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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 (- 4347a  + 15088a b + 1601a*b  - 5491b  - 3713a c + 2283a*b*c -
     ------------------------------------------------------------------------
           2           2          2         3         2               
     10911b c + 6310a*c  + 6364b*c  + 13924c  + 11369a d + 1949a*b*d -
     ------------------------------------------------------------------------
           2                                  2            2          2  
     10242b d + 9658a*c*d - 10886b*c*d + 2564c d - 14156a*d  - 6706b*d  -
     ------------------------------------------------------------------------
             2       3        2                     2               
     13879c*d  + 833d  + 8142a e + 9811a*b*e + 9702b e - 7957a*c*e -
     ------------------------------------------------------------------------
                        2                                               2   
     10510b*c*e - 15914c e - 12081a*d*e - 4207b*d*e - 14739c*d*e - 1871d e -
     ------------------------------------------------------------------------
            2           2          2           2        3        3       2   
     8463a*e  + 13991b*e  + 1342c*e  + 11404d*e  + 2382e , 14269a  + 515a b -
     ------------------------------------------------------------------------
            2         3       2                     2           2           2
     2831a*b  + 13629b  - 464a c + 3493a*b*c - 8105b c + 7703a*c  + 15938b*c 
     ------------------------------------------------------------------------
            3         2                     2                            
     - 5697c  + 11690a d + 8006a*b*d - 2869b d + 6413a*c*d + 10605b*c*d -
     ------------------------------------------------------------------------
          2            2          2          2        3         2   
     5923c d - 10970a*d  + 2755b*d  + 8817c*d  - 4633d  + 14925a e +
     ------------------------------------------------------------------------
                       2                                  2                
     10197a*b*e + 7931b e + 1536a*c*e + 10716b*c*e - 5921c e - 13094a*d*e -
     ------------------------------------------------------------------------
                                  2           2          2        2  
     15637b*d*e - 57c*d*e - 11065d e + 5232a*e  + 3845b*e  + 13c*e  -
     ------------------------------------------------------------------------
            2        3       3        2           2         3         2   
     5405d*e  + 4260e , 6984a  + 5257a b - 9071a*b  + 10401b  + 14581a c -
     ------------------------------------------------------------------------
                        2           2          2        3        2   
     15756a*b*c - 15923b c - 6867a*c  - 6915b*c  - 6628c  + 2077a d -
     ------------------------------------------------------------------------
                       2                                  2          2  
     8034a*b*d - 14244b d + 3354a*c*d - 5174b*c*d + 15779c d - 293a*d  +
     ------------------------------------------------------------------------
            2          2        3         2                     2   
     3102b*d  - 5420c*d  + 6427d  - 11744a e - 6520a*b*e - 5822b e -
     ------------------------------------------------------------------------
                                   2                                         
     15143a*c*e - 5867b*c*e + 6003c e - 7383a*d*e + 12121b*d*e - 14913c*d*e +
     ------------------------------------------------------------------------
         2           2          2           2          2        3
     132d e + 6548a*e  + 8656b*e  - 13123c*e  - 7812d*e  - 7829e )

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+7985b3+13455a2c-2235abc+13757b2c+4646ac2+15518bc2+15212c3+11168a2d
     ------------------------------------------------------------------------
     -14194abd+685b2d-2972acd-7975bcd-15983c2d-11665ad2+1612bd2-12101cd2-
     ------------------------------------------------------------------------
     14711d3-15029a2e+8500abe+1936b2e-6395ace+1327bce+6035c2e+3410ade-5967bde
     ------------------------------------------------------------------------
     +9846cde-9925d2e-1429ae2+9986be2-876ce2-10155de2-2215e3
     ------------------------------------------------------------------------
     a2b+6440b3+1919a2c+5036abc-6940b2c+10032ac2-15387bc2-13948c3-10913a2d+
     ------------------------------------------------------------------------
     3654abd-5198b2d-8715acd+9349bcd-4764c2d+2158ad2+1422bd2+13944cd2-9913d3-
     ------------------------------------------------------------------------
     10471a2e+12983abe-3261b2e+528ace+5057bce+4068c2e+15150ade+115bde-2338cde
     ------------------------------------------------------------------------
     +4209d2e-15920ae2+10659be2-11795ce2-12828de2+8364e3
     ------------------------------------------------------------------------
     a3-9285b3+10255a2c-14692abc+7308b2c-5390ac2-8799bc2-15146c3+12923a2d+
     ------------------------------------------------------------------------
     14051abd+4255b2d+3823acd+6707bcd+746c2d+4331ad2+12223bd2-5882cd2-13042d3
     ------------------------------------------------------------------------
     +8174a2e-15042abe+693b2e+6856ace+15187bce-11041c2e-3287ade+7383bde+
     ------------------------------------------------------------------------
     1051cde-14666d2e-2936ae2-1985be2-5880ce2+823de2+10906e3
     ------------------------------------------------------------------------
     b3c-9610a2c2-1444abc2+9342b2c2+11023ac3+1903bc3-10432c4-10795b3d+
     ------------------------------------------------------------------------
     3234a2cd-3068abcd-8576b2cd-12802ac2d+14106bc2d+6237c3d+2252a2d2-9055abd2
     ------------------------------------------------------------------------
     -15278b2d2+345acd2-12661bcd2+7434c2d2-12516ad3+14958bd3-9434cd3+14497d4+
     ------------------------------------------------------------------------
     4521b3e+7822a2ce-8839abce+4624b2ce+4160ac2e-15365bc2e+15375c3e-15535a2de
     ------------------------------------------------------------------------
     +3906abde-6952b2de-277acde+15943bcde-14647c2de-14693ad2e+3443bd2e+25cd2e
     ------------------------------------------------------------------------
     +174d3e+15114a2e2-2029abe2+15538b2e2-2453ace2+13190bce2+5404c2e2-
     ------------------------------------------------------------------------
     10797ade2+15399bde2+12122cde2-6326d2e2+3664ae3+971be3+6297ce3+3086de3+
     ------------------------------------------------------------------------
     4458e4 b4-9381a2c2-10365abc2-10559b2c2-1529ac3+12011bc3+14386c4-5345b3d-
     ------------------------------------------------------------------------
     4015a2cd-11535abcd+12139b2cd+205ac2d+13194bc2d-12223c3d+12223a2d2-
     ------------------------------------------------------------------------
     338abd2+2310b2d2-5961acd2+6783bcd2-13344c2d2+7097ad3+5846bd3+2592cd3+
     ------------------------------------------------------------------------
     15658d4-7745b3e+13395a2ce+8227abce-7899b2ce+2262ac2e-12069bc2e+7164c3e-
     ------------------------------------------------------------------------
     4342a2de+4619abde+3289b2de+113acde-12062bcde+98c2de+11697ad2e-4036bd2e-
     ------------------------------------------------------------------------
     1900cd2e+5564d3e+9094a2e2-6704abe2-7729b2e2+10093ace2+5408bce2-14858c2e2
     ------------------------------------------------------------------------
     -13707ade2+3801bde2-5396cde2-12374d2e2+6178ae3+12358be3+7289ce3-5953de3+
     ------------------------------------------------------------------------
     8853e4 abc3+7291b2c3-1224ac4+364bc4+8930c5+14708a2c2d+7156abc2d-
     ------------------------------------------------------------------------
     14687b2c2d+14002ac3d-14781bc3d-7612c4d-10560b3d2-13279a2cd2-1164abcd2+
     ------------------------------------------------------------------------
     8818b2cd2-866ac2d2-15544bc2d2-2235c3d2-1149a2d3+635abd3+13719b2d3-
     ------------------------------------------------------------------------
     11824acd3+13183bcd3+15125c2d3+3827ad4+1177bd4+510cd4+9406d5+14795a2c2e+
     ------------------------------------------------------------------------
     7984abc2e-374b2c2e-7127ac3e+3843bc3e-13336c4e-2529b3de+11449a2cde-
     ------------------------------------------------------------------------
     4278abcde-12036b2cde-12729ac2de+11623bc2de-10564c3de+9552a2d2e-8288abd2e
     ------------------------------------------------------------------------
     -11042b2d2e+4232acd2e+10183bcd2e+1645c2d2e+5779ad3e-9001bd3e-2568cd3e-
     ------------------------------------------------------------------------
     15887d4e+4744b3e2+4501a2ce2-15625abce2-1457b2ce2+622ac2e2+2674bc2e2+
     ------------------------------------------------------------------------
     3346c3e2+14178a2de2+2343abde2-1220b2de2-11709acde2-592bcde2+10461c2de2-
     ------------------------------------------------------------------------
     15715ad2e2-2992bd2e2-4751cd2e2-7273d3e2-12331a2e3+3639abe3-930b2e3+
     ------------------------------------------------------------------------
     11252ace3-10826bce3-6808c2e3+7051ade3-515bde3-7486cde3-3320d2e3+12429ae4
     ------------------------------------------------------------------------
     +10268be4-11444ce4-12874de4+8684e5
     ------------------------------------------------------------------------
     a2c3+11468b2c3-11262ac4-12315bc4+7946c5+3899a2c2d-6877abc2d-13043b2c2d+
     ------------------------------------------------------------------------
     521ac3d+2167bc3d+11527c4d-6970b3d2+15968a2cd2-433abcd2-11413b2cd2+
     ------------------------------------------------------------------------
     8244ac2d2+13444bc2d2+8793c3d2+14187a2d3+662abd3-13898b2d3+8123acd3+
     ------------------------------------------------------------------------
     14076bcd3-10997c2d3-909ad4-12385bd4+10505cd4+292d5+10686a2c2e+6809abc2e-
     ------------------------------------------------------------------------
     10835b2c2e+12964ac3e-6488bc3e+10723c4e-3171b3de+4394a2cde+6186abcde+
     ------------------------------------------------------------------------
     4746b2cde+14968ac2de+7880bc2de+3815c3de+3655a2d2e-15145abd2e+11510b2d2e+
     ------------------------------------------------------------------------
     10954acd2e+14959bcd2e+1083c2d2e-11595ad3e+3786bd3e+4635cd3e-674d4e+
     ------------------------------------------------------------------------
     6487b3e2+11862a2ce2-2505abce2-6884b2ce2-13704ac2e2+624bc2e2+6363c3e2+
     ------------------------------------------------------------------------
     12070a2de2+7545abde2+12305b2de2-887acde2+2293bcde2-8181c2de2-15222ad2e2-
     ------------------------------------------------------------------------
     1875bd2e2-4170cd2e2+14708d3e2-13122a2e3+2599abe3+6523b2e3-714ace3+
     ------------------------------------------------------------------------
     7011bce3-14174c2e3-12871ade3-4086bde3+15603cde3+12359d2e3-15680ae4+
     ------------------------------------------------------------------------
     13446be4-9974ce4+13361de4-9113e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R