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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 (3406a  - 10452a b + 6150a*b  + 10083b  + 9672a c + 8041a*b*c +
     ------------------------------------------------------------------------
          2            2          2       3        2                      2 
     6555b c + 12142a*c  + 5150b*c  + 446c  - 3749a d - 4277a*b*d + 12792b d
     ------------------------------------------------------------------------
                                      2            2          2           2  
     + 2330a*c*d - 15096b*c*d - 13777c d - 11130a*d  - 1085b*d  + 11788c*d  +
     ------------------------------------------------------------------------
          3        2                       2                            
     2883d  + 6440a e - 10859a*b*e + 11711b e - 1486a*c*e - 13904b*c*e -
     ------------------------------------------------------------------------
         2                                              2           2  
     666c e - 10364a*d*e - 9872b*d*e - 11327c*d*e + 948d e + 5678a*e  +
     ------------------------------------------------------------------------
            2           2           2        3         3        2           2
     4482b*e  + 14681c*e  + 10760d*e  - 7297e , - 8698a  + 5996a b + 6144a*b 
     ------------------------------------------------------------------------
            3         2                     2           2          2  
     - 5356b  - 10323a c - 9142a*b*c + 8926b c - 4960a*c  + 7474b*c  -
     ------------------------------------------------------------------------
           3        2                     2                           
     12245c  + 1214a d + 2368a*b*d - 7815b d + 6376a*c*d - 3870b*c*d -
     ------------------------------------------------------------------------
          2            2          2          2        3        2             
     5309c d + 13026a*d  - 4434b*d  - 9490c*d  + 1344d  + 3992a e - 7390a*b*e
     ------------------------------------------------------------------------
            2                                   2                           
     + 5381b e - 3860a*c*e + 12176b*c*e - 10844c e + 6365a*d*e + 2243b*d*e -
     ------------------------------------------------------------------------
                       2            2          2          2           2  
     9398c*d*e - 15275d e - 11108a*e  + 9900b*e  - 1119c*e  - 15607d*e  -
     ------------------------------------------------------------------------
           3       3        2           2         3         2                
     10025e , 1929a  + 8435a b - 2510a*b  + 14032b  - 10049a c - 15368a*b*c +
     ------------------------------------------------------------------------
          2           2          2        3         2                      2 
     5978b c - 2607a*c  - 5228b*c  - 7329c  - 15383a d - 3012a*b*d + 14300b d
     ------------------------------------------------------------------------
                                   2          2          2          2       3
     - 5758a*c*d - 160b*c*d - 2845c d - 496a*d  - 4785b*d  + 1564c*d  - 598d 
     ------------------------------------------------------------------------
            2                     2                                  2   
     + 6227a e + 5888a*b*e + 6856b e + 9802a*c*e + 9532b*c*e - 15436c e -
     ------------------------------------------------------------------------
                                               2           2           2  
     10858a*d*e - 5447b*d*e - 3127c*d*e + 5771d e + 7746a*e  + 14965b*e  -
     ------------------------------------------------------------------------
            2           2        3
     4618c*e  - 11709d*e  + 1047e )

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 = | ab2-2441b3+1175a2c+14218abc+4165b2c-2490ac2+3472bc2+6435c3-5536a2d-
     ------------------------------------------------------------------------
     9966abd-14693b2d-10367acd+9322bcd-609c2d+10893ad2-13310bd2+15956cd2+
     ------------------------------------------------------------------------
     7215d3-653a2e+9895abe-4656b2e+2012ace-6288bce-13070c2e+5634ade-777bde-
     ------------------------------------------------------------------------
     11656cde-15454d2e-15794ae2+9148be2+8475ce2+9329de2+4820e3
     ------------------------------------------------------------------------
     a2b-15936b3-8936a2c+1315abc+14862b2c-4917ac2-8098bc2+14634c3-12983a2d-
     ------------------------------------------------------------------------
     10965abd-15955b2d-2004acd-9671bcd-12967c2d+10037ad2-3192bd2-8810cd2-
     ------------------------------------------------------------------------
     8058d3-4119a2e+5223abe+6045b2e-9343ace+11402bce+10007c2e+10180ade-
     ------------------------------------------------------------------------
     9605bde+2889cde+7191d2e+15954ae2+1916be2+667ce2-8009de2+5241e3
     ------------------------------------------------------------------------
     a3+9676b3+4116a2c-13620abc-13261b2c-10608ac2+1336bc2-8637c3-9917a2d-
     ------------------------------------------------------------------------
     7527abd+7753b2d+10766acd+10802bcd+13668c2d-2026ad2-13434bd2+158cd2+
     ------------------------------------------------------------------------
     2301d3+10960a2e+11209abe-767b2e+1935ace-13589bce+2686c2e-14792ade+
     ------------------------------------------------------------------------
     1053bde+5695cde+4194d2e+4339ae2+10335be2+6715ce2-14828de2+6316e3
     ------------------------------------------------------------------------
     b3c+13538a2c2+5654abc2+2184b2c2-4508ac3-10388bc3+4317c4+14873b3d-
     ------------------------------------------------------------------------
     2219a2cd-13974abcd+5366b2cd-9768ac2d+15383bc2d+13372c3d+2197a2d2+
     ------------------------------------------------------------------------
     13629abd2+3374b2d2-15286acd2-8132bcd2+15654c2d2+3188ad3-1835bd3-13202cd3
     ------------------------------------------------------------------------
     +11823d4+10232b3e-15678a2ce-14304abce-9684b2ce+6634ac2e+7944bc2e-
     ------------------------------------------------------------------------
     15467c3e+4082a2de+7759abde-12651b2de+14096acde+10053bcde-2588c2de+
     ------------------------------------------------------------------------
     8876ad2e-9595bd2e+11286cd2e-10829d3e-3834a2e2-13600abe2+1837b2e2+
     ------------------------------------------------------------------------
     9482ace2-11400bce2-14854c2e2-7019ade2+15384bde2-6491cde2-1146d2e2-
     ------------------------------------------------------------------------
     1863ae3-2426be3-1792ce3+15720de3+11949e4
     ------------------------------------------------------------------------
     b4+11057a2c2-15036abc2+8691b2c2-890ac3-9854bc3+988c4-13060b3d-1962a2cd-
     ------------------------------------------------------------------------
     9387abcd+15479b2cd+6253ac2d-14354bc2d-6288c3d-12911a2d2-15301abd2+
     ------------------------------------------------------------------------
     6109b2d2-6566acd2-14556bcd2-10227c2d2+12437ad3+14386bd3-13061cd3+11190d4
     ------------------------------------------------------------------------
     -9250b3e+15455a2ce-13419abce-11403b2ce+2055ac2e-14307bc2e+12057c3e+
     ------------------------------------------------------------------------
     2065a2de-14449abde-13053b2de+12049acde-2944bcde-7814c2de-7685ad2e+
     ------------------------------------------------------------------------
     8740bd2e-14797cd2e-10647d3e+12111a2e2-5550abe2+13221b2e2+4877ace2+
     ------------------------------------------------------------------------
     15991bce2-14840c2e2+2836ade2+6016bde2+5011cde2+14209d2e2-8834ae3+
     ------------------------------------------------------------------------
     13979be3+7064ce3+7497de3-2324e4
     ------------------------------------------------------------------------
     abc3-10068b2c3+5769ac4-13983bc4-15685c5-14384a2c2d-15057abc2d-9065b2c2d-
     ------------------------------------------------------------------------
     7591ac3d+1238bc3d-10013c4d-4220b3d2-10872a2cd2+7065abcd2-147b2cd2-
     ------------------------------------------------------------------------
     1303ac2d2+12738bc2d2-15817c3d2+8924a2d3-11339abd3+4764b2d3+2221acd3-
     ------------------------------------------------------------------------
     15503bcd3-6652c2d3+9768ad4-5281bd4-14121cd4+7063d5+9714a2c2e+15173abc2e+
     ------------------------------------------------------------------------
     12587b2c2e+5351ac3e-4792bc3e+12442c4e-8852b3de+11296a2cde-9410abcde-
     ------------------------------------------------------------------------
     5785b2cde+11979ac2de+4499bc2de+13135c3de-10271a2d2e-11634abd2e+4018b2d2e
     ------------------------------------------------------------------------
     +8712acd2e+5508bcd2e+354c2d2e+6529ad3e+15394bd3e+4027cd3e-14321d4e+
     ------------------------------------------------------------------------
     4282b3e2-11154a2ce2+15384abce2+1980b2ce2+705ac2e2-5245bc2e2-13766c3e2-
     ------------------------------------------------------------------------
     2831a2de2-13407abde2-2091b2de2-6435acde2-7556bcde2-7173c2de2+1744ad2e2+
     ------------------------------------------------------------------------
     9747bd2e2+7596cd2e2+4687d3e2+15804a2e3+7891abe3+12468b2e3-426ace3+
     ------------------------------------------------------------------------
     8348bce3+4826c2e3+13806ade3-7132bde3+277cde3+3085d2e3-710ae4+1990be4+
     ------------------------------------------------------------------------
     821ce4-5268de4+6255e5 a2c3+1350b2c3-7020ac4-8497bc4+13841c5-14542a2c2d+
     ------------------------------------------------------------------------
     6401abc2d-1414b2c2d-139ac3d-3644bc3d+13943c4d+5233b3d2+11610a2cd2+
     ------------------------------------------------------------------------
     195abcd2+11894b2cd2-12163ac2d2-9804bc2d2-4587c3d2-10282a2d3-13931abd3+
     ------------------------------------------------------------------------
     73b2d3+8921acd3+10503bcd3-15956c2d3+15387ad4+7501bd4+14718cd4-8613d5+
     ------------------------------------------------------------------------
     15382a2c2e-2629abc2e-3481b2c2e-14987ac3e+8789bc3e-13014c4e+7245b3de+
     ------------------------------------------------------------------------
     14968a2cde+3251abcde-2176b2cde-4173ac2de-10745bc2de-1601c3de-1954a2d2e+
     ------------------------------------------------------------------------
     6686abd2e+7392b2d2e+4006acd2e-5373bcd2e+2681c2d2e-12690ad3e-3440bd3e-
     ------------------------------------------------------------------------
     5407cd3e+7900d4e-12319b3e2+6355a2ce2+5456abce2-15574b2ce2+2111ac2e2+
     ------------------------------------------------------------------------
     11034bc2e2-3381c3e2+10988a2de2+10639abde2+11627b2de2-14222acde2-
     ------------------------------------------------------------------------
     2669bcde2-7768c2de2+11973ad2e2-3295bd2e2+14509cd2e2+14330d3e2+9104a2e3+
     ------------------------------------------------------------------------
     11545abe3-10750b2e3+14ace3-6239bce3+1589c2e3-1272ade3+10138bde3+9181cde3
     ------------------------------------------------------------------------
     -11311d2e3-8825ae4-7685be4+2459ce4-10374de4+5241e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R