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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 (8223a  + 6471a b + 15610a*b  + 14326b  - 1698a c - 14542a*b*c +
     ------------------------------------------------------------------------
        2           2          2        3         2                     2   
     10b c + 2852a*c  - 1647b*c  + 7404c  + 15172a d + 1001a*b*d + 6197b d -
     ------------------------------------------------------------------------
                                   2           2           2          2  
     8445a*c*d - 14696b*c*d + 3392c d - 4104a*d  - 14024b*d  - 9922c*d  -
     ------------------------------------------------------------------------
          3        2                       2                            
     2098d  - 6492a e + 15957a*b*e + 13844b e - 11445a*c*e - 7331b*c*e +
     ------------------------------------------------------------------------
          2                                               2           2  
     4016c e - 6569a*d*e + 13747b*d*e + 9720c*d*e + 12269d e + 5296a*e  +
     ------------------------------------------------------------------------
             2           2          2         3       3        2            2
     13410b*e  + 13912c*e  - 2736d*e  - 10044e , 3683a  - 7849a b + 14525a*b 
     ------------------------------------------------------------------------
            3         2                      2           2           2  
     + 2307b  + 14306a c + 15633a*b*c - 9677b c + 4252a*c  - 15482b*c  +
     ------------------------------------------------------------------------
          3        2                      2                            
     1019c  - 5188a d + 14832a*b*d + 2989b d + 13093a*c*d - 5723b*c*d -
     ------------------------------------------------------------------------
           2           2           2         2         3        2   
     12680c d + 5373a*d  - 11589b*d  - 476c*d  + 15771d  - 2581a e +
     ------------------------------------------------------------------------
                      2                                 2               
     5209a*b*e - 8156b e - 7184a*c*e - 8507b*c*e - 2387c e + 6755a*d*e +
     ------------------------------------------------------------------------
                                  2           2          2          2  
     2856b*d*e + 3103c*d*e - 6161d e + 1271a*e  + 1547b*e  - 4323c*e  -
     ------------------------------------------------------------------------
           2         3       3        2           2         3         2   
     700d*e  + 12622e , 4091a  - 8981a b + 8674a*b  - 12061b  + 10113a c -
     ------------------------------------------------------------------------
                       2           2          2         3         2   
     15341a*b*c - 9080b c - 7471a*c  + 9364b*c  + 13496c  - 10814a d -
     ------------------------------------------------------------------------
                        2                                   2           2  
     15568a*b*d + 15588b d + 10739a*c*d - 5433b*c*d - 13545c d - 3792a*d  -
     ------------------------------------------------------------------------
             2           2        3       2                      2   
     10714b*d  + 12218c*d  + 2718d  - 394a e + 4450a*b*e + 13002b e -
     ------------------------------------------------------------------------
                                   2                                        
     2441a*c*e + 15260b*c*e - 6668c e - 12753a*d*e + 6828b*d*e + 9145c*d*e +
     ------------------------------------------------------------------------
          2            2           2          2          2       3
     6588d e - 12404a*e  + 11331b*e  + 4096c*e  - 4678d*e  - 503e )

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 = | ab2-13365b3+4775a2c+3139abc+9665b2c-12413ac2+549bc2-2607c3+3761a2d-
     ------------------------------------------------------------------------
     2551abd-9296b2d+11928acd+4615bcd+5287c2d+14102ad2-15213bd2+8955cd2-
     ------------------------------------------------------------------------
     7189d3-618a2e-1429abe+15686b2e-14791ace+14591bce+14264c2e-8823ade-
     ------------------------------------------------------------------------
     1819bde+12775cde-10686d2e-14905ae2-3248be2-8597ce2+1751de2+8405e3
     ------------------------------------------------------------------------
     a2b-55b3+7478a2c+12042abc+12719b2c+7588ac2-15608bc2-3997c3-1587a2d+
     ------------------------------------------------------------------------
     10168abd+10963b2d-5897acd+14949bcd+6266c2d-5738ad2+3240bd2+7752cd2-
     ------------------------------------------------------------------------
     12178d3+2033a2e-8926abe-10301b2e+11002ace+13100bce-5356c2e-8842ade-
     ------------------------------------------------------------------------
     803bde-7886cde+4587d2e+6559ae2+10275be2-9241ce2+6960de2-13687e3
     ------------------------------------------------------------------------
     a3+9658b3-8991a2c+1088abc-14046b2c+7264ac2+8006bc2-12991c3-3114a2d+
     ------------------------------------------------------------------------
     12183abd+1225b2d-7052acd-351bcd+2527c2d+13803ad2-13704bd2+4613cd2-
     ------------------------------------------------------------------------
     14237d3-8472a2e-6825abe+11618b2e+6206ace-12571bce-8373c2e+14790ade+
     ------------------------------------------------------------------------
     9582bde-5345cde+9096d2e-15645ae2-3300be2+10482ce2-15908de2+5186e3
     ------------------------------------------------------------------------
     b3c+7551a2c2-4648abc2+14766b2c2+14878ac3+15631bc3+15540c4+5756b3d+
     ------------------------------------------------------------------------
     4446a2cd+11819abcd-5189b2cd-5204ac2d+13878bc2d-15710c3d+11472a2d2-
     ------------------------------------------------------------------------
     4821abd2+5541b2d2-14153acd2-1234bcd2-10297c2d2+12062ad3-3876bd3-8530cd3-
     ------------------------------------------------------------------------
     4839d4-13095b3e+12621a2ce-4806abce+4935b2ce-15715ac2e-3728bc2e+10079c3e-
     ------------------------------------------------------------------------
     10408a2de+12721abde-1430b2de-4210acde-5115bcde+11564c2de+15449ad2e+
     ------------------------------------------------------------------------
     5280bd2e-13902cd2e-12226d3e+7398a2e2-1687abe2+4429b2e2+10846ace2+
     ------------------------------------------------------------------------
     6836bce2+14188c2e2-1828ade2+10495bde2-13227cde2-384d2e2+10345ae3-2203be3
     ------------------------------------------------------------------------
     -14625ce3-2101de3+4029e4
     ------------------------------------------------------------------------
     b4+10338a2c2+1360abc2+47b2c2+5760ac3-14005bc3-6511c4+7236b3d+298a2cd-
     ------------------------------------------------------------------------
     11285abcd-6311b2cd-11456ac2d-14227bc2d-327c3d+701a2d2-6256abd2+7787b2d2+
     ------------------------------------------------------------------------
     11542acd2+9103bcd2+12608c2d2-3781ad3-14046bd3-7183cd3+10619d4-2659b3e+
     ------------------------------------------------------------------------
     6382a2ce-14111abce+12842b2ce+7411ac2e+9852bc2e+4055c3e+15812a2de+
     ------------------------------------------------------------------------
     12882abde+9333b2de-11980acde+2857bcde+12205c2de-10108ad2e+3952bd2e+
     ------------------------------------------------------------------------
     3274cd2e-1242d3e+14788a2e2-4583abe2+1868b2e2-15994ace2-44bce2-4267c2e2-
     ------------------------------------------------------------------------
     13440ade2+2025bde2+1689cde2+12381d2e2+9880ae3+7241be3-2201ce3+10112de3+
     ------------------------------------------------------------------------
     14968e4 abc3-15628b2c3-929ac4+3656bc4+3540c5+15445a2c2d+15734abc2d-
     ------------------------------------------------------------------------
     1279b2c2d-907ac3d+13391bc3d+10539c4d+8799b3d2-6949a2cd2-10100abcd2+
     ------------------------------------------------------------------------
     2789b2cd2+6337ac2d2+11357bc2d2+11586c3d2+12880a2d3+6731abd3-15900b2d3-
     ------------------------------------------------------------------------
     2895acd3-620bcd3-14414c2d3-6898ad4-11955bd4-8951cd4+14459d5-13268a2c2e+
     ------------------------------------------------------------------------
     9151abc2e-11096b2c2e-8996ac3e+12380bc3e+12847c4e+7955b3de+7692a2cde+
     ------------------------------------------------------------------------
     9406abcde+8176b2cde+12045ac2de-8393bc2de-1884c3de+8840a2d2e-14541abd2e+
     ------------------------------------------------------------------------
     8604b2d2e+8955acd2e-15855bcd2e-12800c2d2e-13151ad3e+7510bd3e-13297cd3e+
     ------------------------------------------------------------------------
     4449d4e+7490b3e2-4754a2ce2-9269abce2-5234b2ce2+12034ac2e2+6444bc2e2+
     ------------------------------------------------------------------------
     2966c3e2+11184a2de2+12892abde2-6572b2de2+7839acde2+3497bcde2-9463c2de2+
     ------------------------------------------------------------------------
     7636ad2e2+1884bd2e2-10616cd2e2+3511d3e2+13536a2e3-7604abe3-9363b2e3-
     ------------------------------------------------------------------------
     2092ace3+4755bce3-3359c2e3+7084ade3-14447bde3-11973cde3-7060d2e3-3097ae4
     ------------------------------------------------------------------------
     -15421be4-3385ce4-12274de4+12872e5
     ------------------------------------------------------------------------
     a2c3+7334b2c3-3555ac4+11311bc4-14514c5+7027a2c2d+6533abc2d-2206b2c2d+
     ------------------------------------------------------------------------
     8831ac3d-3595bc3d-6233c4d-3071b3d2+11409a2cd2+3013abcd2+8579b2cd2-
     ------------------------------------------------------------------------
     1614ac2d2-14717bc2d2+6163c3d2-2316a2d3+1805abd3-13824b2d3+13526acd3-
     ------------------------------------------------------------------------
     8235bcd3-3390c2d3-10209ad4-10810bd4+12084cd4-2480d5+8464a2c2e-13594abc2e
     ------------------------------------------------------------------------
     -10198b2c2e+336ac3e+4978bc3e-12270c4e-9596b3de-7998a2cde+6051abcde-
     ------------------------------------------------------------------------
     7147b2cde+12581ac2de-12152bc2de-3589c3de+284a2d2e+3807abd2e+2232b2d2e+
     ------------------------------------------------------------------------
     11827acd2e+14974bcd2e-6393c2d2e+1961ad3e-4646bd3e-4081cd3e-5128d4e-
     ------------------------------------------------------------------------
     11697b3e2+6397a2ce2-13354abce2+13008b2ce2+7008ac2e2-13638bc2e2+8264c3e2+
     ------------------------------------------------------------------------
     14527a2de2+3951abde2-3805b2de2-4058acde2-1033bcde2+15807c2de2+15824ad2e2
     ------------------------------------------------------------------------
     +10238bd2e2-8095cd2e2-13612d3e2-4016a2e3-14040abe3+5218b2e3+11583ace3-
     ------------------------------------------------------------------------
     10132bce3-1484c2e3-13373ade3+7523bde3+15028cde3-4171d2e3-2525ae4+8300be4
     ------------------------------------------------------------------------
     +6541ce4-4793de4-498e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R