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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 (8593a  + 160a b + 1422a*b  + 650b  + 6686a c + 2383a*b*c +
     ------------------------------------------------------------------------
          2           2          2         3         2                     2 
     4220b c - 7569a*c  - 8192b*c  + 10336c  - 11770a d - 203a*b*d - 12865b d
     ------------------------------------------------------------------------
                                   2           2           2          2  
     + 53a*c*d + 9116b*c*d - 12861c d - 9553a*d  - 15149b*d  - 1547c*d  +
     ------------------------------------------------------------------------
          3        2                      2                            
     9618d  - 4424a e + 2212a*b*e + 14119b e + 14508a*c*e + 6758b*c*e -
     ------------------------------------------------------------------------
           2                                                2           2  
     10493c e - 14661a*d*e - 6813b*d*e - 12429c*d*e - 10077d e + 9852a*e  -
     ------------------------------------------------------------------------
            2         2           2         3         3         2           2
     7421b*e  + 169c*e  - 14470d*e  + 14155e , - 7289a  + 15113a b + 8436a*b 
     ------------------------------------------------------------------------
            3         2                      2           2          2  
     - 8505b  + 14423a c + 5823a*b*c - 13094b c + 1528a*c  - 8749b*c  -
     ------------------------------------------------------------------------
          3         2                       2                            
     4827c  + 10622a d + 11258a*b*d + 11818b d - 8907a*c*d - 11455b*c*d +
     ------------------------------------------------------------------------
           2          2          2           2        3         2   
     12433c d - 863a*d  + 5839b*d  - 10299c*d  + 1766d  + 12388a e +
     ------------------------------------------------------------------------
                       2                                   2              
     3356a*b*e - 15328b e + 1077a*c*e + 11306b*c*e + 10936c e + 300a*d*e +
     ------------------------------------------------------------------------
                                    2            2          2          2  
     13756b*d*e + 14333c*d*e - 7005d e - 15436a*e  + 7964b*e  - 9108c*e  +
     ------------------------------------------------------------------------
            2        3          3        2           2        3         2   
     2336d*e  - 4284e , - 10928a  + 9815a b - 8717a*b  + 1540b  - 15234a c -
     ------------------------------------------------------------------------
                       2            2          2        3       2   
     4612a*b*c - 13123b c + 15079a*c  - 8485b*c  - 7270c  + 896a d -
     ------------------------------------------------------------------------
                       2                                   2           2  
     3614a*b*d + 12269b d + 15110a*c*d + 15674b*c*d + 8340c d - 1327a*d  -
     ------------------------------------------------------------------------
            2          2        3         2                       2   
     1671b*d  - 7987c*d  + 3457d  + 14612a e + 11435a*b*e - 11176b e -
     ------------------------------------------------------------------------
                                   2                                        
     13409a*c*e + 701b*c*e + 14802c e - 6769a*d*e + 10403b*d*e - 3849c*d*e -
     ------------------------------------------------------------------------
          2            2          2           2          2         3
     1301d e - 11257a*e  + 8982b*e  + 10110c*e  + 2374d*e  + 13264e )

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 = | ab2-14573b3-3200a2c+1726abc-7395b2c-12569ac2-11775bc2+13318c3+4648a2d+
     ------------------------------------------------------------------------
     8143abd+12415b2d-449acd+1692bcd+13115c2d-3654ad2-797bd2-10408cd2-6241d3+
     ------------------------------------------------------------------------
     13669a2e+15409abe+295b2e-7451ace+9509bce-5536c2e-7223ade+632bde+24cde-
     ------------------------------------------------------------------------
     2062d2e+15237ae2-3099be2-3970ce2-5947de2+15515e3
     ------------------------------------------------------------------------
     a2b+12731b3-9958a2c-5476abc-2479b2c+9044ac2-12192bc2+3013c3+14776a2d+
     ------------------------------------------------------------------------
     3736abd+8957b2d+15989acd+7553bcd+7432c2d+14828ad2-3022bd2-7436cd2+7148d3
     ------------------------------------------------------------------------
     -465a2e-10273abe+10094b2e+13828ace+12795bce-15098c2e+11177ade-1051bde+
     ------------------------------------------------------------------------
     14545cde+4889d2e+2114ae2-11045be2-7794ce2+4648de2+6852e3
     ------------------------------------------------------------------------
     a3-5963b3-4867a2c+9619abc-7370b2c+1285ac2-12123bc2+12955c3+8064a2d+
     ------------------------------------------------------------------------
     7119abd-14256b2d-4160acd+15662bcd-4042c2d-6853ad2+6514bd2+6881cd2+8774d3
     ------------------------------------------------------------------------
     +11649a2e+15887abe-1304b2e+12355ace+7172bce+1561c2e-9856ade+6212bde-
     ------------------------------------------------------------------------
     239cde-5438d2e+8576ae2-11297be2-8315ce2-5171de2+8446e3
     ------------------------------------------------------------------------
     b3c-8692a2c2-9049abc2-1605b2c2-2288ac3+7104bc3-4341c4+7264b3d-1270a2cd-
     ------------------------------------------------------------------------
     15241abcd+8803b2cd+6715ac2d-7967bc2d-12486c3d+10081a2d2-2027abd2+
     ------------------------------------------------------------------------
     8078b2d2+12414acd2+2934bcd2+11868c2d2+5162ad3-1447bd3-13035cd3+8010d4-
     ------------------------------------------------------------------------
     10999b3e-6144a2ce+3872abce+4256b2ce-5971ac2e-1265bc2e-15041c3e+6052a2de-
     ------------------------------------------------------------------------
     6053abde-193b2de-12472acde+4454bcde+11531c2de+12949ad2e+4838bd2e+
     ------------------------------------------------------------------------
     1958cd2e-2184d3e+5203a2e2+11376abe2-6911b2e2+15847ace2+1083bce2-8543c2e2
     ------------------------------------------------------------------------
     +10629ade2+10567bde2-1414cde2+14859d2e2-13762ae3-6571be3-6069ce3-5963de3
     ------------------------------------------------------------------------
     -9474e4 b4+864a2c2-5636abc2+1262b2c2+1958ac3+8924bc3+8251c4-885b3d-
     ------------------------------------------------------------------------
     6723a2cd+4934abcd-10730b2cd+14824ac2d-9381bc2d-5956c3d-9223a2d2+5098abd2
     ------------------------------------------------------------------------
     -14207b2d2+8418acd2+759bcd2+3260c2d2+615ad3+10778bd3+2708cd3-9107d4-
     ------------------------------------------------------------------------
     1664b3e+4891a2ce-1636abce-8500b2ce+4752ac2e-8167bc2e-15720c3e+673a2de+
     ------------------------------------------------------------------------
     1960abde-10761b2de-7174acde+8710bcde+7436c2de+6271ad2e+12484bd2e-
     ------------------------------------------------------------------------
     8016cd2e-3550d3e-1810a2e2-7906abe2-10225b2e2+10796ace2+6173bce2+7590c2e2
     ------------------------------------------------------------------------
     -7075ade2+4002bde2+6597cde2-7795d2e2+3137ae3-7956be3-6119ce3-8993de3-
     ------------------------------------------------------------------------
     240e4 abc3+2002b2c3+884ac4-11738bc4+11893c5+8005a2c2d-4467abc2d-
     ------------------------------------------------------------------------
     14551b2c2d+15154ac3d-4557bc3d+8563c4d+1570b3d2+6631a2cd2-14235abcd2+
     ------------------------------------------------------------------------
     634b2cd2-8893ac2d2+6693bc2d2+9079c3d2-5484a2d3+6138abd3-3223b2d3+59acd3+
     ------------------------------------------------------------------------
     10923bcd3-11445c2d3+6736ad4-162bd4+12491cd4-2066d5+2019a2c2e+5146abc2e-
     ------------------------------------------------------------------------
     11661b2c2e-9655ac3e-7478bc3e-7199c4e-6938b3de-15315a2cde+3442abcde-
     ------------------------------------------------------------------------
     454b2cde-8348ac2de-14411bc2de-9492c3de+5747a2d2e-621abd2e-3737b2d2e-
     ------------------------------------------------------------------------
     1812acd2e-3220bcd2e-5591c2d2e+7668ad3e+44bd3e-10682cd3e-13803d4e+
     ------------------------------------------------------------------------
     12460b3e2-2080a2ce2+3888abce2+7929b2ce2-8633ac2e2+1879bc2e2-14606c3e2+
     ------------------------------------------------------------------------
     1465a2de2+8197abde2+6951b2de2-15421acde2+10063bcde2-2705c2de2+10946ad2e2
     ------------------------------------------------------------------------
     +15657bd2e2+11936cd2e2-11126d3e2-1148a2e3-11176abe3-10996b2e3+12734ace3+
     ------------------------------------------------------------------------
     14567bce3+7741c2e3-14940ade3+11066bde3-6455cde3+3871d2e3+6860ae4-
     ------------------------------------------------------------------------
     11440be4-10933ce4+3200de4-8669e5
     ------------------------------------------------------------------------
     a2c3+994b2c3-14926ac4-7247bc4+4348c5+2347a2c2d-37abc2d+15678b2c2d-
     ------------------------------------------------------------------------
     9755ac3d-12787bc3d-6955c4d-3423b3d2+6747a2cd2-2619abcd2-670b2cd2-
     ------------------------------------------------------------------------
     9673ac2d2-15179bc2d2+14395c3d2-8286a2d3+2863abd3-8051b2d3+5676acd3-
     ------------------------------------------------------------------------
     14415bcd3-2247c2d3+14346ad4-13548bd4+4214cd4-6371d5+14897a2c2e-3537abc2e
     ------------------------------------------------------------------------
     -45b2c2e+14637ac3e-4893bc3e+8726c4e-8341b3de-9183a2cde-10968abcde-
     ------------------------------------------------------------------------
     9716b2cde-11570ac2de+4165bc2de-7896c3de+4515a2d2e+10117abd2e-3321b2d2e+
     ------------------------------------------------------------------------
     14702acd2e+1515bcd2e-15990c2d2e-9192ad3e+2659bd3e-13450cd3e-6950d4e-
     ------------------------------------------------------------------------
     943b3e2+2458a2ce2+10674abce2-14824b2ce2-2012ac2e2-8792bc2e2-7019c3e2+
     ------------------------------------------------------------------------
     3079a2de2-158abde2-6946b2de2-14652acde2+11523bcde2-7213c2de2+13572ad2e2-
     ------------------------------------------------------------------------
     13749bd2e2+9213cd2e2-2714d3e2-15511a2e3+10506abe3-14012b2e3+10ace3-
     ------------------------------------------------------------------------
     221bce3+718c2e3-4994ade3-9684bde3+10475cde3+3673d2e3-14665ae4-7014be4-
     ------------------------------------------------------------------------
     13445ce4+11564de4-10178e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R