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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 (8052a  - 15960a b - 3576a*b  - 15162b  + 8203a c - 4208a*b*c -
     ------------------------------------------------------------------------
          2           2          2         3         2                     2 
     1450b c + 1754a*c  - 3027b*c  + 11175c  - 10208a d + 5983a*b*d - 5967b d
     ------------------------------------------------------------------------
                                     2           2          2           2  
     + 3751a*c*d - 3639b*c*d + 11393c d - 1694a*d  + 9650b*d  - 12543c*d  -
     ------------------------------------------------------------------------
          3        2                      2                           
     5185d  - 3243a e + 14881a*b*e + 5851b e + 3434a*c*e + 4641b*c*e -
     ------------------------------------------------------------------------
           2                                             2           2  
     13954c e - 7774a*d*e - 2353b*d*e + 8246c*d*e + 9093d e + 1419a*e  -
     ------------------------------------------------------------------------
            2          2           2        3        3         2            2
     9143b*e  + 7806c*e  - 15892d*e  - 6900e , 14836a  + 12681a b - 13556a*b 
     ------------------------------------------------------------------------
            3        2                     2           2          2         3
     - 9719b  + 1920a c + 15586a*b*c - 131b c - 7457a*c  - 8321b*c  + 15976c 
     ------------------------------------------------------------------------
             2                     2                                   2   
     - 14158a d + 9323a*b*d + 7586b d - 8126a*c*d + 11791b*c*d - 14095c d -
     ------------------------------------------------------------------------
             2          2           2         3        2                
     13453a*d  + 8055b*d  - 11942c*d  - 13871d  - 1067a e + 14900a*b*e -
     ------------------------------------------------------------------------
          2                                   2                            
     4164b e + 2776a*c*e - 15292b*c*e - 12836c e + 13315a*d*e - 5135b*d*e +
     ------------------------------------------------------------------------
                     2           2           2           2          2  
     7881c*d*e + 822d e + 8378a*e  - 12551b*e  - 14963c*e  + 2321d*e  -
     ------------------------------------------------------------------------
          3         3        2           2        3         2              
     4823e , - 2746a  + 5829a b + 3600a*b  - 2428b  + 10875a c + 215a*b*c +
     ------------------------------------------------------------------------
          2           2           2         3         2                
     9712b c - 2518a*c  + 11765b*c  + 11071c  - 15547a d + 11570a*b*d -
     ------------------------------------------------------------------------
         2                                   2           2          2  
     495b d + 14045a*c*d + 5619b*c*d + 12956c d - 8938a*d  + 6553b*d  -
     ------------------------------------------------------------------------
             2         3        2                      2               
     14938c*d  + 13415d  - 2676a e + 8885a*b*e + 13727b e - 3971a*c*e +
     ------------------------------------------------------------------------
                        2                                               2   
     12639b*c*e - 10959c e - 1145a*d*e + 5621b*d*e + 13160c*d*e + 14798d e -
     ------------------------------------------------------------------------
            2          2           2         2        3
     5157a*e  + 2557b*e  - 14845c*e  - 208d*e  + 1915e )

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+4015b3-14267a2c+10251abc+10576b2c-12692ac2+5195bc2-5676c3+14319a2d
     ------------------------------------------------------------------------
     +2352abd+11246b2d+809acd-11071bcd+14234c2d-5880ad2+8444bd2+1488cd2+
     ------------------------------------------------------------------------
     10430d3+3339a2e+2958abe+6488b2e-9959ace+5588bce-13739c2e-9116ade+6091bde
     ------------------------------------------------------------------------
     -15673cde+12252d2e+13216ae2-9721be2-4640ce2+8608de2+15499e3
     ------------------------------------------------------------------------
     a2b+10080b3-8722a2c+13830abc+3346b2c+4787ac2-13582bc2-13444c3+745a2d+
     ------------------------------------------------------------------------
     8184abd+2826b2d-10744acd+9822bcd+12041c2d+2134ad2-12653bd2+8679cd2-
     ------------------------------------------------------------------------
     5397d3+12072a2e-8918abe-12970b2e-1670ace+11604bce+13421c2e+11921ade+
     ------------------------------------------------------------------------
     7324bde+8945cde+13471d2e-9441ae2-252be2+14186ce2-4846de2-5647e3
     ------------------------------------------------------------------------
     a3+15823b3-14438a2c-10849abc-1016b2c-8493ac2-11081bc2-7931c3-2833a2d+
     ------------------------------------------------------------------------
     7422abd-7636b2d+15578acd-14936bcd+15138c2d-13175ad2-15931bd2+9599cd2-
     ------------------------------------------------------------------------
     7787d3+15669a2e-12923abe-12353b2e+10590ace-7963bce-9541c2e+14007ade+
     ------------------------------------------------------------------------
     2051bde+11780cde-15706d2e+10014ae2-15879be2+8197ce2-3034de2-3929e3
     ------------------------------------------------------------------------
     b3c-4703a2c2-3642abc2+15899b2c2-12094ac3-13339bc3+10243c4+11387b3d+
     ------------------------------------------------------------------------
     745a2cd+2951abcd-14660b2cd-5125ac2d-10729bc2d-6230c3d-15725a2d2-8062abd2
     ------------------------------------------------------------------------
     +8261b2d2+13919acd2-2305bcd2+8220c2d2-6685ad3-2653bd3-15170cd3-8616d4+
     ------------------------------------------------------------------------
     15719b3e-11083a2ce-13978abce+8194b2ce-3583ac2e-12836bc2e-10864c3e+
     ------------------------------------------------------------------------
     9323a2de-7233abde+7265b2de+13028acde-15027bcde+14664c2de-8207ad2e-
     ------------------------------------------------------------------------
     7682bd2e-4860cd2e+8455d3e-13845a2e2-4445abe2+2799b2e2-13319ace2+4594bce2
     ------------------------------------------------------------------------
     -9244c2e2+2218ade2+900bde2+3419cde2+10675d2e2+335ae3-5031be3-12324ce3-
     ------------------------------------------------------------------------
     10140de3+15931e4 b4+6682a2c2+1123abc2-5229b2c2+10296ac3+3921bc3-7867c4-
     ------------------------------------------------------------------------
     13486b3d-4630a2cd+5063abcd+7902b2cd+8661ac2d+15484bc2d-2650c3d+13853a2d2
     ------------------------------------------------------------------------
     -11754abd2-1143b2d2-270acd2-3638bcd2+144c2d2+11461ad3-881bd3+5312cd3-
     ------------------------------------------------------------------------
     2679d4+15938b3e+11262a2ce-10345abce-2799b2ce-3915ac2e+10530bc2e-5391c3e+
     ------------------------------------------------------------------------
     1965a2de+3463abde-4597b2de+9443acde-3720bcde+10144c2de-11977ad2e+
     ------------------------------------------------------------------------
     12456bd2e+3694cd2e+10497d3e-9603a2e2+15787abe2+11475b2e2+15547ace2+
     ------------------------------------------------------------------------
     12652bce2-3003c2e2+6780ade2+10562bde2-11316cde2+11656d2e2+5731ae3+
     ------------------------------------------------------------------------
     8107be3-6067ce3-11985de3+860e4
     ------------------------------------------------------------------------
     abc3+6384b2c3-1595ac4+1064bc4-3328c5-5385a2c2d+2239abc2d+14252b2c2d-
     ------------------------------------------------------------------------
     6796ac3d+6958bc3d-3396c4d-8673b3d2+10657a2cd2-5016abcd2+5449b2cd2+
     ------------------------------------------------------------------------
     13693ac2d2-14649bc2d2-2329c3d2-2876a2d3+12093abd3-7239b2d3-48acd3+
     ------------------------------------------------------------------------
     9702bcd3-3895c2d3-8369ad4+6383bd4+5897cd4-6866d5+14569a2c2e-4203abc2e+
     ------------------------------------------------------------------------
     3123b2c2e+6587ac3e-14654bc3e+7820c4e-9794b3de+5770a2cde+539abcde+
     ------------------------------------------------------------------------
     4297b2cde-10888ac2de+2584bc2de-10565c3de-7389a2d2e+10083abd2e+5906b2d2e+
     ------------------------------------------------------------------------
     9491acd2e-7987bcd2e+2346c2d2e-11142ad3e-7389bd3e-15405cd3e-393d4e-
     ------------------------------------------------------------------------
     2123b3e2-9990a2ce2+7343abce2-10505b2ce2-9309ac2e2-6825bc2e2+14457c3e2+
     ------------------------------------------------------------------------
     15726a2de2+11801abde2+6507b2de2+9989acde2-13094bcde2-11721c2de2+
     ------------------------------------------------------------------------
     14393ad2e2-9885bd2e2-200cd2e2+10080d3e2-7831a2e3+7854abe3+12001b2e3-
     ------------------------------------------------------------------------
     13573ace3+13202bce3+14623c2e3+10845ade3-4941bde3-8416cde3+14723d2e3-
     ------------------------------------------------------------------------
     12661ae4+12502be4-8187ce4+9170de4+14059e5
     ------------------------------------------------------------------------
     a2c3+13890b2c3-7516ac4+14943bc4-8010c5+4242a2c2d+9961abc2d+8080b2c2d+
     ------------------------------------------------------------------------
     6391ac3d-5827bc3d+13026c4d+5653b3d2-1643a2cd2+5502abcd2-6860b2cd2+
     ------------------------------------------------------------------------
     5737ac2d2-9455bc2d2+4712c3d2-10538a2d3-15189abd3+726b2d3+10513acd3+
     ------------------------------------------------------------------------
     3409bcd3+2959c2d3+5392ad4-2879bd4-5297cd4-14684d5-8983a2c2e-8352abc2e+
     ------------------------------------------------------------------------
     4997b2c2e-13392ac3e-14921bc3e-13732c4e-1340b3de+1683a2cde+11905abcde-
     ------------------------------------------------------------------------
     6594b2cde-10524ac2de-14432bc2de-12387c3de+137a2d2e-9411abd2e-15765b2d2e+
     ------------------------------------------------------------------------
     8293acd2e+5272bcd2e-10312c2d2e-4347ad3e+10341bd3e+7269cd3e-6681d4e+
     ------------------------------------------------------------------------
     2048b3e2-3553a2ce2+4636abce2-10152b2ce2+13235ac2e2-12847bc2e2-15966c3e2-
     ------------------------------------------------------------------------
     10458a2de2-14748abde2+342b2de2-5768acde2+10732bcde2-426c2de2+10145ad2e2-
     ------------------------------------------------------------------------
     13119bd2e2+7363cd2e2+114d3e2+4305a2e3-5060abe3-15889b2e3+8249ace3-
     ------------------------------------------------------------------------
     11318bce3-8792c2e3+5477ade3+11504bde3-14515cde3-8815d2e3+15106ae4-
     ------------------------------------------------------------------------
     9979be4+5014ce4+3385de4-6922e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R