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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 (2335a  - 15668a b - 3880a*b  - 5772b  + 3791a c - 6867a*b*c +
     ------------------------------------------------------------------------
           2           2          2        3        2                      2 
     11688b c + 9770a*c  - 7073b*c  - 4391c  - 2117a d - 12644a*b*d + 4333b d
     ------------------------------------------------------------------------
                                     2            2          2          2  
     - 3237a*c*d + 13854b*c*d + 4629c d - 15834a*d  - 2142b*d  - 1802c*d  -
     ------------------------------------------------------------------------
           3        2                       2                           
     14730d  - 2541a e + 13411a*b*e - 13101b e - 7625a*c*e + 9178b*c*e -
     ------------------------------------------------------------------------
           2                                              2           2  
     15872c e + 107a*d*e - 11102b*d*e + 6142c*d*e + 15151d e - 1077a*e  +
     ------------------------------------------------------------------------
             2          2          2        3          3        2           2
     14243b*e  + 9132c*e  - 6206d*e  - 1533e , - 10530a  + 9203a b - 7547a*b 
     ------------------------------------------------------------------------
            3         2                     2           2           2       3
     + 2717b  - 11048a c + 8703a*b*c - 7674b c - 9584a*c  + 12837b*c  - 758c 
     ------------------------------------------------------------------------
             2                      2                                2   
     - 11502a d + 3714a*b*d - 12096b d + 15929a*c*d + 681b*c*d - 618c d -
     ------------------------------------------------------------------------
            2          2           2        3        2                    2 
     4559a*d  + 7919b*d  - 13115c*d  + 6371d  + 5409a e - 785a*b*e - 8436b e
     ------------------------------------------------------------------------
                                     2                                       
     + 9321a*c*e - 10295b*c*e - 5493c e - 10672a*d*e + 10434b*d*e - 9158c*d*e
     ------------------------------------------------------------------------
            2           2          2          2         2         3         3
     - 1248d e - 7557a*e  - 5386b*e  - 2450c*e  - 422d*e  - 15722e , - 9056a 
     ------------------------------------------------------------------------
            2            2        3        2                      2   
     - 9227a b + 10902a*b  - 5168b  - 2485a c + 14061a*b*c + 6775b c +
     ------------------------------------------------------------------------
            2          2        3        2                      2   
     7324a*c  - 5060b*c  - 7250c  - 2873a d + 3487a*b*d + 11868b d +
     ------------------------------------------------------------------------
                                    2           2          2          2  
     5523a*c*d - 12415b*c*d + 15407c d - 6502a*d  + 5292b*d  - 9913c*d  -
     ------------------------------------------------------------------------
           3         2                     2                            
     14912d  + 10609a e - 394a*b*e + 11117b e - 13272a*c*e - 1008b*c*e -
     ------------------------------------------------------------------------
           2                                             2            2  
     13670c e - 8855a*d*e - 7956b*d*e + 3274c*d*e + 6825d e - 14794a*e  -
     ------------------------------------------------------------------------
            2          2          2        3
     2433b*e  - 6997c*e  - 4199d*e  - 3371e )

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 = | ab2-1752b3+12574a2c-5122abc+11472b2c-830ac2+349bc2-4409c3+15455a2d-
     ------------------------------------------------------------------------
     11042abd-1969b2d-2143acd+12627bcd-5951c2d-13850ad2-8229bd2-2788cd2+
     ------------------------------------------------------------------------
     1126d3-7792a2e+13944abe+1066b2e-6046ace-15525bce+5967c2e+1290ade+7725bde
     ------------------------------------------------------------------------
     +15288cde-11910d2e+10041ae2-5504be2-9253ce2+6988de2+12276e3
     ------------------------------------------------------------------------
     a2b-11738b3+13694a2c-12778abc-2345b2c-14629ac2-11110bc2+5089c3-9088a2d+
     ------------------------------------------------------------------------
     4777abd-532b2d+177acd+19bcd+14712c2d-4376ad2-15532bd2-3023cd2+4746d3-
     ------------------------------------------------------------------------
     13354a2e-3889abe-982b2e+294ace+12010bce-8451c2e+4578ade+11737bde-3868cde
     ------------------------------------------------------------------------
     -13083d2e+4062ae2-5923be2-9404ce2+8275de2+8776e3
     ------------------------------------------------------------------------
     a3-15176b3+12306a2c-11719abc-12991b2c+4134ac2-7074bc2+8015c3+156a2d+
     ------------------------------------------------------------------------
     3983abd+6263b2d+11290acd+10603bcd+12148c2d+6537ad2-4535bd2+2658cd2+529d3
     ------------------------------------------------------------------------
     -9342a2e+11225abe+15927b2e+12701ace+9346bce+15700c2e+14195ade-1036bde+
     ------------------------------------------------------------------------
     8895cde+11134d2e-3591ae2-13221be2+13904ce2-5821de2-8500e3
     ------------------------------------------------------------------------
     b3c-12548a2c2+7037abc2+4476b2c2+2394ac3+10999bc3+10895c4-14436b3d-
     ------------------------------------------------------------------------
     8058a2cd+10099abcd-5130b2cd+8655ac2d+2027bc2d-14270c3d+1967a2d2-
     ------------------------------------------------------------------------
     15436abd2-14308b2d2+5346acd2-10339bcd2-1451c2d2-6601ad3-14222bd3+9433cd3
     ------------------------------------------------------------------------
     +9655d4-1031b3e+5353a2ce-1411abce+13945b2ce+4012ac2e-14884bc2e-145c3e+
     ------------------------------------------------------------------------
     486a2de-11959abde-7074b2de+8318acde+13425bcde+424c2de+9516ad2e-15200bd2e
     ------------------------------------------------------------------------
     -10443cd2e-9495d3e+2338a2e2-4538abe2-12475b2e2-14909ace2+6309bce2+
     ------------------------------------------------------------------------
     4059c2e2+1060ade2-15570bde2-9063cde2+14301d2e2+12017ae3+3748be3-1942ce3-
     ------------------------------------------------------------------------
     2029de3+11068e4 b4-11520a2c2-3644abc2-7170b2c2+8882ac3+9299bc3+13057c4-
     ------------------------------------------------------------------------
     6842b3d+2550a2cd-15935abcd+10398b2cd-11135ac2d-10354bc2d+11052c3d+
     ------------------------------------------------------------------------
     5912a2d2-8185abd2-1063b2d2-2690acd2+9031bcd2-1537c2d2+11833ad3+13044bd3-
     ------------------------------------------------------------------------
     2251cd3+973d4+10009b3e+13600a2ce-6807abce+6497b2ce+12397ac2e-10117bc2e+
     ------------------------------------------------------------------------
     4260c3e+9389a2de-9329abde-8905b2de+3026acde-10707bcde+7798c2de+3848ad2e-
     ------------------------------------------------------------------------
     6616bd2e-14143cd2e-6946d3e-14159a2e2-1492abe2-14129b2e2+76ace2-12536bce2
     ------------------------------------------------------------------------
     +15233c2e2-13620ade2-12091bde2+13579cde2+12854d2e2+6216ae3-8286be3+
     ------------------------------------------------------------------------
     4432ce3+6088de3-514e4 abc3-14208b2c3-14478ac4-1113bc4-10400c5-5513a2c2d-
     ------------------------------------------------------------------------
     13193abc2d-2773b2c2d-7874ac3d+4434bc3d-1205c4d-130b3d2-7124a2cd2-
     ------------------------------------------------------------------------
     9750abcd2+11143b2cd2+9279ac2d2-7350bc2d2-14313c3d2+1025a2d3+7187abd3+
     ------------------------------------------------------------------------
     445b2d3+4909acd3+2490bcd3+1457c2d3-11869ad4-3953bd4-15534cd4+1354d5+
     ------------------------------------------------------------------------
     13208a2c2e-745abc2e+10259b2c2e+12100ac3e-7883bc3e-7350c4e+8911b3de-
     ------------------------------------------------------------------------
     9245a2cde+13504abcde-8858b2cde-919ac2de-5746bc2de-12841c3de-1228a2d2e-
     ------------------------------------------------------------------------
     12277abd2e+15167b2d2e+856acd2e+14739bcd2e+26c2d2e-12755ad3e-6919bd3e-
     ------------------------------------------------------------------------
     9795cd3e+3351d4e+15919b3e2+12766a2ce2-3220abce2-11572b2ce2+10847ac2e2-
     ------------------------------------------------------------------------
     15898bc2e2+15116c3e2-5558a2de2-7752abde2+15689b2de2-4659acde2-15625bcde2
     ------------------------------------------------------------------------
     -7143c2de2-12007ad2e2+5478bd2e2+10656cd2e2-2668d3e2+13746a2e3+5856abe3-
     ------------------------------------------------------------------------
     3783b2e3-5288ace3-10437bce3+6631c2e3-3157ade3+11356bde3-5328cde3-
     ------------------------------------------------------------------------
     6642d2e3-11304ae4-6689be4-2142ce4-8814de4+4525e5
     ------------------------------------------------------------------------
     a2c3+6082b2c3+13616ac4+5626bc4+14017c5+2219a2c2d-6461abc2d-12389b2c2d+
     ------------------------------------------------------------------------
     10062ac3d-8579bc3d-3862c4d-15841b3d2-13292a2cd2-14398abcd2-8724b2cd2+
     ------------------------------------------------------------------------
     1175ac2d2+6442bc2d2+15926c3d2-11556a2d3+4347abd3-11164b2d3+5324acd3+
     ------------------------------------------------------------------------
     308bcd3+13671c2d3+12276ad4-13493bd4-8627cd4+14173d5-11849a2c2e-
     ------------------------------------------------------------------------
     15145abc2e+920b2c2e+14414ac3e+441bc3e+583c4e+1036b3de-4415a2cde-
     ------------------------------------------------------------------------
     15250abcde+4336b2cde+12662ac2de+9010bc2de-12756c3de+13364a2d2e-
     ------------------------------------------------------------------------
     11821abd2e-14454b2d2e-12965acd2e-14025bcd2e+3547c2d2e-8521ad3e+1115bd3e+
     ------------------------------------------------------------------------
     15652cd3e-12761d4e-6477b3e2-12647a2ce2-10929abce2+7636b2ce2+2961ac2e2+
     ------------------------------------------------------------------------
     5931bc2e2+14449c3e2-10217a2de2+6351abde2+7233b2de2-11896acde2-11767bcde2
     ------------------------------------------------------------------------
     -4454c2de2+9320ad2e2-8379bd2e2+4263cd2e2+5508d3e2-6233a2e3-15731abe3-
     ------------------------------------------------------------------------
     14574b2e3-7139ace3+10067bce3+11734c2e3-6395ade3-4111bde3+3466cde3+
     ------------------------------------------------------------------------
     14011d2e3-348ae4-9424be4+13134ce4-14203de4+2596e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R