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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 (- 12097a  - 5878a b - 14343a*b  + 4018b  - 11702a c + 5805a*b*c +
     ------------------------------------------------------------------------
          2            2          2       3        2                      2 
     5562b c - 13686a*c  - 1693b*c  - 509c  + 9584a d - 15040a*b*d - 1289b d
     ------------------------------------------------------------------------
                                     2            2          2           2  
     - 5649a*c*d + 9755b*c*d - 10789c d - 15295a*d  - 4104b*d  + 13421c*d  +
     ------------------------------------------------------------------------
         3        2                    2                                  2 
     607d  + 3819a e + 490a*b*e - 4795b e - 8767a*c*e + 6038b*c*e + 10849c e
     ------------------------------------------------------------------------
                                                  2            2          2  
     - 15105a*d*e - 9099b*d*e + 14705c*d*e - 8996d e - 11634a*e  + 6356b*e  +
     ------------------------------------------------------------------------
           2           2        3       3         2           2        3  
     121c*e  - 14838d*e  + 7052e , 4451a  - 14454a b - 4146a*b  - 6435b  +
     ------------------------------------------------------------------------
          2                       2           2           2         3  
     4866a c + 11674a*b*c - 15274b c + 9846a*c  - 14922b*c  + 13896c  -
     ------------------------------------------------------------------------
           2                     2                                  2   
     14183a d - 6943a*b*d - 2015b d + 15436a*c*d - 1239b*c*d + 3377c d -
     ------------------------------------------------------------------------
            2          2          2        3         2                    2 
     3161a*d  - 7774b*d  + 8013c*d  + 5611d  + 11603a e - 174a*b*e + 2123b e
     ------------------------------------------------------------------------
                                    2                                        
     + 2302a*c*e + 15708b*c*e + 234c e + 2140a*d*e + 6997b*d*e - 14552c*d*e -
     ------------------------------------------------------------------------
           2           2           2         2          2         3         3
     15575d e - 1722a*e  - 15591b*e  - 872c*e  + 6001d*e  + 10692e , - 5773a 
     ------------------------------------------------------------------------
             2           2         3        2                      2   
     - 11215a b - 5235a*b  - 11426b  - 6241a c - 4131a*b*c + 14657b c +
     ------------------------------------------------------------------------
            2          2        3        2                     2             
     2818a*c  + 6513b*c  - 7253c  - 3764a d - 442a*b*d - 10512b d + 6465a*c*d
     ------------------------------------------------------------------------
                         2           2          2          2        3  
     - 1368b*c*d + 11172c d - 3886a*d  - 3874b*d  - 2799c*d  + 2844d  -
     ------------------------------------------------------------------------
          2                       2                                 2   
     2354a e + 12250a*b*e + 12420b e + 6934a*c*e - 2394b*c*e + 9749c e -
     ------------------------------------------------------------------------
                                               2          2          2  
     4250a*d*e - 6387b*d*e + 1534c*d*e + 11800d e - 419a*e  + 4197b*e  -
     ------------------------------------------------------------------------
            2          2        3
     2190c*e  - 2212d*e  + 6491e )

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+10111b3+14387a2c+6271abc-213b2c-12587ac2-14604bc2+14454c3-984a2d-
     ------------------------------------------------------------------------
     7759abd-8830b2d-13525acd+1955bcd+13292c2d+9157ad2-14397bd2-4408cd2+
     ------------------------------------------------------------------------
     9137d3+4951a2e-12625abe-14546b2e+11457ace+7009bce-12460c2e-11248ade+
     ------------------------------------------------------------------------
     8643bde+4930cde-14429d2e+8964ae2+9489be2-3946ce2-5950de2-10051e3
     ------------------------------------------------------------------------
     a2b-2987b3+5747a2c+12648abc+1459b2c-10395ac2-13917bc2-9811c3-11600a2d-
     ------------------------------------------------------------------------
     8672abd-7488b2d+4497acd-11233bcd-4656c2d+4591ad2-10525bd2+14754cd2+
     ------------------------------------------------------------------------
     1346d3-13228a2e-9981abe-12633b2e+9303ace+643bce-7357c2e-8081ade+10177bde
     ------------------------------------------------------------------------
     +2686cde+7123d2e-14674ae2-12412be2+15208ce2-13936de2-5718e3
     ------------------------------------------------------------------------
     a3+328b3-9048a2c+5588abc-11203b2c+9849ac2+14517bc2+4651c3-9002a2d-
     ------------------------------------------------------------------------
     2366abd-4752b2d-13752acd+8613bcd+5538c2d+14493ad2-3911bd2-6293cd2-7170d3
     ------------------------------------------------------------------------
     +7610a2e-7409abe-11763b2e+9915ace-9700bce+9707c2e+3481ade-12983bde+
     ------------------------------------------------------------------------
     1232cde-5678d2e-12656ae2-453be2+6215ce2+1375de2+6052e3
     ------------------------------------------------------------------------
     b3c-6499a2c2+4652abc2-4180b2c2-4515ac3+6254bc3+74c4+13531b3d+8993a2cd+
     ------------------------------------------------------------------------
     15985abcd+10700b2cd-12815ac2d-6887bc2d-15262c3d-7416a2d2+3142abd2+
     ------------------------------------------------------------------------
     10593b2d2-14286acd2-5730bcd2-6468c2d2+5229ad3+5366bd3+13484cd3-2390d4-
     ------------------------------------------------------------------------
     2643b3e-10944a2ce+14934abce-9390b2ce-10943ac2e+1263bc2e+8584c3e-9097a2de
     ------------------------------------------------------------------------
     -12085abde+3489b2de+5872acde+14044bcde-9493c2de-6714ad2e+14697bd2e-
     ------------------------------------------------------------------------
     13509cd2e+10456d3e-8907a2e2+3575abe2-13712b2e2+2626ace2+13695bce2+
     ------------------------------------------------------------------------
     3178c2e2-15203ade2+8304bde2+7173cde2-3413d2e2-1587ae3+9719be3+10150ce3-
     ------------------------------------------------------------------------
     5413de3+8948e4 b4-14126a2c2+13493abc2-14263b2c2-12036ac3+208bc3-8695c4-
     ------------------------------------------------------------------------
     12997b3d+8191a2cd+6934abcd-13457b2cd+8891ac2d-12672bc2d+9235c3d+3192a2d2
     ------------------------------------------------------------------------
     +15839abd2+15052b2d2-12719acd2-3283bcd2-13954c2d2-10326ad3-9238bd3-
     ------------------------------------------------------------------------
     1634cd3+9008d4+11579b3e-388a2ce-5231abce+14978b2ce-5848ac2e+14769bc2e-
     ------------------------------------------------------------------------
     2840c3e+7276a2de-7219abde-10026b2de+5493acde+4773bcde+14567c2de-6177ad2e
     ------------------------------------------------------------------------
     -13246bd2e+11792cd2e+12677d3e-15433a2e2+15301abe2-3297b2e2+4978ace2-
     ------------------------------------------------------------------------
     11692bce2-5806c2e2+2912ade2+8288bde2+5590cde2+1959d2e2+12545ae3-7910be3-
     ------------------------------------------------------------------------
     7430ce3+12341de3+3615e4
     ------------------------------------------------------------------------
     abc3-2047b2c3-9225ac4-1266bc4-12686c5-6544a2c2d+3031abc2d-8171b2c2d+
     ------------------------------------------------------------------------
     5436ac3d+833bc3d+821c4d-10608b3d2-3410a2cd2-10805abcd2+13645b2cd2-
     ------------------------------------------------------------------------
     8977ac2d2-12323bc2d2+2253c3d2+13512a2d3+7464abd3-2363b2d3+10650acd3+
     ------------------------------------------------------------------------
     1667bcd3+14472c2d3+11809ad4-4023bd4-13175cd4+8964d5-4835a2c2e+3638abc2e+
     ------------------------------------------------------------------------
     4003b2c2e-13297ac3e+2806bc3e+2863c4e-12463b3de-15367a2cde+15220abcde-
     ------------------------------------------------------------------------
     9213b2cde+11564ac2de+6237bc2de+7928c3de+7714a2d2e+5915abd2e+10790b2d2e+
     ------------------------------------------------------------------------
     7833acd2e+7585bcd2e+15806c2d2e+411ad3e-14691bd3e-8548cd3e+7469d4e+
     ------------------------------------------------------------------------
     10700b3e2-5563a2ce2-2955abce2+5491b2ce2-11259ac2e2-3797bc2e2-9091c3e2-
     ------------------------------------------------------------------------
     8378a2de2-288abde2+10781b2de2+10770acde2+5381bcde2+11471c2de2+3396ad2e2-
     ------------------------------------------------------------------------
     12035bd2e2+15553cd2e2-9111d3e2-1342a2e3-14911abe3+8457b2e3+3081ace3+
     ------------------------------------------------------------------------
     12024bce3+8855c2e3+9432ade3+480bde3-3783cde3-4012d2e3-1574ae4-14337be4+
     ------------------------------------------------------------------------
     14367ce4-11431de4+7179e5
     ------------------------------------------------------------------------
     a2c3+9118b2c3+15457ac4-9656bc4-5110c5-1876a2c2d+7362abc2d-14724b2c2d+
     ------------------------------------------------------------------------
     4938ac3d-3359bc3d+15116c4d-11514b3d2-4483a2cd2-14618abcd2-12360b2cd2-
     ------------------------------------------------------------------------
     15910ac2d2+2396bc2d2+4345c3d2-12636a2d3+13233abd3+10984b2d3-7702acd3+
     ------------------------------------------------------------------------
     10457bcd3+11799c2d3-5945ad4+13219bd4+6697cd4-13915d5-14747a2c2e+
     ------------------------------------------------------------------------
     7147abc2e+4171b2c2e-3737ac3e-5872bc3e+13851c4e+1562b3de+1946a2cde-
     ------------------------------------------------------------------------
     11267abcde+13963b2cde-655ac2de-2706bc2de-10390c3de-8789a2d2e+14940abd2e+
     ------------------------------------------------------------------------
     7971b2d2e-2654acd2e+10275bcd2e+6665c2d2e+11720ad3e+4076bd3e-1601cd3e+
     ------------------------------------------------------------------------
     3304d4e+6530b3e2-440a2ce2+431abce2-3385b2ce2-2251ac2e2+10697bc2e2+
     ------------------------------------------------------------------------
     15882c3e2+2178a2de2-13097abde2+14277b2de2+9058acde2+4862bcde2+1782c2de2+
     ------------------------------------------------------------------------
     6756ad2e2-9423bd2e2+6521cd2e2-14449d3e2+3567a2e3+15633abe3-5183b2e3-
     ------------------------------------------------------------------------
     1698ace3-9468bce3-15760c2e3-15380ade3-15156bde3+4305cde3-5380d2e3-
     ------------------------------------------------------------------------
     13481ae4+11242be4+7342ce4+10733de4+6875e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R