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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 (- 1734a  + 3642a b - 10661a*b  - 1737b  - 9903a c - 5889a*b*c +
     ------------------------------------------------------------------------
           2          2          2        3        2                       2 
     12285b c - 198a*c  - 3425b*c  - 4211c  - 9644a d + 14428a*b*d - 11388b d
     ------------------------------------------------------------------------
                                     2            2          2           2  
     + 2708a*c*d - 1626b*c*d + 14422c d - 10465a*d  + 3251b*d  - 15496c*d  -
     ------------------------------------------------------------------------
           3        2                      2                            
     12849d  - 9886a e - 10149a*b*e - 9119b e + 9907a*c*e + 14399b*c*e -
     ------------------------------------------------------------------------
          2                                               2           2  
     1906c e - 4538a*d*e - 2602b*d*e + 12186c*d*e - 13632d e + 7802a*e  -
     ------------------------------------------------------------------------
             2          2          2         3         3        2           2
     11641b*e  + 5552c*e  - 3438d*e  + 10495e , - 4487a  - 2993a b - 4171a*b 
     ------------------------------------------------------------------------
             3        2                      2            2           2  
     + 14271b  + 6978a c - 6407a*b*c - 14452b c - 12393a*c  - 10076b*c  -
     ------------------------------------------------------------------------
          3        2                      2                           
     8676c  + 2830a d - 1198a*b*d - 14520b d - 1645a*c*d + 9928b*c*d -
     ------------------------------------------------------------------------
           2           2           2          2         3        2   
     15803c d - 3163a*d  - 12820b*d  - 5472c*d  - 12397d  - 9543a e +
     ------------------------------------------------------------------------
                      2                                2               
     7682a*b*e - 4794b e - 9468a*c*e - 4204b*c*e + 568c e + 2387a*d*e -
     ------------------------------------------------------------------------
                                    2           2          2          2  
     15482b*d*e + 13604c*d*e + 2697d e - 1241a*e  - 5755b*e  + 4227c*e  +
     ------------------------------------------------------------------------
             2        3         3         2           2         3         2 
     12936d*e  - 9025e , - 1052a  + 11251a b + 1346a*b  - 11624b  + 14916a c
     ------------------------------------------------------------------------
                          2            2          2         3       2   
     - 11911a*b*c + 10845b c + 11198a*c  + 9453b*c  - 12318c  - 482a d +
     ------------------------------------------------------------------------
                      2                              2          2           2
     807a*b*d - 14650b d - 911a*c*d + 10b*c*d - 2860c d + 349a*d  - 10930b*d 
     ------------------------------------------------------------------------
             2        3         2                     2               
     - 898c*d  - 2484d  - 10631a e + 3580a*b*e + 5109b e + 4748a*c*e -
     ------------------------------------------------------------------------
                       2                                            2   
     11092b*c*e + 7245c e - 2945a*d*e + 1948b*d*e - 254c*d*e - 2903d e -
     ------------------------------------------------------------------------
            2          2          2          2         3
     5967a*e  + 2150b*e  - 3138c*e  + 1274d*e  - 10780e )

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 = | ab2-4932b3-6625a2c-3943abc+4543b2c+1491ac2-4334bc2-1562c3-6897a2d-
     ------------------------------------------------------------------------
     1105abd+12132b2d-10853acd+12667bcd-9395c2d-3449ad2-3963bd2-2735cd2-
     ------------------------------------------------------------------------
     7253d3-11743a2e+9619abe-3565b2e-8887ace+15405bce-7453c2e+10110ade+
     ------------------------------------------------------------------------
     11286bde+12273cde-15175d2e-15098ae2-9389be2-14767ce2-10980de2-9835e3
     ------------------------------------------------------------------------
     a2b-910b3+12671a2c-14233abc-12269b2c-8788ac2+12563bc2+11829c3+1428a2d-
     ------------------------------------------------------------------------
     3599abd-3378b2d-5188acd-10934bcd+14265c2d+527ad2+953bd2-4040cd2-14159d3-
     ------------------------------------------------------------------------
     5868a2e+4105abe-13595b2e-1976ace+12429bce+1287c2e-11365ade-12002bde-
     ------------------------------------------------------------------------
     5225cde-15592d2e+1193ae2+13134be2-12947ce2-11830de2-3751e3
     ------------------------------------------------------------------------
     a3+5324b3-5034a2c-12145abc+8379b2c-11291ac2+4809bc2+13577c3-11196a2d+
     ------------------------------------------------------------------------
     14305abd+5693b2d-223acd-15004bcd-4473c2d+13939ad2-3903bd2-4968cd2-
     ------------------------------------------------------------------------
     15628d3-10937a2e+15229abe-2238b2e-7137ace+4101bce-585c2e-14121ade+
     ------------------------------------------------------------------------
     10014bde-5102cde+6611d2e+4338ae2+3299be2-3457ce2+12874de2-4594e3
     ------------------------------------------------------------------------
     b3c-856a2c2+8997abc2+5441b2c2+5111ac3-30bc3+11784c4+3365b3d-7123a2cd+
     ------------------------------------------------------------------------
     5149abcd-7134b2cd-8249ac2d+8222bc2d+9940c3d-9911a2d2+1920abd2-15285b2d2-
     ------------------------------------------------------------------------
     9869acd2+11822bcd2+3949c2d2-9713ad3-13057bd3-3944cd3-10620d4-6306b3e-
     ------------------------------------------------------------------------
     14034a2ce+9904abce+473b2ce+11828ac2e+11318bc2e+1704c3e-1951a2de-6446abde
     ------------------------------------------------------------------------
     +15095b2de-12507acde-5162bcde-11469c2de-15757ad2e+11710bd2e-1852cd2e-
     ------------------------------------------------------------------------
     7229d3e+10123a2e2-10338abe2-5770b2e2-1778ace2+1100bce2+3331c2e2+3866ade2
     ------------------------------------------------------------------------
     -2530bde2-2563cde2-10710d2e2+307ae3-11954be3+2629ce3+7594de3-1305e4
     ------------------------------------------------------------------------
     b4+11972a2c2+2392abc2-12b2c2-3521ac3+15173bc3-12515c4+14803b3d-4728a2cd+
     ------------------------------------------------------------------------
     5436abcd-3385b2cd-9526ac2d-4173bc2d+5737c3d-5932a2d2-15121abd2+10678b2d2
     ------------------------------------------------------------------------
     -13968acd2-10492bcd2-13527c2d2+7726ad3-6237bd3+10603cd3-5884d4-7771b3e-
     ------------------------------------------------------------------------
     13597a2ce+5520abce-9351b2ce+10364ac2e-11491bc2e-759c3e-15754a2de+
     ------------------------------------------------------------------------
     15214abde+7939b2de+9787acde-7209bcde-3244c2de-2376ad2e+597bd2e-8816cd2e+
     ------------------------------------------------------------------------
     4879d3e-1198a2e2+3483abe2+5022b2e2-1566ace2+6723bce2+13686c2e2+7948ade2+
     ------------------------------------------------------------------------
     6971bde2-5453cde2-8945d2e2-11092ae3-6425be3+10778ce3-9438de3-1514e4
     ------------------------------------------------------------------------
     abc3+9056b2c3+2749ac4-2450bc4-11228c5+2517a2c2d-7480abc2d-15207b2c2d-
     ------------------------------------------------------------------------
     14737ac3d-1541bc3d-2645c4d-15257b3d2-13207a2cd2+9538abcd2+12310b2cd2-
     ------------------------------------------------------------------------
     7748ac2d2-12609bc2d2+1172c3d2+780a2d3-14025abd3-6037b2d3+6681acd3-
     ------------------------------------------------------------------------
     15512bcd3+11466c2d3+3711ad4-8597bd4+15456cd4+15637d5-10145a2c2e+
     ------------------------------------------------------------------------
     1925abc2e+4556b2c2e-13078ac3e-7523bc3e+12077c4e-110b3de-2933a2cde+
     ------------------------------------------------------------------------
     5961abcde-5601b2cde+292ac2de+8778bc2de-561c3de-7447a2d2e+3110abd2e+
     ------------------------------------------------------------------------
     5560b2d2e-10369acd2e-8875bcd2e+630c2d2e+1412ad3e-12470bd3e-9660cd3e-
     ------------------------------------------------------------------------
     4425d4e-15483b3e2-223a2ce2-6328abce2-158b2ce2-7151ac2e2-4451bc2e2+
     ------------------------------------------------------------------------
     11415c3e2-12590a2de2-9552abde2+123b2de2+3922acde2-6463bcde2+10618c2de2-
     ------------------------------------------------------------------------
     9081ad2e2+6947bd2e2-10811cd2e2-10616d3e2-13270a2e3+5559abe3-3471b2e3+
     ------------------------------------------------------------------------
     12710ace3-5263bce3+6912c2e3-8691ade3+3950bde3+2140cde3-254d2e3+15270ae4+
     ------------------------------------------------------------------------
     12436be4+3296ce4+12639de4+13728e5
     ------------------------------------------------------------------------
     a2c3+1474b2c3+6996ac4+5408bc4+9311c5-9861a2c2d-4143abc2d+1593b2c2d-
     ------------------------------------------------------------------------
     2436ac3d-533bc3d-14614c4d+4252b3d2-8570a2cd2-11034abcd2+13933b2cd2-
     ------------------------------------------------------------------------
     14223ac2d2-12946bc2d2-15901c3d2+15743a2d3-12594abd3-15334b2d3-9601acd3-
     ------------------------------------------------------------------------
     6281bcd3-12493c2d3-7981ad4-10178bd4-9363cd4-3144d5+7709a2c2e+8980abc2e+
     ------------------------------------------------------------------------
     47b2c2e+2764ac3e+2816bc3e+10306c4e+12944b3de+5281a2cde-7344abcde-
     ------------------------------------------------------------------------
     8743b2cde-5858ac2de-7573bc2de-13168c3de-11692a2d2e+1503abd2e+6037b2d2e+
     ------------------------------------------------------------------------
     10171acd2e+15541bcd2e+6865c2d2e-5886ad3e-10522bd3e-12401cd3e-6265d4e-
     ------------------------------------------------------------------------
     3994b3e2+7801a2ce2+10044abce2-3323b2ce2+7005ac2e2-11619bc2e2-3293c3e2-
     ------------------------------------------------------------------------
     7604a2de2+7318abde2-12398b2de2+10613acde2+15037bcde2+5554c2de2-
     ------------------------------------------------------------------------
     13864ad2e2+948bd2e2+13861cd2e2-12095d3e2-8344a2e3+12927abe3+3772b2e3-
     ------------------------------------------------------------------------
     12982ace3+8240bce3-12008c2e3-3188ade3-6933bde3+14795cde3-3022d2e3-
     ------------------------------------------------------------------------
     7754ae4+5590be4-478ce4-1065de4-15200e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R