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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 (7748a  - 3245a b - 1278a*b  + 8177b  - 7210a c - 134a*b*c +
     ------------------------------------------------------------------------
           2           2           2        3        2                     2 
     12690b c + 6874a*c  - 12689b*c  - 5954c  + 7102a d - 7096a*b*d + 8817b d
     ------------------------------------------------------------------------
                                    2           2           2           2  
     - 6767a*c*d + 2724b*c*d - 4520c d - 3836a*d  - 13601b*d  + 14443c*d  -
     ------------------------------------------------------------------------
           3        2                     2                            
     10283d  + 2105a e - 4284a*b*e + 3639b e + 1196a*c*e + 13231b*c*e +
     ------------------------------------------------------------------------
           2                                                2            2  
     14086c e - 12437a*d*e + 11309b*d*e - 8197c*d*e + 11023d e - 14683a*e  +
     ------------------------------------------------------------------------
            2          2          2        3       3         2            2  
     2647b*e  + 1413c*e  + 3391d*e  + 3548e , 8386a  + 12404a b + 14772a*b  -
     ------------------------------------------------------------------------
          3         2                      2           2          2        3
     7029b  + 10154a c - 7959a*b*c - 11849b c - 1209a*c  - 4930b*c  + 4850c 
     ------------------------------------------------------------------------
             2                      2                                   2   
     + 10886a d - 2688a*b*d - 15539b d + 15929a*c*d + 13140b*c*d - 5221c d -
     ------------------------------------------------------------------------
            2          2           2        3         2                
     3926a*d  - 4586b*d  - 14889c*d  - 7375d  + 11060a e + 15700a*b*e +
     ------------------------------------------------------------------------
           2                                 2                            
     12422b e + 10613a*c*e + 3899b*c*e + 899c e - 5496a*d*e - 15291b*d*e +
     ------------------------------------------------------------------------
                       2           2           2           2           2  
     12601c*d*e + 5164d e - 2308a*e  - 12804b*e  - 15616c*e  + 13993d*e  -
     ------------------------------------------------------------------------
           3          3        2           2         3       2              
     14560e , - 12012a  + 3094a b + 9466a*b  - 15434b  + 609a c - 14249a*b*c
     ------------------------------------------------------------------------
            2            2           2        3        2               
     + 3286b c - 16000a*c  + 15087b*c  - 2911c  + 7280a d - 8785a*b*d +
     ------------------------------------------------------------------------
           2                                 2           2          2  
     14426b d + 6911a*c*d - 810b*c*d - 14593c d + 7368a*d  - 3064b*d  -
     ------------------------------------------------------------------------
             2         3        2                     2                
     10191c*d  - 15033d  + 5398a e + 755a*b*e + 10819b e + 11845a*c*e +
     ------------------------------------------------------------------------
                       2                                               2   
     3965b*c*e + 10800c e + 12556a*d*e + 8925b*d*e + 5758c*d*e + 10463d e +
     ------------------------------------------------------------------------
            2          2          2           2         3
     7295a*e  + 1429b*e  + 6470c*e  + 10361d*e  - 15793e )

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+14313b3+8602a2c+1808abc-6930b2c+4996ac2+10604bc2+5527c3+2087a2d+
     ------------------------------------------------------------------------
     5449abd-14308b2d+1164acd+14608bcd+4501c2d+5334ad2+11256bd2+6502cd2-
     ------------------------------------------------------------------------
     15399d3+8066a2e-5898abe-14607b2e+5254ace-9941bce+14707c2e-15548ade-
     ------------------------------------------------------------------------
     3703bde+3332cde+15004d2e+2048ae2+1062be2-10683ce2+4722de2+5862e3
     ------------------------------------------------------------------------
     a2b-13309b3+12420a2c-15483abc+8643b2c+2258ac2+11583bc2-10695c3-14406a2d+
     ------------------------------------------------------------------------
     15016abd-2051b2d-6899acd-1111bcd-1084c2d+9255ad2+6144bd2-14811cd2+
     ------------------------------------------------------------------------
     15812d3+6176a2e-716abe+12632b2e+14611ace-13912bce+2181c2e+5554ade+
     ------------------------------------------------------------------------
     4414bde+4461cde-4578d2e-7565ae2+14578be2-8104ce2+6601de2-6412e3
     ------------------------------------------------------------------------
     a3+10245b3-3847a2c+4714abc+1326b2c-1352ac2-15136bc2+5275c3-7134a2d-
     ------------------------------------------------------------------------
     1165abd+10074b2d-3037acd+11961bcd-11451c2d+720ad2+11231bd2+15028cd2+
     ------------------------------------------------------------------------
     13197d3+4318a2e-7089abe+13245b2e+7362ace-3710bce-6254c2e+5365ade-607bde-
     ------------------------------------------------------------------------
     6158cde+14078d2e+15573ae2-11162be2+15294ce2+13011de2-12193e3
     ------------------------------------------------------------------------
     b3c+8067a2c2+3415abc2+3114b2c2-11654ac3-14742bc3-14705c4-9800b3d+
     ------------------------------------------------------------------------
     8161a2cd+11088abcd-7905b2cd+15992ac2d+12200bc2d+11659c3d-9116a2d2-
     ------------------------------------------------------------------------
     8134abd2+10918b2d2-2693acd2+5802bcd2+9785c2d2-6932ad3+14760bd3+13845cd3+
     ------------------------------------------------------------------------
     10208d4+4483b3e-2740a2ce+3892abce+3172b2ce+10754ac2e+14779bc2e+10095c3e+
     ------------------------------------------------------------------------
     11468a2de+12361abde-1449b2de+10865acde-13465bcde-5373c2de+2753ad2e+
     ------------------------------------------------------------------------
     9202bd2e-4539cd2e-13263d3e+13510a2e2-13479abe2+11296b2e2-2187ace2+
     ------------------------------------------------------------------------
     9743bce2+13061c2e2-358ade2+7042bde2-14749cde2-4286d2e2-11657ae3+3319be3-
     ------------------------------------------------------------------------
     6297ce3-5531de3+235e4 b4+341a2c2-12758abc2+10892b2c2-10579ac3+13906bc3+
     ------------------------------------------------------------------------
     14316c4+7323b3d+8702a2cd+1902abcd+1091b2cd+13301ac2d-6990bc2d-13819c3d-
     ------------------------------------------------------------------------
     13576a2d2-6210abd2+5418b2d2+7177acd2+9720bcd2+9789c2d2+7355ad3-8511bd3+
     ------------------------------------------------------------------------
     10578cd3+1023d4+10976b3e-12964a2ce-13891abce+1776b2ce-129ac2e-4251bc2e+
     ------------------------------------------------------------------------
     308c3e-9820a2de-9587abde+10566b2de+13099acde+6464bcde-15050c2de-
     ------------------------------------------------------------------------
     12685ad2e-12426bd2e+14663cd2e+13060d3e-6336a2e2+15958abe2-3319b2e2-
     ------------------------------------------------------------------------
     13915ace2+997bce2+15710c2e2+10355ade2-15408bde2+10737cde2+7085d2e2+
     ------------------------------------------------------------------------
     5518ae3+11396be3-4157ce3-4405de3-9749e4
     ------------------------------------------------------------------------
     abc3+10714b2c3+11421ac4-2159bc4+7171c5+13870a2c2d-5940abc2d+1012b2c2d-
     ------------------------------------------------------------------------
     1010ac3d+10486bc3d+9318c4d+2692b3d2+4362a2cd2-2142abcd2+2752b2cd2-
     ------------------------------------------------------------------------
     1406ac2d2+14918bc2d2+14786c3d2+13482a2d3-6314abd3-6827b2d3-1655acd3-
     ------------------------------------------------------------------------
     6560bcd3-7863c2d3-1086ad4-8490bd4+9606cd4-7632d5-11524a2c2e-4286abc2e+
     ------------------------------------------------------------------------
     15656b2c2e-9220ac3e+7614bc3e-8484c4e-666b3de+5254a2cde-7106abcde-
     ------------------------------------------------------------------------
     3454b2cde-12648ac2de+2249bc2de-1188c3de-9244a2d2e+2202abd2e+5372b2d2e-
     ------------------------------------------------------------------------
     5402acd2e+784bcd2e+7891c2d2e+15200ad3e+7827bd3e-13670cd3e-1404d4e+
     ------------------------------------------------------------------------
     15198b3e2-14480a2ce2-228abce2-8133b2ce2-742ac2e2-13442bc2e2-15033c3e2+
     ------------------------------------------------------------------------
     8311a2de2+6514abde2-2679b2de2-5952acde2-14760bcde2+14886c2de2+1369ad2e2+
     ------------------------------------------------------------------------
     14628bd2e2-4679cd2e2-6495d3e2-2253a2e3-15147abe3-15895b2e3-7925ace3+
     ------------------------------------------------------------------------
     8205bce3+714c2e3-14262ade3+10320bde3+2365cde3-15590d2e3+13581ae4+1456be4
     ------------------------------------------------------------------------
     +9337ce4+9403de4+13453e5
     ------------------------------------------------------------------------
     a2c3-5116b2c3+7244ac4+136bc4-7831c5+11220a2c2d-3421abc2d+2182b2c2d-
     ------------------------------------------------------------------------
     10801ac3d-10160bc3d+9435c4d-7316b3d2-2004a2cd2-6131abcd2-5162b2cd2+
     ------------------------------------------------------------------------
     10932ac2d2+15579bc2d2-6519c3d2+15390a2d3-10257abd3-4979b2d3-10462acd3+
     ------------------------------------------------------------------------
     11734bcd3+9817c2d3-4146ad4-8662bd4+12542cd4-12534d5+15805a2c2e+7983abc2e
     ------------------------------------------------------------------------
     -9091b2c2e-8317ac3e-8979bc3e-4171c4e-8394b3de+6446a2cde+4497abcde+
     ------------------------------------------------------------------------
     836b2cde+12749ac2de-8511bc2de+6641c3de-7238a2d2e+8232abd2e+9710b2d2e+
     ------------------------------------------------------------------------
     1502acd2e+13588bcd2e+460c2d2e+2906ad3e+12322bd3e+3756cd3e-10824d4e-
     ------------------------------------------------------------------------
     13898b3e2-11263a2ce2-7435abce2-12668b2ce2-13766ac2e2-10006bc2e2+
     ------------------------------------------------------------------------
     12211c3e2+1824a2de2-11521abde2+15375b2de2-11561acde2-12906bcde2-
     ------------------------------------------------------------------------
     9132c2de2+5387ad2e2-5449bd2e2-3320cd2e2-15815d3e2-9373a2e3+10305abe3-
     ------------------------------------------------------------------------
     9123b2e3+4270ace3+10677bce3-10286c2e3-7198ade3+9814bde3+13273cde3-
     ------------------------------------------------------------------------
     9582d2e3-5457ae4-11784be4-96ce4+10226de4+15844e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R