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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 (11760a  + 10052a b + 14506a*b  + 5599b  - 8705a c + 3371a*b*c -
     ------------------------------------------------------------------------
           2           2           2         3         2                
     13032b c - 6118a*c  + 14051b*c  + 15640c  - 14774a d - 12210a*b*d -
     ------------------------------------------------------------------------
          2                                   2            2          2  
     7433b d + 14822a*c*d + 2579b*c*d - 11651c d + 13367a*d  - 2375b*d  -
     ------------------------------------------------------------------------
            2        3       2                       2               
     6039c*d  + 9121d  - 335a e - 10710a*b*e - 15700b e + 4017a*c*e +
     ------------------------------------------------------------------------
                        2                                                2   
     10446b*c*e + 15648c e + 15556a*d*e - 6254b*d*e - 14908c*d*e - 10751d e +
     ------------------------------------------------------------------------
            2          2          2           2         3        3        2 
     4799a*e  + 9010b*e  - 4205c*e  + 13399d*e  - 14860e , 14049a  - 8900a b
     ------------------------------------------------------------------------
              2        3         2                      2            2  
     - 8154a*b  + 8715b  - 14257a c + 5697a*b*c + 11659b c + 12648a*c  -
     ------------------------------------------------------------------------
            2        3        2                     2               
     4253b*c  + 7694c  + 5439a d + 4276a*b*d - 7803b d - 1799a*c*d +
     ------------------------------------------------------------------------
                       2           2           2          2        3  
     12800b*c*d - 6444c d - 1318a*d  + 13633b*d  - 5732c*d  - 6419d  +
     ------------------------------------------------------------------------
           2                      2                                  2   
     12487a e - 15244a*b*e + 6562b e - 11556a*c*e - 8057b*c*e + 5326c e -
     ------------------------------------------------------------------------
                                               2           2          2  
     10211a*d*e + 10395b*d*e + 137c*d*e + 4163d e + 8123a*e  + 4038b*e  -
     ------------------------------------------------------------------------
            2           2         3        3        2          2         3  
     9181c*e  + 11813d*e  - 12880e , 11310a  + 9569a b + 592a*b  + 11370b  +
     ------------------------------------------------------------------------
          2                      2           2           2         3  
     3723a c - 1280a*b*c - 13324b c + 2235a*c  + 13607b*c  + 15223c  -
     ------------------------------------------------------------------------
           2                     2                                  2   
     12191a d + 13217a*b*d - 948b d - 3966a*c*d + 5713b*c*d - 12215c d -
     ------------------------------------------------------------------------
             2         2          2         3        2                     2 
     13276a*d  - 958b*d  - 8439c*d  - 14359d  - 6240a e - 6598a*b*e - 1833b e
     ------------------------------------------------------------------------
                                   2                                         
     + 4166a*c*e + 48b*c*e + 15044c e - 15766a*d*e - 12988b*d*e - 3321c*d*e +
     ------------------------------------------------------------------------
          2           2          2           2          2        3
     4520d e - 7018a*e  - 4424b*e  - 10817c*e  + 5194d*e  + 3678e )

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 = | ab2-13320b3+14718a2c+5510abc-9828b2c+13613ac2-10016bc2-7898c3+2457a2d+
     ------------------------------------------------------------------------
     2925abd+15855b2d+9569acd-2875bcd+4285c2d+4090ad2-7956bd2-10254cd2+7008d3
     ------------------------------------------------------------------------
     -13601a2e+3946abe-13313b2e-14407ace-10459bce+12497c2e-362ade-13996bde+
     ------------------------------------------------------------------------
     3665cde-4008d2e+569ae2+11772be2+1880ce2-13295de2-4944e3
     ------------------------------------------------------------------------
     a2b+356b3-12674a2c+14905abc+11212b2c+446ac2+3754bc2+4020c3+12843a2d+
     ------------------------------------------------------------------------
     8865abd-7799b2d-2346acd-1788bcd+13379c2d-10928ad2+3769bd2-4716cd2+2808d3
     ------------------------------------------------------------------------
     -1777a2e+13117abe+5227b2e+2837ace+1939bce+4359c2e-11306ade-14385bde+
     ------------------------------------------------------------------------
     4560cde-11775d2e+13773ae2+6518be2-15961ce2-2175de2-11194e3
     ------------------------------------------------------------------------
     a3-3655b3-859a2c+14053abc-6562b2c-8857ac2-15217bc2-12078c3+6248a2d+
     ------------------------------------------------------------------------
     4815abd+12104b2d-14532acd+6177bcd-10945c2d-2237ad2-1983bd2-14124cd2-
     ------------------------------------------------------------------------
     4020d3+5002a2e+1799abe-14167b2e-7472ace-7870bce+8384c2e-1209ade-4169bde+
     ------------------------------------------------------------------------
     13966cde-14380d2e+2213ae2-7829be2+2754ce2-11139de2+4116e3
     ------------------------------------------------------------------------
     b3c-6343a2c2+1302abc2+6821b2c2-10498ac3+5211bc3+5341c4-9361b3d+1993a2cd+
     ------------------------------------------------------------------------
     15096abcd+7155b2cd-5175ac2d-1953bc2d-10175c3d+13060a2d2+4767abd2-
     ------------------------------------------------------------------------
     8893b2d2-6320acd2-6234bcd2+4300c2d2-11189ad3-10309bd3-436cd3-5070d4+
     ------------------------------------------------------------------------
     11309b3e+7471a2ce+5988abce-2735b2ce+3145ac2e-13245bc2e+2520c3e-15424a2de
     ------------------------------------------------------------------------
     -11950abde+14726b2de-11039acde-540bcde+8796c2de-14722ad2e-10608bd2e+
     ------------------------------------------------------------------------
     2355cd2e+11306d3e+13471a2e2-15414abe2+12455b2e2+7889ace2+8611bce2-
     ------------------------------------------------------------------------
     12302c2e2+12686ade2+15374bde2+97cde2+6200d2e2+3613ae3+2290be3+8678ce3+
     ------------------------------------------------------------------------
     15806de3+6555e4 b4-6834a2c2+11236abc2+13008b2c2-7624ac3-11732bc3-10914c4
     ------------------------------------------------------------------------
     +8394b3d+558a2cd+15804abcd-6747b2cd+10851ac2d-4991bc2d-11148c3d-1127a2d2
     ------------------------------------------------------------------------
     +15476abd2+2092b2d2+10397acd2+720bcd2+8898c2d2-5171ad3-1437bd3-7123cd3+
     ------------------------------------------------------------------------
     1200d4-12585b3e-14405a2ce-11516abce-10804b2ce+12165ac2e-7591bc2e+7219c3e
     ------------------------------------------------------------------------
     +7714a2de-13857abde-10074b2de-6743acde-14398bcde+12567c2de-14474ad2e-
     ------------------------------------------------------------------------
     3671bd2e+2668cd2e+5245d3e-8440a2e2-14962abe2-6064b2e2+9787ace2+9365bce2-
     ------------------------------------------------------------------------
     1626c2e2+11562ade2-5347bde2-6611cde2+1297d2e2+6083ae3-2910be3+9336ce3+
     ------------------------------------------------------------------------
     4500de3+5824e4 abc3+10205b2c3+129ac4+10383bc4-8995c5+11833a2c2d+
     ------------------------------------------------------------------------
     8750abc2d-3986b2c2d-7688ac3d+13715bc3d-3801c4d+14284b3d2+5583a2cd2-
     ------------------------------------------------------------------------
     10680abcd2-3580b2cd2+1819ac2d2-11397bc2d2+5022c3d2+4921a2d3-6346abd3+
     ------------------------------------------------------------------------
     588b2d3-9801acd3+5283bcd3-15602c2d3-15745ad4-10724bd4-5110cd4+4865d5-
     ------------------------------------------------------------------------
     9419a2c2e+5219abc2e+4904b2c2e+2962ac3e-9674bc3e+14661c4e+12409b3de-
     ------------------------------------------------------------------------
     313a2cde+6087abcde+1654b2cde+10375ac2de+4782bc2de+13568c3de+6761a2d2e-
     ------------------------------------------------------------------------
     12681abd2e-12155b2d2e-1284acd2e-1608bcd2e+8800c2d2e+9832ad3e-4279bd3e-
     ------------------------------------------------------------------------
     3534cd3e+12319d4e-2285b3e2+1166a2ce2-10962abce2+1912b2ce2+360ac2e2-
     ------------------------------------------------------------------------
     12380bc2e2+5852c3e2-10532a2de2-12331abde2+3893b2de2-5214acde2-7314bcde2+
     ------------------------------------------------------------------------
     14154c2de2-8680ad2e2-6985bd2e2+14152cd2e2+6713d3e2+9190a2e3-3024abe3-
     ------------------------------------------------------------------------
     895b2e3+6116ace3+14642bce3+10573c2e3-12549ade3-12131bde3+6219cde3+
     ------------------------------------------------------------------------
     1982d2e3+4618ae4+201be4+11618ce4+644de4-13377e5
     ------------------------------------------------------------------------
     a2c3-10186b2c3-8459ac4-12619bc4+9858c5-10977a2c2d-9530abc2d-10791b2c2d-
     ------------------------------------------------------------------------
     4374ac3d+7212bc3d+11559c4d-3944b3d2+15534a2cd2+15407abcd2-472b2cd2-
     ------------------------------------------------------------------------
     459ac2d2-13931bc2d2-15944c3d2-8354a2d3-5810abd3+15064b2d3+905acd3+
     ------------------------------------------------------------------------
     1316bcd3-14896c2d3-5815ad4+10407bd4-534cd4-3965d5-2533a2c2e+6498abc2e+
     ------------------------------------------------------------------------
     4114b2c2e-1161ac3e+9529bc3e+2934c4e-7672b3de-7580a2cde+13351abcde-
     ------------------------------------------------------------------------
     200b2cde-10316ac2de+7066bc2de-14177c3de-14662a2d2e-6024abd2e-15461b2d2e-
     ------------------------------------------------------------------------
     710acd2e-7835bcd2e+10254c2d2e-15854ad3e+13473bd3e-11164cd3e+12677d4e+
     ------------------------------------------------------------------------
     15698b3e2+6870a2ce2+6983abce2-14369b2ce2-12916ac2e2-9711bc2e2-4762c3e2+
     ------------------------------------------------------------------------
     6939a2de2-1176abde2+14807b2de2+11773acde2+1321bcde2-3747c2de2+9891ad2e2+
     ------------------------------------------------------------------------
     2313bd2e2-15317cd2e2-13439d3e2-11254a2e3+14880abe3+7100b2e3-792ace3-
     ------------------------------------------------------------------------
     14548bce3+15471c2e3-6301ade3+8988bde3+4801cde3+5511d2e3+5980ae4-6871be4+
     ------------------------------------------------------------------------
     15307ce4-7552de4-6757e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R