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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 (- 10142a  - 13176a b + 2290a*b  - 14281b  + 7600a c + 1937a*b*c -
     ------------------------------------------------------------------------
           2           2          2         3        2                     2 
     13457b c - 3338a*c  + 6934b*c  + 14158c  + 1684a d + 254a*b*d + 15643b d
     ------------------------------------------------------------------------
                                    2          2           2           2  
     + 1111a*c*d - 3664b*c*d + 3340c d + 517a*d  + 11931b*d  + 13983c*d  +
     ------------------------------------------------------------------------
          3         2                      2                            
     2912d  - 14688a e + 13899a*b*e + 4272b e + 15959a*c*e - 9855b*c*e +
     ------------------------------------------------------------------------
           2                                             2           2  
     13678c e - 8017a*d*e - 5897b*d*e + 9242c*d*e - 8728d e + 8386a*e  +
     ------------------------------------------------------------------------
             2          2          2        3        3         2           2
     15360b*e  + 2980c*e  + 2540d*e  + 4723e , 14776a  - 13666a b + 3865a*b 
     ------------------------------------------------------------------------
             3       2                       2           2           2  
     + 10969b  + 768a c + 13078a*b*c + 15807b c + 7324a*c  - 11057b*c  -
     ------------------------------------------------------------------------
           3         2                       2                            
     13325c  - 10733a d - 13806a*b*d - 15564b d + 6892a*c*d - 12994b*c*d -
     ------------------------------------------------------------------------
           2            2          2         2         3         2   
     14482c d - 10486a*d  + 3908b*d  + 867c*d  + 10624d  - 13799a e +
     ------------------------------------------------------------------------
                      2                                  2               
     8753a*b*e - 5435b e + 13139a*c*e + 5012b*c*e + 1600c e - 5644a*d*e -
     ------------------------------------------------------------------------
                                   2           2          2          2  
     2509b*d*e - 3858c*d*e - 14054d e + 3255a*e  - 9669b*e  - 8546c*e  -
     ------------------------------------------------------------------------
            2        3         3         2           2         3        2   
     3557d*e  - 5680e , - 5945a  - 11767a b + 1401a*b  + 11842b  - 1276a c +
     ------------------------------------------------------------------------
                      2            2          2        3         2   
     8371a*b*c - 7082b c + 12411a*c  - 4021b*c  - 8172c  + 11586a d +
     ------------------------------------------------------------------------
                      2                                   2          2  
     6438a*b*d + 7275b d + 11554a*c*d - 9205b*c*d - 12653c d - 441a*d  +
     ------------------------------------------------------------------------
             2          2       3         2                      2   
     14888b*d  - 2840c*d  - 538d  - 13053a e + 3960a*b*e + 14222b e -
     ------------------------------------------------------------------------
                                    2                                       
     15295a*c*e + 3099b*c*e + 10080c e + 9088a*d*e + 8664b*d*e + 1197c*d*e -
     ------------------------------------------------------------------------
          2          2           2           2           2        3
     3206d e + 865a*e  + 13072b*e  + 10484c*e  + 11777d*e  - 7384e )

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 = | ab2-590b3+6394a2c-13983abc-5590b2c+15050ac2+2286bc2+14486c3-7557a2d+
     ------------------------------------------------------------------------
     6772abd+15199b2d-7360acd+8917bcd-47c2d+6676ad2+3124bd2+15010cd2+3882d3+
     ------------------------------------------------------------------------
     11842a2e+14021abe+14067b2e-376ace-1156bce+15591c2e-273ade-3659bde-
     ------------------------------------------------------------------------
     14395cde-15835d2e+5125ae2-13253be2+11331ce2+7086de2+7830e3
     ------------------------------------------------------------------------
     a2b+1799b3-2160a2c+517abc-15558b2c+3595ac2+1536bc2+4284c3+11855a2d+
     ------------------------------------------------------------------------
     11104abd-8497b2d-14391acd+12559bcd+12690c2d+7167ad2-13319bd2-15037cd2-
     ------------------------------------------------------------------------
     2119d3+3197a2e+3140abe+15702b2e+15445ace-15461bce-7911c2e-8667ade-
     ------------------------------------------------------------------------
     13112bde+14311cde+2280d2e-14838ae2+13032be2+6756ce2-14884de2-5445e3
     ------------------------------------------------------------------------
     a3-11642b3+5890a2c+10866abc+3095b2c+7879ac2+6516bc2+1907c3-5136a2d-
     ------------------------------------------------------------------------
     1903abd-12444b2d-12151acd-9771bcd-13348c2d-7100ad2-11329bd2-2406cd2+
     ------------------------------------------------------------------------
     12048d3-6022a2e+10751abe-10578b2e-6233ace+14831bce+7940c2e-2619ade+
     ------------------------------------------------------------------------
     504bde+4688cde+9752d2e-12365ae2+4499be2-15414ce2-439de2+3537e3
     ------------------------------------------------------------------------
     b3c-13182a2c2+12021abc2-10911b2c2-15754ac3+6621bc3+7113c4-8857b3d-
     ------------------------------------------------------------------------
     15816a2cd-14933abcd-5150b2cd-7919ac2d+2233bc2d+15140c3d+7758a2d2+
     ------------------------------------------------------------------------
     13202abd2+5420b2d2+13462acd2+13712bcd2+7201c2d2-4220ad3+14635bd3+987cd3+
     ------------------------------------------------------------------------
     10802d4-10412b3e-9027a2ce-7472abce-12687b2ce-3007ac2e-248bc2e-11028c3e-
     ------------------------------------------------------------------------
     3072a2de+4022abde+13560b2de-9382acde-8489bcde-9284c2de+2769ad2e+9570bd2e
     ------------------------------------------------------------------------
     -2907cd2e+13912d3e-5563a2e2-6168abe2+15976b2e2+5746ace2-13827bce2+
     ------------------------------------------------------------------------
     10788c2e2-10600ade2-3794bde2+15710cde2-7076d2e2+4157ae3+1543be3+14246ce3
     ------------------------------------------------------------------------
     -13165de3+1145e4 b4+6656a2c2+3967abc2+7250b2c2+3261ac3+14276bc3+11381c4-
     ------------------------------------------------------------------------
     8650b3d+7469a2cd+5389abcd+7895b2cd-13038ac2d-2357bc2d-14541c3d+2385a2d2-
     ------------------------------------------------------------------------
     7196abd2-11669b2d2+9981acd2-12119bcd2-2753c2d2-12389ad3+9599bd3+3760cd3+
     ------------------------------------------------------------------------
     7742d4+1990b3e+6615a2ce-8709abce-1464b2ce+12121ac2e-5563bc2e+8712c3e-
     ------------------------------------------------------------------------
     13243a2de+12273abde-2725b2de+7391acde-239bcde+7619c2de+3917ad2e+
     ------------------------------------------------------------------------
     14821bd2e-14236cd2e+1438d3e-11925a2e2-13655abe2-12515b2e2+15865ace2+
     ------------------------------------------------------------------------
     8623bce2+13415c2e2-8729ade2+12471bde2+4611cde2-2829d2e2-7484ae3+2181be3-
     ------------------------------------------------------------------------
     13451ce3-4212de3+14356e4
     ------------------------------------------------------------------------
     abc3+3042b2c3+13847ac4+890bc4-12760c5-1370a2c2d+5749abc2d+9910b2c2d-
     ------------------------------------------------------------------------
     9920ac3d+14221bc3d-1691c4d-4896b3d2-10653a2cd2-774abcd2+914b2cd2-
     ------------------------------------------------------------------------
     4566ac2d2+7812bc2d2-5707c3d2+4096a2d3-7325abd3+12199b2d3+611acd3+
     ------------------------------------------------------------------------
     8574bcd3+10544c2d3-10822ad4-7528bd4-491cd4-12639d5-14120a2c2e-15118abc2e
     ------------------------------------------------------------------------
     +5709b2c2e-2291ac3e-12788bc3e+14341c4e+325b3de-2719a2cde-10174abcde-
     ------------------------------------------------------------------------
     12616b2cde+4680ac2de+7798bc2de-12976c3de+11535a2d2e+15033abd2e-8623b2d2e
     ------------------------------------------------------------------------
     -1425acd2e-3204bcd2e+15398c2d2e-6667ad3e+15697bd3e-8565cd3e-13920d4e-
     ------------------------------------------------------------------------
     1493b3e2+8304a2ce2-12572abce2-11645b2ce2+6484ac2e2-5913bc2e2+676c3e2+
     ------------------------------------------------------------------------
     15882a2de2+9060abde2+14717b2de2-13816acde2+6417bcde2-12080c2de2+89ad2e2-
     ------------------------------------------------------------------------
     4733bd2e2+13592cd2e2-14539d3e2+811a2e3-15232abe3-7265b2e3-11761ace3-
     ------------------------------------------------------------------------
     8727bce3-10137c2e3-5899ade3-4408bde3+10057cde3-11417d2e3-14154ae4+565be4
     ------------------------------------------------------------------------
     -937ce4-13676de4+11906e5
     ------------------------------------------------------------------------
     a2c3-9239b2c3+40ac4+2099bc4-11985c5-914a2c2d-5575abc2d+1882b2c2d-101ac3d
     ------------------------------------------------------------------------
     -12038bc3d+13501c4d-10445b3d2-1239a2cd2-5098abcd2+15626b2cd2-15657ac2d2+
     ------------------------------------------------------------------------
     2067bc2d2+9435c3d2+6831a2d3-14182abd3+824b2d3+14213acd3-9057bcd3+
     ------------------------------------------------------------------------
     12327c2d3+14404ad4+3987bd4-15850cd4-5884d5+5923a2c2e+8540abc2e+6885b2c2e
     ------------------------------------------------------------------------
     +4599ac3e+678bc3e+13591c4e-9025b3de+13636a2cde-6536abcde+7668b2cde-
     ------------------------------------------------------------------------
     2233ac2de-9238bc2de+11136c3de+10080a2d2e-493abd2e+1108b2d2e-12962acd2e+
     ------------------------------------------------------------------------
     3445bcd2e-15896c2d2e+13878ad3e-2374bd3e+7656cd3e-3556d4e+4882b3e2-
     ------------------------------------------------------------------------
     3519a2ce2+7925abce2-847b2ce2-3462ac2e2+4725bc2e2+6758c3e2+13133a2de2-
     ------------------------------------------------------------------------
     10343abde2-5597b2de2-10573acde2+1132bcde2+3135c2de2+15120ad2e2-9116bd2e2
     ------------------------------------------------------------------------
     +1422cd2e2+13006d3e2+5208a2e3+346abe3-4239b2e3-6677ace3-4931bce3-
     ------------------------------------------------------------------------
     6880c2e3+122ade3-7636bde3-9281cde3+6901d2e3-1110ae4+10030be4+1665ce4-
     ------------------------------------------------------------------------
     4115de4+2255e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R