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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 (- 8386a  - 15121a b + 7040a*b  + 1261b  + 2842a c - 2014a*b*c +
     ------------------------------------------------------------------------
          2          2           2       3         2                      2 
     5329b c + 907a*c  + 13613b*c  - 132c  + 15356a d - 15454a*b*d + 3251b d
     ------------------------------------------------------------------------
                                    2           2          2          2  
     + 11400a*c*d + 161b*c*d - 4216c d + 7188a*d  + 4209b*d  - 2966c*d  -
     ------------------------------------------------------------------------
          3         2                     2                           
     7562d  + 10910a e - 4791a*b*e - 3722b e + 6377a*c*e - 7420b*c*e +
     ------------------------------------------------------------------------
           2                                               2           2  
     11120c e - 15321a*d*e - 2008b*d*e - 5220c*d*e - 13892d e - 2253a*e  -
     ------------------------------------------------------------------------
         2           2          2        3      3        2           2  
     4b*e  - 10463c*e  - 3937d*e  - 6436e , 694a  + 6705a b - 9710a*b  -
     ------------------------------------------------------------------------
         3        2                       2            2          2         3
     303b  + 5715a c + 12752a*b*c + 10530b c - 13866a*c  + 2764b*c  - 13274c 
     ------------------------------------------------------------------------
            2                      2                                 2   
     - 9189a d - 8639a*b*d - 15678b d - 9862a*c*d - 217b*c*d + 13117c d +
     ------------------------------------------------------------------------
             2          2           2        3         2                
     13044a*d  - 5705b*d  + 15455c*d  + 9964d  + 10149a e - 15085a*b*e +
     ------------------------------------------------------------------------
          2                                 2                          
     8824b e - 8779a*c*e - 2712b*c*e - 3996c e + 883a*d*e + 1449b*d*e -
     ------------------------------------------------------------------------
                       2            2           2          2          2  
     8251c*d*e + 15829d e + 13049a*e  + 15183b*e  + 3284c*e  + 2900d*e  +
     ------------------------------------------------------------------------
          3         3        2          2        3       2                
     8062e , - 5088a  + 9516a b + 268a*b  + 7220b  - 100a c + 13820a*b*c +
     ------------------------------------------------------------------------
          2            2          2        3         2                     2 
     6345b c - 15380a*c  - 1161b*c  - 6045c  - 15806a d + 8534a*b*d - 9613b d
     ------------------------------------------------------------------------
                                   2            2           2           2  
     + 718a*c*d - 6619b*c*d + 3990c d - 12799a*d  + 10231b*d  - 15041c*d  +
     ------------------------------------------------------------------------
           3        2                     2                            
     11156d  + 2503a e - 11204a*b*e + 549b e + 8428a*c*e - 15248b*c*e -
     ------------------------------------------------------------------------
          2                                              2           2  
     2206c e - 5615a*d*e - 7198b*d*e - 14536c*d*e + 3336d e - 2376a*e  -
     ------------------------------------------------------------------------
            2          2           2       3
     5675b*e  - 1415c*e  - 14360d*e  + 574e )

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+7666b3+11216a2c+9097abc+13096b2c+4699ac2-15136bc2-12596c3+10228a2d
     ------------------------------------------------------------------------
     +11994abd-15153b2d+6999acd-6691bcd-4673c2d+15836ad2+13033bd2-15043cd2-
     ------------------------------------------------------------------------
     6822d3+1418a2e-798abe+3153b2e+2413ace+14801bce+10539c2e-9798ade+8231bde-
     ------------------------------------------------------------------------
     8158cde-2038d2e+14322ae2+6765be2-14353ce2-3795de2+9933e3
     ------------------------------------------------------------------------
     a2b+12462b3-13263a2c+8986abc-11855b2c-9572ac2-10900bc2-4686c3+3483a2d-
     ------------------------------------------------------------------------
     10332abd+1677b2d-9061acd-12288bcd+6092c2d+8267ad2-6427bd2-11667cd2+
     ------------------------------------------------------------------------
     5343d3-14251a2e-7233abe+3134b2e-8688ace-13897bce-12242c2e-589ade+9474bde
     ------------------------------------------------------------------------
     -9292cde+7753d2e-11245ae2+5722be2+658ce2-14228de2+15686e3
     ------------------------------------------------------------------------
     a3-5903b3+5071a2c+10691abc+11922b2c-6330ac2-12849bc2+4317c3+980a2d+
     ------------------------------------------------------------------------
     7032abd+535b2d-7810acd+14727bcd+4945c2d+7939ad2-10298bd2-1998cd2-7930d3+
     ------------------------------------------------------------------------
     5732a2e+6862abe-7087b2e-14614ace-7597bce+7763c2e-1170ade+1360bde-5427cde
     ------------------------------------------------------------------------
     -6465d2e-13106ae2-8798be2-3255ce2+6529de2-4168e3
     ------------------------------------------------------------------------
     b3c+7256a2c2+4198abc2+13857b2c2+5337ac3-8217bc3-2734c4+15314b3d-
     ------------------------------------------------------------------------
     14633a2cd+14450abcd-14275b2cd+9015ac2d+4450bc2d-2670c3d-13205a2d2+
     ------------------------------------------------------------------------
     11783abd2+7337b2d2+2135acd2+759bcd2-11758c2d2+776ad3-6733bd3+10183cd3+
     ------------------------------------------------------------------------
     5459d4-15840b3e+63a2ce-2958abce+3789b2ce+5040ac2e+960bc2e+13000c3e+
     ------------------------------------------------------------------------
     13019a2de-11858abde+7647b2de+10526acde+7548bcde+3782c2de+1144ad2e-
     ------------------------------------------------------------------------
     12484bd2e+13349cd2e+7511d3e-6106a2e2-6117abe2-1489b2e2-5014ace2-919bce2+
     ------------------------------------------------------------------------
     1957c2e2+1612ade2+15616bde2+7805cde2+3956d2e2-13484ae3+9697be3-1069ce3-
     ------------------------------------------------------------------------
     3323de3-415e4 b4+14782a2c2+3898abc2+8158b2c2-6858ac3-7164bc3-13628c4+
     ------------------------------------------------------------------------
     5336b3d+9545a2cd+9505abcd-942b2cd+10989ac2d+3852bc2d-13210c3d-1946a2d2-
     ------------------------------------------------------------------------
     5362abd2-9786b2d2+9373acd2+2065bcd2-7942c2d2+11423ad3+7370bd3+4707cd3-
     ------------------------------------------------------------------------
     1221d4+14079b3e+4688a2ce-5379abce-14127b2ce+6402ac2e-13593bc2e+12145c3e-
     ------------------------------------------------------------------------
     8006a2de-11842abde-7626b2de-6948acde+15983bcde-1638c2de+11141ad2e-
     ------------------------------------------------------------------------
     14013bd2e-14493cd2e+15477d3e+3670a2e2+13901abe2-2685b2e2+1614ace2+
     ------------------------------------------------------------------------
     8243bce2-4878c2e2+9580ade2-9043bde2-15685cde2-12045d2e2-2673ae3+5665be3+
     ------------------------------------------------------------------------
     1831ce3-12603de3-13548e4
     ------------------------------------------------------------------------
     abc3+3243b2c3+10617ac4+9540bc4-1715c5+4922a2c2d+14043abc2d+1282b2c2d-
     ------------------------------------------------------------------------
     1094ac3d+4012bc3d-288c4d+13549b3d2+10847a2cd2-15528abcd2-10835b2cd2+
     ------------------------------------------------------------------------
     5957ac2d2+6558bc2d2-11166c3d2-2872a2d3-4715abd3+10801b2d3-5432acd3+
     ------------------------------------------------------------------------
     10810bcd3-14506c2d3-3947ad4+1746bd4+13694cd4+10252d5+8341a2c2e-3697abc2e
     ------------------------------------------------------------------------
     -10419b2c2e-2072ac3e+5104bc3e+15922c4e-13421b3de+8267a2cde+7160abcde-
     ------------------------------------------------------------------------
     4977b2cde+11570ac2de+2209bc2de+237c3de-9652a2d2e+15517abd2e+4614b2d2e-
     ------------------------------------------------------------------------
     15305acd2e+15372bcd2e+15063c2d2e+6281ad3e+7298bd3e-6986cd3e-15578d4e-
     ------------------------------------------------------------------------
     14495b3e2-604a2ce2-8707abce2+7256b2ce2+13405ac2e2+5156bc2e2+15339c3e2-
     ------------------------------------------------------------------------
     10256a2de2-6175abde2-12263b2de2-13120acde2+15724bcde2+2521c2de2-
     ------------------------------------------------------------------------
     4374ad2e2-15731bd2e2+5445cd2e2+8831d3e2+4329a2e3+11403abe3-15795b2e3+
     ------------------------------------------------------------------------
     8270ace3-14179bce3-8918c2e3-5058ade3-4598bde3-942cde3-11615d2e3-14349ae4
     ------------------------------------------------------------------------
     -9396be4+14197ce4+11605de4+8619e5
     ------------------------------------------------------------------------
     a2c3+3305b2c3-8201ac4+14136bc4+12792c5+888a2c2d+2491abc2d+13814b2c2d+
     ------------------------------------------------------------------------
     726ac3d+11910bc3d+1563c4d-2487b3d2+4910a2cd2-11730abcd2-7649b2cd2+
     ------------------------------------------------------------------------
     6902ac2d2+5013bc2d2-13633c3d2+14604a2d3+7299abd3-2486b2d3+12034acd3-
     ------------------------------------------------------------------------
     12145bcd3+15517c2d3+2610ad4+2637bd4+9023cd4-9586d5+8841a2c2e-13329abc2e-
     ------------------------------------------------------------------------
     12665b2c2e-8360ac3e+4362bc3e-10244c4e+7229b3de-14777a2cde-3322abcde+
     ------------------------------------------------------------------------
     5544b2cde+10802ac2de+12667bc2de+1272c3de+8251a2d2e-2266abd2e-2824b2d2e-
     ------------------------------------------------------------------------
     2057acd2e-6380bcd2e+7170c2d2e-7208ad3e+8755bd3e+986cd3e-1274d4e+
     ------------------------------------------------------------------------
     10461b3e2-5364a2ce2-8959abce2-9654b2ce2+15041ac2e2+7031bc2e2+8186c3e2-
     ------------------------------------------------------------------------
     4712a2de2+9975abde2-5534b2de2-282acde2+14905bcde2-13010c2de2+8275ad2e2+
     ------------------------------------------------------------------------
     787bd2e2+15532cd2e2+3709d3e2-10347a2e3+5882abe3-5165b2e3-9378ace3-
     ------------------------------------------------------------------------
     15192bce3-1697c2e3-12643ade3-518bde3-3105cde3+15351d2e3-14687ae4-1054be4
     ------------------------------------------------------------------------
     -14703ce4-7528de4+14528e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R