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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 (13671a  - 9053a b - 12898a*b  - 8565b  - 7978a c - 1483a*b*c -
     ------------------------------------------------------------------------
          2           2         2        3         2                      2 
     8011b c + 4083a*c  - 703b*c  + 9785c  + 12835a d + 13731a*b*d + 7883b d
     ------------------------------------------------------------------------
                                    2           2           2           2  
     - 7732a*c*d - 8199b*c*d - 5160c d - 4493a*d  - 13818b*d  + 10818c*d  -
     ------------------------------------------------------------------------
          3        2                      2                             
     9720d  + 1305a e - 8526a*b*e - 12145b e - 12295a*c*e - 11418b*c*e +
     ------------------------------------------------------------------------
           2                                            2            2  
     14337c e - 3007a*d*e + 3392b*d*e - 760c*d*e + 5488d e - 12459a*e  -
     ------------------------------------------------------------------------
             2           2          2        3        3         2           2
     10574b*e  + 13127c*e  + 9656d*e  - 6882e , 14372a  - 11223a b + 8182a*b 
     ------------------------------------------------------------------------
            3        2                     2           2          2        3
     - 7587b  - 3469a c + 841a*b*c + 15327b c + 1281a*c  - 2759b*c  - 8808c 
     ------------------------------------------------------------------------
             2                      2                                  2   
     - 10309a d - 6590a*b*d - 12414b d - 7532a*c*d + 10017b*c*d - 5069c d +
     ------------------------------------------------------------------------
            2           2          2         3        2                    2 
     7787a*d  + 11311b*d  + 6446c*d  + 11761d  + 8119a e - 314a*b*e - 8317b e
     ------------------------------------------------------------------------
                                     2                                       
     + 2288a*c*e + 6906b*c*e + 10624c e + 2031a*d*e - 9387b*d*e + 1394c*d*e -
     ------------------------------------------------------------------------
          2           2          2           2          2         3        3
     3764d e + 7345a*e  - 2766b*e  - 11845c*e  - 2517d*e  + 12206e , 13047a 
     ------------------------------------------------------------------------
             2           2         3         2                      2   
     - 11585a b + 2435a*b  - 13616b  - 12550a c + 10519a*b*c - 6712b c -
     ------------------------------------------------------------------------
            2          2        3        2                       2   
     5138a*c  - 6347b*c  - 5841c  + 4404a d - 11331a*b*d - 15138b d +
     ------------------------------------------------------------------------
                                  2            2          2           2  
     14245a*c*d - 8304b*c*d + 359c d - 12510a*d  - 6452b*d  - 10944c*d  -
     ------------------------------------------------------------------------
          3        2                      2                                2 
     2827d  + 6005a e + 13976a*b*e + 6138b e - 5222a*c*e + 9900b*c*e - 893c e
     ------------------------------------------------------------------------
                                                  2            2           2
     - 1751a*d*e - 15347b*d*e - 5968c*d*e + 10357d e - 13536a*e  + 15821b*e 
     ------------------------------------------------------------------------
              2           2         3
     + 4802c*e  + 15178d*e  + 11384e )

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+11212b3+11701a2c-13296abc-2226b2c-227ac2-8949bc2+12067c3+6445a2d+
     ------------------------------------------------------------------------
     2463abd+10543b2d+154acd+354bcd+4342c2d-2293ad2+11999bd2+8052cd2+3600d3-
     ------------------------------------------------------------------------
     13547a2e+8288abe+10293b2e-3948ace+7310bce-4421c2e+1580ade+915bde-
     ------------------------------------------------------------------------
     12902cde+5421d2e-15848ae2-1819be2-5298ce2+11660de2-3531e3
     ------------------------------------------------------------------------
     a2b+14791b3-10700a2c-5639abc+7366b2c-8329ac2+5050bc2+2941c3-1661a2d-
     ------------------------------------------------------------------------
     4588abd-9388b2d-10508acd+9734bcd-11061c2d-11399ad2-10622bd2-13271cd2-
     ------------------------------------------------------------------------
     10995d3+14916a2e+3032abe-5570b2e-15590ace+13722bce+11993c2e-5029ade-
     ------------------------------------------------------------------------
     1404bde+13626cde-12772d2e+4299ae2+4256be2+4070ce2+5002de2-3598e3
     ------------------------------------------------------------------------
     a3+2499b3+6451a2c-14078abc-1350b2c-3667ac2+3696bc2-13630c3+2849a2d-
     ------------------------------------------------------------------------
     15754abd-5193b2d+2742acd-4181bcd-14245c2d-12334ad2-5846bd2+331cd2+9718d3
     ------------------------------------------------------------------------
     -11785a2e+5964abe+7878b2e+13370ace-411bce-11772c2e-7650ade+11491bde+
     ------------------------------------------------------------------------
     1570cde+3467d2e-2054ae2-13286be2+11638ce2+3309de2+10019e3
     ------------------------------------------------------------------------
     b3c+13126a2c2-15506abc2+11178b2c2-7041ac3+15198bc3+4935c4-3856b3d-
     ------------------------------------------------------------------------
     15738a2cd+5407abcd+15158b2cd+9747ac2d-2008bc2d-1042c3d-555a2d2+1963abd2-
     ------------------------------------------------------------------------
     12127b2d2+5099acd2-7132bcd2+15993c2d2-13930ad3+168bd3-2003cd3+12214d4+
     ------------------------------------------------------------------------
     11929b3e-3035a2ce-4684abce-8847b2ce-4918ac2e+5820bc2e-15600c3e-15154a2de
     ------------------------------------------------------------------------
     +8280abde-793b2de+14091acde-12705bcde+9543c2de+2747ad2e-3825bd2e+
     ------------------------------------------------------------------------
     11877cd2e+1098d3e+15724a2e2+5819abe2+2220b2e2-6922ace2+13298bce2+
     ------------------------------------------------------------------------
     15769c2e2-13529ade2-14812bde2+4230cde2-15190d2e2-9357ae3-6975be3+7679ce3
     ------------------------------------------------------------------------
     +12469de3+11964e4 b4+10059a2c2+13280abc2-5090b2c2-439ac3-9072bc3+15118c4
     ------------------------------------------------------------------------
     +8958b3d-6472a2cd+7298abcd-8169b2cd+677ac2d-3388bc2d+2837c3d+7709a2d2+
     ------------------------------------------------------------------------
     7131abd2-12666b2d2-12735acd2-9822bcd2-8698c2d2-7060ad3-10393bd3+9909cd3-
     ------------------------------------------------------------------------
     5668d4-9392b3e+10956a2ce-13098abce-5343b2ce+8752ac2e-6012bc2e-5573c3e-
     ------------------------------------------------------------------------
     10188a2de+8717abde-955b2de-15698acde-7306bcde+7260c2de-13979ad2e+
     ------------------------------------------------------------------------
     12415bd2e+11859cd2e+13102d3e-6371a2e2-10834abe2-15656b2e2-13405ace2+
     ------------------------------------------------------------------------
     6952bce2-7819c2e2+10889ade2-2952bde2+14538cde2+4287d2e2-13993ae3+
     ------------------------------------------------------------------------
     10728be3+12053ce3+701de3-4176e4
     ------------------------------------------------------------------------
     abc3-5482b2c3-13792ac4-7886bc4-9885c5-4271a2c2d-9645abc2d-6166b2c2d+
     ------------------------------------------------------------------------
     1735ac3d-12687bc3d+4926c4d+6517b3d2+1861a2cd2-7288abcd2-1833b2cd2+
     ------------------------------------------------------------------------
     4106ac2d2+6375bc2d2+7269c3d2-11127a2d3-13616abd3+1540b2d3-3632acd3-
     ------------------------------------------------------------------------
     11582bcd3-4673c2d3+12565ad4+3552bd4-13370cd4+5149d5+9466a2c2e+5462abc2e-
     ------------------------------------------------------------------------
     10530b2c2e+13709ac3e+14636bc3e-8126c4e-7065b3de+15366a2cde-14290abcde+
     ------------------------------------------------------------------------
     8342b2cde-237ac2de+15015bc2de+1481c3de-14717a2d2e-8729abd2e+4487b2d2e-
     ------------------------------------------------------------------------
     9109acd2e-3281bcd2e-8791c2d2e+14398ad3e+6546bd3e-11150cd3e-15445d4e+
     ------------------------------------------------------------------------
     14470b3e2+11925a2ce2-11910abce2-222b2ce2+4987ac2e2-5634bc2e2+6869c3e2-
     ------------------------------------------------------------------------
     1876a2de2-8099abde2-10290b2de2-6690acde2+12734bcde2-7917c2de2-3138ad2e2+
     ------------------------------------------------------------------------
     14399bd2e2-8462cd2e2-15532d3e2-7719a2e3+10466abe3+8487b2e3-4731ace3-
     ------------------------------------------------------------------------
     10623bce3+8609c2e3+3647ade3+3649bde3-5611cde3-12910d2e3+14912ae4-
     ------------------------------------------------------------------------
     15599be4+6167ce4+8079de4-3174e5
     ------------------------------------------------------------------------
     a2c3-7961b2c3+9639ac4+811bc4-11573c5+620a2c2d-13301abc2d+586b2c2d-
     ------------------------------------------------------------------------
     2720ac3d+10047bc3d+5451c4d+12493b3d2-14410a2cd2+14521abcd2-1899b2cd2+
     ------------------------------------------------------------------------
     1253ac2d2-6250bc2d2+11414c3d2-2989a2d3-1256abd3+1105b2d3-5043acd3-
     ------------------------------------------------------------------------
     4499bcd3+2427c2d3-11686ad4+10253bd4-5810cd4+13072d5-10942a2c2e-7436abc2e
     ------------------------------------------------------------------------
     +13902b2c2e+947ac3e-13590bc3e+4607c4e+14206b3de+10974a2cde-3794abcde+
     ------------------------------------------------------------------------
     7159b2cde-8255ac2de+9867bc2de+3044c3de+9688a2d2e+12643abd2e+12659b2d2e-
     ------------------------------------------------------------------------
     4469acd2e-10220bcd2e-13039c2d2e-2251ad3e+7576bd3e+14893cd3e-13894d4e+
     ------------------------------------------------------------------------
     5333b3e2+2188a2ce2-3373abce2-3839b2ce2-12575ac2e2-13693bc2e2+15221c3e2+
     ------------------------------------------------------------------------
     14438a2de2-12307abde2-5131b2de2+12093acde2-8509bcde2+3087c2de2+9717ad2e2
     ------------------------------------------------------------------------
     +12317bd2e2+10102cd2e2+9329d3e2-3556a2e3-3109abe3-10330b2e3-3771ace3+
     ------------------------------------------------------------------------
     10499bce3-3005c2e3+4297ade3+8063bde3+953cde3-8148d2e3-2095ae4-11295be4-
     ------------------------------------------------------------------------
     13778ce4-15551de4-12848e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R