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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 (14925a  - 13610a b + 389a*b  + 1986b  + 15584a c - 6202a*b*c +
     ------------------------------------------------------------------------
          2           2           2         3        2                     2 
     3980b c + 3974a*c  + 12826b*c  + 14725c  - 6292a d + 10500a*b*d + 295b d
     ------------------------------------------------------------------------
                                  2            2           2           2  
     - 127a*c*d - 108b*c*d + 8558c d + 14765a*d  + 13344b*d  + 10693c*d  -
     ------------------------------------------------------------------------
          3        2                     2                            
     8247d  + 4141a e + 3047a*b*e - 9449b e - 7126a*c*e + 10337b*c*e +
     ------------------------------------------------------------------------
           2                                                2           2  
     12400c e + 15152a*d*e + 4641b*d*e + 14803c*d*e - 14810d e - 3650a*e  -
     ------------------------------------------------------------------------
             2          2          2        3         3        2           2
     13832b*e  - 8450c*e  + 3849d*e  + 1390e , - 7534a  - 1228a b + 3883a*b 
     ------------------------------------------------------------------------
            3        2                     2           2           2        3
     - 1617b  - 7943a c - 6392a*b*c - 3096b c + 3671a*c  + 13142b*c  - 8292c 
     ------------------------------------------------------------------------
            2                      2                                    2   
     - 6054a d + 7240a*b*d + 10514b d - 11607a*c*d - 11876b*c*d + 10245c d -
     ------------------------------------------------------------------------
            2          2           2       3        2                      2 
     6772a*d  + 8870b*d  + 10006c*d  + 521d  - 7557a e - 5976a*b*e - 10515b e
     ------------------------------------------------------------------------
                                     2                                      
     - 8195a*c*e - 14066b*c*e + 1460c e + 4346a*d*e - 9250b*d*e - 11870c*d*e
     ------------------------------------------------------------------------
            2           2           2          2          2        3   
     + 2975d e + 3592a*e  + 15761b*e  - 4265c*e  + 9456d*e  + 4214e , -
     ------------------------------------------------------------------------
          3        2          2        3         2                     2   
     8536a  + 1105a b + 864a*b  + 1788b  - 14812a c - 6324a*b*c - 5162b c -
     ------------------------------------------------------------------------
             2           2        3        2                     2   
     12425a*c  + 12631b*c  - 1011c  + 5150a d + 8148a*b*d - 6280b d +
     ------------------------------------------------------------------------
                                    2           2           2           2  
     5141a*c*d - 10305b*c*d - 13454c d + 3773a*d  + 11774b*d  - 15610c*d  -
     ------------------------------------------------------------------------
          3        2                       2                          
     4783d  - 7517a e + 11441a*b*e + 10874b e - 6639a*c*e - 466b*c*e -
     ------------------------------------------------------------------------
          2                                               2            2  
     8751c e - 5096a*d*e - 11534b*d*e + 13595c*d*e + 6493d e - 15281a*e  -
     ------------------------------------------------------------------------
            2           2          2        3
     8235b*e  - 13787c*e  + 6309d*e  - 3758e )

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+8785b3+2015a2c+8624abc-10517b2c-7031ac2-2799bc2+6323c3-5339a2d-
     ------------------------------------------------------------------------
     11874abd-10243b2d+15213acd-13670bcd+7279c2d+1519ad2-1670bd2+7331cd2-
     ------------------------------------------------------------------------
     11439d3+1279a2e-15937abe+15823b2e-11051ace-15027bce+13665c2e-8428ade-
     ------------------------------------------------------------------------
     2000bde+5620cde-14989d2e-4102ae2-11054be2+14383ce2-12403de2+2271e3
     ------------------------------------------------------------------------
     a2b+1285b3+7836a2c-14355abc+11902b2c-3910ac2-14615bc2+67c3-15334a2d+
     ------------------------------------------------------------------------
     5428abd-4253b2d-13655acd+2522bcd+14522c2d+7412ad2-7473bd2+1455cd2-7616d3
     ------------------------------------------------------------------------
     +15796a2e-11043abe+6812b2e-3740ace-1626bce-14561c2e-10729ade+4195bde-
     ------------------------------------------------------------------------
     11152cde-14866d2e+6807ae2+1791be2-13733ce2-4138de2+6960e3
     ------------------------------------------------------------------------
     a3+1464b3-12157a2c-5015abc-4892b2c-15467ac2+5929bc2-11716c3+15665a2d-
     ------------------------------------------------------------------------
     1220abd-7769b2d-11341acd+13937bcd+3728c2d+1364ad2+12318bd2+14478cd2+
     ------------------------------------------------------------------------
     7316d3-2815a2e+1560abe-12927b2e-166ace+818bce+11969c2e-2740ade-10107bde+
     ------------------------------------------------------------------------
     5336cde-1624d2e-582ae2+5720be2-4077ce2-6692de2-4395e3
     ------------------------------------------------------------------------
     b3c-11446a2c2+13897abc2+10724b2c2-15322ac3+12277bc3+1091c4+3455b3d+
     ------------------------------------------------------------------------
     3054a2cd-11319abcd-14627b2cd-15617ac2d-11929bc2d-13042c3d-157a2d2+
     ------------------------------------------------------------------------
     10345abd2+7575b2d2-6145acd2+10292bcd2-12422c2d2-3813ad3+13732bd3+4145cd3
     ------------------------------------------------------------------------
     +5120d4-15355b3e-6450a2ce-5520abce-14129b2ce+4729ac2e+3264bc2e+10937c3e+
     ------------------------------------------------------------------------
     10863a2de+2006abde-9721b2de-12429acde-13227bcde-14640c2de+12425ad2e+
     ------------------------------------------------------------------------
     269bd2e+10235cd2e+14597d3e-10256a2e2+9142abe2+8160b2e2+12883ace2-
     ------------------------------------------------------------------------
     10351bce2+2297c2e2+10220ade2+15415bde2-13645cde2-13145d2e2-6748ae3-
     ------------------------------------------------------------------------
     4654be3-13644ce3-8581de3-9144e4
     ------------------------------------------------------------------------
     b4+10380a2c2-15402abc2-13754b2c2-15749ac3-8085bc3+7984c4-5526b3d+
     ------------------------------------------------------------------------
     1246a2cd-14987abcd+10358b2cd-14663ac2d+13106bc2d+9901c3d+2887a2d2-
     ------------------------------------------------------------------------
     5591abd2-12549b2d2+13756acd2+6637bcd2+10552c2d2-12281ad3+1417bd3-6714cd3
     ------------------------------------------------------------------------
     +3875d4+8573b3e-5829a2ce-6474abce+9530b2ce-7248ac2e-13799bc2e-15683c3e-
     ------------------------------------------------------------------------
     5384a2de+14912abde-4749b2de+2488acde+14978bcde-478c2de+14438ad2e+
     ------------------------------------------------------------------------
     9744bd2e+6128cd2e+10819d3e-7508a2e2-5579abe2+5091b2e2-11472ace2+
     ------------------------------------------------------------------------
     15268bce2-5832c2e2+7176ade2+7375bde2+11901cde2+5600d2e2-10241ae3-
     ------------------------------------------------------------------------
     13197be3+14606ce3-2098de3-15879e4
     ------------------------------------------------------------------------
     abc3-2122b2c3-650ac4+8356bc4-3949c5-9649a2c2d-15974abc2d+3342b2c2d+
     ------------------------------------------------------------------------
     10896ac3d-6014bc3d-7934c4d-4869b3d2-15589a2cd2-6167abcd2+1718b2cd2+
     ------------------------------------------------------------------------
     11408ac2d2+12435bc2d2+10445c3d2-2258a2d3-15877abd3+15474b2d3-12032acd3-
     ------------------------------------------------------------------------
     3116bcd3+9806c2d3+2754ad4-3929bd4+6002cd4+7828d5+8810a2c2e+8535abc2e-
     ------------------------------------------------------------------------
     14569b2c2e-7295ac3e+2957bc3e+3922c4e-4690b3de+2499a2cde+12489abcde+
     ------------------------------------------------------------------------
     7569b2cde-6508ac2de+13870bc2de-4472c3de-8228a2d2e-8057abd2e-15221b2d2e+
     ------------------------------------------------------------------------
     4722acd2e-11601bcd2e+1216c2d2e-10915ad3e-11599bd3e+14827cd3e-6812d4e+
     ------------------------------------------------------------------------
     10982b3e2+1508a2ce2+6420abce2-3545b2ce2-2315ac2e2-1256bc2e2+14524c3e2+
     ------------------------------------------------------------------------
     9699a2de2+3946abde2+5702b2de2+4616acde2+15033bcde2+5752c2de2-9558ad2e2-
     ------------------------------------------------------------------------
     1000bd2e2+2198cd2e2+5213d3e2+8583a2e3+13141abe3-7526b2e3-3778ace3-
     ------------------------------------------------------------------------
     14294bce3+13120c2e3-8477ade3-3481bde3-10132cde3-13824d2e3-14504ae4+
     ------------------------------------------------------------------------
     4995be4-12761ce4-3365de4-4397e5
     ------------------------------------------------------------------------
     a2c3+14627b2c3-14036ac4-10536bc4-11049c5-409a2c2d-10951abc2d+15099b2c2d-
     ------------------------------------------------------------------------
     2329ac3d-2817bc3d+6953c4d+13650b3d2+3015a2cd2-6381abcd2+10277b2cd2-
     ------------------------------------------------------------------------
     9982ac2d2+13138bc2d2-14797c3d2-8298a2d3-10146abd3-5594b2d3-12325acd3-
     ------------------------------------------------------------------------
     4837bcd3-8930c2d3-1570ad4+2261bd4-2534cd4+10869d5-15136a2c2e+6383abc2e+
     ------------------------------------------------------------------------
     1135b2c2e-5086ac3e-11797bc3e+5233c4e+10067b3de-12218a2cde+15445abcde+
     ------------------------------------------------------------------------
     4263b2cde+2078ac2de+14153bc2de-6796c3de-9727a2d2e-1051abd2e-3956b2d2e-
     ------------------------------------------------------------------------
     8245acd2e-5078bcd2e+13202c2d2e+11036ad3e+7502bd3e+5868cd3e-5781d4e+
     ------------------------------------------------------------------------
     4860b3e2-5946a2ce2+3132abce2+12746b2ce2+15798ac2e2-9982bc2e2-12859c3e2+
     ------------------------------------------------------------------------
     4597a2de2-730abde2+11526b2de2+3649acde2-15898bcde2+14558c2de2+11770ad2e2
     ------------------------------------------------------------------------
     -10644bd2e2+5023cd2e2+122d3e2+10270a2e3+6805abe3-9463b2e3-14139ace3-
     ------------------------------------------------------------------------
     1325bce3+4909c2e3+11057ade3+3800bde3-12729cde3+15232d2e3-12589ae4-
     ------------------------------------------------------------------------
     6204be4-12923ce4-12479de4+2814e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R