next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
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 (- 8154a  - 3150a b + 5696a*b  + 10938b  - 469a c + 2462a*b*c +
     ------------------------------------------------------------------------
           2           2          2        3        2                      2 
     11609b c - 9167a*c  - 7244b*c  + 4254c  + 4043a d + 3988a*b*d + 15720b d
     ------------------------------------------------------------------------
                                      2            2          2          2  
     + 9086a*c*d + 13089b*c*d + 14062c d - 12052a*d  + 2017b*d  + 6179c*d  -
     ------------------------------------------------------------------------
          3        2                     2                            
     8856d  + 4656a e - 8858a*b*e - 8043b e + 15390a*c*e + 6593b*c*e -
     ------------------------------------------------------------------------
          2                                              2            2  
     8436c e - 15568a*d*e + 5302b*d*e - 873c*d*e + 13072d e - 13576a*e  +
     ------------------------------------------------------------------------
             2           2          2        3        3        2           2
     13226b*e  - 14184c*e  + 1586d*e  + 8048e , 14576a  + 9013a b - 2505a*b 
     ------------------------------------------------------------------------
             3       2                      2          2          2        3
     + 12756b  + 971a c - 13815a*b*c + 3339b c - 887a*c  + 7663b*c  - 5551c 
     ------------------------------------------------------------------------
             2                      2                                   2   
     - 10129a d - 9175a*b*d - 13778b d - 7221a*c*d - 13836b*c*d - 11960c d +
     ------------------------------------------------------------------------
            2          2          2         3        2                   2   
     3751a*d  + 6688b*d  + 4381c*d  - 15288d  - 1410a e - 875a*b*e - 118b e -
     ------------------------------------------------------------------------
                                   2                                        
     4335a*c*e + 14557b*c*e + 6890c e - 2801a*d*e + 11951b*d*e - 6687c*d*e +
     ------------------------------------------------------------------------
           2          2         2          2          2        3         3  
     12670d e + 208a*e  + 674b*e  + 9485c*e  - 7379d*e  - 8315e , - 2214a  -
     ------------------------------------------------------------------------
          2            2        3        2                     2            2
     7408a b - 15654a*b  - 2572b  + 1768a c + 5960a*b*c - 9078b c - 14325a*c 
     ------------------------------------------------------------------------
             2         3         2                      2               
     - 767b*c  + 14542c  + 10988a d - 9320a*b*d - 15846b d + 3680a*c*d -
     ------------------------------------------------------------------------
                      2           2          2          2        3        2 
     4186b*c*d - 1695c d + 4573a*d  - 9314b*d  + 5554c*d  + 2746d  + 8828a e
     ------------------------------------------------------------------------
                        2                                   2                
     - 9873a*b*e + 9408b e - 13327a*c*e + 13756b*c*e + 4520c e - 10932a*d*e +
     ------------------------------------------------------------------------
                                  2           2           2          2  
     698b*d*e + 11627c*d*e + 7711d e - 3126a*e  + 14269b*e  - 5787c*e  +
     ------------------------------------------------------------------------
             2         3
     14042d*e  + 13873e )

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 = | ab2-14968b3-4868a2c+8629abc-8854b2c-2284ac2-4060bc2-4758c3-11279a2d-
     ------------------------------------------------------------------------
     12749abd-6109b2d-9711acd+11330bcd+5c2d+4705ad2+4884bd2-10831cd2-2086d3+
     ------------------------------------------------------------------------
     8670a2e-14711abe+2265b2e-1547ace-12540bce+9448c2e+12334ade-12463bde+
     ------------------------------------------------------------------------
     1152cde-15794d2e-399ae2+3522be2-3672ce2-14731de2-14240e3
     ------------------------------------------------------------------------
     a2b-8194b3-5839a2c+10066abc+4445b2c-10069ac2-1805bc2-13010c3-10701a2d+
     ------------------------------------------------------------------------
     7923abd-6866b2d+7594acd-15057bcd+15349c2d+13773ad2+14510bd2-1953cd2+
     ------------------------------------------------------------------------
     3344d3+10129a2e-8638abe-13179b2e+11179ace-12050bce+10908c2e+8204ade+
     ------------------------------------------------------------------------
     4810bde-14275cde+15265d2e+11729ae2+4698be2+9665ce2+13033de2+15600e3
     ------------------------------------------------------------------------
     a3-15636b3-6408a2c-9353abc-15608b2c-8855ac2-1926bc2+642c3-12753a2d+
     ------------------------------------------------------------------------
     6770abd-2920b2d+753acd+2595bcd-3879c2d+9530ad2-14302bd2-7664cd2+9890d3-
     ------------------------------------------------------------------------
     10809a2e+3015abe+4661b2e-919ace-2100bce-12959c2e+4224ade+10794bde+
     ------------------------------------------------------------------------
     12713cde-11900d2e+1189ae2-7512be2+7691ce2+5641de2+3453e3
     ------------------------------------------------------------------------
     b3c+308a2c2+6538abc2-13740b2c2-6569ac3-7528bc3+519c4-2239b3d-15598a2cd-
     ------------------------------------------------------------------------
     5981abcd+626b2cd-11144ac2d-12666bc2d-328c3d-12572a2d2-8631abd2+2152b2d2+
     ------------------------------------------------------------------------
     8982acd2+12285bcd2-8269c2d2+6401ad3-1582bd3-7691cd3+8581d4+15563b3e-
     ------------------------------------------------------------------------
     790a2ce+554abce+3592b2ce-13086ac2e+1305bc2e+8576c3e+3701a2de-5265abde+
     ------------------------------------------------------------------------
     13271b2de+7981acde-7796bcde+9224c2de-15407ad2e+6126bd2e-15853cd2e-
     ------------------------------------------------------------------------
     11402d3e-12517a2e2-78abe2-11064b2e2-11081ace2-4545bce2-3881c2e2-
     ------------------------------------------------------------------------
     13460ade2+11935bde2-6886cde2-15608d2e2-7001ae3-14279be3-1376ce3+9299de3+
     ------------------------------------------------------------------------
     10179e4 b4+4219a2c2+15834abc2+10851b2c2-15151ac3-7918bc3+13112c4+8911b3d
     ------------------------------------------------------------------------
     +4062a2cd+13344abcd+14560b2cd-9479ac2d-6575bc2d+8344c3d+9437a2d2+
     ------------------------------------------------------------------------
     7392abd2-15900b2d2-2709acd2-13148bcd2-4457c2d2+9013ad3+12261bd3-1738cd3-
     ------------------------------------------------------------------------
     3761d4-15297b3e+4130a2ce+9344abce+7904b2ce-13170ac2e+10742bc2e+4963c3e-
     ------------------------------------------------------------------------
     1804a2de-14412abde-13570b2de+7421acde-4455bcde+8942c2de+6415ad2e-
     ------------------------------------------------------------------------
     8641bd2e+10289cd2e-2382d3e-6918a2e2-10748abe2-2184b2e2-5116ace2+
     ------------------------------------------------------------------------
     15337bce2+14057c2e2-7997ade2+11798bde2+9089cde2-2083d2e2+2208ae3-4521be3
     ------------------------------------------------------------------------
     +5530ce3+327de3-13554e4
     ------------------------------------------------------------------------
     abc3+2112b2c3-3043ac4+15444bc4-7722c5+4214a2c2d+12831abc2d+9236b2c2d+
     ------------------------------------------------------------------------
     8849ac3d+14618bc3d+9268c4d+5696b3d2+3039a2cd2-11924abcd2+22b2cd2+
     ------------------------------------------------------------------------
     5651ac2d2-8879bc2d2-7649c3d2-10530a2d3-6214abd3+3030b2d3-6480acd3+
     ------------------------------------------------------------------------
     9546bcd3+3783c2d3-1873ad4+260bd4-8613cd4+8858d5-12089a2c2e+1843abc2e-
     ------------------------------------------------------------------------
     13493b2c2e+3497ac3e+9424bc3e-3845c4e+11029b3de+10091a2cde+1095abcde-
     ------------------------------------------------------------------------
     2255b2cde-2505ac2de+1706bc2de-14598c3de+419a2d2e-4881abd2e+15696b2d2e-
     ------------------------------------------------------------------------
     291acd2e-1940bcd2e+3085c2d2e-376ad3e+6071bd3e+9732cd3e-3207d4e-15879b3e2
     ------------------------------------------------------------------------
     +647a2ce2-14331abce2+10160b2ce2+12871ac2e2+3641bc2e2-11964c3e2-
     ------------------------------------------------------------------------
     10516a2de2+842abde2+5374b2de2-573acde2-2851bcde2-8846c2de2-11265ad2e2+
     ------------------------------------------------------------------------
     5372bd2e2-10322cd2e2-8155d3e2+15947a2e3+6969abe3+2042b2e3-5935ace3+
     ------------------------------------------------------------------------
     6416bce3+2929c2e3-5261ade3+15502bde3+10794cde3-10100d2e3+870ae4+12626be4
     ------------------------------------------------------------------------
     +1209ce4-1143de4-14643e5
     ------------------------------------------------------------------------
     a2c3+12823b2c3+10089ac4-993bc4-6960c5-14740a2c2d-7545abc2d+15298b2c2d-
     ------------------------------------------------------------------------
     9805ac3d-10466bc3d+30c4d-10756b3d2-10797a2cd2+4251abcd2+10582b2cd2+
     ------------------------------------------------------------------------
     8999ac2d2-13451bc2d2+12859c3d2-965a2d3+10181abd3-9227b2d3+2871acd3-
     ------------------------------------------------------------------------
     905bcd3+7635c2d3+3050ad4-6966bd4+15747cd4+6133d5-12877a2c2e-4552abc2e+
     ------------------------------------------------------------------------
     1695b2c2e+15020ac3e+4385bc3e+490c4e-4135b3de-7801a2cde-10774abcde-
     ------------------------------------------------------------------------
     14427b2cde+14075ac2de+12789bc2de-11332c3de-10657a2d2e-7280abd2e-
     ------------------------------------------------------------------------
     9351b2d2e-1042acd2e+2501bcd2e+9670c2d2e+13741ad3e+7280bd3e-8435cd3e-
     ------------------------------------------------------------------------
     4306d4e-12222b3e2+13997a2ce2+2129abce2+15184b2ce2+5051ac2e2-10833bc2e2+
     ------------------------------------------------------------------------
     3025c3e2+5317a2de2+2914abde2+1831b2de2-920acde2+14147bcde2+6201c2de2-
     ------------------------------------------------------------------------
     11551ad2e2-8551bd2e2-3249cd2e2-1435d3e2-12238a2e3+1733abe3+15868b2e3-
     ------------------------------------------------------------------------
     4644ace3-203bce3-9473c2e3-15113ade3-15758bde3+13383cde3+6743d2e3+
     ------------------------------------------------------------------------
     14933ae4+9240be4+7625ce4-13561de4+6492e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R