next | previous | forward | backward | up | top | index | toc | Macaulay2 web site

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 (11850a  - 4820a b - 1957a*b  + 2975b  + 7392a c + 12323a*b*c +
     ------------------------------------------------------------------------
          2           2          2        3        2                       2 
     4539b c - 3409a*c  + 1425b*c  + 6116c  + 1993a d - 13107a*b*d - 11649b d
     ------------------------------------------------------------------------
                                      2           2          2          2  
     - 10944a*c*d - 14186b*c*d + 6908c d + 6446a*d  - 3642b*d  - 7346c*d  +
     ------------------------------------------------------------------------
          3         2                     2                           
     8525d  + 15597a e - 6571a*b*e + 4944b e + 5794a*c*e + 5296b*c*e -
     ------------------------------------------------------------------------
           2                                              2            2  
     13552c e + 7783a*d*e - 10461b*d*e + 7377c*d*e - 9706d e - 13083a*e  -
     ------------------------------------------------------------------------
             2          2           2         3          3      2   
     14926b*e  - 5410c*e  - 13138d*e  - 14393e , - 10361a  + 24a b +
     ------------------------------------------------------------------------
             2         3         2                     2           2  
     13375a*b  + 13150b  + 12566a c - 7810a*b*c - 4190b c + 2758a*c  -
     ------------------------------------------------------------------------
             2       3         2                      2                
     11769b*c  - 482c  - 13802a d + 15182a*b*d + 2518b d - 10538a*c*d -
     ------------------------------------------------------------------------
                      2            2          2          2         3  
     15511b*c*d - 511c d - 13429a*d  - 9197b*d  - 6932c*d  + 14943d  -
     ------------------------------------------------------------------------
          2                     2                                  2   
     8689a e + 1885a*b*e - 5899b e + 13650a*c*e + 2594b*c*e - 6721c e +
     ------------------------------------------------------------------------
                                               2           2          2  
     15045a*d*e + 8167b*d*e - 3824c*d*e + 5086d e + 5247a*e  + 4439b*e  -
     ------------------------------------------------------------------------
             2           2        3        3        2            2         3
     13943c*e  - 14468d*e  + 3197e , 14674a  - 3649a b + 14019a*b  + 10351b 
     ------------------------------------------------------------------------
            2                      2           2          2        3  
     + 2556a c + 8492a*b*c - 15767b c - 4661a*c  - 1592b*c  - 2774c  -
     ------------------------------------------------------------------------
           2                     2                                 2   
     13145a d - 4528a*b*d - 3701b d + 6232a*c*d - 1164b*c*d + 4476c d -
     ------------------------------------------------------------------------
            2          2           2        3         2               
     9377a*d  + 8767b*d  - 15869c*d  - 7492d  - 14234a e - 7488a*b*e -
     ------------------------------------------------------------------------
          2                                  2                            
     5674b e - 10563a*c*e + 8937b*c*e - 8483c e + 4077a*d*e - 14882b*d*e +
     ------------------------------------------------------------------------
                       2           2          2           2          2  
     15704c*d*e - 8722d e + 4114a*e  + 2563b*e  + 15694c*e  - 6313d*e  +
     ------------------------------------------------------------------------
          3
     9966e )

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 = | ab2-5270b3+9237a2c-15637abc+13050b2c-7999ac2-9360bc2+11316c3-9431a2d-
     ------------------------------------------------------------------------
     14401abd-9914b2d+5108acd+2761bcd-8792c2d+13374ad2-1825bd2+7001cd2+1052d3
     ------------------------------------------------------------------------
     +6484a2e+7796abe+7488b2e+14511ace+1347bce-13244c2e+14788ade-4370bde-
     ------------------------------------------------------------------------
     5687cde-15342d2e+12890ae2-12013be2+3765ce2-1973de2-5433e3
     ------------------------------------------------------------------------
     a2b-6725b3+5532a2c-12666abc+14895b2c+4438ac2-4760bc2+11588c3+6545a2d-
     ------------------------------------------------------------------------
     9787abd+14658b2d-6258acd-2873bcd+12209c2d-5946ad2+8910bd2-10294cd2+
     ------------------------------------------------------------------------
     11168d3+14066a2e-10490abe+9477b2e+10376ace+12123bce-311c2e-4758ade+
     ------------------------------------------------------------------------
     6931bde+3532cde-14826d2e+5ae2+1975be2+8659ce2+13611de2+6490e3
     ------------------------------------------------------------------------
     a3-11694b3-9584a2c+7801abc-15857b2c-10146ac2+13708bc2+8349c3-4680a2d+
     ------------------------------------------------------------------------
     12323abd-12477b2d+4687acd-9834bcd+15403c2d+3442ad2+322bd2-13367cd2-
     ------------------------------------------------------------------------
     15087d3-5184a2e-15854abe-2200b2e-3367ace+11379bce-6879c2e-9250ade-
     ------------------------------------------------------------------------
     7958bde-14993cde-4541d2e-3404ae2+5000be2+4616ce2+3435de2-6069e3
     ------------------------------------------------------------------------
     b3c+10197a2c2-6837abc2+6035b2c2-13141ac3-15151bc3-4335c4-11822b3d-
     ------------------------------------------------------------------------
     584a2cd+14162abcd+6267b2cd-4425ac2d-10954bc2d-14503c3d-13880a2d2+
     ------------------------------------------------------------------------
     12501abd2+4193b2d2-5039acd2-2223bcd2-3784c2d2-7636ad3-1008bd3+2425cd3-
     ------------------------------------------------------------------------
     9712d4-3583b3e-11412a2ce+14236abce-13239b2ce+2061ac2e-221bc2e-1943c3e+
     ------------------------------------------------------------------------
     14699a2de+8651abde-9471b2de+7451acde+4413bcde+11489c2de-395ad2e-1288bd2e
     ------------------------------------------------------------------------
     -11945cd2e-7299d3e+6035a2e2+5190abe2-483b2e2-6631ace2+13835bce2+
     ------------------------------------------------------------------------
     12185c2e2-10538ade2+10603bde2+13124cde2-4984d2e2-1666ae3-10271be3+
     ------------------------------------------------------------------------
     3746ce3-13582de3-10800e4
     ------------------------------------------------------------------------
     b4-9767a2c2-7461abc2-10985b2c2-3631ac3-4580bc3+12838c4+4237b3d-7485a2cd+
     ------------------------------------------------------------------------
     7444abcd+6091b2cd-13067ac2d+14887bc2d+3058c3d+1596a2d2+6041abd2-
     ------------------------------------------------------------------------
     15114b2d2-12442acd2-14402bcd2-1217c2d2-15576ad3-5794bd3-1971cd3+14272d4+
     ------------------------------------------------------------------------
     4980b3e+6394a2ce+7853abce-2630b2ce-4117ac2e-3653bc2e-1287c3e+638a2de+
     ------------------------------------------------------------------------
     10073abde+12909b2de+5539acde-4454bcde+5779c2de+10467ad2e+9543bd2e-
     ------------------------------------------------------------------------
     14605cd2e-10511d3e-5932a2e2-11250abe2+3065b2e2+5894ace2+8413bce2+
     ------------------------------------------------------------------------
     7468c2e2+15882ade2+10158bde2-12622cde2-5307d2e2+15434ae3+144be3+7821ce3+
     ------------------------------------------------------------------------
     13790de3+15015e4 abc3-7570b2c3-5759ac4+14612bc4+12625c5+9300a2c2d+
     ------------------------------------------------------------------------
     12804abc2d+3646b2c2d+8398ac3d-3641bc3d+5549c4d+14567b3d2+7991a2cd2+
     ------------------------------------------------------------------------
     12180abcd2+9991b2cd2-13118ac2d2+15948bc2d2+9267c3d2-4062a2d3+8742abd3+
     ------------------------------------------------------------------------
     10642b2d3+861acd3+14219bcd3-3182c2d3+7443ad4-14479bd4+12839cd4-1438d5+
     ------------------------------------------------------------------------
     14144a2c2e+14981abc2e+7987b2c2e+4615ac3e+3395bc3e+4265c4e-5117b3de-
     ------------------------------------------------------------------------
     126a2cde+6005abcde-8406b2cde-8281ac2de-52bc2de-4215c3de+10900a2d2e+
     ------------------------------------------------------------------------
     6471abd2e+1271b2d2e-725acd2e-15746bcd2e+11829c2d2e-1106ad3e-10344bd3e-
     ------------------------------------------------------------------------
     11033cd3e+9884d4e+15828b3e2+15276a2ce2-1190abce2-6172b2ce2+2682ac2e2+
     ------------------------------------------------------------------------
     11755bc2e2-15028c3e2-9065a2de2-14774abde2+6160b2de2-2046acde2-11422bcde2
     ------------------------------------------------------------------------
     -7522c2de2-7894ad2e2-6778bd2e2+1945cd2e2+12321d3e2-6015a2e3-13414abe3+
     ------------------------------------------------------------------------
     11932b2e3-12373ace3+9259bce3+1850c2e3-2691ade3+2765bde3+2133cde3+
     ------------------------------------------------------------------------
     9401d2e3-12062ae4+15936be4-493ce4-14831de4+13627e5
     ------------------------------------------------------------------------
     a2c3-3586b2c3+10509ac4-15903bc4-7326c5+12914a2c2d-11797abc2d+14939b2c2d-
     ------------------------------------------------------------------------
     6459ac3d-846bc3d-5421c4d-196b3d2-2437a2cd2-13276abcd2+14795b2cd2-
     ------------------------------------------------------------------------
     12442ac2d2+8727bc2d2+6740c3d2+9715a2d3+9195abd3+11922b2d3-2781acd3+
     ------------------------------------------------------------------------
     3771bcd3-14443c2d3-1968ad4+14860bd4+1345cd4-14789d5-8575a2c2e+9823abc2e-
     ------------------------------------------------------------------------
     12136b2c2e+600ac3e-15548bc3e+3382c4e+7786b3de-15610a2cde+3876abcde-
     ------------------------------------------------------------------------
     11904b2cde+11174ac2de+3039bc2de+203c3de+15120a2d2e-11116abd2e+9678b2d2e-
     ------------------------------------------------------------------------
     10948acd2e+14147bcd2e+5818c2d2e+10387ad3e-5824bd3e+10925cd3e-12919d4e-
     ------------------------------------------------------------------------
     12720b3e2-3488a2ce2-13579abce2+12700b2ce2-6625ac2e2+8648bc2e2+3930c3e2-
     ------------------------------------------------------------------------
     6525a2de2-9124abde2-3581b2de2-15628acde2+4483bcde2+2008c2de2-4335ad2e2-
     ------------------------------------------------------------------------
     8393bd2e2-3466cd2e2+7127d3e2+5144a2e3-8347abe3+10406b2e3+2998ace3-
     ------------------------------------------------------------------------
     8674bce3-15028c2e3+5560ade3-238bde3+762cde3-2278d2e3-8870ae4-6135be4+
     ------------------------------------------------------------------------
     9621ce4+407de4+11384e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R