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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 (- 7906a  - 12746a b + 1081a*b  - 14496b  + 9052a c - 14801a*b*c -
     ------------------------------------------------------------------------
           2           2          2        3        2                
     10906b c - 7473a*c  - 8380b*c  + 4107c  - 1709a d - 10228a*b*d +
     ------------------------------------------------------------------------
           2                                   2            2          2  
     13141b d - 4915a*c*d + 13976b*c*d + 12433c d + 12525a*d  - 8640b*d  +
     ------------------------------------------------------------------------
            2        3      2                       2                
     3948c*d  - 4768d  + 59a e - 14047a*b*e + 12872b e + 10411a*c*e -
     ------------------------------------------------------------------------
                       2                                             2   
     7084b*c*e + 14150c e + 8485a*d*e + 6128b*d*e - 801c*d*e - 11259d e +
     ------------------------------------------------------------------------
            2           2          2          2         3         3        2 
     1556a*e  + 13272b*e  - 9552c*e  + 8324d*e  + 10071e , - 7795a  + 6612a b
     ------------------------------------------------------------------------
              2        3         2                      2            2  
     - 8781a*b  + 5662b  - 10635a c + 15797a*b*c - 6147b c - 14284a*c  +
     ------------------------------------------------------------------------
            2        3        2                     2                        
     3153b*c  - 2693c  - 6931a d - 1804a*b*d - 5734b d + 993a*c*d - 3547b*c*d
     ------------------------------------------------------------------------
            2            2           2           2         3        2   
     - 6659c d - 10995a*d  - 11647b*d  + 15378c*d  - 13890d  + 7921a e +
     ------------------------------------------------------------------------
                       2                                  2               
     9246a*b*e + 15946b e + 10002a*c*e + 2704b*c*e - 6361c e - 7573a*d*e +
     ------------------------------------------------------------------------
                                   2            2           2          2  
     12394b*d*e + 357c*d*e + 12728d e + 15271a*e  - 15808b*e  + 8344c*e  -
     ------------------------------------------------------------------------
            2         3        3         2           2        3        2   
     2753d*e  - 14774e , 11756a  + 13729a b - 6179a*b  - 8464b  - 2035a c +
     ------------------------------------------------------------------------
                      2            2           2        3        2   
     1762a*b*c + 7596b c - 10695a*c  - 11745b*c  - 3325c  - 7720a d +
     ------------------------------------------------------------------------
                       2                                    2            2  
     13054a*b*d - 7942b d - 10011a*c*d + 13371b*c*d - 11382c d - 10150a*d  -
     ------------------------------------------------------------------------
           2          2        3        2                      2   
     443b*d  + 3196c*d  + 8706d  - 6956a e - 9862a*b*e + 12022b e +
     ------------------------------------------------------------------------
                                     2                                      
     13872a*c*e - 10046b*c*e + 12352c e + 11035a*d*e - 4999b*d*e + 4552c*d*e
     ------------------------------------------------------------------------
            2           2           2           2          2        3
     - 7143d e + 1204a*e  + 14003b*e  - 14574c*e  + 4669d*e  - 1869e )

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+13055b3-15182a2c-13736abc+862b2c+15252ac2-3745bc2-6245c3-3279a2d+
     ------------------------------------------------------------------------
     7565abd-13489b2d+549acd+8821bcd+7233c2d-12456ad2+9563bd2-2252cd2-1083d3-
     ------------------------------------------------------------------------
     9808a2e-13841abe-13113b2e-10177ace+577bce+2824c2e-8731ade+14954bde-
     ------------------------------------------------------------------------
     15206cde+1263d2e+13455ae2+4346be2-793ce2+6291de2-14875e3
     ------------------------------------------------------------------------
     a2b+1391b3-5062a2c+9620abc-199b2c-7373ac2-12360bc2+11460c3-9622a2d+
     ------------------------------------------------------------------------
     11666abd+351b2d-5612acd+8709bcd+11066c2d-9755ad2+5489bd2+7006cd2-8596d3-
     ------------------------------------------------------------------------
     12929a2e+12336abe-11465b2e-12059ace+13463bce-8506c2e+11921ade-7184bde-
     ------------------------------------------------------------------------
     14639cde-2506d2e+4675ae2-7703be2-13557ce2+11151de2+3560e3
     ------------------------------------------------------------------------
     a3-3099b3+14366a2c+4364abc-15525b2c-9339ac2+13445bc2+9054c3+14862a2d+
     ------------------------------------------------------------------------
     2002abd-477b2d-6356acd+5424bcd+14907c2d-14285ad2-3853bd2+8531cd2-3594d3-
     ------------------------------------------------------------------------
     14609a2e-14792abe-2834b2e+10989ace-11647bce-2677c2e+5242ade-1481bde-
     ------------------------------------------------------------------------
     1434cde-4675d2e-8106ae2+9441be2+15730ce2+9011de2+6628e3
     ------------------------------------------------------------------------
     b3c+5094a2c2+4169abc2+12683b2c2-11051ac3-12295bc3-8749c4+15914b3d+
     ------------------------------------------------------------------------
     5509a2cd+9354abcd+13632b2cd+10520ac2d-11116bc2d-5641c3d+14831a2d2+
     ------------------------------------------------------------------------
     3685abd2-1677b2d2+9654acd2+4665bcd2+7283c2d2+7254ad3+12564bd3-3300cd3+
     ------------------------------------------------------------------------
     51d4+9101b3e-10411a2ce+4777abce+3397b2ce-4236ac2e-3192bc2e-10228c3e+
     ------------------------------------------------------------------------
     235a2de-8090abde+12122b2de-10947acde-10020bcde-4985c2de-11067ad2e+
     ------------------------------------------------------------------------
     3524bd2e-4959cd2e+8422d3e-15259a2e2+6457abe2+14930b2e2+1100ace2-2343bce2
     ------------------------------------------------------------------------
     +4202c2e2-13478ade2-1107bde2-721cde2-773d2e2-13445ae3+448be3+11161ce3-
     ------------------------------------------------------------------------
     7149de3-1444e4 b4-11506a2c2-15277abc2+3424b2c2-1042ac3+2122bc3+13646c4-
     ------------------------------------------------------------------------
     9994b3d-14366a2cd-4838abcd+5422b2cd+10764ac2d+2873bc2d-14195c3d+
     ------------------------------------------------------------------------
     13407a2d2-4161abd2+8341b2d2-1324acd2-13188bcd2+9369c2d2-6424ad3-2164bd3+
     ------------------------------------------------------------------------
     10836cd3+13249d4-11286b3e+326a2ce-1038abce-3262b2ce+26ac2e+8742bc2e-
     ------------------------------------------------------------------------
     6952c3e-7801a2de+3824abde+2948b2de+6886acde-10374bcde-15584c2de+4760ad2e
     ------------------------------------------------------------------------
     +12163bd2e+1531cd2e+8055d3e-4280a2e2-15123abe2-5629b2e2-6303ace2-
     ------------------------------------------------------------------------
     13138bce2-4134c2e2+6117ade2+2364bde2-9557cde2+1215d2e2+1136ae3+6166be3-
     ------------------------------------------------------------------------
     11840ce3+10783de3+13786e4
     ------------------------------------------------------------------------
     abc3+11637b2c3+13876ac4-3511bc4+4262c5-8780a2c2d-4680abc2d+8323b2c2d-
     ------------------------------------------------------------------------
     812ac3d-4425bc3d+4529c4d-8561b3d2+10542a2cd2-9413abcd2+6758b2cd2+
     ------------------------------------------------------------------------
     5407ac2d2-12626bc2d2-4408c3d2+7301a2d3+14142abd3-5266b2d3+3288acd3-
     ------------------------------------------------------------------------
     748bcd3+15880c2d3-5892ad4-5522bd4-7729cd4-12931d5-5403a2c2e-4016abc2e+
     ------------------------------------------------------------------------
     6330b2c2e-452ac3e+3495bc3e+15360c4e+707b3de-7360a2cde-7946abcde+
     ------------------------------------------------------------------------
     12372b2cde+6688ac2de+9113bc2de-10658c3de-15113a2d2e+8412abd2e+12257b2d2e
     ------------------------------------------------------------------------
     -13485acd2e-3814bcd2e-12410c2d2e-3381ad3e-15925bd3e+8574cd3e-8289d4e-
     ------------------------------------------------------------------------
     9079b3e2-7667a2ce2-13671abce2-15474b2ce2-6586ac2e2+11937bc2e2+9292c3e2+
     ------------------------------------------------------------------------
     11526a2de2+13235abde2+8204b2de2+2180acde2+7684bcde2-5042c2de2+11632ad2e2
     ------------------------------------------------------------------------
     +9820bd2e2+13581cd2e2+19d3e2-2349a2e3-9960abe3+609b2e3-12746ace3+
     ------------------------------------------------------------------------
     6161bce3+9482c2e3-11791ade3+9409bde3+10221cde3-3922d2e3-8537ae4-14203be4
     ------------------------------------------------------------------------
     -3334ce4-5483de4+9134e5
     ------------------------------------------------------------------------
     a2c3+15324b2c3+4122ac4+8927bc4+12478c5-1376a2c2d-5519abc2d+3120b2c2d+
     ------------------------------------------------------------------------
     3661ac3d+5975bc3d-10777c4d+9649b3d2-2369a2cd2+732abcd2-14717b2cd2+
     ------------------------------------------------------------------------
     2878ac2d2+3567bc2d2+10785c3d2-11471a2d3+11142abd3+8394b2d3-12345acd3+
     ------------------------------------------------------------------------
     5373bcd3+2580c2d3-14966ad4-10129bd4+8745cd4-6671d5-15881a2c2e+5366abc2e+
     ------------------------------------------------------------------------
     10355b2c2e+5810ac3e+4609bc3e-11739c4e-2077b3de-10733a2cde-5600abcde+
     ------------------------------------------------------------------------
     8738b2cde-6885ac2de+11496bc2de+14455c3de-2026a2d2e+8885abd2e+2135b2d2e+
     ------------------------------------------------------------------------
     11013acd2e-15917bcd2e+15870c2d2e-1165ad3e+1823bd3e-12110cd3e-9612d4e+
     ------------------------------------------------------------------------
     1833b3e2+1997a2ce2-7157abce2-3853b2ce2-8481ac2e2+12744bc2e2-5923c3e2-
     ------------------------------------------------------------------------
     13273a2de2+13444abde2-12132b2de2+4216acde2+13752bcde2-7598c2de2+
     ------------------------------------------------------------------------
     9529ad2e2-5125bd2e2+3009cd2e2+13958d3e2+14261a2e3-6003abe3-3096b2e3+
     ------------------------------------------------------------------------
     15243ace3-5159bce3-13490c2e3-13007ade3+10774bde3+9607cde3-13700d2e3-
     ------------------------------------------------------------------------
     3703ae4-13414be4+13590ce4-11665de4-5237e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R