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Macaulay2Doc :: fine control of a Groebner basis computation

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 (- 5040a  - 8529a b + 15952a*b  - 1112b  + 3557a c + 5219a*b*c +
     ------------------------------------------------------------------------
           2           2          2        3        2                      2 
     12188b c - 8203a*c  + 4410b*c  + 4230c  - 3106a d + 13319a*b*d - 3157b d
     ------------------------------------------------------------------------
                                     2          2           2          2  
     + 3065a*c*d + 15288b*c*d - 3697c d - 495a*d  + 13638b*d  - 9168c*d  +
     ------------------------------------------------------------------------
          3         2                      2                            
     1070d  + 11344a e - 11410a*b*e + 3716b e + 8902a*c*e - 10859b*c*e -
     ------------------------------------------------------------------------
           2                                              2            2  
     15517c e + 15187a*d*e - 10287b*d*e + 693c*d*e + 1606d e + 11391a*e  -
     ------------------------------------------------------------------------
             2           2          2        3       3       2           2  
     13064b*e  + 11343c*e  - 5539d*e  + 7607e , 6567a  - 262a b + 9118a*b  -
     ------------------------------------------------------------------------
          3        2                     2           2          2        3  
     8831b  - 7302a c + 3735a*b*c + 4956b c - 6448a*c  - 7715b*c  + 3461c  +
     ------------------------------------------------------------------------
           2                      2                                    2   
     15638a d - 1026a*b*d - 14248b d - 13273a*c*d + 14485b*c*d + 11959c d +
     ------------------------------------------------------------------------
             2        2          2        3        2                      2 
     10707a*d  + 94b*d  + 6456c*d  + 8027d  - 5567a e + 14753a*b*e - 4312b e
     ------------------------------------------------------------------------
                                      2                             
     - 14405a*c*e - 12181b*c*e + 6080c e + 12285a*d*e - 11942b*d*e +
     ------------------------------------------------------------------------
                       2            2          2          2          2  
     9809c*d*e - 15045d e - 11961a*e  - 4771b*e  + 9285c*e  + 5982d*e  -
     ------------------------------------------------------------------------
           3          3         2           2      3        2                
     10381e , - 15987a  - 14402a b - 6551a*b  - 73b  + 2143a c - 15306a*b*c +
     ------------------------------------------------------------------------
          2            2           2        3         2               
     2565b c - 14217a*c  - 12524b*c  - 3128c  - 13151a d - 7121a*b*d -
     ------------------------------------------------------------------------
          2                                  2            2          2  
     9625b d + 664a*c*d + 10219b*c*d - 10493c d + 13093a*d  - 4946b*d  +
     ------------------------------------------------------------------------
            2         3        2                      2               
     9378c*d  - 10584d  + 9877a e - 7676a*b*e - 11965b e + 8673a*c*e +
     ------------------------------------------------------------------------
                       2                                             2   
     10645b*c*e - 6925c e + 46a*d*e + 14288b*d*e - 7855c*d*e + 12389d e +
     ------------------------------------------------------------------------
            2          2          2           2         3
     8293a*e  - 5165b*e  - 1245c*e  + 15192d*e  + 13371e )

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+10325b3+4766a2c-1668abc+3265b2c+14954ac2-4311bc2+13103c3+7282a2d+
     ------------------------------------------------------------------------
     11159abd+8114b2d+14406acd-7242bcd+12231c2d-15871ad2+744bd2+15466cd2+
     ------------------------------------------------------------------------
     11980d3+3305a2e-10821abe+7604b2e+11194ace-6769bce+11666c2e-14231ade+
     ------------------------------------------------------------------------
     2372bde-12298cde-4018d2e-10505ae2+2063be2+12592ce2+13439de2-9855e3
     ------------------------------------------------------------------------
     a2b-11474b3-2120a2c-2685abc-11398b2c-6162ac2+3644bc2-11528c3+7544a2d-
     ------------------------------------------------------------------------
     10476abd-15989b2d-8158acd-8412bcd-3269c2d-4024ad2-15914bd2+687cd2-
     ------------------------------------------------------------------------
     13006d3+8530a2e+457abe+12317b2e-1830ace+3196bce-9962c2e+6379ade-14872bde
     ------------------------------------------------------------------------
     -10205cde-5129d2e-534ae2+2927be2-11284ce2+6303de2-8033e3
     ------------------------------------------------------------------------
     a3+6594b3+15719a2c-6007abc-13038b2c-9694ac2+11086bc2+12683c3+10295a2d+
     ------------------------------------------------------------------------
     13479abd-12676b2d-6275acd+9522bcd-9411c2d-3883ad2+15491bd2+6269cd2+
     ------------------------------------------------------------------------
     2220d3-15419a2e+7428abe+15586b2e-793ace+8798bce-8373c2e-14122ade+
     ------------------------------------------------------------------------
     12783bde+11923cde+10484d2e+15625ae2+9586be2+3330ce2+8630de2-15250e3
     ------------------------------------------------------------------------
     b3c-7795a2c2-10415abc2+199b2c2-4110ac3+14249bc3-11396c4+3279b3d-5002a2cd
     ------------------------------------------------------------------------
     -12925abcd+12193b2cd+11403ac2d+475bc2d-5919c3d-9300a2d2+11151abd2+
     ------------------------------------------------------------------------
     11111b2d2-3835acd2-8960bcd2+7249c2d2+4242ad3-2452bd3-10522cd3-13237d4+
     ------------------------------------------------------------------------
     3790b3e+15471a2ce-13154abce-5477b2ce+3919ac2e-3945bc2e+14530c3e-7736a2de
     ------------------------------------------------------------------------
     -7987abde-7975b2de-14091acde+10754bcde+7238c2de-15005ad2e-12308bd2e+
     ------------------------------------------------------------------------
     7935cd2e+10561d3e+11505a2e2-4193abe2-5784b2e2-6291ace2+2198bce2+3290c2e2
     ------------------------------------------------------------------------
     +3744ade2+13273bde2-1533cde2-7508d2e2+10666ae3-3055be3-7891ce3+8298de3+
     ------------------------------------------------------------------------
     1121e4 b4+557a2c2+9891abc2-11653b2c2-1606ac3-6106bc3+1753c4-6231b3d-
     ------------------------------------------------------------------------
     7303a2cd-11393abcd-472b2cd-4059ac2d+1935bc2d+15985c3d-10421a2d2+3221abd2
     ------------------------------------------------------------------------
     +1828b2d2+2187acd2+10615bcd2-4184c2d2+10310ad3+14397bd3+3531cd3-11872d4-
     ------------------------------------------------------------------------
     14841b3e+7625a2ce-15888abce+7069b2ce-3050ac2e-13206bc2e+13729c3e+
     ------------------------------------------------------------------------
     14966a2de+8921abde-3499b2de-7453acde+14014bcde-4798c2de+12453ad2e+
     ------------------------------------------------------------------------
     5132bd2e+7537cd2e+14160d3e-1217a2e2+13648abe2-11000b2e2+7788ace2+
     ------------------------------------------------------------------------
     15878bce2-3928c2e2-13497ade2+11266bde2+6898cde2-7582d2e2+5994ae3-4992be3
     ------------------------------------------------------------------------
     -8763ce3+3618de3+5401e4
     ------------------------------------------------------------------------
     abc3+1290b2c3+14469ac4+13274bc4-14095c5-3993a2c2d-7586abc2d+397b2c2d-
     ------------------------------------------------------------------------
     6103ac3d+3461bc3d+6400c4d-15466b3d2-9836a2cd2+3669abcd2-12611b2cd2+
     ------------------------------------------------------------------------
     5711ac2d2+4159bc2d2-11349c3d2+8110a2d3-7168abd3+7931b2d3-3022acd3+
     ------------------------------------------------------------------------
     14588bcd3+14915c2d3+9903ad4-8195bd4-9322cd4+4017d5+15881a2c2e-14635abc2e
     ------------------------------------------------------------------------
     +13282b2c2e-12584ac3e-8596bc3e-6459c4e+14812b3de+10247a2cde+12584abcde+
     ------------------------------------------------------------------------
     5328b2cde-12628ac2de-10485bc2de-13985c3de-2935a2d2e-11623abd2e+
     ------------------------------------------------------------------------
     11559b2d2e+5747acd2e+12619bcd2e+5207c2d2e+14590ad3e+4999bd3e+13267cd3e-
     ------------------------------------------------------------------------
     13507d4e-14017b3e2+7588a2ce2+9762abce2-2393b2ce2-7376ac2e2-5689bc2e2+
     ------------------------------------------------------------------------
     6780c3e2+2418a2de2-6806abde2+11186b2de2+6993acde2-2995bcde2+9411c2de2+
     ------------------------------------------------------------------------
     10975ad2e2-9775bd2e2-2270cd2e2-3655d3e2+10736a2e3-4268abe3+5404b2e3+
     ------------------------------------------------------------------------
     5760ace3-6847bce3+11719c2e3-13566ade3-14305bde3+8484cde3-10428d2e3+
     ------------------------------------------------------------------------
     14679ae4-2562be4+12028ce4+8927de4+6242e5
     ------------------------------------------------------------------------
     a2c3-5638b2c3-15715ac4-3552bc4-10402c5+9450a2c2d+2420abc2d+3634b2c2d+
     ------------------------------------------------------------------------
     5896ac3d+4624bc3d-4228c4d-3744b3d2+5031a2cd2-15949abcd2+13735b2cd2-
     ------------------------------------------------------------------------
     6547ac2d2+15146bc2d2+8734c3d2-3397a2d3+8374abd3+9504b2d3+4242acd3+
     ------------------------------------------------------------------------
     13986bcd3+7770c2d3+6257ad4-8135bd4+13714cd4-9958d5+2167a2c2e+5743abc2e-
     ------------------------------------------------------------------------
     6447b2c2e+10530ac3e-9482bc3e+6837c4e+11198b3de+11422a2cde-5525abcde+
     ------------------------------------------------------------------------
     1334b2cde+6683ac2de-9584bc2de+7288c3de-6478a2d2e+10402abd2e-12927b2d2e+
     ------------------------------------------------------------------------
     3199acd2e+8056bcd2e-12076c2d2e+6001ad3e+12161bd3e-14219cd3e-5017d4e+
     ------------------------------------------------------------------------
     13332b3e2-9246a2ce2-5716abce2-8473b2ce2-7574ac2e2+14459bc2e2-7951c3e2+
     ------------------------------------------------------------------------
     1983a2de2-3106abde2+4903b2de2+13949acde2+14558bcde2-765c2de2-10907ad2e2-
     ------------------------------------------------------------------------
     1855bd2e2-4049cd2e2+9120d3e2+9205a2e3+4636abe3+2091b2e3+1774ace3+
     ------------------------------------------------------------------------
     15297bce3+2942c2e3+3369ade3+5626bde3+9964cde3-12213d2e3+12853ae4+1282be4
     ------------------------------------------------------------------------
     -1093ce4+9359de4-15791e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R