next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
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 (- 2336a  - 12640a b - 590a*b  - 8658b  + 4027a c - 10132a*b*c +
     ------------------------------------------------------------------------
          2           2          2        3         2                
     5024b c + 6749a*c  + 3654b*c  + 3961c  - 14189a d - 16000a*b*d +
     ------------------------------------------------------------------------
           2                                 2           2           2  
     12337b d - 225a*c*d - 8360b*c*d + 11051c d + 8287a*d  + 11845b*d  -
     ------------------------------------------------------------------------
             2        3         2                      2              
     11073c*d  + 7395d  - 15673a e - 15760a*b*e + 5344b e + 488a*c*e +
     ------------------------------------------------------------------------
                        2                                              2   
     13193b*c*e - 14585c e + 363a*d*e - 13526b*d*e - 12048c*d*e - 8776d e +
     ------------------------------------------------------------------------
            2          2           2          2        3        3        2   
     1212a*e  + 9610b*e  + 12848c*e  + 9362d*e  - 6372e , 15714a  - 7637a b +
     ------------------------------------------------------------------------
           2        3        2                      2           2          2
     568a*b  + 5671b  - 9728a c + 7818a*b*c + 14687b c + 4628a*c  - 2524b*c 
     ------------------------------------------------------------------------
            3        2                     2                             
     + 7061c  - 7299a d - 6157a*b*d + 3319b d + 12681a*c*d + 10467b*c*d +
     ------------------------------------------------------------------------
           2           2          2          2         3        2            
     15830c d - 5447a*d  - 5437b*d  + 5181c*d  - 12552d  + 4814a e + 577a*b*e
     ------------------------------------------------------------------------
            2                                  2                           
     - 3521b e + 4370a*c*e - 1664b*c*e + 15341c e - 6160a*d*e + 7570b*d*e -
     ------------------------------------------------------------------------
                        2           2          2          2          2  
     14541c*d*e + 15748d e - 5785a*e  + 7612b*e  + 4394c*e  - 3237d*e  -
     ------------------------------------------------------------------------
          3       3        2          2         3        2                
     2756e , 4656a  - 8211a b - 205a*b  + 14270b  - 2528a c - 12247a*b*c -
     ------------------------------------------------------------------------
          2            2          2         3         2                
     4969b c + 15964a*c  + 1434b*c  + 11858c  - 11031a d + 13167a*b*d +
     ------------------------------------------------------------------------
          2                                 2           2          2  
     4566b d + 1850a*c*d + 4284b*c*d + 1922c d + 3900a*d  + 7186b*d  -
     ------------------------------------------------------------------------
            2         3        2                      2               
     6918c*d  + 13414d  - 8559a e - 14706a*b*e - 8654b e - 9510a*c*e +
     ------------------------------------------------------------------------
                        2                                              2   
     13920b*c*e - 11106c e - 12461a*d*e + 4421b*d*e - 719c*d*e - 14569d e +
     ------------------------------------------------------------------------
            2           2           2          2         3
     7139a*e  - 15623b*e  + 11319c*e  - 6623d*e  + 10887e )

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+12346b3-5545a2c-10825abc-4840b2c-8867ac2+12250bc2-4289c3-6934a2d-
     ------------------------------------------------------------------------
     969abd-1077b2d-8443acd-3646bcd-15131c2d+3676ad2+13338bd2-14227cd2-7406d3
     ------------------------------------------------------------------------
     +13169a2e-13863abe+1850b2e+6159ace-4266bce+3107c2e-10669ade-14984bde-
     ------------------------------------------------------------------------
     9058cde-14093d2e+7592ae2-12636be2+15256ce2-11051de2+8953e3
     ------------------------------------------------------------------------
     a2b-6819b3+13273a2c-12588abc-7145b2c+13394ac2+1756bc2-6142c3+124a2d-
     ------------------------------------------------------------------------
     2811abd-14354b2d+1728acd+13941bcd-6844c2d+526ad2-8524bd2+6268cd2-6882d3+
     ------------------------------------------------------------------------
     10212a2e+9369abe+1845b2e-8279ace-7134bce+4352c2e+604ade+3616bde+1130cde+
     ------------------------------------------------------------------------
     9539d2e+8766ae2+5224be2-9730ce2+12188de2-10132e3
     ------------------------------------------------------------------------
     a3+5698b3-4675a2c-2443abc+5029b2c-13890ac2-8131bc2-852c3-10901a2d+
     ------------------------------------------------------------------------
     14448abd+4189b2d+8003acd-37bcd+6586c2d-12368ad2-7735bd2+8357cd2-12776d3+
     ------------------------------------------------------------------------
     9033a2e-10444abe-3822b2e+3320ace-9879bce-5106c2e-3985ade-7912bde-
     ------------------------------------------------------------------------
     13521cde-5226d2e+1120ae2-10311be2+8019ce2-5622de2+7383e3
     ------------------------------------------------------------------------
     b3c+11349a2c2+9399abc2+11508b2c2-9215ac3+10597bc3+14165c4+8424b3d-
     ------------------------------------------------------------------------
     1013a2cd+3317abcd-7418b2cd+1542ac2d-5323bc2d+13085c3d+3379a2d2-10271abd2
     ------------------------------------------------------------------------
     -3577b2d2+1839acd2+11096bcd2+1761c2d2-10755ad3+15976bd3-12186cd3+166d4+
     ------------------------------------------------------------------------
     726b3e+12655a2ce-8970abce+3793b2ce-4078ac2e-15769bc2e-1183c3e-7088a2de-
     ------------------------------------------------------------------------
     10531abde-12106b2de-13239acde+15569bcde+11655c2de-14059ad2e+9436bd2e+
     ------------------------------------------------------------------------
     8162cd2e+4755d3e-9483a2e2-2270abe2+7932b2e2-12958ace2+11424bce2+1130c2e2
     ------------------------------------------------------------------------
     +1460ade2+15440bde2-1940cde2-13856d2e2+14854ae3-15942be3+5782ce3+3343de3
     ------------------------------------------------------------------------
     -9775e4 b4-5338a2c2-15983abc2-946b2c2-8116ac3-4550bc3-4771c4-15047b3d-
     ------------------------------------------------------------------------
     6998a2cd+12255abcd-12837b2cd-13060ac2d+6681bc2d+4567c3d+11297a2d2+
     ------------------------------------------------------------------------
     1968abd2-2768b2d2-8096acd2-675bcd2-11298c2d2+5750ad3-3315bd3-15374cd3+
     ------------------------------------------------------------------------
     844d4+6836b3e+7114a2ce-4163abce-10407b2ce+3027ac2e-1662bc2e+9599c3e-
     ------------------------------------------------------------------------
     10363a2de-8929abde-11149b2de+10298acde-1727bcde+5658c2de-15475ad2e+
     ------------------------------------------------------------------------
     9991bd2e-14289cd2e-14514d3e+5414a2e2+118abe2-14354b2e2-10006ace2+
     ------------------------------------------------------------------------
     6860bce2-13930c2e2+14391ade2-12431bde2-1094cde2-7958d2e2-9701ae3+2641be3
     ------------------------------------------------------------------------
     -10952ce3+2894de3+12128e4
     ------------------------------------------------------------------------
     abc3-10917b2c3-12085ac4+12686bc4-11354c5+4278a2c2d+13783abc2d+9834b2c2d+
     ------------------------------------------------------------------------
     5254ac3d+8148bc3d-13852c4d-11010b3d2+5007a2cd2+4125abcd2-15075b2cd2+
     ------------------------------------------------------------------------
     7697ac2d2-11728bc2d2-12362c3d2+14211a2d3-9319abd3+2412b2d3-9250acd3-
     ------------------------------------------------------------------------
     6233bcd3-7685c2d3+5397ad4-6885bd4-9360cd4-5679d5+5722a2c2e-3856abc2e+
     ------------------------------------------------------------------------
     9281b2c2e-11046ac3e+9487bc3e-1889c4e-6580b3de+4505a2cde-13484abcde+
     ------------------------------------------------------------------------
     13086b2cde-5413ac2de-3590bc2de-8473c3de-12189a2d2e+3342abd2e+1981b2d2e+
     ------------------------------------------------------------------------
     678acd2e+5368bcd2e+5734c2d2e-13654ad3e+4758bd3e-7666cd3e-4316d4e+
     ------------------------------------------------------------------------
     1782b3e2-14698a2ce2-2191abce2-3595b2ce2-10740ac2e2+13294bc2e2+10629c3e2+
     ------------------------------------------------------------------------
     8712a2de2-4309abde2+4758b2de2-8548acde2-13458bcde2+5899c2de2+7414ad2e2+
     ------------------------------------------------------------------------
     9969bd2e2-3189cd2e2-14000d3e2-14268a2e3+7550abe3-15502b2e3-5835ace3-
     ------------------------------------------------------------------------
     11151bce3+5345c2e3+10104ade3+9290bde3+11610cde3+11882d2e3-11646ae4+
     ------------------------------------------------------------------------
     578be4+6916ce4+13725de4+11762e5
     ------------------------------------------------------------------------
     a2c3+15727b2c3+15221ac4-3305bc4+8423c5+10663a2c2d+13291abc2d+6478b2c2d+
     ------------------------------------------------------------------------
     8525ac3d-660bc3d+3429c4d+8363b3d2+1728a2cd2+7563abcd2+15067b2cd2+
     ------------------------------------------------------------------------
     15559ac2d2+9856bc2d2+5065c3d2+6956a2d3-2033abd3-5843b2d3+2068acd3-
     ------------------------------------------------------------------------
     15803bcd3+6372c2d3-10874ad4+2446bd4+921cd4-2173d5+7095a2c2e-564abc2e-
     ------------------------------------------------------------------------
     12185b2c2e+13793ac3e-8719bc3e+1087c4e-10189b3de-11910a2cde+8786abcde+
     ------------------------------------------------------------------------
     1951b2cde-15679ac2de+3937bc2de-15448c3de+7421a2d2e-14226abd2e+8895b2d2e-
     ------------------------------------------------------------------------
     820acd2e-6791bcd2e-14624c2d2e+5785ad3e+8195bd3e+12835cd3e-9481d4e+
     ------------------------------------------------------------------------
     5818b3e2+767a2ce2-1917abce2-14983b2ce2-6261ac2e2+111bc2e2+1912c3e2-
     ------------------------------------------------------------------------
     12263a2de2+2964abde2-6197b2de2-547acde2-14854bcde2+7265c2de2+6758ad2e2+
     ------------------------------------------------------------------------
     10490bd2e2+15449cd2e2-664d3e2+13313a2e3+13184abe3-2842b2e3-545ace3-
     ------------------------------------------------------------------------
     11465bce3-15494c2e3-6282ade3-16bde3+4496cde3-15849d2e3-7943ae4+9618be4-
     ------------------------------------------------------------------------
     8229ce4-5322de4-9463e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R