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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 (- 7277a  - 2891a b - 2798a*b  + 390b  + 4860a c - 4830a*b*c +
     ------------------------------------------------------------------------
          2           2          2        3         2                
     7789b c + 5210a*c  + 5602b*c  + 5627c  + 10692a d - 14494a*b*d -
     ------------------------------------------------------------------------
           2                                   2            2         2  
     14753b d + 13335a*c*d - 10582b*c*d - 3688c d + 15843a*d  + 779b*d  +
     ------------------------------------------------------------------------
             2        3         2                      2               
     11418c*d  - 6423d  - 13230a e - 15738a*b*e + 9072b e - 5062a*c*e -
     ------------------------------------------------------------------------
                        2                                              2   
     15065b*c*e - 15792c e + 4852a*d*e + 14927b*d*e - 1998c*d*e + 4048d e -
     ------------------------------------------------------------------------
            2          2           2           2         3       3        2 
     7998a*e  + 7708b*e  - 15388c*e  - 12964d*e  + 14501e , 9239a  + 8982a b
     ------------------------------------------------------------------------
              2         3        2                     2           2  
     + 8506a*b  + 13287b  - 8594a c - 8927a*b*c - 9165b c - 8147a*c  +
     ------------------------------------------------------------------------
             2         3        2                      2               
     10584b*c  + 12163c  + 4914a d - 3191a*b*d + 10214b d - 7095a*c*d -
     ------------------------------------------------------------------------
                      2            2          2          2        3  
     4052b*c*d - 1154c d - 13422a*d  + 6454b*d  - 9704c*d  + 9455d  -
     ------------------------------------------------------------------------
           2                      2                                 2   
     10176a e - 6180a*b*e + 11493b e - 2047a*c*e + 3806b*c*e + 1504c e -
     ------------------------------------------------------------------------
                                               2           2          2  
     8946a*d*e + 12865b*d*e - 2513c*d*e + 7360d e + 5290a*e  - 4067b*e  +
     ------------------------------------------------------------------------
            2          2        3       3        2           2         3  
     3583c*e  - 5630d*e  - 5442e , 6519a  + 3585a b + 3330a*b  + 15229b  +
     ------------------------------------------------------------------------
           2                    2           2          2        3        2   
     10378a c - 717a*b*c - 8935b c + 7456a*c  - 4649b*c  - 3001c  - 8142a d +
     ------------------------------------------------------------------------
                       2                                2            2  
     6636a*b*d - 10546b d + 5348a*c*d - 171b*c*d - 8041c d + 10975a*d  -
     ------------------------------------------------------------------------
           2          2         3        2                       2   
     891b*d  - 8599c*d  + 13721d  + 1186a e - 13076a*b*e - 10160b e +
     ------------------------------------------------------------------------
                                  2                                       
     7751a*c*e + 9486b*c*e - 2832c e - 1541a*d*e - 2903b*d*e + 6009c*d*e -
     ------------------------------------------------------------------------
          2            2          2          2          2        3
     4159d e + 12180a*e  - 1034b*e  + 8303c*e  - 8948d*e  + 1636e )

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 = | ab2-4041b3-3833a2c-5320abc-14904b2c+2459ac2-568bc2-2070c3-6651a2d-
     ------------------------------------------------------------------------
     11284abd+1658b2d-710acd+1161bcd+15725c2d-1965ad2+585bd2-7707cd2-9120d3-
     ------------------------------------------------------------------------
     2726a2e+4443abe+5871b2e-1674ace-15377bce+1372c2e-11355ade-4954bde-
     ------------------------------------------------------------------------
     3126cde-14510d2e-6353ae2-14688be2-5741ce2+15736de2+9064e3
     ------------------------------------------------------------------------
     a2b-13789b3-11116a2c+2943abc+14941b2c-469ac2-3425bc2-14519c3-10444a2d-
     ------------------------------------------------------------------------
     5826abd+8334b2d+3967acd-2998bcd+914c2d+3995ad2-12845bd2+4439cd2+1884d3+
     ------------------------------------------------------------------------
     9322a2e-12243abe+6361b2e-11800ace-11960bce+13519c2e-12749ade+13930bde-
     ------------------------------------------------------------------------
     8768cde+491d2e+5261ae2-14913be2+13937ce2+10888de2+7690e3
     ------------------------------------------------------------------------
     a3+14706b3-11790a2c+11423abc-1508b2c+5164ac2+5035bc2+13116c3+3499a2d-
     ------------------------------------------------------------------------
     6657abd+14696b2d-7066acd+11468bcd+8469c2d-6032ad2+11787bd2-13297cd2-
     ------------------------------------------------------------------------
     6881d3-371a2e+14746abe-14373b2e-7549ace-2356bce-5043c2e+10710ade-
     ------------------------------------------------------------------------
     12018bde+2988cde+7534d2e+15214ae2+11747be2+8107ce2-4037de2+10130e3
     ------------------------------------------------------------------------
     b3c-3733a2c2-6256abc2-13059b2c2+10740ac3+538bc3+7657c4-13042b3d-8565a2cd
     ------------------------------------------------------------------------
     +7426abcd+7626b2cd+12263ac2d+13970bc2d+11720c3d+13032a2d2-8061abd2+
     ------------------------------------------------------------------------
     8797b2d2-848acd2+3102bcd2+6514c2d2-15656ad3+640bd3-10304cd3-7265d4-
     ------------------------------------------------------------------------
     11033b3e+413a2ce-14056abce-3362b2ce-4068ac2e-4580bc2e-1369c3e-3644a2de-
     ------------------------------------------------------------------------
     7971abde+4967b2de+15102acde+13062bcde+524c2de+12006ad2e+718bd2e-3886cd2e
     ------------------------------------------------------------------------
     +2414d3e-11518a2e2-1793abe2-14382b2e2+5423ace2+5989bce2-8960c2e2+
     ------------------------------------------------------------------------
     2116ade2-14650bde2+5175cde2+13702d2e2-7723ae3+9971be3+7196ce3-8852de3-
     ------------------------------------------------------------------------
     2599e4 b4+4577a2c2-15191abc2-15566b2c2+662ac3+7464bc3-8396c4-1056b3d-
     ------------------------------------------------------------------------
     4424a2cd+15172abcd+14012b2cd+3941ac2d+2521bc2d-4792c3d+6463a2d2+
     ------------------------------------------------------------------------
     11151abd2+3638b2d2-5093acd2+12559bcd2-4595c2d2+3198ad3+12814bd3+15794cd3
     ------------------------------------------------------------------------
     -10530d4+15243b3e+1006a2ce+11097abce+4602b2ce+15380ac2e+5591bc2e+
     ------------------------------------------------------------------------
     15920c3e+2487a2de+12647abde-15770b2de+6613acde-12873bcde-1267c2de+
     ------------------------------------------------------------------------
     13138ad2e+6624bd2e-10821cd2e-14648d3e+13570a2e2+4684abe2-2075b2e2+
     ------------------------------------------------------------------------
     6977ace2-3473bce2+14802c2e2-9518ade2+4249bde2+10203cde2+14535d2e2+
     ------------------------------------------------------------------------
     2462ae3-10572be3+7026ce3-10310de3+507e4
     ------------------------------------------------------------------------
     abc3+6514b2c3-2808ac4-15682bc4-13435c5+15743a2c2d-5806abc2d+9367b2c2d+
     ------------------------------------------------------------------------
     6020ac3d+11702bc3d+5759c4d+10294b3d2-14188a2cd2+6249abcd2-241b2cd2-
     ------------------------------------------------------------------------
     6538ac2d2+14898bc2d2-9478c3d2+1818a2d3-9160abd3+10833b2d3+5223acd3+
     ------------------------------------------------------------------------
     15804bcd3+3047c2d3+9628ad4+2506bd4-13904cd4-8306d5-2901a2c2e+115abc2e+
     ------------------------------------------------------------------------
     6278b2c2e-5323ac3e+15969bc3e-12061c4e-8149b3de+6480a2cde-10037abcde-
     ------------------------------------------------------------------------
     1084b2cde+3393ac2de-1167bc2de+12253c3de+2618a2d2e-1450abd2e-2822b2d2e+
     ------------------------------------------------------------------------
     987acd2e-14007bcd2e-7053c2d2e-6231ad3e+5072bd3e-8373cd3e+2506d4e+
     ------------------------------------------------------------------------
     9650b3e2+1270a2ce2-14011abce2+10934b2ce2+1862ac2e2+11860bc2e2-1347c3e2+
     ------------------------------------------------------------------------
     13462a2de2+2969abde2-14383b2de2-2644acde2+5510bcde2+5834c2de2+4077ad2e2+
     ------------------------------------------------------------------------
     1849bd2e2-10730cd2e2+15682d3e2-12422a2e3-6090abe3+8321b2e3+7041ace3-
     ------------------------------------------------------------------------
     11726bce3-9174c2e3+4593ade3+9187bde3-389cde3-11724d2e3+415ae4-6001be4+
     ------------------------------------------------------------------------
     12458ce4-958de4+1454e5 a2c3+8738b2c3-13048ac4-8147bc4-5507c5+1140a2c2d-
     ------------------------------------------------------------------------
     12951abc2d+1144b2c2d-1651ac3d-7638bc3d-10859c4d-1338b3d2+13508a2cd2+
     ------------------------------------------------------------------------
     2993abcd2+2260b2cd2+6080ac2d2-437bc2d2-13465c3d2+10144a2d3-7501abd3-
     ------------------------------------------------------------------------
     11618b2d3-8601acd3-4325bcd3+5713c2d3+3274ad4-8665bd4+10308cd4-7715d5-
     ------------------------------------------------------------------------
     9716a2c2e-12318abc2e-14055b2c2e-6475ac3e+11486bc3e-14139c4e-11525b3de-
     ------------------------------------------------------------------------
     3230a2cde-3806abcde-13051b2cde-6165ac2de-11405bc2de-4482c3de-9943a2d2e-
     ------------------------------------------------------------------------
     10163abd2e+4557b2d2e+1969acd2e-1336bcd2e-11212c2d2e+7704ad3e-4275bd3e-
     ------------------------------------------------------------------------
     2906cd3e-596d4e+4591b3e2+7459a2ce2+10148abce2+1133b2ce2-13799ac2e2+
     ------------------------------------------------------------------------
     10749bc2e2+12246c3e2-1424a2de2-11193abde2+854b2de2-14999acde2+8240bcde2-
     ------------------------------------------------------------------------
     4278c2de2+14202ad2e2+8978bd2e2-15665cd2e2-2862d3e2+4465a2e3-11267abe3-
     ------------------------------------------------------------------------
     14287b2e3+13844ace3-1999bce3-8094c2e3-2539ade3+13623bde3+1183cde3-
     ------------------------------------------------------------------------
     11705d2e3-8205ae4-5396be4-9804ce4-3841de4-10989e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R