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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 (- 14726a  + 364a b - 10501a*b  - 15229b  - 11998a c + 13792a*b*c
     ------------------------------------------------------------------------
             2           2           2        3        2                
     - 10701b c + 9775a*c  + 12801b*c  - 5639c  - 3884a d + 14103a*b*d -
     ------------------------------------------------------------------------
          2                                 2           2          2  
     9861b d + 2912a*c*d - 8948b*c*d - 9071c d - 2621a*d  + 2739b*d  +
     ------------------------------------------------------------------------
             2         3        2                     2               
     14096c*d  - 15430d  + 3776a e - 7509a*b*e + 8248b e - 7427a*c*e +
     ------------------------------------------------------------------------
                      2                                               2   
     9351b*c*e - 4929c e + 3900a*d*e + 8013b*d*e + 10289c*d*e + 13848d e +
     ------------------------------------------------------------------------
            2          2          2          2        3        3        2   
     4933a*e  + 5400b*e  - 8456c*e  - 2936d*e  + 9214e , 10553a  - 2857a b +
     ------------------------------------------------------------------------
             2        3        2                     2           2          2
     15266a*b  - 7056b  + 9665a c - 2100a*b*c + 9137b c - 1241a*c  + 5435b*c 
     ------------------------------------------------------------------------
            3        2                      2                            
     + 1472c  + 4256a d + 15230a*b*d + 4660b d - 1774a*c*d - 10397b*c*d +
     ------------------------------------------------------------------------
          2           2          2           2       3         2             
     1544c d - 8954a*d  - 4586b*d  + 12948c*d  - 902d  + 10229a e + 6883a*b*e
     ------------------------------------------------------------------------
            2                                 2                            
     - 1883b e + 5466a*c*e - 8914b*c*e - 2508c e - 1187a*d*e - 11241b*d*e -
     ------------------------------------------------------------------------
                      2           2          2           2           2  
     9096c*d*e - 1903d e - 3434a*e  - 8944b*e  + 10442c*e  - 14770d*e  -
     ------------------------------------------------------------------------
          3         3         2           2        3        2                
     8088e , - 2018a  + 15019a b + 1222a*b  - 5305b  + 7126a c - 10791a*b*c -
     ------------------------------------------------------------------------
          2            2          2         3        2                
     7923b c + 15992a*c  + 6655b*c  - 12171c  + 1480a d - 13394a*b*d -
     ------------------------------------------------------------------------
          2                                 2           2          2  
     6068b d - 5104a*c*d + 9468b*c*d + 9565c d + 6292a*d  + 7696b*d  -
     ------------------------------------------------------------------------
            2         3         2                      2               
     9981c*d  - 13515d  - 12233a e - 13857a*b*e - 4698b e + 2298a*c*e +
     ------------------------------------------------------------------------
                       2                                              2   
     12637b*c*e + 6735c e - 7162a*d*e - 14393b*d*e + 405c*d*e - 12629d e +
     ------------------------------------------------------------------------
             2          2           2          2         3
     13585a*e  + 2432b*e  + 12171c*e  + 2209d*e  + 13110e )

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+14663b3+14186a2c-2504abc-5661b2c+6406ac2-7193bc2+2915c3-15135a2d+
     ------------------------------------------------------------------------
     456abd-6905b2d-3470acd-9113bcd-12552c2d-3156ad2-7945bd2+13917cd2-9832d3-
     ------------------------------------------------------------------------
     3768a2e-2368abe+3962b2e-7175ace-5209bce+6276c2e-7434ade+3069bde-11804cde
     ------------------------------------------------------------------------
     -10041d2e+14859ae2-7856be2+5380ce2+11605de2-14497e3
     ------------------------------------------------------------------------
     a2b-7594b3-11931a2c-1054abc+9607b2c+6072ac2-11256bc2+10560c3-10214a2d-
     ------------------------------------------------------------------------
     15049abd+9721b2d-8461acd+12942bcd-4308c2d-1715ad2-2853bd2+876cd2-548d3+
     ------------------------------------------------------------------------
     1794a2e+3252abe-7130b2e+9213ace+9492bce+4213c2e-1011ade-13000bde+3502cde
     ------------------------------------------------------------------------
     -6947d2e-11687ae2+36be2+7224ce2+13885de2-13773e3
     ------------------------------------------------------------------------
     a3-14698b3-13270a2c+5314abc-4557b2c+8210ac2-4699bc2-3608c3+5592a2d+
     ------------------------------------------------------------------------
     608abd-8031b2d+10180acd+6017bcd+1771c2d-3466ad2-15090bd2-7615cd2+2487d3+
     ------------------------------------------------------------------------
     11663a2e-4961abe-13903b2e+3467ace-2945bce-12075c2e-1635ade+9638bde-
     ------------------------------------------------------------------------
     670cde-12326d2e+4032ae2-9597be2+2732ce2-11620de2+7856e3
     ------------------------------------------------------------------------
     b3c+11392a2c2-5543abc2+979b2c2+3694ac3+1560bc3-4199c4+12138b3d+10586a2cd
     ------------------------------------------------------------------------
     +5366abcd-4037b2cd+5634ac2d-9604bc2d-5723c3d+533a2d2-545abd2+10414b2d2+
     ------------------------------------------------------------------------
     11411acd2-610bcd2+5682c2d2-7621ad3+6541bd3+13178cd3+1388d4+10771b3e+
     ------------------------------------------------------------------------
     10911a2ce+13156abce-12447b2ce-1821ac2e-1072bc2e-15947c3e+9393a2de+
     ------------------------------------------------------------------------
     8970abde-10301b2de+8214acde+13945bcde-6473c2de-12431ad2e-1642bd2e+
     ------------------------------------------------------------------------
     11079cd2e-5008d3e+7055a2e2+4663abe2+8192b2e2+9072ace2+1522bce2-3960c2e2-
     ------------------------------------------------------------------------
     1329ade2-6601bde2+14687cde2+10119d2e2+13813ae3-2619be3+14820ce3-1465de3-
     ------------------------------------------------------------------------
     6527e4 b4+15020a2c2+220abc2-9765b2c2+10380ac3-7408bc3+11209c4+12146b3d+
     ------------------------------------------------------------------------
     11657a2cd+10078abcd+2351b2cd-6399ac2d+2310bc2d-9680c3d-4067a2d2+
     ------------------------------------------------------------------------
     11416abd2+15335b2d2-4249acd2+4428bcd2-7771c2d2+2384ad3-11470bd3+4197cd3-
     ------------------------------------------------------------------------
     9823d4-5008b3e+6825a2ce-2581abce-589b2ce-12068ac2e-13209bc2e-6893c3e-
     ------------------------------------------------------------------------
     11029a2de-5500abde+14459b2de-1971acde-862bcde+5248c2de-7738ad2e-
     ------------------------------------------------------------------------
     11233bd2e+486cd2e-10793d3e-11760a2e2-15406abe2-8740b2e2-15172ace2-
     ------------------------------------------------------------------------
     10940bce2+456c2e2-13521ade2+2314bde2-12854cde2-11301d2e2+1153ae3+2835be3
     ------------------------------------------------------------------------
     +14280ce3+3976de3-10734e4
     ------------------------------------------------------------------------
     abc3+9270b2c3+11767ac4-10425bc4+12629c5-8060a2c2d-10688abc2d+10072b2c2d+
     ------------------------------------------------------------------------
     679ac3d+1182bc3d-12818c4d-14688b3d2+9941a2cd2-10501abcd2-8911b2cd2+
     ------------------------------------------------------------------------
     6023ac2d2+4623bc2d2+12151c3d2-2482a2d3-9476abd3+1103b2d3-6975acd3-
     ------------------------------------------------------------------------
     8456bcd3+13682c2d3-12904ad4-11738bd4-1791cd4+5266d5+15794a2c2e-2823abc2e
     ------------------------------------------------------------------------
     -4885b2c2e+10071ac3e+5661bc3e+13153c4e+7232b3de+7838a2cde+13460abcde+
     ------------------------------------------------------------------------
     2226b2cde+5929ac2de-5761bc2de+9215c3de-15967a2d2e+558abd2e+15462b2d2e-
     ------------------------------------------------------------------------
     4369acd2e+3856bcd2e-10899c2d2e+14505ad3e+15095bd3e-15255cd3e+15939d4e+
     ------------------------------------------------------------------------
     7389b3e2+1205a2ce2+8196abce2-11797b2ce2+12697ac2e2-7348bc2e2+14065c3e2-
     ------------------------------------------------------------------------
     10474a2de2+448abde2-7467b2de2-13026acde2+3536bcde2+15740c2de2-8251ad2e2-
     ------------------------------------------------------------------------
     10967bd2e2-6066cd2e2-15124d3e2-14873a2e3+15735abe3-4866b2e3+10401ace3-
     ------------------------------------------------------------------------
     3843bce3+14107c2e3-2191ade3+1591bde3-4029cde3-15044d2e3-8575ae4-3706be4+
     ------------------------------------------------------------------------
     4500ce4-133de4-2320e5 a2c3-10217b2c3+475ac4+8820bc4+14066c5+14249a2c2d-
     ------------------------------------------------------------------------
     6340abc2d-10612b2c2d+11018ac3d-2555bc3d-2050c4d+8202b3d2+1419a2cd2+
     ------------------------------------------------------------------------
     10680abcd2+12013b2cd2+10997ac2d2-15253bc2d2-1754c3d2+3368a2d3+10682abd3-
     ------------------------------------------------------------------------
     10286b2d3+4656acd3-11273bcd3-10383c2d3+3876ad4+4915bd4-6343cd4+667d5-
     ------------------------------------------------------------------------
     15866a2c2e-12577abc2e-3598b2c2e+3260ac3e+11271bc3e-10684c4e+5005b3de+
     ------------------------------------------------------------------------
     9a2cde+7902abcde-13305b2cde+1889ac2de-10134bc2de-3360c3de-4072a2d2e+
     ------------------------------------------------------------------------
     12040abd2e+5392b2d2e+10755acd2e-11927bcd2e-7398c2d2e+9171ad3e+10772bd3e-
     ------------------------------------------------------------------------
     7394cd3e+14125d4e-8545b3e2+6140a2ce2+6181abce2+2251b2ce2+7683ac2e2-
     ------------------------------------------------------------------------
     5032bc2e2+3545c3e2+1671a2de2-11125abde2+14274b2de2+14149acde2+1438bcde2+
     ------------------------------------------------------------------------
     10325c2de2+4782ad2e2+9881bd2e2+6552cd2e2+14052d3e2+9393a2e3+488abe3+
     ------------------------------------------------------------------------
     12840b2e3-15514ace3+6533bce3-10231c2e3+8763ade3+14052bde3-4819cde3-
     ------------------------------------------------------------------------
     13620d2e3-13553ae4-9357be4-3250ce4-11773de4-12292e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R