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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 (- 14045a  + 5408a b - 13418a*b  + 3317b  - 10647a c + 5072a*b*c +
     ------------------------------------------------------------------------
          2           2          2        3        2                     2   
     9402b c + 7868a*c  - 8031b*c  - 6274c  - 7702a d + 5907a*b*d - 1311b d -
     ------------------------------------------------------------------------
                                   2           2          2          2  
     2560a*c*d + 5016b*c*d + 11527c d - 8167a*d  - 2441b*d  + 7105c*d  +
     ------------------------------------------------------------------------
           3        2                     2                             
     10116d  + 9186a e - 5986a*b*e + 4146b e + 13478a*c*e - 14424b*c*e -
     ------------------------------------------------------------------------
         2                                             2           2  
     714c e + 19a*d*e + 11046b*d*e + 12602c*d*e - 3984d e - 7542a*e  -
     ------------------------------------------------------------------------
            2          2           2         3         3         2   
     7162b*e  + 9293c*e  - 14442d*e  + 12264e , - 5449a  - 10604a b +
     ------------------------------------------------------------------------
             2       3        2                     2            2          2
     11530a*b  - 682b  + 3947a c - 6241a*b*c - 8398b c + 14045a*c  - 2942b*c 
     ------------------------------------------------------------------------
           3        2                      2                            
     + 868c  + 7835a d + 15913a*b*d + 4124b d + 10787a*c*d - 2388b*c*d +
     ------------------------------------------------------------------------
          2           2           2           2         3         2   
     3852c d + 9135a*d  - 12406b*d  - 12741c*d  + 10794d  - 12532a e -
     ------------------------------------------------------------------------
                        2                                  2               
     10299a*b*e - 15115b e - 7885a*c*e + 6627b*c*e - 11152c e + 5169a*d*e +
     ------------------------------------------------------------------------
                                    2           2          2           2  
     11468b*d*e - 5438c*d*e + 10951d e - 8030a*e  - 7219b*e  + 11630c*e  -
     ------------------------------------------------------------------------
           2        3       3         2           2        3         2   
     839d*e  - 4128e , 1088a  - 11151a b + 7074a*b  + 2781b  + 12042a c +
     ------------------------------------------------------------------------
                       2            2          2        3         2   
     15310a*b*c - 7908b c + 14477a*c  + 2878b*c  + 9202c  - 11495a d -
     ------------------------------------------------------------------------
                    2                                  2          2  
     477a*b*d - 244b d + 8810a*c*d + 14670b*c*d + 9761c d + 237a*d  -
     ------------------------------------------------------------------------
             2          2       3        2                     2             
     13111b*d  + 2539c*d  + 666d  + 7659a e + 4690a*b*e + 2301b e - 6994a*c*e
     ------------------------------------------------------------------------
                         2                                               2   
     + 11780b*c*e + 8335c e - 1415a*d*e + 15731b*d*e + 14494c*d*e + 1722d e +
     ------------------------------------------------------------------------
            2           2          2           2         3
     4277a*e  + 12371b*e  + 2167c*e  - 11710d*e  - 14082e )

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 = | ab2-8915b3-96a2c+11592abc+6044b2c-11095ac2-3739bc2-5836c3+3378a2d+
     ------------------------------------------------------------------------
     14772abd+10024b2d+6512acd+6182bcd+6788c2d-6936ad2-8908bd2-7973cd2-9414d3
     ------------------------------------------------------------------------
     +8921a2e+8464abe+3236b2e+13628ace+625bce+6219c2e+15362ade+7168bde+
     ------------------------------------------------------------------------
     4860cde+5472d2e+6556ae2+14896be2-12717ce2+10711de2+11394e3
     ------------------------------------------------------------------------
     a2b+13410b3-7995a2c-13121abc-13765b2c-6901ac2+3981bc2+341c3-11395a2d-
     ------------------------------------------------------------------------
     2627abd+14513b2d+7298acd+4024bcd-10580c2d-974ad2+5095bd2-12846cd2-
     ------------------------------------------------------------------------
     11620d3+378a2e-9286abe-11297b2e-7086ace-16bce+1002c2e-15044ade-12468bde+
     ------------------------------------------------------------------------
     10312cde-9955d2e-3575ae2+6339be2-10531ce2+7545de2+7178e3
     ------------------------------------------------------------------------
     a3-700b3-13741a2c-1961abc-14338b2c+14600ac2-5392bc2+3121c3-11456a2d-
     ------------------------------------------------------------------------
     14548abd-14586b2d-14362acd+9121bcd+7013c2d+2376ad2+8057bd2+7690cd2+
     ------------------------------------------------------------------------
     2885d3+3619a2e+11462abe-6986b2e+10660ace+14432bce-13362c2e+7043ade-
     ------------------------------------------------------------------------
     5331bde-7140cde+8790d2e+4157ae2-10222be2-14305ce2+6942de2-9469e3
     ------------------------------------------------------------------------
     b3c+14618a2c2-5022abc2-575b2c2-8443ac3+5438bc3+9109c4+8018b3d-14255a2cd+
     ------------------------------------------------------------------------
     15664abcd-15783b2cd-926ac2d+10294bc2d+15815c3d-5123a2d2-10728abd2+
     ------------------------------------------------------------------------
     4299b2d2-14071acd2+8963bcd2+9808c2d2+13799ad3+13782bd3-14438cd3+9393d4-
     ------------------------------------------------------------------------
     6323b3e-5985a2ce-7601abce+12859b2ce+15914ac2e+5362bc2e+10544c3e+
     ------------------------------------------------------------------------
     15145a2de+3608abde+3796b2de-9020acde+13266bcde-2711c2de-2065ad2e-
     ------------------------------------------------------------------------
     15169bd2e+2020cd2e+10941d3e+764a2e2-13962abe2-2383b2e2+8593ace2+244bce2+
     ------------------------------------------------------------------------
     856c2e2+15025ade2+6426bde2+13992cde2-13670d2e2+3549ae3+863be3+7292ce3-
     ------------------------------------------------------------------------
     5188de3+15361e4 b4+12183a2c2+13302abc2-13799b2c2+15560ac3-13384bc3-105c4
     ------------------------------------------------------------------------
     -14244b3d+12742a2cd-7828abcd+5488b2cd-1400ac2d-6313bc2d+12285c3d+
     ------------------------------------------------------------------------
     15897a2d2-3292abd2+10387b2d2-6225acd2+6117bcd2-11204c2d2+6654ad3-8567bd3
     ------------------------------------------------------------------------
     -8770cd3-1824d4+13910b3e-1348a2ce-7067abce+14238b2ce-1258ac2e-5455bc2e-
     ------------------------------------------------------------------------
     13133c3e-5852a2de-1339abde-545b2de+10360acde+11849bcde+4545c2de+301ad2e-
     ------------------------------------------------------------------------
     4083bd2e-5308cd2e-6040d3e-10750a2e2+11700abe2-8510b2e2-5270ace2-
     ------------------------------------------------------------------------
     15538bce2-8282c2e2-11978ade2-3639bde2+9734cde2+7248d2e2-811ae3-4700be3+
     ------------------------------------------------------------------------
     12184ce3+8603de3+5049e4
     ------------------------------------------------------------------------
     abc3-12715b2c3-2508ac4-5702bc4+836c5+5511a2c2d+15356abc2d-10845b2c2d+
     ------------------------------------------------------------------------
     3863ac3d+3599bc3d+9635c4d-4544b3d2-9880a2cd2+13540abcd2-15060b2cd2-
     ------------------------------------------------------------------------
     7937ac2d2-15331bc2d2+12495c3d2+15030a2d3+9412abd3-8492b2d3-883acd3-
     ------------------------------------------------------------------------
     3088bcd3-14161c2d3-9156ad4-12856bd4+1402cd4-14001d5-4303a2c2e-3521abc2e-
     ------------------------------------------------------------------------
     1852b2c2e+6861ac3e+293bc3e-7484c4e-1106b3de+5164a2cde-8326abcde+
     ------------------------------------------------------------------------
     5797b2cde+13884ac2de+14626bc2de+5854c3de-2281a2d2e+13559abd2e+7302b2d2e-
     ------------------------------------------------------------------------
     6122acd2e-12357bcd2e+15169c2d2e-5107ad3e+8214bd3e+13543cd3e+7119d4e+
     ------------------------------------------------------------------------
     7216b3e2-14560a2ce2-1798abce2-4118b2ce2-8266ac2e2-14485bc2e2+8609c3e2+
     ------------------------------------------------------------------------
     14705a2de2-12695abde2+9422b2de2-9422acde2+1986bcde2-2068c2de2-665ad2e2+
     ------------------------------------------------------------------------
     15427bd2e2+7803cd2e2-10184d3e2+7838a2e3-2410abe3-14345b2e3-141ace3-
     ------------------------------------------------------------------------
     5434bce3+14859c2e3+3321ade3+6090bde3-11219cde3+3083d2e3+10429ae4-2305be4
     ------------------------------------------------------------------------
     +5375ce4-7530de4-10214e5
     ------------------------------------------------------------------------
     a2c3-13085b2c3-5662ac4+450bc4+13174c5-14231a2c2d+10582abc2d-10218b2c2d+
     ------------------------------------------------------------------------
     11998ac3d-7548bc3d+6911c4d+3505b3d2+12395a2cd2+3941abcd2+12996b2cd2+
     ------------------------------------------------------------------------
     10396ac2d2-1510bc2d2-11218c3d2-1327a2d3-15913abd3+4521b2d3+11403acd3+
     ------------------------------------------------------------------------
     8530bcd3-6034c2d3+12106ad4+13390bd4-11142cd4-6873d5-15087a2c2e-7690abc2e
     ------------------------------------------------------------------------
     -4382b2c2e-15968ac3e+1999bc3e-7338c4e+3013b3de+6405a2cde-14974abcde-
     ------------------------------------------------------------------------
     3812b2cde+9584ac2de+1208bc2de+3473c3de-1326a2d2e-11246abd2e-10867b2d2e-
     ------------------------------------------------------------------------
     12416acd2e+4999bcd2e-5768c2d2e-9939ad3e+13983bd3e+13548cd3e+8537d4e-
     ------------------------------------------------------------------------
     15322b3e2+9617a2ce2+12187abce2-10488b2ce2+4342ac2e2-162bc2e2+12395c3e2+
     ------------------------------------------------------------------------
     9785a2de2-2420abde2+2662b2de2+3471acde2+14912bcde2-10774c2de2-2752ad2e2+
     ------------------------------------------------------------------------
     4181bd2e2-11496cd2e2-3599d3e2+11957a2e3-5612abe3-14989b2e3-3843ace3+
     ------------------------------------------------------------------------
     5649bce3+492c2e3+5989ade3+10908bde3-2215cde3-13857d2e3+3201ae4-4863be4+
     ------------------------------------------------------------------------
     214ce4+6123de4+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