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 (- 3879a  + 13379a b - 3808a*b  + 6680b  + 1492a c - 9345a*b*c -
     ------------------------------------------------------------------------
           2            2           2        3        2               
     13805b c + 11078a*c  + 15101b*c  - 4581c  + 1389a d + 8465a*b*d +
     ------------------------------------------------------------------------
          2                                  2            2           2  
     7897b d + 10326a*c*d + 3653b*c*d + 8387c d + 15979a*d  - 15949b*d  +
     ------------------------------------------------------------------------
             2        3         2                      2               
     12993c*d  + 2485d  + 10781a e + 7371a*b*e - 11985b e - 7806a*c*e -
     ------------------------------------------------------------------------
                      2                                              2   
     2255b*c*e - 4965c e + 3699a*d*e - 5399b*d*e + 4293c*d*e + 12209d e -
     ------------------------------------------------------------------------
            2          2          2           2        3       3         2   
     5560a*e  + 7022b*e  + 6011c*e  + 10472d*e  + 9420e , 7732a  - 10327a b +
     ------------------------------------------------------------------------
            2        3        2                      2           2  
     4233a*b  - 5411b  - 2814a c + 15280a*b*c - 1580b c + 2576a*c  -
     ------------------------------------------------------------------------
             2         3        2                       2                
     14228b*c  - 10937c  + 2099a d - 14171a*b*d - 15211b d + 15663a*c*d +
     ------------------------------------------------------------------------
                      2            2          2           2         3  
     13669b*c*d + 836c d + 12739a*d  + 2630b*d  - 11820c*d  + 14565d  +
     ------------------------------------------------------------------------
          2                      2                                2   
     9673a e + 12041a*b*e - 4477b e - 751a*c*e + 581b*c*e - 15229c e +
     ------------------------------------------------------------------------
                                               2          2           2  
     8134a*d*e - 11448b*d*e - 5634c*d*e - 4249d e + 917a*e  + 14047b*e  +
     ------------------------------------------------------------------------
            2           2         3         3        2           2        3  
     2916c*e  - 13051d*e  - 12297e , - 8046a  - 6207a b - 8462a*b  + 3517b  -
     ------------------------------------------------------------------------
          2                      2            2           2        3  
     6188a c - 6050a*b*c - 11771b c + 13115a*c  + 13421b*c  - 1956c  +
     ------------------------------------------------------------------------
           2                     2                                  2   
     14088a d + 6687a*b*d - 8674b d - 10809a*c*d - 1207b*c*d + 1869c d -
     ------------------------------------------------------------------------
            2         2          2        3        2                     2   
     4621a*d  - 473b*d  + 7670c*d  + 1714d  + 4755a e - 9185a*b*e - 1943b e +
     ------------------------------------------------------------------------
                                     2                                      
     13448a*c*e - 11267b*c*e + 13201c e + 1932a*d*e - 3935b*d*e - 12954c*d*e
     ------------------------------------------------------------------------
            2           2          2           2          2        3
     + 8170d e - 7322a*e  + 7212b*e  + 14708c*e  + 9956d*e  + 3099e )

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+2449b3+3785a2c-5927abc+10739b2c+15747ac2+1426bc2+13650c3-7104a2d-
     ------------------------------------------------------------------------
     327abd-6697b2d-7624acd-6379bcd+3221c2d+11259ad2-12038bd2-4846cd2+9294d3+
     ------------------------------------------------------------------------
     4572a2e-5119abe+14858b2e-13464ace-4208bce+2495c2e-10227ade+10664bde+
     ------------------------------------------------------------------------
     3988cde+12811d2e+15059ae2-5905be2-7716ce2-3488de2+7842e3
     ------------------------------------------------------------------------
     a2b+8542b3+11583a2c-1716abc+5618b2c-11553ac2+4974bc2+6170c3+2162a2d+
     ------------------------------------------------------------------------
     7275abd-5920b2d+9031acd+15610bcd+15450c2d+13574ad2+14635bd2+230cd2+
     ------------------------------------------------------------------------
     8119d3+2086a2e-15412abe-1560b2e-9366ace+7440bce-8715c2e-8763ade+2380bde-
     ------------------------------------------------------------------------
     9794cde-14626d2e+11983ae2-3816be2-2962ce2-8115de2-13554e3
     ------------------------------------------------------------------------
     a3+3089b3+13340a2c-14016abc-6029b2c+6255ac2+10480bc2-1837c3+7162a2d+
     ------------------------------------------------------------------------
     8143abd+10418b2d-5550acd+14964bcd+7767c2d+14277ad2+7814bd2+12197cd2-
     ------------------------------------------------------------------------
     15517d3-15117a2e+6706abe+12716b2e-4828ace-15023bce+14256c2e-8008ade+
     ------------------------------------------------------------------------
     6594bde+12185cde-12501d2e+2177ae2-4776be2+2992ce2-2391de2-8710e3
     ------------------------------------------------------------------------
     b3c-11458a2c2+1318abc2-6348b2c2-5755ac3+3126bc3+4890c4-6693b3d-13588a2cd
     ------------------------------------------------------------------------
     +3951abcd-3628b2cd+14995ac2d+12812bc2d+10532c3d+365a2d2+6011abd2+
     ------------------------------------------------------------------------
     10162b2d2-15798acd2+13383bcd2-6676c2d2-6500ad3-11758bd3-11509cd3-2253d4-
     ------------------------------------------------------------------------
     10538b3e-2509a2ce+5833abce+7874b2ce-2978ac2e-14525bc2e-8779c3e-11768a2de
     ------------------------------------------------------------------------
     +12720abde-15799b2de+15519acde-3822bcde-15252c2de+7869ad2e+2257bd2e-
     ------------------------------------------------------------------------
     9295cd2e-9448d3e+13442a2e2+283abe2+12455b2e2+8052ace2+2587bce2+13159c2e2
     ------------------------------------------------------------------------
     +13399ade2+15348bde2-15778cde2+5449d2e2+14134ae3-1054be3-14503ce3+
     ------------------------------------------------------------------------
     4358de3-669e4 b4-6021a2c2+3199abc2+10027b2c2+2495ac3-8969bc3-8092c4-
     ------------------------------------------------------------------------
     7193b3d-5062a2cd+1509abcd+7036b2cd-11768ac2d-12239bc2d+14312c3d-
     ------------------------------------------------------------------------
     15247a2d2+4198abd2-10237b2d2+6121acd2-13744bcd2+15894c2d2-15686ad3-
     ------------------------------------------------------------------------
     1971bd3-15681cd3+2471d4+269b3e-13975a2ce-12389abce+2725b2ce+10853ac2e+
     ------------------------------------------------------------------------
     306bc2e+6502c3e-7784a2de+7607abde-8716b2de-12680acde+12177bcde+15269c2de
     ------------------------------------------------------------------------
     -5296ad2e+323bd2e-616cd2e-8698d3e-5677a2e2+13757abe2+15637b2e2+12306ace2
     ------------------------------------------------------------------------
     +1666bce2-8670c2e2+6475ade2+4545bde2+12451cde2+2575d2e2+2088ae3-8835be3-
     ------------------------------------------------------------------------
     3460ce3+6111de3+11804e4
     ------------------------------------------------------------------------
     abc3-11314b2c3-759ac4+14320bc4-6998c5+2870a2c2d-6604abc2d-12324b2c2d-
     ------------------------------------------------------------------------
     715ac3d-13483bc3d-10139c4d-14427b3d2-11392a2cd2+2059abcd2-11863b2cd2+
     ------------------------------------------------------------------------
     15383ac2d2-11414bc2d2+1213c3d2-5701a2d3-5056abd3-630b2d3-13327acd3+
     ------------------------------------------------------------------------
     13254bcd3+9601c2d3-1296ad4-10584bd4-4078cd4-13289d5-13937a2c2e+
     ------------------------------------------------------------------------
     13789abc2e+6371b2c2e-1421ac3e+15746bc3e-14156c4e+1906b3de-9482a2cde-
     ------------------------------------------------------------------------
     14142abcde-1091b2cde-975ac2de-4051bc2de-10900c3de+15495a2d2e+4446abd2e+
     ------------------------------------------------------------------------
     3541b2d2e-10624acd2e-7566bcd2e+1727c2d2e-11448ad3e-14606bd3e+12611cd3e+
     ------------------------------------------------------------------------
     10625d4e-13274b3e2+14045a2ce2-13810abce2+10920b2ce2+11384ac2e2+9652bc2e2
     ------------------------------------------------------------------------
     -4563c3e2-14140a2de2-8575abde2+8858b2de2-15289acde2+5835bcde2+11332c2de2
     ------------------------------------------------------------------------
     +13612ad2e2-9487bd2e2+5382cd2e2-15306d3e2-1087a2e3+11263abe3+7968b2e3+
     ------------------------------------------------------------------------
     15693ace3+13479bce3+14766c2e3-3664ade3-2360bde3+1931cde3+8041d2e3-
     ------------------------------------------------------------------------
     1248ae4-450be4+12947ce4-10191de4+11471e5
     ------------------------------------------------------------------------
     a2c3-3592b2c3-12494ac4-1941bc4+7289c5+15264a2c2d+2477abc2d+15552b2c2d-
     ------------------------------------------------------------------------
     5216ac3d-7640bc3d-12038c4d+2380b3d2+10263a2cd2-14754abcd2+15322b2cd2-
     ------------------------------------------------------------------------
     10208ac2d2+5609bc2d2+11531c3d2+12072a2d3-2529abd3+7259b2d3-13900acd3+
     ------------------------------------------------------------------------
     13923bcd3-15657c2d3+13047ad4-14799bd4+9789cd4-1125d5+12194a2c2e+
     ------------------------------------------------------------------------
     9600abc2e-9300b2c2e-12475ac3e-9212bc3e+11039c4e-7066b3de-10202a2cde+
     ------------------------------------------------------------------------
     14607abcde+15597b2cde+4664ac2de-5717bc2de+3748c3de+15807a2d2e-165abd2e-
     ------------------------------------------------------------------------
     11303b2d2e-12489acd2e-765bcd2e-8709c2d2e+946ad3e+14268bd3e-15985cd3e+
     ------------------------------------------------------------------------
     8432d4e-10839b3e2+5890a2ce2+13463abce2+3892b2ce2-2241ac2e2+11673bc2e2+
     ------------------------------------------------------------------------
     6257c3e2-14702a2de2+76abde2+299b2de2-1172acde2+2682bcde2+7344c2de2-
     ------------------------------------------------------------------------
     2446ad2e2+4023bd2e2+4166cd2e2+5738d3e2+14095a2e3-3876abe3-12257b2e3-
     ------------------------------------------------------------------------
     11691ace3+2062bce3+554c2e3-11963ade3+14282bde3+599cde3+12418d2e3-9543ae4
     ------------------------------------------------------------------------
     -10938be4+7144ce4+10440de4-5029e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R