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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 (1978a  + 10590a b + 5662a*b  - 14228b  + 7252a c + 12845a*b*c +
     ------------------------------------------------------------------------
          2            2           2         3        2               
     1989b c - 13127a*c  - 15033b*c  + 14161c  + 2002a d - 8355a*b*d +
     ------------------------------------------------------------------------
           2                                2            2          2  
     13297b d - 525a*c*d + 2999b*c*d + 4930c d - 13766a*d  + 8295b*d  +
     ------------------------------------------------------------------------
             2        3        2                     2                
     12095c*d  + 1674d  - 7323a e + 8092a*b*e + 8885b e + 13814a*c*e -
     ------------------------------------------------------------------------
                       2                                                2   
     2596b*c*e - 13072c e + 12019a*d*e + 14437b*d*e + 11159c*d*e - 2613d e +
     ------------------------------------------------------------------------
             2           2         2          2        3         3         2 
     14935a*e  + 15943b*e  - 427c*e  + 7782d*e  - 2164e , - 6264a  - 11293a b
     ------------------------------------------------------------------------
              2        3        2                       2            2  
     + 4839a*b  - 9210b  + 8323a c + 10319a*b*c + 15871b c + 13127a*c  +
     ------------------------------------------------------------------------
            2         3         2                     2                
     2497b*c  - 11463c  + 14703a d + 13456a*b*d - 913b d + 14618a*c*d -
     ------------------------------------------------------------------------
                       2            2          2           2         3  
     15295b*c*d - 6574c d + 10147a*d  + 7492b*d  + 15333c*d  + 11249d  +
     ------------------------------------------------------------------------
          2                     2                                  2   
     5047a e - 2049a*b*e - 8537b e + 13986a*c*e - 6429b*c*e - 7680c e +
     ------------------------------------------------------------------------
                                              2            2          2  
     9654a*d*e - 8021b*d*e - 5479c*d*e + 9651d e + 13728a*e  - 3433b*e  +
     ------------------------------------------------------------------------
             2           2        3         3         2           2       3  
     13028c*e  - 13782d*e  + 4906e , - 3486a  + 13429a b - 4337a*b  - 266b  +
     ------------------------------------------------------------------------
          2                       2            2          2        3  
     4537a c + 11537a*b*c + 10885b c - 12769a*c  + 1110b*c  - 9810c  -
     ------------------------------------------------------------------------
           2                      2                                  2   
     13501a d - 11221a*b*d - 1821b d + 8592a*c*d + 15855b*c*d - 9113c d +
     ------------------------------------------------------------------------
             2          2          2         3        2                
     14446a*d  - 7745b*d  - 4162c*d  + 15457d  - 2648a e + 15614a*b*e +
     ------------------------------------------------------------------------
         2                                   2                            
     704b e - 2285a*c*e - 15476b*c*e - 14955c e - 10235a*d*e - 8688b*d*e +
     ------------------------------------------------------------------------
                        2            2          2          2           2  
     10043c*d*e + 12592d e + 11120a*e  - 8192b*e  + 3494c*e  + 13738d*e  +
     ------------------------------------------------------------------------
           3
     11553e )

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+12071b3+11215a2c+8747abc+12489b2c-12249ac2+3396bc2+9257c3-12057a2d
     ------------------------------------------------------------------------
     +8954abd-13299b2d+15647acd-1328bcd-6953c2d-11728ad2-7899bd2+12474cd2+
     ------------------------------------------------------------------------
     10446d3-11389a2e-8105abe-6114b2e-4325ace-4825bce-9284c2e-7899ade+7749bde
     ------------------------------------------------------------------------
     -15850cde-13609d2e-2438ae2-2027be2+13049ce2-4007de2+2044e3
     ------------------------------------------------------------------------
     a2b+4777b3+7211a2c-2987abc-9857b2c-14401ac2-4884bc2-8321c3-8573a2d-
     ------------------------------------------------------------------------
     10714abd-1718b2d+14366acd+101bcd+7096c2d+12917ad2+15086bd2-8811cd2+
     ------------------------------------------------------------------------
     3894d3-9835a2e-9188abe+13907b2e+1218ace+4214bce-8086c2e-2289ade+1870bde+
     ------------------------------------------------------------------------
     204cde-14200d2e+7065ae2-11989be2-8418ce2-9730de2+431e3
     ------------------------------------------------------------------------
     a3-563b3-5794a2c+3726abc-9364b2c+12508ac2-2494bc2-1761c3+12265a2d+
     ------------------------------------------------------------------------
     6244abd-8433b2d-11214acd+6223bcd+1103c2d+5601ad2+6289bd2-11389cd2-1369d3
     ------------------------------------------------------------------------
     +1621a2e-3971abe+4968b2e-282ace+7396bce-2106c2e+4859ade+2422bde+12653cde
     ------------------------------------------------------------------------
     -1723d2e-10469ae2-7453be2+7603ce2-12185de2+14427e3
     ------------------------------------------------------------------------
     b3c+2554a2c2-6801abc2+5663b2c2+13897ac3+10802bc3+393c4+9922b3d-15960a2cd
     ------------------------------------------------------------------------
     -7657abcd-2788b2cd+13136ac2d-8418bc2d+12272c3d-10957a2d2+4435abd2-
     ------------------------------------------------------------------------
     6317b2d2-111acd2-872bcd2-12828c2d2+15016ad3-11830bd3-7850cd3-13110d4-
     ------------------------------------------------------------------------
     3321b3e-2691a2ce+7241abce-6709b2ce-3780ac2e-4287bc2e-5962c3e-3038a2de+
     ------------------------------------------------------------------------
     12746abde+8259b2de+3442acde-10041bcde+14758c2de-3893ad2e+2728bd2e+
     ------------------------------------------------------------------------
     8944cd2e-8870d3e+13879a2e2-4145abe2-13907b2e2+4452ace2+5337bce2-3723c2e2
     ------------------------------------------------------------------------
     -9808ade2-15432bde2-7744cde2-12470d2e2-5109ae3-362be3+6104ce3+6386de3-
     ------------------------------------------------------------------------
     781e4 b4-3423a2c2+14634abc2-12049b2c2+9702ac3-1591bc3+11739c4+8889b3d+
     ------------------------------------------------------------------------
     14775a2cd-13323abcd+12304b2cd-10464ac2d+314bc2d+13059c3d-14997a2d2+
     ------------------------------------------------------------------------
     9965abd2-3331b2d2-14002acd2+4153bcd2-11731c2d2+5114ad3+15348bd3-15412cd3
     ------------------------------------------------------------------------
     -10448d4+6939b3e-13495a2ce-1039abce-5959b2ce-8210ac2e+1642bc2e-9131c3e-
     ------------------------------------------------------------------------
     931a2de+5000abde-11910b2de+11601acde-11927bcde+7431c2de-7394ad2e-
     ------------------------------------------------------------------------
     13553bd2e-15715cd2e-3383d3e+13580a2e2+14116abe2-5826b2e2+3865ace2-
     ------------------------------------------------------------------------
     1639bce2+1722c2e2+8725ade2-10181bde2+342cde2+15539d2e2+14158ae3+3854be3-
     ------------------------------------------------------------------------
     9701ce3-11637de3-4879e4
     ------------------------------------------------------------------------
     abc3-5039b2c3+5406ac4-8143bc4-12557c5+4117a2c2d-1448abc2d+7377b2c2d+
     ------------------------------------------------------------------------
     7844ac3d+13969bc3d+2903c4d+3420b3d2+10649a2cd2+7987abcd2+9307b2cd2-
     ------------------------------------------------------------------------
     5387ac2d2-2249bc2d2+7166c3d2-7261a2d3-3716abd3-7557b2d3-14182acd3-
     ------------------------------------------------------------------------
     8396bcd3-15585c2d3-2976ad4+9015bd4-12139cd4-549d5-7862a2c2e+6829abc2e+
     ------------------------------------------------------------------------
     12402b2c2e+233ac3e+15730bc3e+9129c4e-4156b3de+940a2cde-11498abcde-
     ------------------------------------------------------------------------
     2553b2cde+7735ac2de-6932bc2de+8175c3de-12446a2d2e-9618abd2e-6278b2d2e-
     ------------------------------------------------------------------------
     5880acd2e-13168bcd2e+11581c2d2e-30ad3e+8203bd3e+7624cd3e-14025d4e-
     ------------------------------------------------------------------------
     12799b3e2+9250a2ce2-4930abce2-12321b2ce2-11194ac2e2-11907bc2e2+15563c3e2
     ------------------------------------------------------------------------
     -5865a2de2-13734abde2-8750b2de2+8500acde2-3231bcde2+14663c2de2-8098ad2e2
     ------------------------------------------------------------------------
     -5232bd2e2-7584cd2e2-7245d3e2+12125a2e3+9725abe3+12052b2e3+12551ace3+
     ------------------------------------------------------------------------
     818bce3+10655c2e3+12747ade3-5116bde3+8009cde3-10658d2e3+7831ae4-5568be4-
     ------------------------------------------------------------------------
     1102ce4+15637de4+8276e5
     ------------------------------------------------------------------------
     a2c3+13659b2c3+14032ac4+1898bc4-666c5+14546a2c2d+12685abc2d-10681b2c2d+
     ------------------------------------------------------------------------
     2582ac3d+7725bc3d+4592c4d+6151b3d2-15254a2cd2-10595abcd2-7498b2cd2-
     ------------------------------------------------------------------------
     3787ac2d2-14748bc2d2-8861c3d2-8526a2d3-467abd3+8327b2d3-4464acd3+
     ------------------------------------------------------------------------
     6447bcd3+6423c2d3-13095ad4-9666bd4-4471cd4+932d5-15963a2c2e-4800abc2e+
     ------------------------------------------------------------------------
     11866b2c2e-12986ac3e-1066bc3e-7613c4e+8637b3de-6108a2cde-15500abcde-
     ------------------------------------------------------------------------
     8494b2cde-5135ac2de-12070bc2de+3319c3de+12772a2d2e+4849abd2e+5243b2d2e+
     ------------------------------------------------------------------------
     8637acd2e-8338bcd2e-12935c2d2e+11145ad3e+14546bd3e-15717cd3e+15060d4e+
     ------------------------------------------------------------------------
     5922b3e2-7682a2ce2+10708abce2-558b2ce2-660ac2e2-15547bc2e2+9044c3e2+
     ------------------------------------------------------------------------
     14278a2de2+3283abde2-7712b2de2-3787acde2-2454bcde2+11971c2de2+3994ad2e2-
     ------------------------------------------------------------------------
     14740bd2e2-7521cd2e2-6109d3e2-15207a2e3-11136abe3+824b2e3-14013ace3-
     ------------------------------------------------------------------------
     11905bce3-15492c2e3+3751ade3-7567bde3-15144cde3+1226d2e3-3561ae4+
     ------------------------------------------------------------------------
     12488be4-1351ce4-13815de4+5795e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R