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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 (14738a  + 8354a b - 14978a*b  - 4113b  + 6998a c + 8602a*b*c -
     ------------------------------------------------------------------------
          2            2           2        3        2                     2 
     7615b c - 12872a*c  + 12281b*c  + 5169c  - 8993a d - 4945a*b*d + 2971b d
     ------------------------------------------------------------------------
                                    2           2          2          2  
     + 8405a*c*d + 9092b*c*d - 6928c d + 8300a*d  - 9896b*d  - 4093c*d  +
     ------------------------------------------------------------------------
           3        2                     2                            
     10971d  + 8573a e - 6068a*b*e + 8741b e - 14357a*c*e - 3557b*c*e -
     ------------------------------------------------------------------------
          2                                              2           2  
     2570c e - 1363a*d*e - 14328b*d*e + 7934c*d*e + 1597d e - 9697a*e  -
     ------------------------------------------------------------------------
             2          2          2        3        3         2            2
     13773b*e  + 1510c*e  - 5438d*e  - 6776e , 15117a  + 12751a b + 10697a*b 
     ------------------------------------------------------------------------
            3        2                       2           2           2  
     + 2451b  + 6982a c + 12744a*b*c + 15346b c - 2206a*c  + 10446b*c  +
     ------------------------------------------------------------------------
          3         2                     2                            
     5998c  - 14777a d + 335a*b*d - 14048b d + 15988a*c*d + 9569b*c*d -
     ------------------------------------------------------------------------
          2            2         2          2        3        2             
     4285c d - 13237a*d  - 225b*d  + 3775c*d  + 2304d  - 6421a e - 6096a*b*e
     ------------------------------------------------------------------------
             2                                   2                          
     + 10701b e - 14313a*c*e - 8347b*c*e - 14009c e - 7802a*d*e - 242b*d*e -
     ------------------------------------------------------------------------
                       2            2          2          2           2  
     9546c*d*e - 12960d e + 15235a*e  - 2735b*e  - 3123c*e  + 13898d*e  -
     ------------------------------------------------------------------------
          3         3       2            2        3         2               
     4610e , - 7881a  - 388a b + 15400a*b  + 2142b  - 15979a c + 6189a*b*c -
     ------------------------------------------------------------------------
         2            2          2        3        2                     2   
     315b c - 13244a*c  + 2485b*c  - 7584c  + 1866a d - 305a*b*d - 13069b d +
     ------------------------------------------------------------------------
                                  2            2          2          2  
     7669a*c*d + 2758b*c*d - 3193c d - 10589a*d  + 3959b*d  + 9796c*d  -
     ------------------------------------------------------------------------
          3         2                      2                           
     8463d  + 12449a e - 11205a*b*e + 5222b e - 1476a*c*e - 6265b*c*e -
     ------------------------------------------------------------------------
           2                                                2           2  
     14516c e + 10137a*d*e + 13128b*d*e - 10840c*d*e - 2642d e - 5155a*e  -
     ------------------------------------------------------------------------
            2          2          2         3
     1602b*e  - 1024c*e  + 9981d*e  + 11415e )

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 = | ab2-14603b3-15215a2c-5552abc-2389b2c+13863ac2+8391bc2-3168c3-2604a2d+
     ------------------------------------------------------------------------
     3560abd-11504b2d-10031acd-5632bcd-1904c2d-13291ad2-5625bd2-14473cd2-
     ------------------------------------------------------------------------
     4688d3+11493a2e+8108abe-1159b2e-12586ace-8108bce-7525c2e-8768ade+
     ------------------------------------------------------------------------
     12664bde+15985cde+1938d2e-611ae2+9361be2+12188ce2-6138de2-15960e3
     ------------------------------------------------------------------------
     a2b-11776b3+7352a2c-897abc-10371b2c+1342ac2+4402bc2+15982c3+1340a2d-
     ------------------------------------------------------------------------
     6069abd-12355b2d+11933acd+8209bcd-1747c2d+3397ad2-5367bd2-13133cd2-
     ------------------------------------------------------------------------
     9059d3+15628a2e-15497abe+8295b2e+3237ace-2215bce-554c2e+1358ade+12823bde
     ------------------------------------------------------------------------
     +4337cde-2204d2e+1119ae2-11447be2-6327ce2+4913de2-8866e3
     ------------------------------------------------------------------------
     a3+5968b3+1047a2c-6623abc-6988b2c+12337ac2+10665bc2-7955c3+11722a2d+
     ------------------------------------------------------------------------
     754abd+22b2d-5043acd+5280bcd+5795c2d+15246ad2+15322bd2-518cd2-9676d3+
     ------------------------------------------------------------------------
     8518a2e+9997abe-13577b2e+7989ace+7766bce+7923c2e-14903ade+5718bde+
     ------------------------------------------------------------------------
     8133cde+10856d2e-8172ae2+6844be2+1359ce2-6678de2+15740e3
     ------------------------------------------------------------------------
     b3c+7351a2c2-5448abc2-4752b2c2+11428ac3-13070bc3+4207c4-9333b3d-5310a2cd
     ------------------------------------------------------------------------
     +6925abcd-12334b2cd-2265ac2d-2044bc2d+12305c3d-6879a2d2-2663abd2-
     ------------------------------------------------------------------------
     9904b2d2-6224acd2-2871bcd2+19c2d2-1414ad3+13052bd3-1732cd3-8477d4+
     ------------------------------------------------------------------------
     1854b3e+10923a2ce+11095abce-7127b2ce-1211ac2e+12495bc2e+637c3e-9893a2de+
     ------------------------------------------------------------------------
     9274abde+6458b2de+11398acde-8121bcde-12051c2de-7625ad2e-10155bd2e-
     ------------------------------------------------------------------------
     5626cd2e+5574d3e+12828a2e2+13abe2+6505b2e2-8141ace2-6290bce2-2210c2e2+
     ------------------------------------------------------------------------
     11363ade2+11518bde2-10474cde2+6692d2e2-2443ae3+5537be3-10188ce3-11995de3
     ------------------------------------------------------------------------
     -2551e4 b4-1339a2c2+7466abc2+12591b2c2-1570ac3-7612bc3-1302c4-8968b3d-
     ------------------------------------------------------------------------
     14415a2cd-13714abcd+1182b2cd+9103ac2d+1616bc2d-3781c3d+3718a2d2-
     ------------------------------------------------------------------------
     14771abd2+12926b2d2-1261acd2+1174bcd2+8332c2d2+8059ad3-7146bd3-6922cd3+
     ------------------------------------------------------------------------
     9743d4-2903b3e-4754a2ce-3741abce-8362b2ce-6730ac2e+1751bc2e+7674c3e+
     ------------------------------------------------------------------------
     5251a2de+4316abde-14422b2de+11966acde+9428bcde-9766c2de+6666ad2e+
     ------------------------------------------------------------------------
     13776bd2e-10645cd2e+9728d3e+11427a2e2+10943abe2+10284b2e2-5563ace2+
     ------------------------------------------------------------------------
     8802bce2+15812c2e2-4096ade2+13524bde2+598cde2-8803d2e2-1107ae3+9121be3-
     ------------------------------------------------------------------------
     13984ce3-6573de3+11133e4
     ------------------------------------------------------------------------
     abc3+14528b2c3-10103ac4+5657bc4+10349c5-10075a2c2d+11613abc2d-8035b2c2d+
     ------------------------------------------------------------------------
     3598ac3d-8312bc3d-1803c4d+7565b3d2+682a2cd2+4454abcd2-12230b2cd2+
     ------------------------------------------------------------------------
     10886ac2d2-15653bc2d2+4726c3d2+12042a2d3+3445abd3-1809b2d3-3061acd3-
     ------------------------------------------------------------------------
     2023bcd3+15950c2d3+1570ad4+12612bd4-2751cd4-2766d5+11601a2c2e+13536abc2e
     ------------------------------------------------------------------------
     +12494b2c2e-7490ac3e+1282bc3e+10409c4e-12585b3de+654a2cde-4565abcde-
     ------------------------------------------------------------------------
     689b2cde-10136ac2de-765bc2de+7452c3de-6236a2d2e+8837abd2e+15286b2d2e+
     ------------------------------------------------------------------------
     2605acd2e-7738bcd2e+14480c2d2e-8885ad3e+11560bd3e+4578cd3e+1417d4e-
     ------------------------------------------------------------------------
     1258b3e2+15732a2ce2+4983abce2-4704b2ce2+15071ac2e2-4955bc2e2-6924c3e2+
     ------------------------------------------------------------------------
     1849a2de2+8652abde2+6107b2de2-14300acde2+13102bcde2-13219c2de2+6749ad2e2
     ------------------------------------------------------------------------
     +10259bd2e2-12694cd2e2+101d3e2+6390a2e3-12000abe3-7299b2e3+11075ace3+
     ------------------------------------------------------------------------
     11383bce3+6554c2e3-7351ade3-13225bde3-9961cde3-11423d2e3-15905ae4-
     ------------------------------------------------------------------------
     7557be4-10791ce4-7584de4-1998e5
     ------------------------------------------------------------------------
     a2c3+12657b2c3+8126ac4-15051bc4-9386c5+2750a2c2d-10644abc2d-8987b2c2d-
     ------------------------------------------------------------------------
     9041ac3d+4082bc3d-6220c4d+1023b3d2-9461a2cd2-6645abcd2+9947b2cd2-
     ------------------------------------------------------------------------
     1879ac2d2-9698bc2d2+13594c3d2-15064a2d3+10444abd3-14314b2d3+2441acd3-
     ------------------------------------------------------------------------
     6233bcd3-3431c2d3-11630ad4-6535bd4+14218cd4+7661d5+10502a2c2e+5564abc2e+
     ------------------------------------------------------------------------
     2037b2c2e+1446ac3e+1388bc3e-8902c4e+1574b3de-14620a2cde-3715abcde+
     ------------------------------------------------------------------------
     893b2cde-8222ac2de-9477bc2de+11388c3de-8808a2d2e-14435abd2e-14961b2d2e-
     ------------------------------------------------------------------------
     12384acd2e-184bcd2e+6801c2d2e-13237ad3e+10739bd3e-13898cd3e-159d4e+
     ------------------------------------------------------------------------
     1404b3e2+2314a2ce2-6903abce2+2803b2ce2-12921ac2e2-2661bc2e2-9439c3e2+
     ------------------------------------------------------------------------
     13660a2de2-14689abde2-14447b2de2+3259acde2+1589bcde2+1271c2de2+
     ------------------------------------------------------------------------
     12325ad2e2-13451bd2e2-4043cd2e2-11133d3e2+12209a2e3+4755abe3+15857b2e3+
     ------------------------------------------------------------------------
     4521ace3-8699bce3+6160c2e3+6016ade3-7485bde3+12803cde3-3953d2e3-5044ae4+
     ------------------------------------------------------------------------
     6848be4+9476ce4-10122de4+14745e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R