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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 (13076a  - 2045a b - 15109a*b  + 11962b  - 13311a c - 5835a*b*c +
     ------------------------------------------------------------------------
          2           2           2        3         2                
     4932b c + 4893a*c  + 15856b*c  - 4955c  - 15467a d + 12779a*b*d +
     ------------------------------------------------------------------------
           2                                  2            2         2  
     15282b d + 13551a*c*d - 4020b*c*d + 1971c d + 10008a*d  + 103b*d  -
     ------------------------------------------------------------------------
             2         3        2                      2               
     12434c*d  - 12990d  + 6260a e - 11596a*b*e - 4303b e + 6186a*c*e +
     ------------------------------------------------------------------------
                       2                                              2   
     5940b*c*e - 13598c e + 4792a*d*e - 6375b*d*e + 15809c*d*e - 5494d e -
     ------------------------------------------------------------------------
            2          2           2           2        3        3        2 
     7518a*e  + 3914b*e  + 12782c*e  - 15575d*e  + 5382e , 15291a  + 1395a b
     ------------------------------------------------------------------------
             2        3        2                      2           2  
     + 817a*b  - 9912b  + 2474a c - 6726a*b*c + 10110b c + 6626a*c  -
     ------------------------------------------------------------------------
            2        3       2                     2               
     2203b*c  - 7228c  - 823a d - 2776a*b*d - 5528b d - 4906a*c*d +
     ------------------------------------------------------------------------
                        2            2          2           2        3  
     11986b*c*d + 10498c d + 15807a*d  + 5361b*d  + 10269c*d  + 1074d  +
     ------------------------------------------------------------------------
          2                      2                                  2   
     2475a e - 11775a*b*e + 2469b e + 5218a*c*e - 13201b*c*e + 9413c e -
     ------------------------------------------------------------------------
                                              2           2          2  
     714a*d*e + 3242b*d*e - 6399c*d*e + 10667d e - 1403a*e  + 4159b*e  +
     ------------------------------------------------------------------------
             2           2         3        3        2            2       3  
     13958c*e  + 12450d*e  - 15997e , 15458a  - 3090a b + 14330a*b  + 134b  -
     ------------------------------------------------------------------------
           2                       2           2          2        3  
     15242a c - 13109a*b*c + 12653b c - 5839a*c  + 6231b*c  - 2309c  +
     ------------------------------------------------------------------------
          2                     2                                  2   
     6326a d - 7609a*b*d - 2534b d + 13123a*c*d - 7466b*c*d - 4289c d +
     ------------------------------------------------------------------------
            2         2          2         3         2                     2 
     1006a*d  - 872b*d  - 9699c*d  - 10617d  + 14713a e - 2691a*b*e - 7089b e
     ------------------------------------------------------------------------
                                    2                                        
     + 4760a*c*e - 2258b*c*e + 4357c e + 13748a*d*e + 9034b*d*e - 7584c*d*e +
     ------------------------------------------------------------------------
          2            2           2          2           2        3
     2980d e + 13789a*e  - 11951b*e  + 4739c*e  - 15089d*e  + 8260e )

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 = | ab2-11714b3-14761a2c+1192abc+5721b2c+6680ac2-6730bc2-13412c3-11119a2d-
     ------------------------------------------------------------------------
     13264abd+9239b2d-12638acd+7115bcd+6918c2d+1367ad2+11858bd2+14396cd2-
     ------------------------------------------------------------------------
     10757d3+11749a2e+4141abe-5540b2e+4688ace-6990bce+5761c2e+24ade-6234bde+
     ------------------------------------------------------------------------
     2109cde+14075d2e-7829ae2-11614be2+4559ce2+8948de2+7115e3
     ------------------------------------------------------------------------
     a2b+10739b3+2367a2c-3491abc+4530b2c+2427ac2+12893bc2-9332c3+8433a2d-
     ------------------------------------------------------------------------
     2896abd+11157b2d-10837acd-11389bcd-9386c2d+2032ad2+12910bd2-15113cd2-
     ------------------------------------------------------------------------
     15238d3+11654a2e+3148abe+7731b2e-13634ace-14596bce+567c2e-15891ade+
     ------------------------------------------------------------------------
     4528bde+136cde+5870d2e-110ae2-844be2-6856ce2-7095de2+11614e3
     ------------------------------------------------------------------------
     a3+9093b3-8456a2c-3785abc-329b2c-13958ac2-8659bc2-14096c3+8615a2d-
     ------------------------------------------------------------------------
     14831abd+6435b2d+5006acd+14766bcd+11898c2d+1553ad2+13819bd2+537cd2+
     ------------------------------------------------------------------------
     3677d3+6840a2e+374abe+7544b2e+12419ace-9336bce-11734c2e-14506ade-5940bde
     ------------------------------------------------------------------------
     +11980cde-5299d2e+1301ae2+12098be2+2662ce2+8548de2+14206e3
     ------------------------------------------------------------------------
     b3c+9171a2c2+5297abc2-15054b2c2+15719ac3-914bc3-15109c4-9971b3d+
     ------------------------------------------------------------------------
     15210a2cd+4738abcd-2526b2cd-14681ac2d-5355bc2d-302c3d-12766a2d2-
     ------------------------------------------------------------------------
     11229abd2+2809b2d2-3395acd2-3635bcd2+3215c2d2-2783ad3-13460bd3-5169cd3+
     ------------------------------------------------------------------------
     10468d4+5759b3e-11225a2ce+803abce-14916b2ce-15156ac2e+9303bc2e-15820c3e+
     ------------------------------------------------------------------------
     12377a2de-4716abde+2289b2de+2984acde+5166bcde+248c2de+884ad2e+8576bd2e+
     ------------------------------------------------------------------------
     15151cd2e-12293d3e+9218a2e2+67abe2-4275b2e2-11075ace2-5240bce2+8873c2e2-
     ------------------------------------------------------------------------
     10620ade2+12942bde2+9679cde2+4301d2e2-107ae3-2980be3-8471ce3+15093de3+
     ------------------------------------------------------------------------
     5188e4 b4+13818a2c2+13651abc2+2685b2c2+15443ac3-8035bc3+6970c4+383b3d-
     ------------------------------------------------------------------------
     14151a2cd-604abcd-4524b2cd-13874ac2d-1190bc2d-3921c3d-6892a2d2+8663abd2-
     ------------------------------------------------------------------------
     10916b2d2-13543acd2+8497bcd2-15373c2d2-15972ad3-1646bd3-5675cd3-12654d4-
     ------------------------------------------------------------------------
     1455b3e+5430a2ce+10008abce+6150b2ce-14126ac2e-10093bc2e-6118c3e+9110a2de
     ------------------------------------------------------------------------
     +14652abde-12155b2de-14254acde+12598bcde-2028c2de-8478ad2e-12683bd2e-
     ------------------------------------------------------------------------
     8937cd2e+6941d3e+15017a2e2-15250abe2-1976b2e2-13343ace2-1753bce2+
     ------------------------------------------------------------------------
     14564c2e2+6416ade2+1972bde2+15586cde2+11976d2e2-11960ae3-13250be3+120ce3
     ------------------------------------------------------------------------
     -2809de3+7593e4 abc3+14961b2c3+5809ac4+5146bc4-13627c5+1905a2c2d+
     ------------------------------------------------------------------------
     5261abc2d+7201b2c2d-1755ac3d-5677bc3d-73c4d-1513b3d2+10920a2cd2-
     ------------------------------------------------------------------------
     11039abcd2+9397b2cd2-10433ac2d2-2873bc2d2-286c3d2+5679a2d3+5460abd3-
     ------------------------------------------------------------------------
     12750b2d3-175acd3-14278bcd3-13527c2d3-805ad4-10625bd4-11119cd4-12556d5-
     ------------------------------------------------------------------------
     12570a2c2e+11028abc2e-5125b2c2e+7898ac3e-11743bc3e+4675c4e+467b3de+
     ------------------------------------------------------------------------
     13613a2cde-11501abcde-15699b2cde-1163ac2de+12852bc2de-13975c3de+
     ------------------------------------------------------------------------
     11196a2d2e-6112abd2e+4160b2d2e-9831acd2e-7155bcd2e-229c2d2e+3004ad3e-
     ------------------------------------------------------------------------
     13361bd3e-3170cd3e+11906d4e+14363b3e2+13346a2ce2+6230abce2-1077b2ce2-
     ------------------------------------------------------------------------
     5992ac2e2-9665bc2e2+839c3e2-997a2de2-8324abde2-11590b2de2+4968acde2-
     ------------------------------------------------------------------------
     14009bcde2-8712c2de2+2672ad2e2+13738bd2e2-1594cd2e2-5619d3e2+13989a2e3+
     ------------------------------------------------------------------------
     8921abe3+4343b2e3+5759ace3-2341bce3+9461c2e3+457ade3-6581bde3-10924cde3+
     ------------------------------------------------------------------------
     4792d2e3-12379ae4+8850be4+12475ce4+5887de4-7456e5
     ------------------------------------------------------------------------
     a2c3+4112b2c3-11757ac4+15182bc4-7758c5+3798a2c2d+3721abc2d-8704b2c2d+
     ------------------------------------------------------------------------
     5385ac3d+3530bc3d-6830c4d-1347b3d2-15046a2cd2+12519abcd2-650b2cd2-
     ------------------------------------------------------------------------
     1264ac2d2+10787bc2d2-13285c3d2-6763a2d3+221abd3-10730b2d3+10572acd3+
     ------------------------------------------------------------------------
     5800bcd3-6017c2d3-1368ad4-7907bd4+13576cd4+223d5+13660a2c2e+15872abc2e-
     ------------------------------------------------------------------------
     9162b2c2e-12074ac3e-1925bc3e+8375c4e+9889b3de+5935a2cde+6608abcde-
     ------------------------------------------------------------------------
     6149b2cde-4034ac2de+8682bc2de+12328c3de+8586a2d2e+11056abd2e-5617b2d2e-
     ------------------------------------------------------------------------
     4606acd2e-645bcd2e+12641c2d2e-9069ad3e-7456bd3e-1082cd3e+15786d4e+
     ------------------------------------------------------------------------
     1843b3e2-9188a2ce2-1413abce2-9801b2ce2+2705ac2e2+5958bc2e2+6481c3e2-
     ------------------------------------------------------------------------
     9277a2de2+13377abde2+9816b2de2+15283acde2-3626bcde2-138c2de2-6762ad2e2+
     ------------------------------------------------------------------------
     14620bd2e2-15296cd2e2-3582d3e2+3827a2e3-10611abe3-320b2e3+10737ace3-
     ------------------------------------------------------------------------
     12519bce3+3660c2e3-13582ade3+14943bde3+14636cde3+14974d2e3-2872ae4-
     ------------------------------------------------------------------------
     7469be4-14294ce4-6702de4-13818e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R