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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 (7489a  + 9781a b + 6670a*b  + 4309b  - 5474a c + 1769a*b*c -
     ------------------------------------------------------------------------
           2           2          2        3         2                     2 
     11243b c - 5886a*c  + 9024b*c  - 4284c  - 13015a d + 3111a*b*d + 9005b d
     ------------------------------------------------------------------------
                                      2           2           2           2  
     - 13388a*c*d + 5681b*c*d + 10190c d - 6061a*d  - 15818b*d  - 10104c*d  -
     ------------------------------------------------------------------------
          3         2                      2                            
     8633d  - 10055a e - 1864a*b*e + 12484b e + 10994a*c*e - 5848b*c*e +
     ------------------------------------------------------------------------
           2                                              2          2  
     15163c e - 1447a*d*e - 13277b*d*e - 5287c*d*e - 9795d e + 530a*e  +
     ------------------------------------------------------------------------
            2          2           2        3         3        2            2
     3625b*e  - 6569c*e  - 12930d*e  + 2750e , - 7794a  + 9722a b - 15831a*b 
     ------------------------------------------------------------------------
            3        2                     2            2         2       3  
     - 4523b  - 3908a c - 1599a*b*c - 8692b c - 10055a*c  + 497b*c  - 306c  -
     ------------------------------------------------------------------------
          2                      2                                2   
     7779a d + 15370a*b*d + 2475b d + 272a*c*d - 4655b*c*d + 6519c d -
     ------------------------------------------------------------------------
            2          2          2        3        2                    2   
     8174a*d  + 8367b*d  + 4851c*d  + 1222d  + 1612a e - 4577a*b*e + 241b e -
     ------------------------------------------------------------------------
                                    2                                       
     1789a*c*e - 11703b*c*e - 15332c e + 2424a*d*e - 12638b*d*e - 12212c*d*e
     ------------------------------------------------------------------------
            2           2          2          2           2        3   
     - 1033d e + 8685a*e  + 8368b*e  + 6115c*e  - 10939d*e  - 5659e , -
     ------------------------------------------------------------------------
           3        2            2         3        2                
     14334a  - 1091a b - 15971a*b  + 10591b  + 2071a c - 11367a*b*c -
     ------------------------------------------------------------------------
           2            2           2         3        2               
     14714b c + 10398a*c  + 13265b*c  - 11772c  - 4572a d + 8853a*b*d -
     ------------------------------------------------------------------------
           2                                   2           2        2  
     12959b d - 11559a*c*d - 12103b*c*d - 9726c d - 3579a*d  + 30b*d  +
     ------------------------------------------------------------------------
            2         3        2                     2               
     9982c*d  + 14914d  - 1322a e - 2031a*b*e - 8999b e + 1790a*c*e +
     ------------------------------------------------------------------------
                       2                                               2   
     13719b*c*e + 1898c e - 14401a*d*e + 10108b*d*e - 5354c*d*e + 9431d e +
     ------------------------------------------------------------------------
             2          2          2           2         3
     10226a*e  - 9070b*e  + 5488c*e  - 14359d*e  + 15225e )

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 = | ab2-11693b3+1686a2c-3156abc-5437b2c-14374ac2-5738bc2-13221c3+8977a2d-
     ------------------------------------------------------------------------
     13778abd-12846b2d+15763acd+5371bcd+10937c2d+7002ad2+13692bd2+15928cd2+
     ------------------------------------------------------------------------
     13856d3-12834a2e-15325abe-1640b2e+2887ace-14312bce+10721c2e+7601ade-
     ------------------------------------------------------------------------
     15649bde+5810cde-1505d2e+12113ae2+6862be2+14787ce2-5560de2+15564e3
     ------------------------------------------------------------------------
     a2b+12327b3-1202a2c-7376abc-12898b2c+11810ac2-13334bc2+11007c3-9478a2d-
     ------------------------------------------------------------------------
     13733abd+7039b2d-411acd+10593bcd+7970c2d-1007ad2-12626bd2+11666cd2-
     ------------------------------------------------------------------------
     8264d3-2754a2e-6786abe+2341b2e-3043ace-6461bce+1155c2e-13518ade+10640bde
     ------------------------------------------------------------------------
     +13339cde-13736d2e+15197ae2+15070be2+12914ce2-6722de2+2360e3
     ------------------------------------------------------------------------
     a3-4890b3-6804a2c-9717abc-441b2c+10731ac2+3288bc2-6977c3-3259a2d+
     ------------------------------------------------------------------------
     12422abd-1520b2d-11782acd-6926bcd-15978c2d+10851ad2-12129bd2-15309cd2+
     ------------------------------------------------------------------------
     1229d3-7268a2e+3209abe-12099b2e+10058ace+13642bce-111c2e-7332ade+1736bde
     ------------------------------------------------------------------------
     +15671cde-6267d2e-7603ae2+13030be2+2530ce2-3163de2-2829e3
     ------------------------------------------------------------------------
     b3c-7932a2c2-49abc2+4515b2c2+4061ac3+7032bc3+4752c4+15670b3d-4319a2cd-
     ------------------------------------------------------------------------
     12177abcd+10276b2cd-14069ac2d-4177bc2d-15170c3d-1463a2d2+8716abd2+
     ------------------------------------------------------------------------
     13664b2d2-11360acd2-7218bcd2-4470c2d2-6976ad3+7402bd3+5502cd3-12451d4-
     ------------------------------------------------------------------------
     13209b3e+9752a2ce+12233abce+10708b2ce-12951ac2e+7972bc2e-328c3e+8060a2de
     ------------------------------------------------------------------------
     +3116abde+3992b2de-12489acde-10277bcde-6454c2de+13228ad2e+1478bd2e+
     ------------------------------------------------------------------------
     5139cd2e-8016d3e-9198a2e2-7589abe2-14796b2e2+10087ace2+1423bce2-7679c2e2
     ------------------------------------------------------------------------
     +7612ade2-3580bde2+15042cde2-14680d2e2+6820ae3-955be3-1628ce3+5024de3-
     ------------------------------------------------------------------------
     4241e4 b4+5031a2c2+1862abc2+8384b2c2+6138ac3-13130bc3+11255c4-11753b3d-
     ------------------------------------------------------------------------
     14822a2cd+1193abcd+13689b2cd-11107ac2d-13865bc2d-6828c3d+10754a2d2-
     ------------------------------------------------------------------------
     14347abd2+1826b2d2-7933acd2-7531bcd2-7446c2d2+3145ad3-4096bd3-8953cd3+
     ------------------------------------------------------------------------
     6446d4+15786b3e+6034a2ce-11080abce-1133b2ce-10002ac2e+659bc2e+15302c3e+
     ------------------------------------------------------------------------
     1753a2de+2933abde-14793b2de+3804acde+8746bcde-9408c2de+13462ad2e+
     ------------------------------------------------------------------------
     10377bd2e+15961cd2e-1292d3e-12417a2e2+3017abe2+993b2e2+3531ace2+8182bce2
     ------------------------------------------------------------------------
     -13459c2e2+4440ade2+7045bde2+6916cde2-11112d2e2+15861ae3+5914be3-
     ------------------------------------------------------------------------
     11446ce3-6882de3-8147e4
     ------------------------------------------------------------------------
     abc3-9212b2c3+12958ac4-13525bc4+6603c5-5210a2c2d+5844abc2d+2576b2c2d-
     ------------------------------------------------------------------------
     9812ac3d-11820bc3d-6027c4d+15978b3d2-3830a2cd2-732abcd2-1464b2cd2+
     ------------------------------------------------------------------------
     14127ac2d2+12603bc2d2+10142c3d2+9730a2d3+12253abd3-2481b2d3-3172acd3+
     ------------------------------------------------------------------------
     13210bcd3-832c2d3-1382ad4-14104bd4-12187cd4-3567d5+3798a2c2e-14373abc2e+
     ------------------------------------------------------------------------
     963b2c2e-9853ac3e-14229bc3e+12849c4e+1035b3de+11342a2cde+6340abcde+
     ------------------------------------------------------------------------
     6225b2cde-9589ac2de+8186bc2de+11489c3de+15267a2d2e+6473abd2e-12048b2d2e+
     ------------------------------------------------------------------------
     11263acd2e-13708bcd2e+9843c2d2e+8139ad3e-10234bd3e+417cd3e+9357d4e-
     ------------------------------------------------------------------------
     14169b3e2-4891a2ce2-8949abce2-13824b2ce2-33ac2e2-10573bc2e2-6726c3e2-
     ------------------------------------------------------------------------
     15674a2de2-8821abde2-5956b2de2+4601acde2-14311bcde2-2767c2de2+12786ad2e2
     ------------------------------------------------------------------------
     -1705bd2e2+4812cd2e2+11422d3e2+1717a2e3+8034abe3+12304b2e3-1048ace3+
     ------------------------------------------------------------------------
     5353bce3-10485c2e3-6034ade3+3430bde3-6331cde3-11773d2e3+2143ae4-13669be4
     ------------------------------------------------------------------------
     +238ce4-12837de4-3249e5
     ------------------------------------------------------------------------
     a2c3-10839b2c3-8184ac4-13599bc4+6660c5+2082a2c2d-1848abc2d-12407b2c2d+
     ------------------------------------------------------------------------
     10707ac3d+8589bc3d-4585c4d+3731b3d2+15947a2cd2+7886abcd2-14381b2cd2-
     ------------------------------------------------------------------------
     4004ac2d2+10519bc2d2-5162c3d2-7639a2d3-8036abd3+3032b2d3-2980acd3-
     ------------------------------------------------------------------------
     13200bcd3-11072c2d3-5476ad4-1353bd4+1110cd4-10068d5-12062a2c2e-8751abc2e
     ------------------------------------------------------------------------
     -15329b2c2e-5478ac3e-4018bc3e+14590c4e+8447b3de-1560a2cde+14331abcde+
     ------------------------------------------------------------------------
     14542b2cde+9201ac2de+2230bc2de+4902c3de-12272a2d2e-7715abd2e+1900b2d2e+
     ------------------------------------------------------------------------
     8568acd2e+8860bcd2e+9426c2d2e+4586ad3e+6416bd3e-8079cd3e-12228d4e+
     ------------------------------------------------------------------------
     9134b3e2+629a2ce2-4031abce2-13454b2ce2+12291ac2e2+1937bc2e2-8995c3e2-
     ------------------------------------------------------------------------
     1009a2de2-9688abde2+11650b2de2+7633acde2-5059bcde2-9562c2de2+5609ad2e2+
     ------------------------------------------------------------------------
     3233bd2e2-2769cd2e2-314d3e2-8638a2e3-7676abe3-5411b2e3+3936ace3-9441bce3
     ------------------------------------------------------------------------
     -3014c2e3-4189ade3-10475bde3+619cde3+897d2e3-5962ae4+5763be4-900ce4-
     ------------------------------------------------------------------------
     7760de4+3316e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R