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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 (- 8195a  + 13247a b + 14446a*b  + 9702b  + 13181a c + 14803a*b*c
     ------------------------------------------------------------------------
            2            2         2        3         2               
     + 6896b c + 15038a*c  + 239b*c  + 8442c  + 15531a d + 9223a*b*d -
     ------------------------------------------------------------------------
          2                                  2            2          2  
     6298b d + 2351a*c*d - 15369b*c*d + 2811c d + 14090a*d  - 6982b*d  +
     ------------------------------------------------------------------------
            2         3         2                     2               
     4455c*d  - 10356d  + 10104a e + 8442a*b*e + 2665b e - 8778a*c*e -
     ------------------------------------------------------------------------
                       2                                               2   
     8854b*c*e - 10876c e + 3817a*d*e + 14581b*d*e - 11304c*d*e - 1509d e -
     ------------------------------------------------------------------------
             2           2          2           2        3        3        2 
     13967a*e  + 15716b*e  + 2828c*e  + 11888d*e  - 5520e , 11258a  - 9965a b
     ------------------------------------------------------------------------
               2         3        2                      2            2  
     - 15381a*b  + 15365b  - 8840a c + 7518a*b*c + 15223b c + 12894a*c  +
     ------------------------------------------------------------------------
            2         3        2                     2                
     4977b*c  - 14030c  - 5828a d + 7314a*b*d + 9712b d - 14661a*c*d +
     ------------------------------------------------------------------------
                    2           2          2           2         3        2 
     830b*c*d + 435c d + 9937a*d  - 6821b*d  - 14098c*d  - 11623d  + 9933a e
     ------------------------------------------------------------------------
                        2                                  2              
     + 12505a*b*e - 217b e + 8153a*c*e - 6419b*c*e + 12035c e - 159a*d*e -
     ------------------------------------------------------------------------
                                  2           2           2           2  
     6275b*d*e + 3164c*d*e - 8043d e + 5980a*e  + 13073b*e  + 12968c*e  +
     ------------------------------------------------------------------------
            2         3        3        2           2         3        2   
     7853d*e  + 10677e , 11209a  + 3393a b + 9148a*b  + 11357b  - 7952a c +
     ------------------------------------------------------------------------
                      2           2          2         3        2   
     6712a*b*c + 1353b c + 2819a*c  + 9573b*c  + 10225c  + 7435a d -
     ------------------------------------------------------------------------
                       2                                   2            2  
     13113a*b*d - 9371b d + 15747a*c*d + 6612b*c*d - 10321c d + 12368a*d  -
     ------------------------------------------------------------------------
            2          2         3         2                       2   
     9071b*d  - 3208c*d  + 11923d  - 11030a e + 13534a*b*e + 13116b e +
     ------------------------------------------------------------------------
                                  2                                        
     9106a*c*e + 2396b*c*e - 2798c e - 1106a*d*e - 12472b*d*e - 6841c*d*e +
     ------------------------------------------------------------------------
          2            2           2          2          2         3
     4265d e - 12183a*e  + 15251b*e  - 5837c*e  + 1288d*e  - 14035e )

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+9198b3+13a2c-461abc+9592b2c-7340ac2+12741bc2+13662c3-9266a2d-
     ------------------------------------------------------------------------
     8560abd+11954b2d-8720acd+10620bcd+10789c2d-7009ad2-9128bd2+327cd2-
     ------------------------------------------------------------------------
     11185d3+14219a2e-9208abe-596b2e+2368ace-7076bce-13936c2e+15928ade+
     ------------------------------------------------------------------------
     2933bde-11465cde+13992d2e-838ae2+174be2+6199ce2+14257de2+14655e3
     ------------------------------------------------------------------------
     a2b+5380b3-3952a2c-6677abc+5385b2c+4276ac2-5595bc2+13547c3+6888a2d+
     ------------------------------------------------------------------------
     6067abd+15836b2d-186acd+12392bcd-9460c2d-6269ad2-10937bd2-11528cd2-
     ------------------------------------------------------------------------
     6684d3+6910a2e+13961abe-2882b2e-3852ace+726bce-13241c2e-4656ade-11345bde
     ------------------------------------------------------------------------
     -13071cde+10627d2e-10058ae2-10500be2-5821ce2-8849de2+15813e3
     ------------------------------------------------------------------------
     a3-6125b3+12003a2c+4388abc+3267b2c-14827ac2-2631bc2+3988c3-6131a2d-
     ------------------------------------------------------------------------
     7771abd+3117b2d-3992acd-11744bcd+5929c2d+9235ad2+4404bd2-15333cd2+
     ------------------------------------------------------------------------
     10793d3+10557a2e+7647abe-15785b2e+14452ace-14833bce+11961c2e+12924ade-
     ------------------------------------------------------------------------
     15783bde+9824cde+11500d2e+8544ae2-1559be2-1833ce2-1268de2-2250e3
     ------------------------------------------------------------------------
     b3c-10923a2c2-11076abc2+10004b2c2+5170ac3+525bc3+11367c4-8568b3d+
     ------------------------------------------------------------------------
     2038a2cd-7199abcd-14884b2cd-7812ac2d-13966bc2d-12092c3d+8358a2d2+879abd2
     ------------------------------------------------------------------------
     -11778b2d2-1014acd2+10498bcd2-1562c2d2+7933ad3+3542bd3-3854cd3-5561d4-
     ------------------------------------------------------------------------
     2298b3e-9332a2ce-15902abce+6683b2ce-1012ac2e+12930bc2e+8173c3e+8736a2de+
     ------------------------------------------------------------------------
     9315abde-13888b2de+4643acde+3181bcde-6297c2de-10364ad2e+366bd2e-2670cd2e
     ------------------------------------------------------------------------
     -7438d3e+5519a2e2-14418abe2-13551b2e2+3940ace2-8996bce2+14957c2e2-
     ------------------------------------------------------------------------
     2399ade2+5111bde2+7246cde2-7061d2e2-4033ae3+12447be3+4666ce3-5365de3-
     ------------------------------------------------------------------------
     11156e4 b4+8139a2c2+12371abc2-12223b2c2-8902ac3+11592bc3-6082c4-13565b3d
     ------------------------------------------------------------------------
     -1392a2cd+4673abcd+10948b2cd-8217ac2d-8708bc2d+3112c3d+8528a2d2-3701abd2
     ------------------------------------------------------------------------
     +8895b2d2-11161acd2+6513bcd2+9738c2d2-15222ad3-6643bd3+12518cd3-5944d4+
     ------------------------------------------------------------------------
     12097b3e+14724a2ce-2875abce+1916b2ce-2958ac2e+9851bc2e+6598c3e+101a2de-
     ------------------------------------------------------------------------
     1315abde+11804b2de-12936acde-11184bcde-4819c2de+9686ad2e+6208bd2e+
     ------------------------------------------------------------------------
     446cd2e+3132d3e+358a2e2-3740abe2+13015b2e2-13220ace2-10865bce2+7953c2e2-
     ------------------------------------------------------------------------
     1551ade2-8228bde2-4916cde2-4341d2e2-15061ae3+4433be3+6709ce3+7513de3+
     ------------------------------------------------------------------------
     9894e4 abc3-4012b2c3-15021ac4+4749bc4-15017c5-11950a2c2d-7123abc2d+
     ------------------------------------------------------------------------
     11307b2c2d+535ac3d-11444bc3d-14306c4d-3094b3d2+1216a2cd2+10280abcd2-
     ------------------------------------------------------------------------
     12729b2cd2-7516ac2d2-10163bc2d2-10624c3d2-7621a2d3-7753abd3-7928b2d3+
     ------------------------------------------------------------------------
     12228acd3-14653bcd3-11878c2d3+6856ad4+10551bd4-4130cd4+4678d5-5773a2c2e-
     ------------------------------------------------------------------------
     7845abc2e-14059b2c2e-3659ac3e-6566bc3e+13709c4e+14639b3de-1019a2cde+
     ------------------------------------------------------------------------
     15098abcde+1722b2cde-15575ac2de+12086bc2de+6137c3de-7080a2d2e+7538abd2e+
     ------------------------------------------------------------------------
     4326b2d2e-11243acd2e+5225bcd2e-9709c2d2e-10258ad3e+7726bd3e+10524cd3e+
     ------------------------------------------------------------------------
     5492d4e+1406b3e2-3800a2ce2-15120abce2+14474b2ce2+9105ac2e2+8991bc2e2-
     ------------------------------------------------------------------------
     14753c3e2+6879a2de2-9892abde2-11961b2de2+866acde2-4860bcde2-498c2de2+
     ------------------------------------------------------------------------
     10181ad2e2-10440bd2e2-8705cd2e2-6728d3e2-9773a2e3-10699abe3-9506b2e3+
     ------------------------------------------------------------------------
     6198ace3-10667bce3+13114c2e3-8945ade3-15800bde3+3997cde3-12243d2e3-
     ------------------------------------------------------------------------
     15238ae4-12530be4+15625ce4+1889de4-10762e5
     ------------------------------------------------------------------------
     a2c3-9379b2c3-9123ac4+139bc4+1569c5+13395a2c2d-1595abc2d+8852b2c2d+
     ------------------------------------------------------------------------
     13057ac3d+4534bc3d-11299c4d+6730b3d2+8097a2cd2-1231abcd2+11889b2cd2+
     ------------------------------------------------------------------------
     6115ac2d2+15213bc2d2-15603c3d2-3840a2d3-499abd3+3695b2d3-6249acd3-
     ------------------------------------------------------------------------
     11426bcd3+13777c2d3+5110ad4+8316bd4+9105cd4-9549d5+6278a2c2e+787abc2e+
     ------------------------------------------------------------------------
     12206b2c2e-11900ac3e-11327bc3e-11035c4e-4241b3de-7998a2cde+13195abcde+
     ------------------------------------------------------------------------
     7449b2cde+5437ac2de+4491bc2de-9429c3de-498a2d2e-5854abd2e+5247b2d2e+
     ------------------------------------------------------------------------
     2952acd2e+7852bcd2e+9597c2d2e-14945ad3e-11503bd3e+2726cd3e-6496d4e-
     ------------------------------------------------------------------------
     4766b3e2-15250a2ce2+8873abce2+14333b2ce2-8756ac2e2+9486bc2e2-10847c3e2-
     ------------------------------------------------------------------------
     905a2de2+3945abde2+3895b2de2+13779acde2-6598bcde2-9209c2de2-15682ad2e2+
     ------------------------------------------------------------------------
     179bd2e2+4050cd2e2-5651d3e2+14640a2e3-10642abe3+987b2e3+681ace3-6374bce3
     ------------------------------------------------------------------------
     +5500c2e3-7075ade3+1007bde3+12503cde3+15000d2e3+13604ae4-7194be4+
     ------------------------------------------------------------------------
     15333ce4-3098de4-8760e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R