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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 (9912a  + 851a b - 5301a*b  + 3872b  + 5092a c - 5749a*b*c +
     ------------------------------------------------------------------------
          2           2          2        3         2                
     8882b c - 7862a*c  - 3590b*c  - 4494c  + 14251a d + 15230a*b*d -
     ------------------------------------------------------------------------
           2                                 2          2           2  
     11541b d + 1345a*c*d + 5976b*c*d + 4871c d + 608a*d  - 14911b*d  +
     ------------------------------------------------------------------------
             2        3         2                      2                
     11612c*d  - 1943d  - 15650a e + 11549a*b*e + 2119b e + 11341a*c*e -
     ------------------------------------------------------------------------
                        2                                              2   
     15963b*c*e + 12735c e + 9305a*d*e - 11212b*d*e - 8903c*d*e - 1056d e -
     ------------------------------------------------------------------------
             2           2          2          2        3         3        2 
     15759a*e  - 13469b*e  - 2729c*e  + 5509d*e  + 2468e , - 1534a  + 9256a b
     ------------------------------------------------------------------------
               2        3        2                     2            2  
     + 15962a*b  - 8459b  + 8314a c + 1886a*b*c + 2669b c + 12798a*c  -
     ------------------------------------------------------------------------
            2        3         2                    2               
     8962b*c  - 6014c  + 10338a d + 564a*b*d + 1681b d + 4888a*c*d -
     ------------------------------------------------------------------------
                       2            2          2          2       3  
     10936b*c*d + 8202c d + 12932a*d  + 9233b*d  + 2475c*d  - 440d  +
     ------------------------------------------------------------------------
           2                      2                                  2   
     12939a e - 15860a*b*e + 1485b e + 4812a*c*e - 13010b*c*e - 8262c e -
     ------------------------------------------------------------------------
                                               2           2           2  
     6191a*d*e + 15143b*d*e + 9312c*d*e + 9880d e + 6275a*e  - 12626b*e  -
     ------------------------------------------------------------------------
             2          2        3          3         2            2        3
     15515c*e  - 8856d*e  - 9879e , - 15975a  - 13877a b - 14450a*b  - 1916b 
     ------------------------------------------------------------------------
            2                     2           2          2        3        2 
     - 3459a c + 2301a*b*c - 5086b c - 2746a*c  + 9303b*c  + 1907c  + 4086a d
     ------------------------------------------------------------------------
                        2                                  2           2  
     + 6000a*b*d + 5881b d - 3451a*c*d + 14719b*c*d + 2607c d + 3213a*d  +
     ------------------------------------------------------------------------
           2          2        3        2                      2             
     608b*d  + 8551c*d  - 5246d  - 8334a e + 12533a*b*e + 1863b e - 7511a*c*e
     ------------------------------------------------------------------------
                         2                                              2   
     - 14844b*c*e - 7159c e + 8089a*d*e + 12000b*d*e + 8622c*d*e + 5601d e +
     ------------------------------------------------------------------------
             2           2           2         2         3
     14895a*e  - 12982b*e  + 13894c*e  - 691d*e  - 12055e )

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 = | ab2-4589b3-8589a2c-6709abc+14799b2c+1504ac2-2995bc2-12043c3+3524a2d+
     ------------------------------------------------------------------------
     4693abd-1988b2d-1968acd+6340bcd-15392c2d-3395ad2+6385bd2+2950cd2+6727d3+
     ------------------------------------------------------------------------
     5067a2e-8472abe-9418b2e-2919ace+7497bce+958c2e+13748ade-3780bde+9121cde+
     ------------------------------------------------------------------------
     756d2e-2387ae2-6943be2-11386ce2+13116de2+9231e3
     ------------------------------------------------------------------------
     a2b+14397b3+1214a2c-2070abc+4263b2c+726ac2+8520bc2-10051c3-15422a2d-
     ------------------------------------------------------------------------
     3128abd-10389b2d+4370acd-6683bcd+14320c2d+4431ad2-7712bd2-332cd2-531d3+
     ------------------------------------------------------------------------
     13652a2e+3274abe+13078b2e-1093ace-5896bce-14435c2e+11608ade+13861bde-
     ------------------------------------------------------------------------
     520cde+9300d2e+13586ae2+9953be2-5175ce2+3863de2+3586e3
     ------------------------------------------------------------------------
     a3-11258b3+14123a2c+8742abc-4358b2c+10634ac2+11947bc2+763c3-1733a2d-
     ------------------------------------------------------------------------
     14103abd-3950b2d-5796acd-15404bcd-13093c2d-5386ad2-8536bd2-3875cd2+
     ------------------------------------------------------------------------
     12635d3-2038a2e-2089abe-41b2e+7048ace-13302bce-8947c2e+9253ade+15065bde+
     ------------------------------------------------------------------------
     5561cde+1388d2e+952ae2-11514be2-9100ce2-2809de2+15158e3
     ------------------------------------------------------------------------
     b3c-4117a2c2+11668abc2+10199b2c2+2128ac3-3206bc3-1176c4+3876b3d-
     ------------------------------------------------------------------------
     15453a2cd+12232abcd-8391b2cd+14761ac2d+3673bc2d-12624c3d+2693a2d2-
     ------------------------------------------------------------------------
     244abd2-851b2d2-8568acd2+9232bcd2-8545c2d2+4716ad3+7013bd3-3645cd3+
     ------------------------------------------------------------------------
     2080d4-12381b3e-11736a2ce-5054abce+2108b2ce-3698ac2e+5513bc2e-11347c3e+
     ------------------------------------------------------------------------
     2589a2de-1416abde-5729b2de-4995acde+4215bcde+8315c2de-12216ad2e-
     ------------------------------------------------------------------------
     13289bd2e+8874cd2e-9078d3e-4597a2e2-7675abe2+8583b2e2-357ace2+2911bce2-
     ------------------------------------------------------------------------
     2869c2e2+7248ade2+9776bde2+13185cde2+15776d2e2-12387ae3-2967be3-13902ce3
     ------------------------------------------------------------------------
     -9975de3+6405e4 b4+13294a2c2-11149abc2-15622b2c2+9962ac3-1744bc3+3327c4+
     ------------------------------------------------------------------------
     8958b3d+14315a2cd+4041abcd+15683b2cd-285ac2d+14123bc2d+4462c3d+1175a2d2+
     ------------------------------------------------------------------------
     6597abd2-692b2d2-9233acd2-11137bcd2-4426c2d2-681ad3+4905bd3+10403cd3-
     ------------------------------------------------------------------------
     3968d4+1871b3e-7494a2ce+15619abce-6011b2ce+5488ac2e+804bc2e-9570c3e+
     ------------------------------------------------------------------------
     8475a2de+3701abde+5167b2de+92acde+10906bcde-5014c2de-7492ad2e-3569bd2e+
     ------------------------------------------------------------------------
     7001cd2e-6130d3e-1591a2e2+13786abe2+14933b2e2-11342ace2+9971bce2-320c2e2
     ------------------------------------------------------------------------
     -15963ade2-4091bde2+15271cde2-8030d2e2+5565ae3-13785be3-8520ce3+3610de3-
     ------------------------------------------------------------------------
     2341e4 abc3-2568b2c3+3967ac4+7679bc4-6832c5+14005a2c2d+3616abc2d-
     ------------------------------------------------------------------------
     15164b2c2d-4659ac3d-2616bc3d-13751c4d+5816b3d2-4098a2cd2-15676abcd2+
     ------------------------------------------------------------------------
     13347b2cd2-7714ac2d2-10964bc2d2-7552c3d2+12057a2d3+3192abd3+8189b2d3+
     ------------------------------------------------------------------------
     6127acd3+13293bcd3+7491c2d3-623ad4-905bd4+14763cd4+5170d5-12325a2c2e+
     ------------------------------------------------------------------------
     7301abc2e-9146b2c2e-12651ac3e+5308bc3e-8508c4e+11974b3de+5400a2cde-
     ------------------------------------------------------------------------
     1770abcde+5664b2cde+8730ac2de+12939bc2de-10867c3de-2618a2d2e+691abd2e-
     ------------------------------------------------------------------------
     10546b2d2e+11854acd2e-7832bcd2e-13428c2d2e-8698ad3e+7418bd3e-11867cd3e-
     ------------------------------------------------------------------------
     3874d4e+6281b3e2+1516a2ce2+11394abce2+1924b2ce2-5107ac2e2-5132bc2e2+
     ------------------------------------------------------------------------
     9445c3e2+11572a2de2-15520abde2-10074b2de2+2452acde2-11350bcde2+149c2de2-
     ------------------------------------------------------------------------
     9206ad2e2-5654bd2e2+7462cd2e2-12760d3e2+14527a2e3+5066abe3+5331b2e3+
     ------------------------------------------------------------------------
     14174ace3+15079bce3-15172c2e3+10315ade3-8530bde3-3980cde3+6177d2e3+
     ------------------------------------------------------------------------
     6635ae4-12012be4+5235ce4+2445de4+4818e5
     ------------------------------------------------------------------------
     a2c3-8546b2c3+7203ac4-1776bc4+2475c5-4155a2c2d+15237abc2d+2463b2c2d-
     ------------------------------------------------------------------------
     13599ac3d+9555bc3d+10079c4d-12277b3d2+12052a2cd2+12127abcd2-2703b2cd2+
     ------------------------------------------------------------------------
     96ac2d2+1593bc2d2+1698c3d2-206a2d3+683abd3-12377b2d3+10029acd3+9970bcd3+
     ------------------------------------------------------------------------
     6358c2d3+9445ad4+8614bd4-4873cd4+10587d5+12282a2c2e-4476abc2e+15763b2c2e
     ------------------------------------------------------------------------
     +10138ac3e-1551bc3e+11601c4e-9495b3de-4507a2cde+11509abcde-15683b2cde+
     ------------------------------------------------------------------------
     6499ac2de-314bc2de+5076c3de-2752a2d2e+9519abd2e+8215b2d2e-3879acd2e+
     ------------------------------------------------------------------------
     6100bcd2e+3791c2d2e+2888ad3e-530bd3e-13435cd3e-10001d4e+1140b3e2+
     ------------------------------------------------------------------------
     776a2ce2-15016abce2+13083b2ce2-11988ac2e2+1838bc2e2+15935c3e2+822a2de2-
     ------------------------------------------------------------------------
     14011abde2-6154b2de2-12753acde2+5088bcde2+6839c2de2-9087ad2e2+9880bd2e2-
     ------------------------------------------------------------------------
     6565cd2e2-8289d3e2-11991a2e3+10596abe3-6291b2e3-11592ace3-5165bce3-
     ------------------------------------------------------------------------
     5709c2e3+7090ade3-4144bde3+9276cde3+3080d2e3-1889ae4+5894be4-5790ce4-
     ------------------------------------------------------------------------
     15070de4-10192e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R