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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 (1651a  + 14967a b - 12957a*b  + 764b  + 8639a c + 14257a*b*c -
     ------------------------------------------------------------------------
          2           2          2        3         2                      2 
     7078b c + 2867a*c  + 3834b*c  - 6709c  + 12985a d - 1204a*b*d + 15331b d
     ------------------------------------------------------------------------
                                     2           2          2          2  
     - 14694a*c*d + 8423b*c*d + 9656c d - 9234a*d  + 9269b*d  + 7854c*d  -
     ------------------------------------------------------------------------
           3        2                     2                             
     14233d  - 2710a e + 10796a*b*e - 552b e + 13948a*c*e + 14490b*c*e -
     ------------------------------------------------------------------------
          2                                             2           2  
     7131c e - 146a*d*e + 304b*d*e - 14200c*d*e - 10168d e - 1629a*e  -
     ------------------------------------------------------------------------
             2           2          2        3        3       2           2  
     11848b*e  + 15169c*e  + 8748d*e  + 4159e , 13246a  + 604a b - 5426a*b  -
     ------------------------------------------------------------------------
          3        2                     2           2          2        3  
     1733b  - 4133a c + 9557a*b*c + 4571b c + 4574a*c  - 8072b*c  + 9332c  +
     ------------------------------------------------------------------------
         2                      2                                  2   
     701a d - 8708a*b*d + 10345b d + 6602a*c*d + 8290b*c*d + 14407c d +
     ------------------------------------------------------------------------
            2           2          2         3        2                    2 
     2593a*d  - 13327b*d  + 7203c*d  + 13994d  + 1730a e + 337a*b*e + 8772b e
     ------------------------------------------------------------------------
                                    2                                        
     - 7677a*c*e + 5793b*c*e - 6530c e - 3014a*d*e + 6604b*d*e + 14963c*d*e +
     ------------------------------------------------------------------------
          2           2         2           2           2        3       3  
     6667d e + 5197a*e  - 597b*e  + 14960c*e  - 14806d*e  - 8146e , 7340a  +
     ------------------------------------------------------------------------
          2           2        3         2                      2   
     1375a b - 2638a*b  - 2074b  - 15300a c - 4604a*b*c - 11915b c +
     ------------------------------------------------------------------------
             2           2         3        2                      2   
     13501a*c  - 11230b*c  - 10123c  - 8777a d + 1726a*b*d + 10289b d -
     ------------------------------------------------------------------------
                                  2           2          2           2  
     8324a*c*d + 8615b*c*d + 7928c d - 6265a*d  - 8646b*d  - 14986c*d  +
     ------------------------------------------------------------------------
           3        2                     2                             
     14825d  - 7525a e + 3307a*b*e + 7604b e - 10605a*c*e + 14190b*c*e -
     ------------------------------------------------------------------------
          2                                             2            2  
     8392c e - 4546a*d*e + 3993b*d*e - 3461c*d*e + 3422d e + 11626a*e  -
     ------------------------------------------------------------------------
            2          2          2        3
     5934b*e  + 8232c*e  + 7179d*e  - 7885e )

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+15628b3+9967a2c+6442abc-14548b2c+14812ac2-9276bc2-1658c3-14292a2d+
     ------------------------------------------------------------------------
     9303abd+3333b2d+9443acd+5976bcd+8817c2d+4643ad2-11355bd2+12812cd2-8905d3
     ------------------------------------------------------------------------
     +4688a2e+13730abe+7463b2e+12896ace-702bce-10240c2e-4347ade-4278bde-
     ------------------------------------------------------------------------
     9844cde+1665d2e-10288ae2-9545be2+2046ce2-5359de2+7732e3
     ------------------------------------------------------------------------
     a2b-12884b3-8558a2c-15344abc+12886b2c+12604ac2+10022bc2-8557c3+14240a2d-
     ------------------------------------------------------------------------
     9419abd+9394b2d-3872acd-3928bcd-9996c2d-5543ad2-2708bd2-13248cd2+6443d3-
     ------------------------------------------------------------------------
     2155a2e+13763abe-7242b2e-9220ace-8419bce+1905c2e+9184ade+162bde-15609cde
     ------------------------------------------------------------------------
     -8066d2e+11597ae2+8716be2-8153ce2-8679de2+1003e3
     ------------------------------------------------------------------------
     a3-12506b3-11263a2c-14972abc-5887b2c-14995ac2+4798bc2-7261c3-9763a2d+
     ------------------------------------------------------------------------
     15943abd+2182b2d+13405acd-8979bcd-15354c2d-14987ad2+15749bd2+10180cd2-
     ------------------------------------------------------------------------
     4013d3+9552a2e-6250abe-2570b2e-4544ace-3090bce+8122c2e+3623ade-1624bde+
     ------------------------------------------------------------------------
     11184cde+11205d2e+6475ae2+4127be2-5955ce2-8034de2+13307e3
     ------------------------------------------------------------------------
     b3c-11965a2c2+8089abc2-15852b2c2-12158ac3+15604bc3+11396c4+4509b3d-
     ------------------------------------------------------------------------
     13555a2cd-2305abcd-12078b2cd-1910ac2d+11528bc2d-15450c3d-11928a2d2+
     ------------------------------------------------------------------------
     3310abd2+1161b2d2-4645acd2+5433bcd2+4105c2d2-1251ad3+1584bd3+9471cd3-
     ------------------------------------------------------------------------
     1499d4-13901b3e-1261a2ce-11952abce+2256b2ce+2282ac2e-579bc2e-1872c3e+
     ------------------------------------------------------------------------
     4170a2de-7406abde-10640b2de-5617acde-12142bcde+14383c2de-7020ad2e-
     ------------------------------------------------------------------------
     8736bd2e+11209cd2e+7006d3e+9646a2e2-10970abe2+4273b2e2+1635ace2-
     ------------------------------------------------------------------------
     11298bce2-15276c2e2+2803ade2-4751bde2-2559cde2+280d2e2-2309ae3+5251be3-
     ------------------------------------------------------------------------
     5289ce3+8411de3-6158e4 b4-12579a2c2+5299abc2-8762b2c2+10502ac3-3740bc3-
     ------------------------------------------------------------------------
     2295c4-15178b3d+15354a2cd+5838abcd+2895b2cd+850ac2d-14111bc2d+2893c3d-
     ------------------------------------------------------------------------
     5381a2d2-13501abd2+6970b2d2+15465acd2-5740bcd2-7120c2d2-418ad3-14322bd3-
     ------------------------------------------------------------------------
     13668cd3+504d4+14970b3e+14803a2ce-8204abce+15872b2ce+4426ac2e+5749bc2e-
     ------------------------------------------------------------------------
     5641c3e-11419a2de-15195abde-8309b2de+6946acde+12057bcde+12560c2de+
     ------------------------------------------------------------------------
     4317ad2e+7677bd2e-10087cd2e-10619d3e-6441a2e2+3600abe2+11717b2e2+
     ------------------------------------------------------------------------
     9325ace2+11293bce2+5297c2e2-12212ade2-14172bde2-5859cde2-13442d2e2+
     ------------------------------------------------------------------------
     11411ae3-5552be3-12203ce3+11887de3-8807e4
     ------------------------------------------------------------------------
     abc3+4297b2c3+15127ac4-4297bc4-1435c5+11738a2c2d+14995abc2d-3296b2c2d+
     ------------------------------------------------------------------------
     15086ac3d-10847bc3d+3932c4d+11058b3d2+345a2cd2-14704abcd2+1775b2cd2+
     ------------------------------------------------------------------------
     15843ac2d2-14042bc2d2-5277c3d2+6594a2d3+8756abd3+4789b2d3-3221acd3+
     ------------------------------------------------------------------------
     11988bcd3-4357c2d3+10898ad4+13433bd4+5397cd4+12787d5+8302a2c2e+2678abc2e
     ------------------------------------------------------------------------
     +15622b2c2e-2108ac3e-1274bc3e+8571c4e+3194b3de-12085a2cde-13945abcde+
     ------------------------------------------------------------------------
     11844b2cde-10788ac2de+1534bc2de-1797c3de-346a2d2e+6259abd2e-5762b2d2e+
     ------------------------------------------------------------------------
     14494acd2e-12855bcd2e-11252c2d2e+15362ad3e+8362bd3e+12816cd3e+8097d4e-
     ------------------------------------------------------------------------
     2033b3e2-5650a2ce2-1700abce2+11163b2ce2-13587ac2e2+13596bc2e2-10926c3e2+
     ------------------------------------------------------------------------
     12747a2de2-3756abde2-6006b2de2+6736acde2+516bcde2+4202c2de2+4890ad2e2-
     ------------------------------------------------------------------------
     10933bd2e2-13232cd2e2+1260d3e2+2067a2e3+6205abe3+7302b2e3-4617ace3-
     ------------------------------------------------------------------------
     15583bce3-9745c2e3-11976ade3-8245bde3-2444cde3+8215d2e3+9587ae4-2467be4+
     ------------------------------------------------------------------------
     10086ce4-7958de4+13852e5
     ------------------------------------------------------------------------
     a2c3-9009b2c3+4378ac4+14106bc4-5651c5-6072a2c2d-2437abc2d+15329b2c2d-
     ------------------------------------------------------------------------
     15840ac3d-6127bc3d-5018c4d-13836b3d2+2406a2cd2+6597abcd2-9027b2cd2-
     ------------------------------------------------------------------------
     8388ac2d2-14889bc2d2+15218c3d2-709a2d3+11235abd3-12940b2d3-15672acd3-
     ------------------------------------------------------------------------
     4695bcd3-3929c2d3-11763ad4-5495bd4+6337cd4+7200d5+1903a2c2e+15098abc2e-
     ------------------------------------------------------------------------
     12618b2c2e-10121ac3e+683bc3e-7351c4e+5186b3de-5191a2cde+12706abcde-
     ------------------------------------------------------------------------
     7254b2cde-9709ac2de+13895bc2de+3987c3de-1554a2d2e-11698abd2e-11910b2d2e+
     ------------------------------------------------------------------------
     12825acd2e-11811bcd2e+13312c2d2e+11443ad3e+10864bd3e+8132cd3e-12013d4e+
     ------------------------------------------------------------------------
     5573b3e2+4764a2ce2-1403abce2-12873b2ce2+13034ac2e2+12664bc2e2+8323c3e2-
     ------------------------------------------------------------------------
     2232a2de2+7478abde2-13825b2de2-11921acde2-9362bcde2-3572c2de2+9844ad2e2+
     ------------------------------------------------------------------------
     6409bd2e2+8579cd2e2+8806d3e2-222a2e3-1203abe3+13721b2e3-6668ace3-
     ------------------------------------------------------------------------
     13053bce3+11890c2e3+14896ade3-5188bde3+2597cde3+14889d2e3-6954ae4+
     ------------------------------------------------------------------------
     13196be4+14882ce4+9449de4+3804e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R