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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 (8163a  + 5186a b + 6031a*b  - 11878b  + 4903a c + 7468a*b*c +
     ------------------------------------------------------------------------
           2           2           2         3         2               
     10334b c - 9078a*c  - 12669b*c  + 11428c  + 14551a d - 5433a*b*d -
     ------------------------------------------------------------------------
          2                                  2           2           2  
     6103b d + 8117a*c*d - 11636b*c*d - 4675c d - 4483a*d  + 14213b*d  -
     ------------------------------------------------------------------------
             2        3         2                     2                
     15783c*d  - 3247d  - 11097a e + 7786a*b*e + 7802b e + 15906a*c*e +
     ------------------------------------------------------------------------
                      2                                               2   
     1889b*c*e - 6771c e - 2401a*d*e - 12523b*d*e + 11313c*d*e - 7109d e -
     ------------------------------------------------------------------------
             2          2          2          2        3         3        2 
     10582a*e  - 4724b*e  + 1471c*e  + 4326d*e  + 5056e , - 3533a  - 9081a b
     ------------------------------------------------------------------------
               2         3       2                       2          2  
     - 10420a*b  + 11556b  + 933a c + 10532a*b*c - 15342b c - 659a*c  +
     ------------------------------------------------------------------------
             2         3        2                       2               
     14968b*c  - 13393c  - 5538a d + 14278a*b*d + 13225b d - 2746a*c*d +
     ------------------------------------------------------------------------
                      2           2          2           2         3  
     8588b*c*d - 3680c d + 7985a*d  + 7155b*d  + 10311c*d  - 12688d  -
     ------------------------------------------------------------------------
          2                      2                                  2   
     7182a e - 9597a*b*e - 12209b e + 2259a*c*e + 2523b*c*e - 13205c e -
     ------------------------------------------------------------------------
                                              2           2          2  
     702a*d*e + 14604b*d*e - 8399c*d*e - 2498d e + 6836a*e  - 3421b*e  +
     ------------------------------------------------------------------------
             2          2        3         3         2            2         3
     12568c*e  - 6127d*e  + 6745e , - 2516a  - 13156a b + 12710a*b  - 10570b 
     ------------------------------------------------------------------------
           2                      2           2           2         3  
     - 979a c - 8189a*b*c + 11483b c - 5979a*c  - 10866b*c  + 11552c  +
     ------------------------------------------------------------------------
          2                     2                                 2   
     6168a d - 4436a*b*d - 4160b d + 3520a*c*d + 14100b*c*d - 781c d +
     ------------------------------------------------------------------------
             2          2           2        3         2               
     13134a*d  - 6987b*d  + 10061c*d  + 2785d  - 15598a e - 3526a*b*e +
     ------------------------------------------------------------------------
           2                                 2                            
     14151b e + 8390a*c*e + 1239b*c*e + 1252c e - 6848a*d*e + 13185b*d*e +
     ------------------------------------------------------------------------
                      2           2          2          2          2  
     7932c*d*e + 6003d e + 9371a*e  + 8202b*e  - 1446c*e  + 1723d*e  -
     ------------------------------------------------------------------------
          3
     4938e )

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+4225b3+9226a2c+10512abc+3607b2c+2953ac2+7023bc2-2501c3+6826a2d+
     ------------------------------------------------------------------------
     4714abd-10338b2d+756acd-11852bcd+3795c2d+9773ad2-9178bd2+13769cd2-8887d3
     ------------------------------------------------------------------------
     +14293a2e-413abe-9793b2e-3438ace+7264bce-12037c2e-4890ade-6003bde+118cde
     ------------------------------------------------------------------------
     -7883d2e+6813ae2-10636be2-12439ce2-13671de2+6450e3
     ------------------------------------------------------------------------
     a2b+15491b3-3629a2c+3311abc-11606b2c-8134ac2-3701bc2-15636c3+3214a2d+
     ------------------------------------------------------------------------
     4053abd+5542b2d-7259acd+688bcd-15467c2d-15154ad2-11956bd2-2835cd2-3593d3
     ------------------------------------------------------------------------
     +13522a2e-10939abe-7287b2e-2492ace-12051bce-11865c2e+1505ade+12339bde+
     ------------------------------------------------------------------------
     907cde-9282d2e-15307ae2+14979be2+5620ce2-7523de2-3888e3
     ------------------------------------------------------------------------
     a3+6489b3+2480a2c-15938abc+9034b2c+7705ac2+15454bc2-11599c3+10704a2d-
     ------------------------------------------------------------------------
     6027abd+1223b2d+3666acd+2006bcd-12561c2d-10347ad2+2660bd2-172cd2+15168d3
     ------------------------------------------------------------------------
     +14580a2e-15048abe+4997b2e-8538ace-3258bce-11664c2e+3860ade+13586bde-
     ------------------------------------------------------------------------
     7813cde+11038d2e+13750ae2+13839be2-743ce2-3840de2+11576e3
     ------------------------------------------------------------------------
     b3c-1574a2c2+1247abc2+37b2c2-9415ac3-4779bc3-4928c4-330b3d+3160a2cd+
     ------------------------------------------------------------------------
     14958abcd+14128b2cd-6123ac2d+45bc2d+6514c3d+12339a2d2-6034abd2-1755b2d2-
     ------------------------------------------------------------------------
     12934acd2-12107bcd2+1541c2d2-15186ad3-5288bd3+14335cd3-15793d4+11451b3e-
     ------------------------------------------------------------------------
     7095a2ce+562abce+13780b2ce-10929ac2e-14045bc2e+15926c3e-11150a2de+
     ------------------------------------------------------------------------
     11782abde+13719b2de-12849acde-7171bcde-11119c2de-15103ad2e+1395bd2e+
     ------------------------------------------------------------------------
     12105cd2e+693d3e+1609a2e2-8076abe2-4807b2e2-15616ace2-11333bce2+6426c2e2
     ------------------------------------------------------------------------
     -1051ade2+3973bde2+15905cde2+10511d2e2+1041ae3-928be3-9818ce3+7022de3-
     ------------------------------------------------------------------------
     3362e4 b4-14343a2c2+6613abc2-8247b2c2-8226ac3+4092bc3+10663c4+4689b3d-
     ------------------------------------------------------------------------
     12880a2cd+14083abcd-1290b2cd-13988ac2d+13485bc2d-3177c3d+8353a2d2-
     ------------------------------------------------------------------------
     5589abd2-6569b2d2+13130acd2-3457bcd2-15931c2d2+8697ad3-5919bd3+5527cd3+
     ------------------------------------------------------------------------
     3593d4-1359b3e+9492a2ce-10935abce-10734b2ce-1573ac2e+8172bc2e+8376c3e-
     ------------------------------------------------------------------------
     12544a2de+9138abde+6072b2de+7572acde-2454bcde+15936c2de-10335ad2e+
     ------------------------------------------------------------------------
     7676bd2e-11069cd2e+9736d3e-2875a2e2-8725abe2-13516b2e2-13672ace2-
     ------------------------------------------------------------------------
     15311bce2-5417c2e2+15875ade2-89bde2+370cde2-11896d2e2-1893ae3-15649be3+
     ------------------------------------------------------------------------
     8570ce3-1781de3+5523e4 abc3-13161b2c3+12901ac4+686bc4+12710c5+4493a2c2d-
     ------------------------------------------------------------------------
     15685abc2d-6347b2c2d+11995ac3d+3237bc3d-5232c4d+4009b3d2+9208a2cd2+
     ------------------------------------------------------------------------
     785abcd2-6902b2cd2-13274ac2d2+13477bc2d2-14287c3d2-11641a2d3+2717abd3+
     ------------------------------------------------------------------------
     6862b2d3-3687acd3+9858bcd3+372c2d3+6098ad4+6939bd4-11366cd4-2228d5+
     ------------------------------------------------------------------------
     4418a2c2e+11174abc2e+4896b2c2e+2229ac3e-6299bc3e-9593c4e+10442b3de+
     ------------------------------------------------------------------------
     1059a2cde-5628abcde+15405b2cde+2806ac2de-1129bc2de+14032c3de+7146a2d2e+
     ------------------------------------------------------------------------
     6763abd2e+10015b2d2e+4831acd2e-6324bcd2e-4343c2d2e+12759ad3e+2735bd3e+
     ------------------------------------------------------------------------
     6575cd3e-3545d4e+11503b3e2-10310a2ce2-4963abce2+11202b2ce2+4612ac2e2+
     ------------------------------------------------------------------------
     3182bc2e2-9479c3e2-12204a2de2+3982abde2+5528b2de2-13024acde2-1148bcde2-
     ------------------------------------------------------------------------
     11033c2de2-8953ad2e2+8663bd2e2-1134cd2e2+6696d3e2-928a2e3-1516abe3-
     ------------------------------------------------------------------------
     6112b2e3+989ace3+10716bce3+5521c2e3-13309ade3-9165bde3-13020cde3-
     ------------------------------------------------------------------------
     1489d2e3+9280ae4-4046be4-14921ce4-1436de4-6862e5
     ------------------------------------------------------------------------
     a2c3+14320b2c3+1617ac4+6491bc4+14359c5-14872a2c2d-2682abc2d+2786b2c2d-
     ------------------------------------------------------------------------
     8762ac3d-5165bc3d+15065c4d-3886b3d2-14092a2cd2+9668abcd2-258b2cd2+
     ------------------------------------------------------------------------
     14488ac2d2-3266bc2d2-5718c3d2+1515a2d3+14068abd3-13325b2d3+14485acd3+
     ------------------------------------------------------------------------
     2182bcd3+8365c2d3-10439ad4+14443bd4-7123cd4+9332d5-14275a2c2e+4013abc2e+
     ------------------------------------------------------------------------
     8217b2c2e-375ac3e+2649bc3e-8191c4e+6825b3de-2659a2cde-1535abcde-
     ------------------------------------------------------------------------
     15988b2cde-11647ac2de+6671bc2de-8118c3de+6930a2d2e-10195abd2e+8048b2d2e-
     ------------------------------------------------------------------------
     10596acd2e-680bcd2e+1716c2d2e+4235ad3e+5988bd3e-1362cd3e+9407d4e+
     ------------------------------------------------------------------------
     4500b3e2-3137a2ce2+13141abce2+8653b2ce2+2963ac2e2+9334bc2e2-249c3e2+
     ------------------------------------------------------------------------
     4651a2de2+2598abde2+3952b2de2-5602acde2+216bcde2+9773c2de2+3748ad2e2+
     ------------------------------------------------------------------------
     9654bd2e2-15638cd2e2+11294d3e2+13615a2e3+2684abe3-2967b2e3-5017ace3-
     ------------------------------------------------------------------------
     8825bce3-8936c2e3-9230ade3-2415bde3+5196cde3-11697d2e3-2255ae4+15247be4+
     ------------------------------------------------------------------------
     14481ce4-10858de4-7259e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R