------------------------------------------------------------
     11213abd2-11656b2d2-9909acd2+11220bcd2+13851c2d2+5253ad3+1498bd3-4784cd3
     ------------------------------------------------------------------------
     -6101d4+8955b3e-14367a2ce-4755abce-13355b2ce-8289ac2e-7304bc2e-15011c3e-
     ------------------------------------------------------------------------
     15764a2de+6930abde+9139b2de-12423acde+10546bcde-3780c2de+2131ad2e+
     ------------------------------------------------------------------------
     9357bd2e-9221cd2e-11209d3e-280a2e2-13952abe2-14011b2e2-15403ace2+
     ------------------------------------------------------------------------
     6913bce2+7252c2e2+7460ade2+15989bde2-5115cde2-5087d2e2+4565ae3-10475be3-
     ------------------------------------------------------------------------
     14803ce3+11056de3-14011e4
     ------------------------------------------------------------------------
     abc3-12554b2c3+14818ac4+14799bc4-12146c5+12931a2c2d+13045abc2d-
     ------------------------------------------------------------------------
     12498b2c2d+8772ac3d+3542bc3d-13001c4d-785b3d2-11908a2cd2-10485abcd2+
     ------------------------------------------------------------------------
     11973b2cd2+2362ac2d2+13162bc2d2-2223c3d2+1882a2d3-5252abd3+3120b2d3+
     ------------------------------------------------------------------------
     10977acd3-11427bcd3-740c2d3+11418ad4+234bd4-10503cd4+7987d5+621a2c2e+
     ------------------------------------------------------------------------
     14664abc2e-7852b2c2e-10093ac3e-1323bc3e-3993c4e-760b3de-15603a2cde+
     ------------------------------------------------------------------------
     9226abcde+7347b2cde+8322ac2de+2204bc2de-6024c3de+4717a2d2e-51abd2e-
     ------------------------------------------------------------------------
     6287b2d2e-10136acd2e+7486bcd2e+15095c2d2e-12597ad3e-15549bd3e-14695cd3e+
     ------------------------------------------------------------------------
     4340d4e-1454b3e2-3011a2ce2+2432abce2-9665b2ce2+5325ac2e2-12270bc2e2-
     ------------------------------------------------------------------------
     1046c3e2-7672a2de2+231abde2+9562b2de2+290acde2-11428bcde2-14844c2de2+
     ------------------------------------------------------------------------
     8148ad2e2+12929bd2e2+8806cd2e2-2670d3e2+14348a2e3-1059abe3+3281b2e3+
     ------------------------------------------------------------------------
     10021ace3-6652bce3+3197c2e3-12912ade3+9658bde3-11250cde3-14024d2e3-
     ------------------------------------------------------------------------
     10177ae4-6265be4-1708ce4-2741de4-5624e5
     ------------------------------------------------------------------------
     a2c3-4082b2c3+10857ac4+8887bc4-12727c5-5456a2c2d+11022abc2d-12674b2c2d-
     ------------------------------------------------------------------------
     15881ac3d+5004bc3d-13378c4d-389b3d2-11962a2cd2-11111abcd2-10988b2cd2+
     ------------------------------------------------------------------------
     15406ac2d2-48bc2d2-9859c3d2+7993a2d3+7703abd3-336b2d3+6923acd3-13218bcd3
     ------------------------------------------------------------------------
     -1071c2d3-2485ad4+5504bd4-1493cd4+3927d5-5099a2c2e+4370abc2e-438b2c2e-
     ------------------------------------------------------------------------
     10501ac3e-2573bc3e+6299c4e-9929b3de+1043a2cde-7416abcde+91b2cde+
     ------------------------------------------------------------------------
     11414ac2de+9030bc2de+10983c3de-14029a2d2e+7461abd2e-8681b2d2e+5946acd2e-
     ------------------------------------------------------------------------
     3469bcd2e-13009c2d2e-8523ad3e-10168bd3e+14125cd3e-11440d4e+4167b3e2-
     ------------------------------------------------------------------------
     8061a2ce2-12666abce2-2186b2ce2+3022ac2e2+8496bc2e2-8911c3e2-7382a2de2-
     ------------------------------------------------------------------------
     9125abde2-2161b2de2+13186acde2-716bcde2-9202c2de2+7448ad2e2-11352bd2e2+
     ------------------------------------------------------------------------
     1292cd2e2+8062d3e2+13531a2e3-11714abe3+2617b2e3-4877ace3-12976bce3-
     ------------------------------------------------------------------------
     12003c2e3-5019ade3+10465bde3+11845cde3+9108d2e3-15916ae4-9427be4-
     ------------------------------------------------------------------------
     13776ce4-7521de4-13197e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R