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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 (- 6211a  - 15111a b + 1033a*b  + 11196b  + 11877a c - 1123a*b*c +
     ------------------------------------------------------------------------
           2            2           2         3        2                
     12487b c - 12624a*c  + 11547b*c  - 12683c  - 9121a d + 14702a*b*d +
     ------------------------------------------------------------------------
          2                                  2            2          2  
     7860b d + 1555a*c*d - 8563b*c*d - 10097c d + 11062a*d  - 8630b*d  +
     ------------------------------------------------------------------------
            2       3        2                      2               
     8144c*d  + 154d  + 2022a e + 13516a*b*e - 9927b e - 1205a*c*e +
     ------------------------------------------------------------------------
                       2                                               2   
     9259b*c*e + 14922c e - 12234a*d*e - 4721b*d*e + 11920c*d*e - 3409d e -
     ------------------------------------------------------------------------
            2          2           2          2        3          3  
     2241a*e  - 9164b*e  + 11019c*e  + 4898d*e  + 4175e , - 13216a  -
     ------------------------------------------------------------------------
           2          2        3        2                       2           2
     14364a b - 818a*b  - 2471b  - 7185a c + 12264a*b*c - 13681b c - 3933a*c 
     ------------------------------------------------------------------------
              2        3        2                     2               
     - 7356b*c  - 9385c  + 6749a d + 6676a*b*d - 9363b d + 2372a*c*d -
     ------------------------------------------------------------------------
                       2           2          2          2        3  
     6406b*c*d - 14432c d + 2037a*d  + 1277b*d  - 5823c*d  - 2709d  -
     ------------------------------------------------------------------------
           2                     2                                  2   
     12514a e + 9031a*b*e + 7951b e + 2518a*c*e - 13232b*c*e + 1248c e +
     ------------------------------------------------------------------------
                                                2           2          2  
     10954a*d*e - 2427b*d*e - 1635c*d*e - 15024d e - 4186a*e  - 7132b*e  -
     ------------------------------------------------------------------------
             2          2        3          3        2            2         3
     15414c*e  + 7013d*e  - 2240e , - 11923a  - 2304a b + 11025a*b  - 15855b 
     ------------------------------------------------------------------------
           2                      2            2          2        3  
     - 936a c - 7319a*b*c - 13732b c + 12037a*c  - 2973b*c  - 9504c  -
     ------------------------------------------------------------------------
          2                     2                                 2   
     6595a d - 6343a*b*d - 2651b d + 7272a*c*d + 589b*c*d - 13571c d -
     ------------------------------------------------------------------------
             2           2          2        3         2                
     13191a*d  + 12282b*d  + 7053c*d  - 8020d  + 11368a e - 11786a*b*e +
     ------------------------------------------------------------------------
          2                                   2                            
     5655b e + 13223a*c*e + 3274b*c*e + 10484c e + 4979a*d*e - 11588b*d*e +
     ------------------------------------------------------------------------
                        2            2          2           2          2  
     13484c*d*e - 10913d e - 14835a*e  - 2748b*e  - 13258c*e  - 9369d*e  +
     ------------------------------------------------------------------------
           3
     10710e )

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+10356b3-2752a2c+2015abc+15385b2c-13488ac2+13492bc2+11510c3+
     ------------------------------------------------------------------------
     12841a2d-1440abd-3914b2d+12502acd+6882bcd+2096c2d-2343ad2-2179bd2-
     ------------------------------------------------------------------------
     3559cd2+6970d3+9494a2e+3955abe+4505b2e-7160ace+15787bce+8383c2e-8753ade-
     ------------------------------------------------------------------------
     8473bde+3928cde-14260d2e+6627ae2-9359be2-8222ce2-2763de2+880e3
     ------------------------------------------------------------------------
     a2b+13009b3+1233a2c+2040abc-3380b2c-9170ac2+1087bc2-7047c3+4700a2d+
     ------------------------------------------------------------------------
     11652abd-1063b2d-13598acd-14054bcd-14616c2d-15416ad2-13683bd2-4662cd2-
     ------------------------------------------------------------------------
     5987d3-11103a2e-7550abe+34b2e+1160ace+15968bce+11487c2e+10017ade+
     ------------------------------------------------------------------------
     10149bde+6592cde+1508d2e+5518ae2-9853be2-5397ce2+11635de2-14933e3
     ------------------------------------------------------------------------
     a3-2229b3-9555a2c-4159abc+10033b2c+12412ac2+7244bc2-8732c3-2017a2d+
     ------------------------------------------------------------------------
     1944abd+6762b2d+5617acd-7114bcd-5785c2d+4107ad2-6262bd2+8719cd2-15948d3+
     ------------------------------------------------------------------------
     5209a2e-4111abe+13019b2e+3139ace-4727bce-14694c2e+15448ade+11823bde+
     ------------------------------------------------------------------------
     15488cde+14452d2e-3666ae2+15507be2-13873ce2+1669de2+13764e3
     ------------------------------------------------------------------------
     b3c-1042a2c2-5318abc2+196b2c2+15269ac3-6542bc3+1776c4-358b3d+6746a2cd-
     ------------------------------------------------------------------------
     12422abcd-14632b2cd+15160ac2d-11097bc2d+664c3d-14256a2d2+1085abd2-
     ------------------------------------------------------------------------
     11306b2d2+8994acd2+15590bcd2+425c2d2+10936ad3-2030bd3+12555cd3-6488d4-
     ------------------------------------------------------------------------
     12177b3e+7441a2ce+5033abce+708b2ce+13618ac2e+4061bc2e-6027c3e+296a2de-
     ------------------------------------------------------------------------
     13997abde+1326b2de-8607acde+9157bcde+11016c2de+6791ad2e+15872bd2e-
     ------------------------------------------------------------------------
     11974cd2e+14307d3e-10996a2e2-11707abe2-13776b2e2-6212ace2-15950bce2+
     ------------------------------------------------------------------------
     7717c2e2+5219ade2-10224bde2+8882cde2-9131d2e2+1096ae3-4069be3-4410ce3+
     ------------------------------------------------------------------------
     14076de3-5755e4 b4+6557a2c2+7202abc2-11335b2c2-15406ac3-7742bc3+6601c4-
     ------------------------------------------------------------------------
     15672b3d+3665a2cd+3456abcd+1285b2cd+10820ac2d-2249bc2d-12901c3d+
     ------------------------------------------------------------------------
     12589a2d2+13770abd2-12837b2d2+11812acd2+5448bcd2-4843c2d2-10172ad3-
     ------------------------------------------------------------------------
     15956bd3+10898cd3+7561d4-9405b3e-4731a2ce+2764abce+10435b2ce+3553ac2e+
     ------------------------------------------------------------------------
     14500bc2e-12805c3e+1939a2de-14547abde+635b2de+15347acde-10597bcde+
     ------------------------------------------------------------------------
     4538c2de-15442ad2e+10609bd2e-8263cd2e+7611d3e+13580a2e2+2441abe2-
     ------------------------------------------------------------------------
     13844b2e2-9451ace2+2177bce2-3695c2e2-4654ade2+7244bde2+2761cde2+
     ------------------------------------------------------------------------
     14202d2e2+14704ae3+11241be3+7232ce3+7240de3+1102e4
     ------------------------------------------------------------------------
     abc3+7350b2c3-2965ac4-13520bc4+5604c5+12589a2c2d-1435abc2d+8436b2c2d+
     ------------------------------------------------------------------------
     3658ac3d+7879bc3d+12431c4d-8807b3d2+329a2cd2-8671abcd2+5960b2cd2+
     ------------------------------------------------------------------------
     9200ac2d2+12190bc2d2+239c3d2-6035a2d3+11565abd3+15645b2d3+4737acd3+
     ------------------------------------------------------------------------
     2398bcd3-11599c2d3-10742ad4+13656bd4-13030cd4+9914d5-13248a2c2e-
     ------------------------------------------------------------------------
     4472abc2e-10752b2c2e+14934ac3e-14623bc3e+4451c4e+1087b3de+15589a2cde-
     ------------------------------------------------------------------------
     4858abcde-14450b2cde+2229ac2de-3680bc2de+3463c3de-4903a2d2e-1394abd2e+
     ------------------------------------------------------------------------
     8835b2d2e+11669acd2e-8455bcd2e+15435c2d2e+3450ad3e-195bd3e+1361cd3e-
     ------------------------------------------------------------------------
     12504d4e+11818b3e2+892a2ce2+6490abce2-7686b2ce2+14675ac2e2+7950bc2e2+
     ------------------------------------------------------------------------
     14335c3e2+11126a2de2-15064abde2+10188b2de2+12449acde2-9135bcde2+239c2de2
     ------------------------------------------------------------------------
     -219ad2e2+1275bd2e2+4972cd2e2+14736d3e2+3352a2e3-12826abe3+6627b2e3-
     ------------------------------------------------------------------------
     6250ace3-13443bce3-685c2e3-14842ade3-8106bde3-14494cde3-7525d2e3+9427ae4
     ------------------------------------------------------------------------
     -8234be4-4757ce4-8904de4-14529e5
     ------------------------------------------------------------------------
     a2c3+14749b2c3-9746ac4+5392bc4-15080c5-13266a2c2d-1138abc2d-450b2c2d+
     ------------------------------------------------------------------------
     12676ac3d-14862bc3d-4254c4d+13367b3d2+10891a2cd2+8345abcd2-13643b2cd2-
     ------------------------------------------------------------------------
     10942ac2d2-4296bc2d2-15923c3d2-3141a2d3-5617abd3+1044b2d3+11915acd3+
     ------------------------------------------------------------------------
     1525bcd3+12896c2d3+12184ad4-2693bd4+3528cd4+13151d5+8613a2c2e-9832abc2e-
     ------------------------------------------------------------------------
     14836b2c2e+15358ac3e-9324bc3e-6817c4e-12966b3de-11844a2cde-9433abcde-
     ------------------------------------------------------------------------
     10804b2cde+5057ac2de-13633bc2de-462c3de-1415a2d2e-6443abd2e+12569b2d2e+
     ------------------------------------------------------------------------
     1945acd2e-1246bcd2e-14105c2d2e-1925ad3e-911bd3e-8862cd3e+4937d4e-
     ------------------------------------------------------------------------
     7092b3e2-2169a2ce2-11531abce2+11343b2ce2+12690ac2e2+12416bc2e2-12712c3e2
     ------------------------------------------------------------------------
     -10010a2de2+13383abde2+13159b2de2+9063acde2-12347bcde2-13411c2de2+
     ------------------------------------------------------------------------
     7254ad2e2-5480bd2e2-2668cd2e2+4797d3e2+11693a2e3-3593abe3-8369b2e3+
     ------------------------------------------------------------------------
     3547ace3-3173bce3-7948c2e3+10052ade3-11224bde3-6678cde3-10187d2e3-
     ------------------------------------------------------------------------
     9172ae4+10332be4+8986ce4+2606de4-15446e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R