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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 (5765a  + 4372a b + 247a*b  + 15585b  + 11069a c + 9728a*b*c +
     ------------------------------------------------------------------------
           2         2         2        3         2                     2   
     13495b c - 76a*c  + 272b*c  - 1672c  - 15931a d - 8731a*b*d - 3195b d -
     ------------------------------------------------------------------------
                                 2           2           2          2  
     2885a*c*d + 711b*c*d + 7699c d + 1342a*d  + 15655b*d  - 6488c*d  +
     ------------------------------------------------------------------------
           3         2                      2                            
     13370d  - 14100a e + 6131a*b*e + 11201b e + 3676a*c*e + 13011b*c*e +
     ------------------------------------------------------------------------
         2                                              2            2  
     129c e - 9209a*d*e - 2005b*d*e + 15542c*d*e - 6540d e + 14802a*e  -
     ------------------------------------------------------------------------
            2          2          2         3         3        2           2
     7223b*e  + 4988c*e  + 7960d*e  - 12037e , - 6230a  - 1791a b - 5182a*b 
     ------------------------------------------------------------------------
            3        2                     2            2          2  
     - 6002b  - 6513a c + 6263a*b*c - 8760b c - 12061a*c  + 4401b*c  +
     ------------------------------------------------------------------------
           3        2                      2                            
     13608c  + 4547a d + 5172a*b*d - 14626b d - 2301a*c*d - 12659b*c*d +
     ------------------------------------------------------------------------
          2           2           2           2        3         2   
     4804c d - 4211a*d  + 15227b*d  + 11045c*d  + 3930d  + 12487a e +
     ------------------------------------------------------------------------
                       2                                  2               
     10921a*b*e + 2722b e + 11869a*c*e + 2909b*c*e + 4911c e + 9117a*d*e -
     ------------------------------------------------------------------------
                                   2            2         2          2  
     15453b*d*e + 4308c*d*e - 7066d e - 12415a*e  + 243b*e  - 5140c*e  +
     ------------------------------------------------------------------------
             2         3          3        2           2         3         2 
     13003d*e  - 15874e , - 10614a  - 2981a b + 9295a*b  - 10088b  - 10870a c
     ------------------------------------------------------------------------
                        2          2          2        3         2   
     + 8801a*b*c + 8678b c + 225a*c  + 3174b*c  + 7897c  - 13339a d +
     ------------------------------------------------------------------------
                      2                                 2            2  
     3223a*b*d - 1422b d + 6899a*c*d - 1050b*c*d - 4887c d - 11766a*d  -
     ------------------------------------------------------------------------
            2          2         3         2                      2   
     9857b*d  + 7435c*d  - 15887d  - 11212a e + 11796a*b*e - 2007b e -
     ------------------------------------------------------------------------
                                   2                                      
     15714a*c*e - 3915b*c*e - 7120c e - 5369a*d*e + 9078b*d*e + 753c*d*e -
     ------------------------------------------------------------------------
           2           2           2           2           2        3
     12014d e + 5560a*e  + 13236b*e  + 11999c*e  + 11050d*e  - 2961e )

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+10710b3-15026a2c+8269abc-4499b2c-2746ac2+12675bc2+3316c3-15481a2d-
     ------------------------------------------------------------------------
     1358abd-6365b2d-10461acd+11387bcd-5541c2d+10899ad2+563bd2+11106cd2+
     ------------------------------------------------------------------------
     14164d3+310a2e-2722abe+13661b2e-3883ace-14314bce-12511c2e-9632ade+
     ------------------------------------------------------------------------
     4729bde-8932cde+4139d2e+5618ae2+11135be2-823ce2+832de2-13762e3
     ------------------------------------------------------------------------
     a2b-1364b3+13914a2c+8651abc-4252b2c+933ac2+15478bc2-13469c3-2776a2d-
     ------------------------------------------------------------------------
     8316abd-9569b2d+12857acd-10914bcd-4434c2d+11422ad2+3982bd2+12502cd2+
     ------------------------------------------------------------------------
     6082d3+5087a2e+9159abe+3598b2e+15479ace-2398bce+5008c2e+3277ade+5970bde+
     ------------------------------------------------------------------------
     6962cde+10048d2e+15983ae2+12204be2-14334ce2-5199de2-6019e3
     ------------------------------------------------------------------------
     a3-9142b3-10800a2c+3240abc+7894b2c-8667ac2-3882bc2-7431c3+12919a2d+
     ------------------------------------------------------------------------
     540abd+11104b2d-7282acd+11786bcd-1689c2d-2162ad2-15254bd2+15178cd2+
     ------------------------------------------------------------------------
     9072d3-4301a2e+1643abe-8730b2e-6287ace-2451bce+4954c2e+8712ade+9070bde-
     ------------------------------------------------------------------------
     4528cde+656d2e-646ae2-5892be2+337ce2+8999de2-12140e3
     ------------------------------------------------------------------------
     b3c+2230a2c2+2357abc2+3018b2c2+10297ac3+15295bc3+4747c4-14319b3d-
     ------------------------------------------------------------------------
     1301a2cd-1908abcd+10388b2cd-2199ac2d+12017bc2d+8583c3d-11642a2d2-
     ------------------------------------------------------------------------
     8574abd2-9975b2d2-12370acd2+10047bcd2-8687c2d2-7706ad3+6123bd3-14471cd3+
     ------------------------------------------------------------------------
     10263d4+7050b3e-9820a2ce+3352abce+2307b2ce-3604ac2e-7777bc2e-11533c3e+
     ------------------------------------------------------------------------
     4566a2de-5312abde+8290b2de+14762acde-8787bcde+8741c2de-7567ad2e-9509bd2e
     ------------------------------------------------------------------------
     +2323cd2e-1092d3e-1302a2e2+14414abe2+12289b2e2+8437ace2+9237bce2-
     ------------------------------------------------------------------------
     3246c2e2-6471ade2+5727bde2-11763cde2+14753d2e2+12530ae3+9990be3-7078ce3-
     ------------------------------------------------------------------------
     2637de3-14364e4 b4+5322a2c2-14463abc2-10825b2c2-6120ac3-7190bc3+9415c4-
     ------------------------------------------------------------------------
     13265b3d-12945a2cd+1912abcd-9954b2cd+13591ac2d+10061bc2d+9765c3d-
     ------------------------------------------------------------------------
     14199a2d2-1000abd2-12151b2d2+15243acd2+6370bcd2-9398c2d2-7588ad3-7430bd3
     ------------------------------------------------------------------------
     -11722cd3+9300d4-5768b3e-13784a2ce+13089abce+12501b2ce-7236ac2e+5574bc2e
     ------------------------------------------------------------------------
     -5921c3e-11266a2de-8698abde-1603b2de+9766acde+15091bcde+15145c2de+
     ------------------------------------------------------------------------
     15234ad2e+3228bd2e-9023cd2e+2526d3e+4587a2e2-7006abe2+2768b2e2-1572ace2-
     ------------------------------------------------------------------------
     2492bce2-1715c2e2-14800ade2+15183bde2+13400cde2-10309d2e2-5597ae3-
     ------------------------------------------------------------------------
     12885be3+7062ce3+5158de3-5627e4
     ------------------------------------------------------------------------
     abc3-5488b2c3-14756ac4-6887bc4-4397c5-2076a2c2d-9203abc2d+1948b2c2d+
     ------------------------------------------------------------------------
     6027ac3d-5007bc3d-6110c4d-14584b3d2-4969a2cd2+14422abcd2+7105b2cd2+
     ------------------------------------------------------------------------
     5513ac2d2-12361bc2d2-12021c3d2-2578a2d3+12303abd3+10155b2d3-14572acd3+
     ------------------------------------------------------------------------
     5235bcd3+6796c2d3-13202ad4-15407bd4+13537cd4-4737d5+5032a2c2e+6134abc2e-
     ------------------------------------------------------------------------
     1856b2c2e+5433ac3e-11437bc3e+705c4e-9119b3de-4115a2cde-2351abcde-
     ------------------------------------------------------------------------
     9428b2cde-1227ac2de+6474bc2de-15678c3de-7697a2d2e-13820abd2e+11346b2d2e-
     ------------------------------------------------------------------------
     2326acd2e-2765bcd2e+13454c2d2e+6985ad3e+161bd3e+12149cd3e+15910d4e+
     ------------------------------------------------------------------------
     21b3e2-12245a2ce2-5019abce2-10166b2ce2+2442ac2e2-98bc2e2+12482c3e2-
     ------------------------------------------------------------------------
     9541a2de2+9964abde2+13442b2de2+10769acde2-13783bcde2+1024c2de2+
     ------------------------------------------------------------------------
     13606ad2e2+3715bd2e2+1743cd2e2+7820d3e2+4961a2e3+969abe3+10930b2e3-
     ------------------------------------------------------------------------
     9680ace3+783bce3+7360c2e3+7706ade3+95bde3-14889cde3+8204d2e3-15587ae4+
     ------------------------------------------------------------------------
     10017be4+8924ce4-6865de4+9344e5
     ------------------------------------------------------------------------
     a2c3-2575b2c3-12974ac4-14569bc4+10765c5+14363a2c2d-12261abc2d-13886b2c2d
     ------------------------------------------------------------------------
     +8948ac3d+10740bc3d+13691c4d+13111b3d2-15107a2cd2+852abcd2-12310b2cd2+
     ------------------------------------------------------------------------
     1365ac2d2+15090bc2d2+680c3d2+4115a2d3-7901abd3-10387b2d3-8912acd3+
     ------------------------------------------------------------------------
     1281bcd3+2996c2d3+6056ad4+7128bd4-9199cd4-9909d5-12738a2c2e+3747abc2e-
     ------------------------------------------------------------------------
     1290b2c2e-4007ac3e-2307bc3e-4162c4e-144b3de+9525a2cde+4716abcde-
     ------------------------------------------------------------------------
     10570b2cde+920ac2de-9205bc2de+4386c3de+15626a2d2e+28abd2e-15187b2d2e-
     ------------------------------------------------------------------------
     6824acd2e-8711bcd2e-9142c2d2e-11312ad3e-11531bd3e+14791cd3e+14215d4e+
     ------------------------------------------------------------------------
     6141b3e2-7351a2ce2-13959abce2-906b2ce2-13099ac2e2+15046bc2e2-12061c3e2+
     ------------------------------------------------------------------------
     7620a2de2+11860abde2+11601b2de2+11508acde2-1167bcde2-13167c2de2-
     ------------------------------------------------------------------------
     9962ad2e2-5859bd2e2-15903cd2e2-8083d3e2-2667a2e3-5955abe3-436b2e3-
     ------------------------------------------------------------------------
     9791ace3-1172bce3-11091c2e3+8238ade3+5299bde3-10993cde3-5539d2e3+2301ae4
     ------------------------------------------------------------------------
     +14582be4+8542ce4+2231de4-8915e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R